diff --git a/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/-oZSLACDJP8.srt b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/-oZSLACDJP8.srt
new file mode 100644
index 0000000000000000000000000000000000000000..770677410322250951f492d89da3fb7f8d05a203
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+++ b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/-oZSLACDJP8.srt
@@ -0,0 +1,1950 @@
+1
+00:00:21,190 --> 00:00:23,730
+بسم الله الرحمن الرحيم السلام عليكم ورحمة الله
+
+2
+00:00:23,730 --> 00:00:26,610
+وبركاته إحنا إن شاء الله اليوم هنكمل ال boundary
+
+3
+00:00:26,610 --> 00:00:30,230
+conditions إحنا قلنا هناخد boundary conditions بين
+
+4
+00:00:30,230 --> 00:00:33,770
+dielectric و dielectric و conductor و dielectric و
+
+5
+00:00:33,770 --> 00:00:38,270
+conductor في space و هنستعين بيه ال y2 max with
+
+6
+00:00:38,270 --> 00:00:42,110
+equations لـ ال closed integral دي dot dl بتساوي
+
+7
+00:00:42,110 --> 00:00:45,450
+zero هي قلنا conservative force اللي هو ال work و
+
+8
+00:00:45,450 --> 00:00:50,360
+ال closed integral دي dot DS بتساوي الـ الخاصية اللي هو Gauss
+
+9
+00:00:50,360 --> 00:00:55,440
+law قلنا عشان نفهم إيش بيصير عند ال boundary إنه
+
+10
+00:00:55,440 --> 00:00:57,780
+نكتب الـ fields على شكل tangential و normal
+
+11
+00:00:57,780 --> 00:01:00,720
+components فعندنا الـ field هنكتبه على شكل
+
+12
+00:01:00,720 --> 00:01:04,200
+tangential زي الـ normal وبالتالي الـ fields الباقية هم
+
+13
+00:01:04,200 --> 00:01:07,260
+هنكتبه بهذه الطريقة بعدين نميز بال dielectric
+
+14
+00:01:07,260 --> 00:01:10,180
+dielectric boundaries قلنا لو كان عندي two
+
+15
+00:01:10,180 --> 00:01:14,670
+dielectrics بينهم هيكون boundary قلنا بعد نفس
+
+16
+00:01:14,670 --> 00:01:16,330
+الحاجة الـ electric field اللي هو في ال media الـ
+
+17
+00:01:16,330 --> 00:01:20,670
+أول E1 هسميه لـ tangential و normal component و E2
+
+18
+00:01:20,670 --> 00:01:23,430
+اللي هو في ال media الثاني هسميه لـ normal و
+
+19
+00:01:23,430 --> 00:01:26,990
+tangential component و هدرس إيش بيصير لـ tangential
+
+20
+00:01:26,990 --> 00:01:31,360
+component و إيش بيصير لـ normal component استفدنا من
+
+21
+00:01:31,360 --> 00:01:34,040
+استخدامنا لـ two Maxwell's equation أن الـ
+
+22
+00:01:34,040 --> 00:01:36,140
+tangential component للـ electric field على الـ
+
+23
+00:01:36,140 --> 00:01:38,680
+boundary between two dielectric مالها continuous
+
+24
+00:01:38,680 --> 00:01:43,720
+يعني E tangential واحد تساوي E tangential اثنين لكن الـ
+
+25
+00:01:43,720 --> 00:01:48,680
+intensity اللي هو D بتكون discontinuous هتكون D
+
+26
+00:01:48,680 --> 00:01:52,420
+واحد T على Epsilon واحد تساوي D اثنين T على Epsilon
+
+27
+00:01:52,420 --> 00:01:59,380
+اثنين كذلك لما نحكي عن normal components بدنا بالـ D
+
+28
+00:01:59,380 --> 00:02:03,880
+و أخذنا tangential للـ normal components لاقينا أن الـ
+
+29
+00:02:03,880 --> 00:02:08,820
+normal component للـ D بتكون continuous فقط في حالة
+
+30
+00:02:08,820 --> 00:02:12,820
+أن الـ surface charged على ال interface بتساوي 0
+
+31
+00:02:12,820 --> 00:02:17,000
+لكن لو كانت الـ surface charged لها تساوي 0 هيكون
+
+32
+00:02:17,000 --> 00:02:19,740
+ال difference بين الـ normal components بتساوي الـ
+
+33
+00:02:19,740 --> 00:02:26,330
+surface charged الـ free charged density رو مع إنه
+
+34
+00:02:26,330 --> 00:02:29,810
+الـ normal components continuous للـ D هلاحظ أنه الـ
+
+35
+00:02:29,810 --> 00:02:33,730
+normal component للـ E مالها discontinuous أنه E1
+
+36
+00:02:33,730 --> 00:02:37,270
+E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1
+
+37
+00:02:37,270 --> 00:02:38,130
+E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1
+
+38
+00:02:38,130 --> 00:02:38,490
+E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1
+
+39
+00:02:38,490 --> 00:02:42,070
+E1 E1 E1 E1 E1 E1 E1 E1 E1 E1
+
+40
+00:02:42,070 --> 00:02:43,610
+E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1
+
+41
+00:02:43,610 --> 00:02:45,690
+E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1
+
+42
+00:02:45,690 --> 00:02:54,050
+E1 E1 الـ 2 ده الـ electrics فيها E1 و E2 و E1 و D1
+
+43
+00:02:54,050 --> 00:02:58,670
+و E1 و D1 زي ما تشوفين هدول في ال media الأولى هذا
+
+44
+00:02:58,670 --> 00:03:06,490
+ال normal على ال surface هذا normal على ال surface هذه
+
+45
+00:03:06,490 --> 00:03:13,110
+يعني E1 و D1 برضه هجزئها لـ tangential components و
+
+46
+00:03:13,110 --> 00:03:16,790
+normal components نفس الحاجة بالنسبة لـ E2 و D2
+
+47
+00:03:17,080 --> 00:03:21,200
+هجزئهم لـ tangential components و normal components
+
+48
+00:03:21,200 --> 00:03:25,080
+واضح الـ components اللي ما قلناش فيها مشكلة طب إحنا
+
+49
+00:03:25,080 --> 00:03:26,960
+بدنا نشوف إيش قانون ال refraction ال refraction
+
+50
+00:03:26,960 --> 00:03:30,560
+بتاعه اللي هو انكسار بين two dielectric medium على
+
+51
+00:03:30,560 --> 00:03:36,480
+أساس أن θ1 و θ2 بمثل θ1 هي الزاوية ما بين الـ
+
+52
+00:03:36,480 --> 00:03:41,420
+electric field و ال normal على ال surface أو θ اثنين هي
+
+53
+00:03:41,420 --> 00:03:44,840
+الزاوية بين الـ field و ال normal على ال surface على
+
+54
+00:03:44,840 --> 00:03:47,500
+ال interface يعني وين ال interface بحط normal
+
+55
+00:03:47,500 --> 00:03:51,400
+عليها و الزاوية بين الـ field و ال normal هي بتكون θتا
+
+56
+00:03:51,400 --> 00:03:54,540
+طب نيجي على ال tangential component ال tangential
+
+57
+00:03:54,540 --> 00:04:00,960
+component لـ E إيش بتساوي E1 sin θ1 صح و E2
+
+58
+00:04:00,960 --> 00:04:07,150
+tangential إيش هتكون E2 sin ثتا اثنين طب إحنا عارفين
+
+59
+00:04:07,150 --> 00:04:09,890
+أن E واحد tangential بتساوي E اثنين tangential اللي
+
+60
+00:04:09,890 --> 00:04:11,730
+إسبقنا أثبتناها في المحاضرة الماضية و ارجعناها
+
+61
+00:04:11,730 --> 00:04:14,410
+اليوم ال tangential component للـ electric field
+
+62
+00:04:14,410 --> 00:04:17,790
+between two dielectrics مالها continuous إذا E
+
+63
+00:04:17,790 --> 00:04:21,550
+واحد tangential بتساوي E اثنين tangential لكن إحنا
+
+64
+00:04:21,550 --> 00:04:26,430
+عارفين من الرسمة اللي رسمناها الـ field وهي ال theta
+
+65
+00:04:26,430 --> 00:04:29,870
+واحد اللي بين الـ field و ال normal ال tangential
+
+66
+00:04:29,870 --> 00:04:33,690
+بتحدد أشهر كم قيمتها E واحد sin θتا واحد و نفس
+
+67
+00:04:33,690 --> 00:04:37,950
+القضية بالنسبة لـ E2 وهي θ ثتا اثنين هي الزاوية بين الـ
+
+68
+00:04:37,950 --> 00:04:40,610
+field و ال normal هتكون ال tangential component
+
+69
+00:04:40,610 --> 00:04:43,790
+بتساوي E2 sin θتا اثنين اللي هو زي ما إحنا
+
+70
+00:04:43,790 --> 00:04:48,710
+شايفين هذا من ال boundary condition أن E1
+
+71
+00:04:48,710 --> 00:04:51,890
+tangential بتساوي E2 tangential E1 tangential
+
+72
+00:04:51,890 --> 00:04:55,570
+بتساوي E1 sin θتا اثنين و E2 tangential بتساوي E2
+
+73
+00:04:55,570 --> 00:04:57,590
+sin θتا اثنين إيش كمان بعض ال conditions التاني
+
+74
+00:04:57,590 --> 00:05:02,390
+قالنا أن الـ D normal هي ال continuous D1 normal بتساوي D2
+
+75
+00:05:02,390 --> 00:05:05,510
+normal إذا ما كانش هنا free charge يعني إذا كانت هذه
+
+76
+00:05:05,510 --> 00:05:09,690
+رو بتساوي zero الـ free charge بتساوي zero إذا D1
+
+77
+00:05:09,690 --> 00:05:13,830
+normal بتساوي D2 normal D1 normal شو هتساوي الـ normal
+
+78
+00:05:13,830 --> 00:05:18,090
+component لـ D1 هاي دي D1 الـ normal اللي هي هاي
+
+79
+00:05:18,090 --> 00:05:25,150
+هتكون D1 cosine θتا 1 جيب تمام θتا 1
+
+80
+00:05:49,950 --> 00:05:51,960
+D1D1D1D1D1D1D1D1D1D1D1D1D1D1D1D1D1D1D1D1D1D1D1 ساين
+
+81
+00:05:51,960 --> 00:05:55,500
+على كوساين اللي هي tan θ1 ألا Epsilon 1 بتساوي tan
+
+82
+00:05:55,500 --> 00:06:00,400
+θ2 على Epsilon 2 إذا عوضنا عن Epsilon 1 و Epsilon
+
+83
+00:06:00,400 --> 00:06:04,480
+2 بقيمتهم ده لاتر ال relative permittivity Epsilon
+
+84
+00:06:04,480 --> 00:06:06,540
+1 هتكون Epsilon not في relative permittivity
+
+85
+00:06:06,540 --> 00:06:09,660
+للـ media الأولى و Epsilon 2 هتكون Epsilon not في
+
+86
+00:06:09,660 --> 00:06:13,680
+Epsilon relative للـ media الثانية هيكون ال tan θ1
+
+87
+00:06:13,680 --> 00:06:16,480
+على tan θ2 بتساوي relative permittivity للـ media
+
+88
+00:06:16,480 --> 00:06:20,400
+الأولى على relative permittivity للـ media الثانية
+
+89
+00:06:29,190 --> 00:06:32,770
+نيجي لـ ال conductor dielectric إيش الفرق بين
+
+90
+00:06:32,770 --> 00:06:35,330
+dielectric و dielectric؟ بين dielectric و
+
+91
+00:06:35,330 --> 00:06:38,190
+conductor إحنا قلنا ال conductor إيش بيكون الـ
+
+92
+00:06:38,190 --> 00:06:41,930
+electric field في قلبه zero يعني خصائص الـ
+
+93
+00:06:41,930 --> 00:06:44,210
+conductor الـ electric field بيكون بتساوي صفر في
+
+94
+00:06:44,210 --> 00:06:47,410
+قلبه لأن ال charges بيروح على ال surface بطل فيه
+
+95
+00:06:47,410 --> 00:06:50,470
+charges in plus في ال conductor وبالتالي بيكون الـ
+
+96
+00:06:50,470 --> 00:06:53,310
+electric field بتساوي zero قلنا معدى إذا إحنا
+
+97
+00:06:53,310 --> 00:06:57,630
+أجبرناه و وصلنا معه أسلاب، فاكرين؟ لأن هو في ال
+
+98
+00:06:57,630 --> 00:07:02,090
+free space وحطينا electric field هلاقي أنه في قلب
+
+99
+00:07:02,090 --> 00:07:06,670
+ال conductor electric field بتساوي 0 إذا أنا عندي
+
+100
+00:07:06,670 --> 00:07:10,110
+هاي ال conductor وهي ال electric field الـ
+
+101
+00:07:10,110 --> 00:07:12,850
+dielectric وهي ال boundary اللي بين ال two medium
+
+102
+00:07:12,850 --> 00:07:16,170
+اللي هو الخط هذا، هذا هو ال boundary، هذا خط الـ
+
+103
+00:07:16,170 --> 00:07:22,630
+boundary لو استخدمنا Maxwell's equations هلاقي نفس
+
+104
+00:07:22,630 --> 00:07:25,870
+القضية أن E tangential لازم تكون continuous اللي
+
+105
+00:07:25,870 --> 00:07:28,890
+هي ال closed انتجرا لـ E dot dl لكن ال tangential
+
+106
+00:07:28,890 --> 00:07:32,510
+component في ال conductor أشبه بتساوي 0 ال electric
+
+107
+00:07:32,510 --> 00:07:35,810
+field في ال conductor أشبه بتساوي 0 فال tangential
+
+108
+00:07:35,810 --> 00:07:41,270
+component 0 إذا E tangential في اللي هو ال media
+
+109
+00:07:41,270 --> 00:07:44,410
+اللي هي ال dielectric بتساوي 0 لو أخذنا ال normal
+
+110
+00:07:44,410 --> 00:07:48,530
+components اللي هي DN هلاحظ أنه مالها إحنا قلنا
+
+111
+00:07:48,530 --> 00:07:52,290
+بتكون ال D continuous إذا كانت رو بتساوي 0 لا توا
+
+112
+00:07:52,290 --> 00:07:58,230
+بتساوي 0 هتكون DN أشبه بتساوي رو فالـ E tangential هي 0
+
+113
+00:07:58,230 --> 00:08:02,330
+لأن E tangential في ال conductor هي 0 إنتوا باخدين
+
+114
+00:08:02,330 --> 00:08:05,530
+أن إحنا بس بحطين E واحدة مش E واحد و E اثنين E
+
+115
+00:08:05,530 --> 00:08:08,390
+اللي هي ال dielectric فال tangential component
+
+116
+00:08:08,390 --> 00:08:12,250
+بتاعتها 0 لأن E tangential في ال conductor هي 0 و
+
+117
+00:08:12,250 --> 00:08:17,830
+ال normal component لـ D هتكون بتساوي رو D مش هيكون
+
+118
+00:08:17,830 --> 00:08:22,970
+D على 1 ناقص D على 2 لأن D على 2 هي 0 ال conductor عنده
+
+119
+00:08:22,970 --> 00:08:26,810
+ال electric field بتساوي 0 إذا رو 0 إذا D بتساوي 0
+
+120
+00:08:26,810 --> 00:08:31,010
+لو
+
+121
+00:08:31,010 --> 00:08:35,990
+كان ال electric field قلنا بيبقى أنه أنه مافيش
+
+122
+00:08:35,990 --> 00:08:39,490
+electric field في قلب ال conductor لو كان رو بتساوي 0
+
+123
+00:08:39,490 --> 00:08:45,610
+لأ في قلب ال conductor اللي أنا حكيته أنه
+
+124
+00:08:45,610 --> 00:08:48,330
+أي charges إيش بتصير اللي هو قلنا بتصير على الباندر
+
+125
+00:08:48,330 --> 00:08:50,850
+لو موجودة charges بتروح كلها على الباندر وبالتالي
+
+126
+00:08:50,850 --> 00:08:54,330
+ال electric field لو أخدت Gauss law بتساوي zero هذا
+
+127
+00:08:54,330 --> 00:08:57,990
+اللي بنحكي هنا أن مافيش أنا عندي أي field exist في
+
+128
+00:08:57,990 --> 00:09:00,610
+قلب ال conductor معناه أن رو V بتساوي zero و E
+
+129
+00:09:00,610 --> 00:09:03,210
+بتساوي zero E بتساوي zero أن إحنا ال electric
+
+130
+00:09:03,210 --> 00:09:06,290
+field إيش اللي بنعبر عنه برضه ال potential scalar
+
+131
+00:09:06,290 --> 00:09:09,570
+potential أنه E بتساوي minus grade V إيش قلنا
+
+132
+00:09:09,570 --> 00:09:12,250
+echo potential surfaces لل conductor من الذاكرين
+
+133
+00:09:12,250 --> 00:09:16,710
+قلنا أن V بتساوي zero معناه أن ال conductor
+
+134
+00:09:16,710 --> 00:09:18,770
+بتتصرف as echo potential body
+
+135
+00:09:28,080 --> 00:09:31,460
+طبعا إذا إحنا قلنا معناه أن ال electric field مالها
+
+136
+00:09:31,460 --> 00:09:34,400
+zero على ال conductor إذا معناه زي ما إنتوا شايفين
+
+137
+00:09:34,400 --> 00:09:38,140
+أن E T tangential لنا بتساوي Zero برضه E T
+
+138
+00:09:38,140 --> 00:09:41,320
+بتساوي Zero لأن E T إيش علاقتها بـ E T بال Epsilon
+
+139
+00:09:41,320 --> 00:09:44,520
+Epsilon لـ ال media لل conductor إذا ما هتكون برضه Zero
+
+140
+00:09:44,520 --> 00:09:48,800
+لكن DN اللي إحنا قلناه هتساوي ρو S وين بتكون
+
+141
+00:09:48,800 --> 00:09:53,460
+External لل conductor و عمودي عليه يعني فقط هي اللي
+
+142
+00:09:53,460 --> 00:09:57,320
+بيكون موجود لو كان عندي conductor هيكون الـ
+
+143
+00:09:57,320 --> 00:10:00,260
+tangential component بتساوي 0 دائما، external
+
+144
+00:10:00,260 --> 00:10:05,080
+لل conductor هتكون ال tangential component 0، وإيش
+
+145
+00:10:05,080 --> 00:10:08,080
+هتكون فقط ال external، اللي هي ال normal component
+
+146
+00:10:08,080 --> 00:10:12,480
+فقط ال non-zero component هي ال normal component،
+
+147
+00:10:12,480 --> 00:10:16,180
+ال tangential بتساوي 0، ال normal .. يعني نقدر نقول
+
+148
+00:10:16,180 --> 00:10:20,860
+ببساطة أن ال electric field خارج ال conductor هيكون
+
+149
+00:10:20,860 --> 00:10:23,480
+دائما على ال normal direction لأن ال tangential
+
+150
+00:10:23,480 --> 00:10:25,280
+component دائما بتساوي 0
+
+151
+00:10:36,070 --> 00:10:38,570
+عشان هذا الشيء أن ال electric field في قلب أي
+
+152
+00:10:38,570 --> 00:10:42,350
+conductor بتساوي zero إحنا بنسمي ال conductor as a
+
+153
+00:10:42,350 --> 00:10:46,430
+shield يعني مثلا لو إحنا اعتبرنا اللي هي ال a هذه
+
+154
+00:10:46,430 --> 00:10:51,950
+هي عبارة عن conductor بحط هنا body اللي هو b في
+
+155
+00:10:51,950 --> 00:10:56,120
+قلب اللي هو ال conductor a ال conductor A إيش
+
+156
+00:10:56,120 --> 00:11:00,760
+بيعمل؟ بيمنع اختراق أي electric field لـ inside الـ
+
+157
+00:11:00,760 --> 00:11:05,460
+A فمعناه أن B مش هتشعر بالمرة في وجود ال C و نفس
+
+158
+00:11:05,460 --> 00:11:08,360
+الشيء ال C مش هتشعر بالمرة في وجود ال B لأن الـ
+
+159
+00:11:08,360 --> 00:11:13,660
+conductor A إيش عمل؟ ك shield كدرع واقي هيمنع أن
+
+160
+00:11:13,660 --> 00:11:18,040
+ال body B أنه يشعر في وجود ال C و نفس العضية الـ
+
+161
+00:11:18,040 --> 00:11:22,140
+body C مش هيشعر في وجود ال body B أنه إحنا شرحناه
+
+162
+00:11:22,140 --> 00:11:24,920
+بمنع اختراق ال electric field إله فقط هيكون
+
+163
+00:11:24,920 --> 00:11:28,460
+external و normal إله، مش هيكون في قلبه، وبالتالي
+
+164
+00:11:28,460 --> 00:11:33,060
+ال body B هيشعر إنه محمي من اللي هو أي تأثير لـ
+
+165
+00:11:33,060 --> 00:11:38,460
+ال body C ياه، بنسميه electrostatic screening or
+
+166
+00:11:38,460 --> 00:11:40,920
+shielding، shielding اللي هو الحماية و ال screen هو
+
+167
+00:11:40,920 --> 00:11:44,580
+برضه زي إحنا بنحمي حالنا بالشبكة من البعض و من
+
+168
+00:11:44,580 --> 00:11:47,160
+الحشرات والدارة
+
+169
+00:11:54,690 --> 00:11:57,090
+آخر حاجة اللي هي conductor of free space إحنا قلنا
+
+170
+00:11:57,090 --> 00:11:59,410
+بال free space ما هو إلا ال dielectric و الـ
+
+171
+00:11:59,410 --> 00:12:02,850
+Epsilon بتساوي Epsilon node يعني اللي حكيناه قبل
+
+172
+00:12:02,850 --> 00:12:06,350
+قليل على conductor dielectric حالة خاصة منه اللي
+
+173
+00:12:06,350 --> 00:12:09,710
+هي ال free space يعني بقدر أقول إنه ال electric
+
+174
+00:12:09,710 --> 00:12:14,690
+field هيكون external لل conductor و normal عليه بمعنى
+
+175
+00:12:14,690 --> 00:12:18,710
+أن ال tangential component بتساوي 0 و ال normal
+
+176
+00:12:18,710 --> 00:12:22,390
+component بتساوي ρو S و ال D normal مش بتساوي
+
+177
+00:12:22,390 --> 00:12:28,520
+Epsilon node Em واضح؟ لأن Epsilon relative بالنسبة
+
+178
+00:12:28,520 --> 00:12:33,260
+لل space بتساوي واحد لنشوف بعض الأمثلة بنا
+
+179
+00:12:33,260 --> 00:12:35,920
+نستفيد من boundary condition إ
+
+201
+00:14:06,950 --> 00:14:11,890
+هي أنا الـ two medias اللي هي الـ 1 و 2 Epsilon R1
+
+202
+00:14:11,890 --> 00:14:15,850
+للميديا الأولى التي الديالكتريك 1 و الديالكتريك
+
+203
+00:14:15,850 --> 00:14:20,410
+للميديا Epsilon R2 Epsilon R1 قيمتها 4 و Epsilon 
+
+204
+00:14:20,410 --> 00:14:24,570
+R2 قيمتها 3 و زي ما قلنا إن الـ Epsilon الميديا
+
+205
+00:14:24,570 --> 00:14:28,170
+الأولى في Z أكبر من أو تساوي 0 و الميديا الثانية
+
+206
+00:14:28,170 --> 00:14:32,960
+في Z أقل من أو تساوي 0 في الـ media الأولى كان في
+
+207
+00:14:32,960 --> 00:14:37,280
+عندي electric field E1 أنا عارفة كل معلوماته إنه
+
+208
+00:14:37,280 --> 00:14:41,240
+الـ component في الـ X direction قيمتها خمسة و في ال
+
+209
+00:14:41,240 --> 00:14:44,200
+Y مقدرها ماينس اثنين و في الـ Z مقدرها ثلاثة
+
+210
+00:14:44,200 --> 00:14:50,160
+كيلوفولت بالمتر اللي طالب هو الحاجة E2 for Z أقل
+
+211
+00:14:50,160 --> 00:14:53,240
+من Zero عشان أجيب E2 إيش لازم أجيب الـ tangential
+
+212
+00:14:53,240 --> 00:14:57,940
+component و الـ normal component طب احنا عرفنا إنه
+
+213
+00:14:57,940 --> 00:14:59,840
+بين الـ dielectric و الـ dielectric tangential
+
+214
+00:14:59,840 --> 00:15:04,060
+component مالهم continuous يعني E tangential واحد
+
+215
+00:15:04,060 --> 00:15:07,040
+بساوي E tangential اثنين مين الـ tangential component
+
+216
+00:15:07,040 --> 00:15:10,160
+في هالحالة؟ اللي هي الـ X و الـ Y مين اللي على ال
+
+217
+00:15:10,160 --> 00:15:13,040
+interface اللي فرجتكم إياه بالدفترين؟ هيكون الـ X و ال
+
+218
+00:15:13,040 --> 00:15:17,220
+Y اللي عمودي عليهم مين؟ الـ Z component إذا بطلع
+
+219
+00:15:17,220 --> 00:15:20,200
+وين الـ X component و الـ Y component؟ خمسة X minus
+
+220
+00:15:20,200 --> 00:15:27,290
+اثنين Y هي E واحد tangential E1 norm هي 3 AZ hat إذا
+
+221
+00:15:27,290 --> 00:15:31,030
+من الـ boundary condition E1 tangential بتساوي E2
+
+222
+00:15:31,030 --> 00:15:35,370
+tangential بتالي E2 tangential إيش قيمتها 5X hat
+
+223
+00:15:35,370 --> 00:15:39,350
+minus 2Y hat واضح؟ طب الـ normal component قولنا
+
+224
+00:15:39,350 --> 00:15:46,490
+مين من الـ normal اللي هي DN1 بتساوي DN2 أو D1 DN1
+
+225
+00:15:46,490 --> 00:15:50,950
+minus DN2 بتساوي raw free بس هو مجرد نسيرة أي free
+
+226
+00:15:50,950 --> 00:15:55,710
+charges معناه raw بتساوي صفر الـ surface charge
+
+227
+00:15:55,710 --> 00:16:01,470
+بتساوي zero إذا دي واحد norm بتساوي دي اثنين norm
+
+228
+00:16:01,470 --> 00:16:05,210
+طب دي واحد norm مش بتساوي epsilon واحد في E واحد
+
+229
+00:16:05,210 --> 00:16:10,300
+norm التي قيمتها ثلاثة اي واحد نورم اي ابسلون ار
+
+230
+00:16:10,300 --> 00:16:14,580
+واحد هي أربعة 4 في 3 هي اللي هي دي واحد
+
+231
+00:16:14,580 --> 00:16:18,180
+نورم هي تساوي دي اثنين norm وبالتالي بقدر أقول اي
+
+232
+00:16:18,180 --> 00:16:21,280
+اثنين norm لأن اي اثنين norm مش متساوي دي اثنين
+
+233
+00:16:21,280 --> 00:16:25,620
+نورم على ابسلون اثنين ار واضح كده شفنا ال
+
+234
+00:16:25,620 --> 00:16:29,460
+components كلهم هي المحلول المحضوطة هي اي واحد
+
+235
+00:16:29,460 --> 00:16:32,920
+نورم متساوي اي واحد dot and hat اللي هي الثلاثة
+
+236
+00:16:35,690 --> 00:16:39,190
+واللي هي total E E norm plus E tangential وكذا أنا
+
+237
+00:16:39,190 --> 00:16:41,710
+قلت لكم يا tangential component اللي في الـ X وY
+
+238
+00:16:41,710 --> 00:16:44,850
+component الـ tangential اثنين هتساوي E tangential
+
+239
+00:16:44,850 --> 00:16:48,050
+واحد دي اثنين norm بتساوي D واحد norm لأن الـ free
+
+240
+00:16:48,050 --> 00:16:51,150
+charge على الـ surface اللي قلنا بتساوي Zero وD واحد
+
+241
+00:16:51,150 --> 00:16:55,570
+norm إيش بتساوي Epsilon واحد في E واحد N وبنجيب دي
+
+242
+00:16:55,570 --> 00:16:59,040
+اثنين N وبالتالي بقدر أجيب E اثنين N لأنها هتكون دي
+
+243
+00:16:59,040 --> 00:17:03,780
+اثنين N على Epsilon اثنين إذا جبنا E اثنين tangential
+
+244
+00:17:03,780 --> 00:17:07,200
+أو E اثنين norm بالتالي بقدر أقول إن E اثنين أو E
+
+245
+00:17:07,200 --> 00:17:11,480
+tangential زائد E اثنين norm و بقدر أحسب قيمة الـ E
+
+246
+00:17:11,480 --> 00:17:16,800
+اثنين واضح كده إذا أنا معرفتي المعطيات عن الـ field
+
+247
+00:17:16,800 --> 00:17:20,620
+في الـ media الأولى عرفت أول شي بالـ media الـ field
+
+248
+00:17:20,620 --> 00:17:23,780
+في الـ media الثانية لأن عارفة الـ conditions بتاعة
+
+249
+00:17:23,780 --> 00:17:28,450
+الـ boundary بين الـ two dielectrics طب الزوايا بين
+
+250
+00:17:28,450 --> 00:17:33,240
+E1 و E2 اللي بيعملوهم على الـ interface بتوازي الزاوية
+
+251
+00:17:33,240 --> 00:17:36,100
+اللي بيعملوها مع الـ interface طبعا عندي two
+
+252
+00:17:36,100 --> 00:17:41,020
+components يعني عندي XY component على الـ XY plane
+
+253
+00:17:41,020 --> 00:17:44,620
+يعني عندي E1 لو أنا بدأت أفكر في الزاوية اللي بين
+
+254
+00:17:44,620 --> 00:17:49,080
+الـ XY plane في الـ XY plane هتكون أصعب من إن لو
+
+255
+00:17:49,080 --> 00:17:51,720
+فكرت في الـ Z component لأن عندي one component في
+
+256
+00:17:51,720 --> 00:17:55,420
+الـ Z component يعني لما طلعت على الـ Z component للـ
+
+257
+00:17:55,420 --> 00:17:59,380
+electric field بقول إن الـ Z component مش متساوي E
+
+258
+00:17:59,380 --> 00:18:04,140
+جبت من 90 واحد صح؟ إذا جيبت الـ 90 واحد أنا هجيب الـ
+
+259
+00:18:04,140 --> 00:18:07,420
+alpha واحد بمنتهى البساطة بقدر أقول إن E alpha
+
+260
+00:18:07,420 --> 00:18:11,100
+واحد بالساوي اللي هي الـ difference بين الـ 90 ناقص
+
+261
+00:18:11,100 --> 00:18:16,520
+الـ 90 واحد أو بدي أجيب قيمة الـ E واحد tangential
+
+262
+00:18:16,520 --> 00:18:19,880
+اللي هي الـ square root لـ X تربيع زائد E X تربيع زائد E
+
+263
+00:18:19,880 --> 00:18:22,700
+Y تربيع بس هسأل ليه إن أجيب الزاوية ما بين الـ Z
+
+264
+00:18:22,700 --> 00:18:29,090
+component و الـ norm على الـ interface الـ E1 والنورم
+
+265
+00:18:29,090 --> 00:18:32,370
+على الـ interface وبالتالي بقدر أجيب اللي مع ال
+
+266
+00:18:32,370 --> 00:18:35,670
+interface أنا هتكون تسعين ناقص سيتا اللي مع ال
+
+267
+00:18:35,670 --> 00:18:41,270
+norm لأن هذه هي الخطوة الثانية بتأجيب سيتا واحد و
+
+268
+00:18:41,270 --> 00:18:44,290
+سيتا اثنين و احنا قلنا إنه أنا عارفة الـ normal
+
+269
+00:18:44,290 --> 00:18:47,710
+component و الـ tangential component للـ fields بقدر
+
+270
+00:18:47,710 --> 00:18:51,930
+أقول إن سيتا واحد يعني أصلاً بعملها بهذه الطريقة إن
+
+271
+00:18:51,930 --> 00:18:57,280
+سيتا واحد بتساوي إياها سواء اللي هو الـ .. بأجيب دلالتي
+
+272
+00:18:57,860 --> 00:19:01,460
+الـ tangential component إن هي cosine أو التان إن
+
+273
+00:19:01,460 --> 00:19:05,700
+بقول magnitude تبع الـ E1 tangential على اللي هي الـ
+
+274
+00:19:05,700 --> 00:19:10,400
+E1Z هي بتكون تان ثتا واحد إذا حسبناها بأي طريقة زي
+
+275
+00:19:10,400 --> 00:19:12,860
+ما احنا هنا حاسبينها إن جيبت المقياس تبع الـ E1
+
+276
+00:19:12,860 --> 00:19:16,040
+tangential هي الـ square root المربع الأول زائد
+
+277
+00:19:16,040 --> 00:19:18,980
+المربع الثانية و الـ A norm احنا عارفين إن هي في الـ
+
+278
+00:19:18,980 --> 00:19:22,280
+Z component بقدر و هي تان ثتا واحد E1 tangential
+
+279
+00:19:22,280 --> 00:19:26,110
+اي واحد norm بأجيب ثتا واحد بأجيب الفا واحد لأن الفا
+
+280
+00:19:26,110 --> 00:19:29,290
+واحد مش هتساوي تسعين minus ستة واحد نفس الحكي
+
+281
+00:19:29,290 --> 00:19:33,390
+بطبقه على اللي هو الـ E في الـ media الثانية و بقدر
+
+282
+00:19:33,390 --> 00:19:38,810
+أجيب اللي هي الفا اثنين بعد أشهر بعدها ال energy
+
+283
+00:19:38,810 --> 00:19:43,690
+densities in both dielectrics و احنا برضه شوفنا إن
+
+284
+00:19:43,690 --> 00:19:46,750
+الـ energy density بتساوي نصف الـ dielectric في ال
+
+285
+00:19:46,750 --> 00:19:51,010
+magnitude لفير تربيع فإذا في الـ media الأولى هتكون
+
+286
+00:19:51,010 --> 00:19:54,830
+الـ energy density نصف ابسلون واحد اي واحد تربيع في
+
+287
+00:19:54,830 --> 00:19:57,670
+الـ media الثانية هتكون نصف ابسلون اثنين اي
+
+288
+00:19:57,670 --> 00:20:00,230
+magnitude تربيع هو ما أعطانا الـ relative
+
+289
+00:20:00,230 --> 00:20:05,640
+permittivity ابسلون ار واحد ابسلون ار اثنين لكن أنا
+
+290
+00:20:05,640 --> 00:20:09,100
+بدي ابسلون فاش بس إذا بضرب هذا ابسلون نوت إذا ربنا
+
+291
+00:20:09,100 --> 00:20:12,280
+ابسلون relative ابسلون نوت بحصل على ابسلون في
+
+292
+00:20:12,280 --> 00:20:15,820
+الميديا فإذا ابسلون واحد إيش هتكون ابسلون نوت اللي
+
+293
+00:20:15,820 --> 00:20:19,000
+هي عشرة أس ناقص تسعة ستة وتلاتين باي في ابسلون
+
+294
+00:20:19,000 --> 00:20:22,120
+relative اللي هي أربعة في واحد تربيع اللي هي طبعا
+
+295
+00:20:22,120 --> 00:20:27,000
+الـ magnitude هو جذر التربيع ل EX تربيع زائد ال EY
+
+296
+00:20:27,000 --> 00:20:30,420
+تربيع زائد EZ تربيع تربيعها بخلص من الجذر
+
+297
+00:20:34,000 --> 00:20:37,080
+لأنها كانت كل القيم المعطينها إياه بال kilo volt
+
+298
+00:20:37,080 --> 00:20:41,360
+فلما أربعها إيش بتصير عشرة أس ستة انتبهوا للـ
+
+299
+00:20:41,360 --> 00:20:44,520
+units احنا عند الـ electric field المعطيناه إياه بـ kilo
+
+300
+00:20:44,520 --> 00:20:48,500
+volt per meter لما أخد الـ magnitude ل E تربيع
+
+301
+00:20:48,500 --> 00:20:52,200
+هتصير إيش هتكون K تربيع يعني kilo تربيع يعني عشرة
+
+302
+00:20:52,200 --> 00:20:57,660
+أس ستة فهذه صارت عندي في عشرة أس ستة لو حسبت
+
+303
+00:20:57,660 --> 00:21:00,820
+بيطلع بيضل عندي في الـ micro لأن عشرة أس ناقص ستة
+
+304
+00:21:00,820 --> 00:21:05,220
+وفي عندي اللي هي بعض الـ .. الـ .. هيطلع لنا بعض الـ
+
+305
+00:21:05,220 --> 00:21:09,420
+.. برضه الـ .. الترمال فهيكون ستمية واثنين وسبعين
+
+306
+00:21:09,420 --> 00:21:12,300
+micro هي point ستة سبعة تلات .. سبعة اثنين
+
+307
+00:21:12,300 --> 00:21:16,280
+millijoule ده التسهير 672 microjoule per meter
+
+308
+00:21:16,280 --> 00:21:19,270
+cube نفس الحاجة الـ energy density في الـ media
+
+309
+00:21:19,270 --> 00:21:22,750
+الثانية ما ننساش الـ units إن هي كانت بالـ kilo volt
+
+310
+00:21:22,750 --> 00:21:25,930
+هيطلع عندها عشرة أس ستة بالنهاية بيطلع مع الجواب
+
+311
+00:21:25,930 --> 00:21:29,310
+بالـ micro joule أخر حاجة هو طالب الـ total energy
+
+312
+00:21:31,290 --> 00:21:38,050
+within the cube of side 2m centered at 3,4,-5 بيده
+
+313
+00:21:38,050 --> 00:21:43,430
+الـ total energy اللي في قلب مكعب اللي وين عند 3,4,
+
+314
+00:21:43,550 --> 00:21:45,770
+-5 بتعرف وين هو في الـ media الأولى ولا في ال
+
+315
+00:21:45,770 --> 00:21:50,270
+media الثانية ما إنها سالب z سالب z وين media
+
+316
+00:21:50,270 --> 00:21:57,670
+الثانية وهذا الـ cube centered عن مين عند x3 و y4 و
+
+317
+00:21:57,670 --> 00:22:02,150
+minus 5 بالنسبة لـ الـ z component هذا الـ center تبعه
+
+318
+00:22:02,150 --> 00:22:04,870
+عشان أنا أعرف اللي هي من ومن بدي أخد الـ X لـ Y و
+
+319
+00:22:04,870 --> 00:22:10,530
+الـ Z إذا هو الـ center تبع
+
+320
+00:22:10,530 --> 00:22:16,030
+الـ X مثلاً عند الثلاثة إذا قد إيش هيروح طول الضلع واحد
+
+321
+00:22:16,030 --> 00:22:20,190
+يعني هيروح من وين من من 2 لـ 4
+
+322
+00:22:24,560 --> 00:22:28,820
+هيكون بيبدأ الـ integration من 1 لـ 4 و Y الـ center
+
+323
+00:22:28,820 --> 00:22:33,980
+دي عند الـ 4 إذا ما هيروح من وين لـ 3 لـ 5 واضح؟ و
+
+324
+00:22:33,980 --> 00:22:38,040
+هكذا إذا ما هنعمل الـ total integral اللي هو X من 2
+
+325
+00:22:38,040 --> 00:22:42,800
+لـ 4 و Y من 3 لـ 5 زي ما هيكون من minus 6 لـ minus 4
+
+326
+00:22:42,800 --> 00:22:47,560
+بعمل الـ integration بحصل على الـ total energy واضح؟
+
+327
+00:22:47,560 --> 00:22:52,110
+في أسف صح لحد هنا؟ طبعاً أخذنا هيك واضح ليش لأن قلنا
+
+328
+00:22:52,110 --> 00:22:55,870
+الـ X centered عند الثلاثة إذا هيكون الطول بيروح من
+
+329
+00:22:55,870 --> 00:23:01,390
+2 لـ 4 لأن طوله 2 Y centered عند 4 إذا بيكون من 3 ل
+
+330
+00:23:01,390 --> 00:23:05,810
+5 Z centered عند الـ minus 5 إذا بيروح من minus 6 ل
+
+331
+00:23:05,810 --> 00:23:12,450
+minus 4 طب كده المثال المثال طبعاً مهلكة عن
+
+332
+00:23:12,450 --> 00:23:14,770
+conductor و dielectric احنا شوفنا بين dielectric و
+
+333
+00:23:14,770 --> 00:23:16,870
+dielectric نشوف بين conductor و dielectric
+
+334
+00:23:24,290 --> 00:23:27,890
+عند الـ cube الأولاني الـ extension في الـ XZ
+
+335
+00:23:27,890 --> 00:23:32,970
+والثاني في الـ XZ اتقابل عند الـ Y equal 0 زي ما
+
+336
+00:23:32,970 --> 00:23:37,590
+تشوفي في الرسمة هي الـ Y axis و الـ two media اللي
+
+337
+00:23:37,590 --> 00:23:40,430
+هي الـ dielectric conductor اتقابل الـ interface
+
+338
+00:23:40,430 --> 00:23:45,090
+تبعهم أو البلين عند Y equal 0 تبع التقاطع واضح؟
+
+339
+00:23:48,320 --> 00:23:51,440
+for y أقل من أو تساوي زيرو الـ conductor for y أكبر
+
+340
+00:23:51,440 --> 00:23:55,960
+من أو تساوي زيرو الـ dielectric الـ ipsim relative
+
+341
+00:23:55,960 --> 00:24:00,500
+بتساوي اثنين if there is a surface charge هنا
+
+342
+00:24:00,500 --> 00:24:03,620
+معطينا surface charge مقدارها اثنين نانو كولوم بالمتر
+
+343
+00:24:03,620 --> 00:24:10,040
+تربيع من دا conductor E and D at أول حاجة بده
+
+344
+00:24:10,040 --> 00:24:14,660
+قيمة E و D عند A اللي موجودة في الكوندكتور ليش
+
+345
+00:24:14,660 --> 00:24:18,600
+موجودة في الكوندكتور عندما Y مالها سالبة قولنا Y
+
+346
+00:24:18,600 --> 00:24:22,580
+سالبة بيكون الكوندكتور و Y موجبة ده electric طب
+
+347
+00:24:22,580 --> 00:24:24,620
+احنا عارفين الـ electric الكوندكتور إيش الـ electric
+
+348
+00:24:24,620 --> 00:24:28,500
+فيه اللي بيكون عنده في قلبه Zero إذا الجواب
+
+349
+00:24:28,500 --> 00:24:31,760
+الأولاني سهل احنا أول حاجة بيقولوا إيه هذه النقطة
+
+350
+00:24:31,760 --> 00:24:36,580
+اللي ثلاثة ناقص اثنين اثنين بتكون في الكوندكتور لأن Y
+
+351
+00:24:36,580 --> 00:24:40,520
+مالها أقل من Zero وبالتالي E و D بيساوي 0 أطول
+
+352
+00:24:40,520 --> 00:24:43,120
+احنا قولنا الكوندكتور ما يحتويش على الـ electric
+
+353
+00:24:43,120 --> 00:24:45,320
+field لأن الـ charges كلها بتروح على الـ surfaces
+
+354
+00:24:45,320 --> 00:24:48,360
+بطل فيه عندي enclosed charges جوا بيكون الـ
+
+355
+00:24:48,360 --> 00:24:55,800
+electric و الـ D بالتالي بيساوي 0 النقطة B X-4Y1Z5
+
+356
+00:24:55,800 --> 00:24:58,000
+وين بيكون في Y أكبر من 0
+
+357
+00:25:22,250 --> 00:25:25,170
+واضح؟ لو كانت ما فيش free charge، هتكون برضه ال
+
+358
+00:25:25,170 --> 00:25:28,670
+normal component بتساوي zero طب إذا دي norm بتساوي
+
+359
+00:25:28,670 --> 00:25:32,290
+رقص، اللي هي اثنين نانو كولوم بالمتر تربيع، و دي
+
+360
+00:25:32,290 --> 00:25:37,060
+إيش هتساوي اتجاهها as a vector عشان نحددها ال
+
+361
+00:25:37,060 --> 00:25:39,920
+normal اللي هي مالها هتكون اتجاه الـ Y component
+
+362
+00:25:39,920 --> 00:25:43,500
+الـ tangential هي في الـ XZ component مالها صفر
+
+363
+00:25:43,500 --> 00:25:47,600
+وبالتالي بقدر أقول إنه E إيش بتساوي D على ال
+
+364
+00:25:47,600 --> 00:25:49,960
+epsilon اللي هي عبارة عن epsilon note في epsilon
+
+365
+00:25:49,960 --> 00:25:54,440
+relative و معطيني الـ dielectric لـ الـ media ال
+
+366
+00:25:54,440 --> 00:25:59,080
+relative dialectic لـ الـ dielectric ابسون ار
+
+367
+00:25:59,080 --> 00:26:01,400
+للديايلكتريك أو الـ relative permittivity
+
+368
+00:26:01,400 --> 00:26:04,060
+للديايلكتريك بتساوي اثنين طالعة على الرسمة مش في
+
+369
+00:26:04,060 --> 00:26:08,520
+السؤال فإذا أنا هقول إن E بتساوي D على E not E ر
+
+370
+00:26:08,520 --> 00:26:13,080
+بتساوي المتدرج دمنا اللي هو ستة وتلاتين باي و I
+
+371
+00:26:13,080 --> 00:26:20,120
+hat في اي سلسلة حد هنا إيه
+
+372
+00:26:20,120 --> 00:2
+
+401
+00:28:16,210 --> 00:28:22,230
+epsilon minus بدل الـ E من الـ E وحطتلها minus del V
+
+402
+00:28:22,230 --> 00:28:27,250
+بيسوي رو V طب احنا الـ diverge الـ del طبعا الـ
+
+403
+00:28:27,250 --> 00:28:31,320
+epsilon اذا أخدتها برضه متجانسةهذه طبعا الحالة اللى
+
+404
+00:28:31,320 --> 00:28:35,840
+عندنا هى المعادلة اللى بنوصل للـ متجانس يعنى y مالها
+
+405
+00:28:35,840 --> 00:28:39,240
+بعتمد على x و y و z اللى متجانس معناه ماقدرش
+
+406
+00:28:39,240 --> 00:28:43,120
+أطلعه من الـ differential انا بيصير له تفاضل لو هو
+
+407
+00:28:43,120 --> 00:28:47,180
+متجانس معناه y مالها بتعتمد على الـ x y z بتعتمد
+
+408
+00:28:47,180 --> 00:28:49,680
+على الـ position يعنى برضه نفس الـ epsilon function
+
+409
+00:28:49,680 --> 00:28:53,170
+في x y z مش بس potentialلكن لو أنا اعتبرتها
+
+410
+00:28:53,170 --> 00:28:56,590
+homogeneous، معناه يوماله لا يعتمد على الـX وY، إذا 
+
+411
+00:28:56,590 --> 00:28:59,630
+كنت بقدر أطلعه من الـdifferential، بالتالي إذا 
+
+412
+00:28:59,630 --> 00:29:01,950
+طلعت الـY من برة الـdifferential، minus يومالي،
+
+413
+00:29:01,950 --> 00:29:04,830
+حأحسب عندي الـdivergent دل، و الـdivergent دل احنا
+
+414
+00:29:04,830 --> 00:29:08,550
+شفناها قبل كده هي كـ دلتر بيع، إذا هيكون دلتر بيع الـV
+
+415
+00:29:08,550 --> 00:29:11,630
+بتساوي minus rho V على يومالي هي، بس هو equation
+
+416
+00:29:11,630 --> 00:29:17,070
+لمين؟ للـhomogenous medium تمام؟ إذا المبسطون الـ
+
+417
+00:29:17,070 --> 00:29:20,590
+equation للـ in homogenous media بتقول لي diverse
+
+418
+00:29:20,590 --> 00:29:25,790
+minus epsilon دل V بتساوي rho V للـ homogenous دل
+
+419
+00:29:25,790 --> 00:29:30,170
+تربيع V بتساوي minus rho V على epsilon لو كانت rho
+
+420
+00:29:30,170 --> 00:29:34,250
+V بتساوي zero بحصل على plus equation هيكون عندي
+
+421
+00:29:35,600 --> 00:29:39,040
+diverge minus epsilon دي الـ V بتساوي Zero لـ الـ
+
+422
+00:29:39,040 --> 00:29:42,840
+homogenous و دي الـ تربيع V بتساوي Zero لـ الـ
+
+423
+00:29:42,840 --> 00:29:47,200
+homogenous يعني لما الـ free chart بتساوي Zero بحصل
+
+424
+00:29:47,200 --> 00:29:50,900
+على plus equation لما رو V لا تساوي Zero بكون بحكي
+
+425
+00:29:50,900 --> 00:29:55,700
+على plus equation واضح؟ طب إيش الـ plus equation يا
+
+426
+00:29:55,700 --> 00:29:59,340
+عزيزي؟ طب لما إيش plus equation؟ واحد دلتين، الـ
+
+427
+00:29:59,340 --> 00:30:04,630
+homogenous و الـ inhomogenous تمام في الـ divergence
+
+428
+00:30:04,630 --> 00:30:08,430
+سالب إبسلون و gradient الـ voltage like this و بعد
+
+429
+00:30:08,430 --> 00:30:12,290
+ما عوضنا للخارج، صاروا ستان و نصر تمام، حد لمين؟
+
+430
+00:30:12,290 --> 00:30:14,910
+للمتجانس ولا لغير المتجانس؟ للمتجانس، إيه؟ ليش
+
+431
+00:30:14,910 --> 00:30:17,370
+للمتجانس؟ لأن إبسلون لسه موجودة، ما تقولوش أنها
+
+432
+00:30:17,370 --> 00:30:20,890
+بجد، ليش؟ لأنها determined على x, y, z، المتجانس،
+
+433
+00:30:20,890 --> 00:30:24,250
+طب و التعنية إيش بتكون؟ لما نضغط على سلب Epsilon
+
+434
+00:30:24,250 --> 00:30:30,030
+مرة أخرى، نعتمد عليه فعلا إلى Δ P بساوي رو P على
+
+435
+00:30:30,030 --> 00:30:32,470
+Epsilon مرة أخرى، minus rho V على Epsilon هنا لأن
+
+436
+00:30:32,470 --> 00:30:35,570
+Epsilon تصبح متجانسة، مع أنها لا تعتمد على X,
+
+437
+00:30:35,630 --> 00:30:39,350
+Y, Z، في حالة rho V بتساوي zero، بنحصل على الـ plus
+
+438
+00:30:39,350 --> 00:30:43,590
+أسواق اللي هم متجانس ولا اللي هم الجناس mediaطب الـ
+
+439
+00:30:43,590 --> 00:30:48,090
+Laplace احنا شوفنا قبل كده لكن للتذكير بتساوي في
+
+440
+00:30:48,090 --> 00:30:50,250
+الـ Cartesian أو الـ cylindrical أو الـ spherical
+
+441
+00:30:50,250 --> 00:30:54,390
+ماقدرنا نشتقها أو يعني نتذكرها أو نعرف اللى بدنا
+
+442
+00:30:54,390 --> 00:30:57,870
+إيه أو يعطي ليه في الامتحان أسهل واحدة فيهم اللى
+
+443
+00:30:57,870 --> 00:31:01,330
+في الـ Cartesian هي D2V بقي DX تربيع زي D2V بقي DY
+
+444
+00:31:01,330 --> 00:31:05,010
+تربيع زي D2V بقي DZ تربيع بتساوي Zero طبعا هذه
+
+445
+00:31:05,010 --> 00:31:09,050
+Laplace equation دل تربيع V بتساوي Zero لمين؟
+
+446
+00:31:09,050 --> 00:31:12,170
+للمتجانس لأن أُس من أنا طلعتها برا دل تربيع V
+
+447
+00:31:12,170 --> 00:31:17,110
+بتساوي Zero المتجانس أصلا plus equation بس هنا في
+
+448
+00:31:17,110 --> 00:31:19,930
+الـ cylindrical و هنا في الـ spherical coordinate
+
+449
+00:31:19,930 --> 00:31:24,970
+لأن الـ plus equation أصلا المتجانس السببية طب
+
+450
+00:31:24,970 --> 00:31:27,550
+uniqueness في الـ realm؟ إيش معناه uniqueness يا رم؟
+
+451
+00:31:27,550 --> 00:31:30,950
+إنه أنا لو أنا بدي solution يكون وحيداني، يعني أنا
+
+452
+00:31:30,950 --> 00:31:34,470
+بحكي عن الـ mouse هاي الزرقاء، بدي أنا اللي احصل
+
+453
+00:31:34,470 --> 00:31:36,470
+عليه في نهاية الـ mouse الزرقاء، ما بديش احصل على الـ
+
+454
+00:31:36,470 --> 00:31:39,390
+mouse الحمراء و الخضراء و الصفراء، ما لها الدنيا
+
+455
+00:31:39,390 --> 00:31:43,290
+mouseات، لكن أنا بحكي عن mouse معينة، بحكي عن موجة
+
+456
+00:31:43,290 --> 00:31:45,350
+معينة، بدي احصل على هذه الموجة معينة، هاي الـ
+
+457
+00:31:45,350 --> 00:31:47,910
+uniqueness مش الـ solution تبعه هذا mathematical
+
+458
+00:31:47,910 --> 00:31:51,510
+هذا الـ solution تبعه mathematical أو يعني هذه
+
+459
+00:31:51,510 --> 00:31:54,870
+المعادلات رياضية المعادلات الرياضية هي بتعطيني بس
+
+460
+00:31:54,870 --> 00:31:58,010
+الـ solution مليون solution أكملت solution واحد
+
+461
+00:31:58,010 --> 00:32:01,270
+منهم اللي بيخليها uniqueness اللي هي الـ boundary
+
+462
+00:32:01,270 --> 00:32:04,590
+conditions بحط الـ conditions بتاعت الـ problem
+
+463
+00:32:04,590 --> 00:32:07,630
+بتاعتي بتعطيني الـ solution تبعه أو بتعطيني الـ
+
+464
+00:32:07,630 --> 00:32:10,430
+wave بتاعتي أو الـ potential تبعاه بدون الـ boundary
+
+465
+00:32:10,430 --> 00:32:14,630
+conditions تعوني بيكون عندي solution مالها عام  بينفع
+
+466
+00:32:14,630 --> 00:32:22,030
+لأي حد ثاني، بينفع لنا و لعبير و لهديل و ل .. و
+
+467
+00:32:22,030 --> 00:32:26,030
+لهبة، بينفع للجميع، لكن أنا بس بدي الـ solution تبع
+
+468
+00:32:26,030 --> 00:32:30,190
+مين هديل، بدي بالنهاية يكون بنطبق الحلقة هديل مع
+
+469
+00:32:30,190 --> 00:32:32,790
+نبض أو الـ boundary conditions، لبسة جلبيه بلونها
+
+470
+00:32:32,790 --> 00:32:39,410
+بالنيباته، حاطه إشارب على شكل جلد النمر و هكذا بحط
+
+471
+00:32:39,410 --> 00:32:42,970
+الـ boundary condition بتاعتي بتطلع لي الموجة اللي
+
+472
+00:32:42,970 --> 00:32:46,050
+أنا بدور عنها هذه هي الـ uniqueness إذا إن هي دي
+
+473
+00:32:46,050 --> 00:32:49,650
+تلاتة تربيع V اللي هي الـ Laplace equation لـ الـ
+
+474
+00:32:49,650 --> 00:32:54,850
+homogeneous media بتساوي Zero بتقول لي إنه أنا عندي
+
+475
+00:32:54,850 --> 00:32:58,930
+solutions متعددة عشان أحقق أو يعني أوصل لـ solution
+
+476
+00:32:58,930 --> 00:33:03,630
+بديها أو الـ only solution اللي أنا بديها فقط بتحقق
+
+477
+00:33:03,630 --> 00:33:06,150
+هذا الحكي إذا طبقت الـ right boundary conditions
+
+478
+00:33:09,710 --> 00:33:16,410
+عشان احصل على الـ solution تبعي أولا بالدين أختار
+
+479
+00:33:16,410 --> 00:33:22,000
+المعادلة المناسبة أنا بدي مين؟ لبلاس ولا بسان؟ إيش
+
+480
+00:33:22,000 --> 00:33:25,460
+بأكمل على إن في عندي free charge ولا لأ؟ هل هي الـ
+
+481
+00:33:25,460 --> 00:33:28,680
+homogenous ولا الـ homogenous؟ بأكمل هل الـ
+
+482
+00:33:28,680 --> 00:33:32,580
+permittivity بتاعتك بتاعتك مد على الـ XYZ ولا لأ؟
+
+483
+00:33:32,580 --> 00:33:37,160
+إذا أول حاجة بدي أختار المعادلة الصحيحة بعدين بدي
+
+484
+00:33:37,160 --> 00:33:41,900
+أشوف المنطقة اللي بحل فيها عشان أختار اللي هي
+
+485
+00:33:45,560 --> 00:33:48,720
+أول حاجة بختار المعادلة الصحيحة بعدين بشوف الـ
+
+486
+00:33:48,720 --> 00:33:52,940
+region بتاعتي و بحل و بختار بعض الـ conditions
+
+487
+00:33:52,940 --> 00:33:59,440
+الصحيحة إذا الـ zero zero solution كانت مرة أول حاجة
+
+488
+00:33:59,440 --> 00:34:03,400
+بنحل لـ plus إذا كانت row v بتساوي zero أو بصمم
+
+489
+00:34:03,400 --> 00:34:07,580
+إذا كانت row v بتساوي zero بتساوي نستخدم الـ direct
+
+490
+00:34:07,580 --> 00:34:10,560
+integration ولا نستخدم الـ direct integration لو
+
+491
+00:34:10,560 --> 00:34:13,360
+أنا خلينا ناخد أسئلة واحدة اللي هي الـ plus
+
+492
+00:34:13,360 --> 00:34:16,820
+equation للـ homogenous media اللي هي تقبيع V لو
+
+493
+00:34:16,820 --> 00:34:20,520
+كانت الاعتمادية بتاعة الـ potential على Y بتساوي 0
+
+494
+00:34:21,140 --> 00:34:23,080
+الاعتمادية التانية من شاء على z بتساوي Zero إيش
+
+495
+00:34:23,080 --> 00:34:25,420
+هيكون عندي فقط الاعتمادية على الـ x، عندي تانين v
+
+496
+00:34:25,420 --> 00:34:28,140
+by dx تربيع بتساوي Zero Zero، مش هيبقى حلها by
+
+497
+00:34:28,140 --> 00:34:31,360
+direct integration بكامل أول مرة و ثاني مرة،
+
+498
+00:34:31,360 --> 00:34:34,460
+الحالة تبقى زي هيكون نفس الشيء هنا، لو كان مثلا
+
+499
+00:34:34,460 --> 00:34:36,800
+بعتمدش على الـ row و بعتمدش على الـ z ده، بس جد الـ
+
+500
+00:34:36,800 --> 00:34:41,150
+phi componentباستخدام الـ integral نفس الحاجة في الـ
+
+501
+00:34:41,150 --> 00:34:43,690
+spherical لو هدولة بقتملش على أعلى وتسيطر عن
+
+502
+00:34:43,690 --> 00:34:47,730
+نفسها على الـ five double integral بحل إذا بطلع لو
+
+503
+00:34:47,730 --> 00:34:50,470
+أنا الـ potential تبعي فقط بعتمد على one variable
+
+504
+00:34:50,470 --> 00:34:53,670
+دايما بسهل علي الحل بكون إني بقدر أعمل بالـ double
+
+505
+00:34:53,670 --> 00:34:56,730
+integral بجيب الـ solution لك لو بعتمد عليهم كلها
+
+506
+00:34:58,750 --> 00:35:02,530
+بنحلل بحاجة بنسميها separation of variables بندق
+
+507
+00:35:02,530 --> 00:35:05,310
+أستخدم الـ separation of variables يعني الحل الأول
+
+508
+00:35:05,310 --> 00:35:09,130
+طريقة الأول هي direct integration إذا كانت في فقط
+
+509
+00:35:09,130 --> 00:35:12,590
+فقط content variable واحد أو بستخدم الـ separation
+
+510
+00:35:12,590 --> 00:35:15,430
+of variables إذا كانت فيه مالها بتعتمد على أكثر من
+
+511
+00:35:15,430 --> 00:35:16,910
+variable واضحة هذه النقطة؟
+
+512
+00:35:19,800 --> 00:35:23,440
+لحدها لقيت الحل اللي حليته أسبوع بالدوبل انتجرال و
+
+513
+00:35:23,440 --> 00:35:26,260
+لا بالـ separation of variables الناتج تبعي مالها مش
+
+514
+00:35:26,260 --> 00:35:31,840
+unique لأنه عام لسه ما حطيتش عليه constraints بدي
+
+515
+00:35:31,840 --> 00:35:34,540
+أحط الـ boundary conditions وبالتالي بحصل على الـ
+
+516
+00:35:34,540 --> 00:35:38,770
+unique solution واضح؟ لما أحط الـ boundary
+
+517
+00:35:38,770 --> 00:35:41,250
+conditions أفرضها على الـ solution اللي حصلت عليه
+
+518
+00:35:41,250 --> 00:35:45,070
+بتساوي من اللي هي الـ double integral ولا من الـ
+
+519
+00:35:45,070 --> 00:35:47,550
+separation variable بحصل على الـ unique solution
+
+520
+00:35:47,550 --> 00:35:51,350
+إذا حصلت على V بسهولة عليا أجيب E لأن E مش بتساوي
+
+521
+00:35:51,350 --> 00:35:55,830
+minus grade V إذا جبت E بجيب D لأن D مش بتساوي
+
+522
+00:35:55,830 --> 00:36:01,670
+epsilon E واضح؟ كمان بقدر أجيب Q لأن Q مش بتساوي
+
+523
+00:36:01,670 --> 00:36:06,890
+الـ integral لـ rho S DS و rho S مش بتساوي DN إذا
+
+524
+00:36:06,890 --> 00:36:09,990
+بقدر أجيب أي حاجة إذا عرفت هذا الحكاية أقدر أجيب
+
+525
+00:36:09,990 --> 00:36:12,950
+مين is the distance between two media لأن الـ C
+
+526
+00:36:12,950 --> 00:36:15,950
+بتساوي و Q على V إذا كنت عارف الـ potential already
+
+527
+00:36:15,950 --> 00:36:19,530
+بقدر أجيب اللي هي الـ capacitance بالذات لو أنا كنت
+
+528
+00:36:19,530 --> 00:36:24,390
+أحكي على two conductors طبعا خلي الأمثلة القادمة
+
+529
+00:36:24,390 --> 00:36:27,850
+إن شاء الله بس راجعوا اللي حكيناه عشان تكونوا
+
+530
+00:36:27,850 --> 00:36:33,130
+معنا في أحل الأمثلة يعني احنا تقريبا هيك خلصنا الـ
+
+531
+00:36:33,130 --> 00:36:37,240
+chapter الباقي أسئلة يعني إن كان أقول لكم المقال
+
+532
+00:36:37,240 --> 00:36:41,680
+الجانب ده chapter 7 بس عشان تستفيدوا من حل الأمثلة
+
+533
+00:36:41,680 --> 00:36:45,640
+راجعوا أن تطلعوا عليه، تطلعوا على اللي حكيناه و
+
+534
+00:36:45,640 --> 00:36:47,860
+تطلعوا على الأمثلة نفسها عشان لو فيكم أي
+
+535
+00:36:47,860 --> 00:36:50,980
+استفسارات تحصلوا على الإجابات و احنا بنحكيها مع
+
+536
+00:36:50,980 --> 00:36:54,160
+بعض، تسألون ليش هي النقطة هيك و ليش النقطة هيك،
+
+537
+00:36:54,160 --> 00:36:57,420
+أما هيك باعتبار الـ chapter خلص، يعطيكم العفو
diff --git a/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/-oZSLACDJP8_postprocess.srt b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/-oZSLACDJP8_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..445b8f13bcfde71d4d5a499a8974c1d466f82ec5
--- /dev/null
+++ b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/-oZSLACDJP8_postprocess.srt
@@ -0,0 +1,2148 @@
+1
+00:00:21,190 --> 00:00:23,730
+بسم الله الرحمن الرحيم السلام عليكم ورحمة الله
+
+2
+00:00:23,730 --> 00:00:26,610
+وبركاته احنا ان شاء الله اليوم هنكمل ال boundary
+
+3
+00:00:26,610 --> 00:00:30,230
+conditions احنا قلنا هناخد boundary conditions بين
+
+4
+00:00:30,230 --> 00:00:33,770
+dielectric و dielectric conductor و dielectric و
+
+5
+00:00:33,770 --> 00:00:38,270
+conductor في space و هنستيين بيه ال y2 max with
+
+6
+00:00:38,270 --> 00:00:42,110
+equations ل ال clause integral دي dot dl بساوة
+
+7
+00:00:42,110 --> 00:00:45,450
+zero هي قلنا conservative force اللي هو ال work و
+
+8
+00:00:45,450 --> 00:00:50,360
+ال clause integral دي dot DS بتساويالخاص هو Gauss
+
+9
+00:00:50,360 --> 00:00:55,440
+law قلنا عشان نفهم إيش بيصير عند ال boundary إنه
+
+10
+00:00:55,440 --> 00:00:57,780
+نكتب ال fields ع شكل tangential و normal
+
+11
+00:00:57,780 --> 00:01:00,720
+components فعندنا اللي كتب field هنكتبه ع شكل
+
+12
+00:01:00,720 --> 00:01:04,200
+tangential زي normal وبالتالي ال fields البقية هم
+
+13
+00:01:04,200 --> 00:01:07,260
+نكتبه بهذه الطريقة بعدين نميز بال dialectric
+
+14
+00:01:07,260 --> 00:01:10,180
+dialectric boundaries قلنا لو كان عندى two
+
+15
+00:01:10,180 --> 00:01:14,670
+dialectrics بينهم هيكون boundaryقلنا بعد نفس
+
+16
+00:01:14,670 --> 00:01:16,330
+الحاجة ال electric field اللي هو في ال media ال
+
+17
+00:01:16,330 --> 00:01:20,670
+1E1 هاسمه ل tangential و normal component و E2
+
+18
+00:01:20,670 --> 00:01:23,430
+اللي هو في ال media التاني هاسمه ل normal و
+
+19
+00:01:23,430 --> 00:01:26,990
+tangential component و هدرس إيش بيصير ل tangential
+
+20
+00:01:26,990 --> 00:01:31,360
+component و إيش بيصير ل normal componentاستفدنا من
+
+21
+00:01:31,360 --> 00:01:34,040
+استخدامنا لل two Maxwell's equation ان ال
+
+22
+00:01:34,040 --> 00:01:36,140
+tangential component للـ electric field على ال
+
+23
+00:01:36,140 --> 00:01:38,680
+boundary between two dielectric مالها continuous
+
+24
+00:01:38,680 --> 00:01:43,720
+يعني E tangential واحد سو E tangential تنين لكن ال
+
+25
+00:01:43,720 --> 00:01:48,680
+intensity اللي هو D بتكون discontinuous هتكون D
+
+26
+00:01:48,680 --> 00:01:52,420
+واحد T على Epsilon واحد سو D تنين T على Epsilon
+
+27
+00:01:52,420 --> 00:01:59,380
+تنينكذلك لما نحكي عن normal components بدنا بال D
+
+28
+00:01:59,380 --> 00:02:03,880
+و أخدنا تنجينشال لل normal components لاقينا ان ال
+
+29
+00:02:03,880 --> 00:02:08,820
+normal component لل D بتكون continuous فقط في حالة
+
+30
+00:02:08,820 --> 00:02:12,820
+ان ال surface charged على ال interface بتساوي 0
+
+31
+00:02:12,820 --> 00:02:17,000
+لكن لو كانت ال surface charged لها تساوي 0 هيكون
+
+32
+00:02:17,000 --> 00:02:19,740
+ال difference بين ال normal components بساوي ال
+
+33
+00:02:19,740 --> 00:02:26,330
+surface charged ال free charged density رؤسمع انه
+
+34
+00:02:26,330 --> 00:02:29,810
+ال normal components continuous لل D هلاحظ انه ال
+
+35
+00:02:29,810 --> 00:02:33,730
+normal component لل E مارها discontinuous انه E1
+
+36
+00:02:33,730 --> 00:02:37,270
+E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1
+
+37
+00:02:37,270 --> 00:02:38,130
+E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1
+
+38
+00:02:38,130 --> 00:02:38,490
+E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1
+
+39
+00:02:38,490 --> 00:02:42,070
+E1 E1 E1 E1 E1 E1 E1 E1 E1 E1
+
+40
+00:02:42,070 --> 00:02:43,610
+E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1
+
+41
+00:02:43,610 --> 00:02:45,690
+E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1
+
+42
+00:02:45,690 --> 00:02:54,050
+E1 E1الـ 2 ده ال electrics فيها E1 و E2 و E1 و D1
+
+43
+00:02:54,050 --> 00:02:58,670
+E1 و D1 زى ما تشايفين هدولة فى ال media الأولى هدا
+
+44
+00:02:58,670 --> 00:03:06,490
+ال norm على ال surface هدا norm على ال surface هده
+
+45
+00:03:06,490 --> 00:03:13,110
+يعنى E1 و D1 برضه هجزقها ل tangential components و
+
+46
+00:03:13,110 --> 00:03:16,790
+normal components نفس الحاجة بالنسبة ل E2 و D2
+
+47
+00:03:17,080 --> 00:03:21,200
+هجزقهم ل tangential components و normal components
+
+48
+00:03:21,200 --> 00:03:25,080
+واضح ال components اللي ماقلتش فيها مشكلة طب احنا
+
+49
+00:03:25,080 --> 00:03:26,960
+بدنا نشوف ايش قانون ال refraction ال refraction
+
+50
+00:03:26,960 --> 00:03:30,560
+بتاعه اللي هو انكسار بين two dielectric medium على
+
+51
+00:03:30,560 --> 00:03:36,480
+اساس ان θ1 و θ2 بمثله θ1 هي الزاوية المابين ال
+
+52
+00:03:36,480 --> 00:03:41,420
+electric field و ال norm على ال surfaceأو θتنين هي
+
+53
+00:03:41,420 --> 00:03:44,840
+الزاور بين ال field و ال norm على ال surface على
+
+54
+00:03:44,840 --> 00:03:47,500
+ال interface يعني وين ال interface بحط normal
+
+55
+00:03:47,500 --> 00:03:51,400
+عليها و الزاور بين ال field و ال norm هي بتكون θتا
+
+56
+00:03:51,400 --> 00:03:54,540
+طب نيجي على ال tangential component ال tangential
+
+57
+00:03:54,540 --> 00:04:00,960
+component لE ايش بتساوي E1 sin θ1 صح و E2
+
+58
+00:04:00,960 --> 00:04:07,150
+tangential ايش هتكون E2 sinثاتنين طب احنا عارفين
+
+59
+00:04:07,150 --> 00:04:09,890
+ان اي واحد tangential بتسوي اتنين tangential اللي
+
+60
+00:04:09,890 --> 00:04:11,730
+اسبقنا اثبتناها في المحاضرة الماضية وارجعناها
+
+61
+00:04:11,730 --> 00:04:14,410
+اليوم ال tangential component لل electric field
+
+62
+00:04:14,410 --> 00:04:17,790
+between two dielectrics مالها continuous اذا اي
+
+63
+00:04:17,790 --> 00:04:21,550
+واحد tangential بتسوي اتنين tangentials لكن احنا
+
+64
+00:04:21,550 --> 00:04:26,430
+عارفنا من الرسمة اللي قمناها ال field وهي ال theta
+
+65
+00:04:26,430 --> 00:04:29,870
+واحد اللي بين ال field و ال non ال tangential
+
+66
+00:04:29,870 --> 00:04:33,690
+بتحدي اشهر كم قيمتها اي واحد sin theta واحدو نفس
+
+67
+00:04:33,690 --> 00:04:37,950
+بقضية بالنسبة ل E2 وهي θتة اتنين هي الزاوية بين ال
+
+68
+00:04:37,950 --> 00:04:40,610
+field و ال norm هتكون ال tangential component
+
+69
+00:04:40,610 --> 00:04:43,790
+بتساوي E2 K sin θتة اتنين اللي هو زي ما احنا
+
+70
+00:04:43,790 --> 00:04:48,710
+شايفين هذا من ال boundary condition ان E1
+
+71
+00:04:48,710 --> 00:04:51,890
+tangential بتساوي E2 tangential E1 tangential
+
+72
+00:04:51,890 --> 00:04:55,570
+بتساوي E1 sin θتة اتنين و E2 tangential بتساوي E2
+
+73
+00:04:55,570 --> 00:04:57,590
+sin θتة اتنين ايش كمان بعض ال condition التاني
+
+74
+00:04:57,590 --> 00:05:02,390
+قالنا ان ال D norm هي ال continuousD1 non بتسوي D2
+
+75
+00:05:02,390 --> 00:05:05,510
+non إذا ماكانش هنا free charge يعني إذا كانت هذه
+
+76
+00:05:05,510 --> 00:05:09,690
+row بتسوي zero ال free charge بتسوي zero إذا D1
+
+77
+00:05:09,690 --> 00:05:13,830
+non بتسوي D2 non D1 non شو هتسوي ال normal
+
+78
+00:05:13,830 --> 00:05:18,090
+component ل D1 هاي دي D1 ال normal اللي هي هاي
+
+79
+00:05:18,090 --> 00:05:25,150
+هتكون D1 cosine theta 1 جيب تمام theta 1
+
+80
+00:05:49,950 --> 00:05:51,960
+D1D1D1D1D1D1D1D1D1D1D1D1D1D1D1D1D1D1D1D1D1D1D1ساين
+
+81
+00:05:51,960 --> 00:05:55,500
+على كوساين اللي هي tan θ1 أقى epsilon 1 بيساوي tan
+
+82
+00:05:55,500 --> 00:06:00,400
+θ2 على epsilon 2 إذا عبضنا عن epsilon 1 و epsilon
+
+83
+00:06:00,400 --> 00:06:04,480
+2 بقيمتهم ده لاتر ال relative permittivity epsilon
+
+84
+00:06:04,480 --> 00:06:06,540
+1 هتكون epsilon not في relative permittivity
+
+85
+00:06:06,540 --> 00:06:09,660
+للmedia الأولى و epsilon 2 هتكون epsilon not في
+
+86
+00:06:09,660 --> 00:06:13,680
+epsilon relative للmedia التانية هيكون الtan θ1
+
+87
+00:06:13,680 --> 00:06:16,480
+على tan θ2 بيساوي relative permittivity للmedia
+
+88
+00:06:16,480 --> 00:06:20,400
+الأولى على relative permittivity للmedia التانية
+
+89
+00:06:29,190 --> 00:06:32,770
+نجي لقى ال conductor dielectric ايش الفرق بين
+
+90
+00:06:32,770 --> 00:06:35,330
+dielectric و dielectric؟ بين dielectric و
+
+91
+00:06:35,330 --> 00:06:38,190
+conductor احنا قلنا ال conductor ايش بيكون ال
+
+92
+00:06:38,190 --> 00:06:41,930
+electric field في قلبه zero يعني خصائص ال
+
+93
+00:06:41,930 --> 00:06:44,210
+conductor ال electric field بيكون بساوة سفر في
+
+94
+00:06:44,210 --> 00:06:47,410
+قلبه لأن ال charges بيروح على ال surface بطل فيه
+
+95
+00:06:47,410 --> 00:06:50,470
+charges in plus في ال conductor وبالتالي بيكون ال
+
+96
+00:06:50,470 --> 00:06:53,310
+electric field بساوة zero قولنا معدى اذا احنا
+
+97
+00:06:53,310 --> 00:06:57,630
+أجبرناه ووصلنا معاه أسلاب، مفذكرين؟ لإن هو في ال
+
+98
+00:06:57,630 --> 00:07:02,090
+free spaceوحطيها electric field هلاقي انه في قلب
+
+99
+00:07:02,090 --> 00:07:06,670
+ال conductor electric field بساوي 0 اذا أنا عندي
+
+100
+00:07:06,670 --> 00:07:10,110
+هاي ال conductor وهي ال electric field ال
+
+101
+00:07:10,110 --> 00:07:12,850
+dielectric وهي ال boundary اللي بين ال two medium
+
+102
+00:07:12,850 --> 00:07:16,170
+اللي هو الخط هذا، هذا هو ال boundary، هذا خط ال
+
+103
+00:07:16,170 --> 00:07:22,630
+boundary لو استخدمنا Maxwell's equations هلاقي نفس
+
+104
+00:07:22,630 --> 00:07:25,870
+القضية ان E tangential لازم تكون continuous اللي
+
+105
+00:07:25,870 --> 00:07:28,890
+هي ال clause انتجرة لE dot dlلكن الـ tangential
+
+106
+00:07:28,890 --> 00:07:32,510
+component في القندكتور أشبه الساوي 0 ال electric
+
+107
+00:07:32,510 --> 00:07:35,810
+field في القندكتور أشبه الساوي 0 فال tangential
+
+108
+00:07:35,810 --> 00:07:41,270
+component 0 إذا E tangential في اللي هو ال media
+
+109
+00:07:41,270 --> 00:07:44,410
+اللي هي الدايليكتريك الساوي 0 لو أخدنا النمر
+
+110
+00:07:44,410 --> 00:07:48,530
+components اللي هي DN هلاحظ أنه مالها احنا قلنا
+
+111
+00:07:48,530 --> 00:07:52,290
+بتكون ال D continuous إذا كانت رقص ساوي 0 لاتوا
+
+112
+00:07:52,290 --> 00:07:58,230
+ساوي 0 هتكون DN أشبه ساوي رقصفال E tangential هي 0
+
+113
+00:07:58,230 --> 00:08:02,330
+لأن E tangential في الconductor هي 0 انتوا باخدين
+
+114
+00:08:02,330 --> 00:08:05,530
+ان احنا بس بحطين E واحدة مش E واحد و E اتنين E
+
+115
+00:08:05,530 --> 00:08:08,390
+اللي هي ال direct trip فال tangential component
+
+116
+00:08:08,390 --> 00:08:12,250
+بتاعتها 0 لأن E tangential في ال conductor هي 0 و
+
+117
+00:08:12,250 --> 00:08:17,830
+ال normal component لD هتكون بالسوء raw D مش هيكون
+
+118
+00:08:17,830 --> 00:08:22,970
+D على 1 نقص D على 2 لأن D على 2 هي 0الكندكتور عنده
+
+119
+00:08:22,970 --> 00:08:26,810
+ال electric field بيساوي 0 إذا A0 إذا D بيساوي 0
+
+120
+00:08:26,810 --> 00:08:31,010
+لو
+
+121
+00:08:31,010 --> 00:08:35,990
+كان ال electric field قلنا بيبقى انه انه مافيش
+
+122
+00:08:35,990 --> 00:08:39,490
+electric field في قلب الكندكتور لو كان Trophy
+
+123
+00:08:39,490 --> 00:08:45,610
+بيساوي 0لأ في قلب ال conductor اللي انا حكيته انه
+
+124
+00:08:45,610 --> 00:08:48,330
+اي charges ايش بتصير اللي هقولنا بتصير على الباندر
+
+125
+00:08:48,330 --> 00:08:50,850
+لو موجودة charges بتروح كلها على الباندر وبالتالي
+
+126
+00:08:50,850 --> 00:08:54,330
+ال electric field لو أخدت gauss law بساوة zeroفهذا
+
+127
+00:08:54,330 --> 00:08:57,990
+اللي بنحكي هنا ان مافيش انا عندى اي field exist فى
+
+128
+00:08:57,990 --> 00:09:00,610
+قلب ال conductor معناه ان رو V بالثاوة زيرو و E
+
+129
+00:09:00,610 --> 00:09:03,210
+بالثاوة زيرو E بالثاوة زيرو ان احنا ال electric
+
+130
+00:09:03,210 --> 00:09:06,290
+field ايش اللي بنعبر عنه برضه ال potential scalar
+
+131
+00:09:06,290 --> 00:09:09,570
+potential انه E بالثاوة minus grade V ايش قولنا
+
+132
+00:09:09,570 --> 00:09:12,250
+echo potential surfaces للكندكتور من الذاكرين
+
+133
+00:09:12,250 --> 00:09:16,710
+قولنا دل V بالثاوة زيرو معناه ان ال conductor
+
+134
+00:09:16,710 --> 00:09:18,770
+بتصرف as echo potential body
+
+135
+00:09:28,080 --> 00:09:31,460
+طبعا اذا احنا قلنا معناه ان ال electric field مانه
+
+136
+00:09:31,460 --> 00:09:34,400
+zero على ال conductor اذا معناه زى ما انتوا شايفين
+
+137
+00:09:34,400 --> 00:09:38,140
+ان E T tangential لنا بالساوة Zero برضه E T
+
+138
+00:09:38,140 --> 00:09:41,320
+بالساوة Zero لان E T ايش علاقتها ب E T بال Epsilon
+
+139
+00:09:41,320 --> 00:09:44,520
+Epsilon ل ال media للكندكتور اذا ماحتكون برضه Zero
+
+140
+00:09:44,520 --> 00:09:48,800
+لكن DN اللى احنا قلناه هتساوي ρو S وين بتكون
+
+141
+00:09:48,800 --> 00:09:53,460
+External للكندكتور و عمودي عليه يعني فقط هى اللى
+
+142
+00:09:53,460 --> 00:09:57,320
+بيكون موجود لو كان عندى conductorهيكون الـ
+
+143
+00:09:57,320 --> 00:10:00,260
+tangential component تسوى 0 دائما، external
+
+144
+00:10:00,260 --> 00:10:05,080
+للكندكتور هتكون ال tangential component 0، وإيش
+
+145
+00:10:05,080 --> 00:10:08,080
+هتكون فقط ال external، اللي هي ال normal component
+
+146
+00:10:08,080 --> 00:10:12,480
+فقط ال non-zero component هي ال normal component،
+
+147
+00:10:12,480 --> 00:10:16,180
+ال tangential تسوى 0، ال normal .. يعني نقدر نقول
+
+148
+00:10:16,180 --> 00:10:20,860
+بساطة إن ال electric field خارج الكندكتور هيكون
+
+149
+00:10:20,860 --> 00:10:23,480
+دائما على ال normal direction لأن ال tangential
+
+150
+00:10:23,480 --> 00:10:25,280
+component دائما بتسوى 0
+
+151
+00:10:36,070 --> 00:10:38,570
+عشان هذا الاشي ان ال electric field في قلب اي
+
+152
+00:10:38,570 --> 00:10:42,350
+conductor بيساوي zero احنا بنسمي ال conductor as a
+
+153
+00:10:42,350 --> 00:10:46,430
+shield يعني مثلا لو احنا اعتبرنا اللي هي ال a هذه
+
+154
+00:10:46,430 --> 00:10:51,950
+هي عبارة عن conductor بحط هنا body اللي هو b في
+
+155
+00:10:51,950 --> 00:10:56,120
+قلب اللي هو ال conductor aال conductor A ايش
+
+156
+00:10:56,120 --> 00:11:00,760
+بيعمل؟ بيمنع اختراق اي electric field ل inside ال
+
+157
+00:11:00,760 --> 00:11:05,460
+A فمعناه ان B مش هتشعر بالمرة في وجود ال C و نفس
+
+158
+00:11:05,460 --> 00:11:08,360
+الشيء ال C مش هتشعر بالمرة في وجود ال B لأن ال
+
+159
+00:11:08,360 --> 00:11:13,660
+conductor A ايش عمل؟ ك shield كدرع واقي هيمنع ان
+
+160
+00:11:13,660 --> 00:11:18,040
+ال body B انه يشعر في وجود ال C و نفس العضية ال
+
+161
+00:11:18,040 --> 00:11:22,140
+body C مش هيعشعر في وجود ال body Bأنه إحنا شرناه
+
+162
+00:11:22,140 --> 00:11:24,920
+بمنع اختراف ال electric field إله فقط هيكون
+
+163
+00:11:24,920 --> 00:11:28,460
+external و normal إله، مش هيكون في قلبه، وبالتالي
+
+164
+00:11:28,460 --> 00:11:33,060
+ال body بيه هيشعر إنه محمي من اللي هو أي تأثير ل
+
+165
+00:11:33,060 --> 00:11:38,460
+ال body تسييه، بنسميه electrostatic screening or
+
+166
+00:11:38,460 --> 00:11:40,920
+shielding، shielding اللي هو حالي و ال screen هو
+
+167
+00:11:40,920 --> 00:11:44,580
+برضه زي إحنا بنحمي حالنا الشبكة من البعض و من
+
+168
+00:11:44,580 --> 00:11:47,160
+الحشبات الدارة
+
+169
+00:11:54,690 --> 00:11:57,090
+أخر حاجة اللي هي conductor of free space احنا قلنا
+
+170
+00:11:57,090 --> 00:11:59,410
+بالـ free space ما هو إلا الـ dielectric و الـ
+
+171
+00:11:59,410 --> 00:12:02,850
+epsilon بتساوي epsilon node يعني اللي حكيناه قبل
+
+172
+00:12:02,850 --> 00:12:06,350
+قليل على conductor dielectric حالة خاصة منه اللي
+
+173
+00:12:06,350 --> 00:12:09,710
+هي الـ free space يعني بقدر أقول إنه ال electric
+
+174
+00:12:09,710 --> 00:12:14,690
+field هيكون external للكندكتور و normal عليه بمعنى
+
+175
+00:12:14,690 --> 00:12:18,710
+إن ال tangential component بتساوي 0 و ال normal
+
+176
+00:12:18,710 --> 00:12:22,390
+component بتساوي ρو S و ال D norm مش بتساوي
+
+177
+00:12:22,390 --> 00:12:28,520
+epsilon node Emواضح؟ لأن Epsilon relative بالنسبة
+
+178
+00:12:28,520 --> 00:12:33,260
+للـ space بالساوي واحد لنشوف بعض الأمثلة بنا
+
+179
+00:12:33,260 --> 00:12:35,920
+نستفيد من power condition احنا في حالتنا عشان نحل
+
+180
+00:12:35,920 --> 00:12:39,200
+الأمثلة ان لو انا كنت عارفة بعض المعلومات عن ال
+
+181
+00:12:39,200 --> 00:12:42,040
+electric field في media كيف اقدر اجيبها في media
+
+182
+00:12:42,040 --> 00:12:46,140
+تانية يعني مثل ان هذا المثل اللي قدامنا الناتو
+
+183
+00:12:46,140 --> 00:12:50,130
+extensive homogeneousisotropic، dielectric،
+
+184
+00:12:50,130 --> 00:12:52,850
+homogenous إيش معناه؟ قلنا إبسلون لتعتمد على X
+
+185
+00:12:52,850 --> 00:12:56,530
+والـ Y إيستروبك إنه الـ D والـ E بيكونوا في اتجاه
+
+186
+00:12:56,530 --> 00:13:02,030
+واحد meet أن بلان Z بالساوة Zero يعني هاي ال two
+
+187
+00:13:02,030 --> 00:13:05,950
+planes هاي الأولاني، هاي المكعب الأولاني أو ال
+
+188
+00:13:05,950 --> 00:13:08,890
+media الأولى وهي ال media التانية وانتقعوا تعاون،
+
+189
+00:13:08,890 --> 00:13:14,730
+قعدوا على بعض يعني Z equal Zero هاي ال Z-axis هاي
+
+190
+00:13:14,730 --> 00:13:22,430
+ال Z-axisوهذه z equals 0 احنا ال two media قاعدة
+
+191
+00:13:22,430 --> 00:13:26,070
+على بعض ال z equals 0 اذا ال interface بيكون ال
+
+192
+00:13:26,070 --> 00:13:29,170
+plan تبع ال interface بيكون ال z equals 0 واضح
+
+193
+00:13:29,170 --> 00:13:33,410
+مبتد في ال x y plan ويكون زي ما قلنا احنا لو
+
+194
+00:13:33,410 --> 00:13:37,350
+دفترين او مكعبين يعني لو قعدتكم دفترين افرجكم ايش
+
+195
+00:13:37,350 --> 00:13:44,030
+اصلا في ال two medias و ال interfaceهذه الميديا
+
+196
+00:13:44,030 --> 00:13:47,810
+الأولى وهذه الميديا الثانية وانطلاقها هذا هو ما
+
+197
+00:13:47,810 --> 00:13:51,370
+نسميه ال interface اللي هو جلد الدفتر بالتمام احنا
+
+198
+00:13:51,370 --> 00:13:55,250
+كنا حاطين جلد الدفتر عن z equal 0 هدوله two plans
+
+199
+00:13:55,250 --> 00:13:59,530
+يعني موجودين في ال XY plan لكن في ال z axis واحدة
+
+200
+00:13:59,530 --> 00:14:06,950
+هتكون في minus z والتانية في plus z شكرا لكم لذا
+
+201
+00:14:06,950 --> 00:14:11,890
+هى انا ال two mediasاللي هي الـ 1 و 2 Epsilon R1
+
+202
+00:14:11,890 --> 00:14:15,850
+للميديا الأولى التي الديالكتريك 1 و الديالكتريك
+
+203
+00:14:15,850 --> 00:14:20,410
+للميديا Epsilon R2 Epsilon R1 قيمتها 4 و Epsilon
+
+204
+00:14:20,410 --> 00:14:24,570
+R2 قيمتها 3 و زى ما قلنا ان ال Epsilon الميديا
+
+205
+00:14:24,570 --> 00:14:28,170
+الأولى في Z أكبر من أو تساوي 0 و الميديا التانية
+
+206
+00:14:28,170 --> 00:14:32,960
+في Z أقل من أو تساوي 0في ال media الأولى كان في
+
+207
+00:14:32,960 --> 00:14:37,280
+عندي electric field E1 انا عارفة كل معلوماته انه
+
+208
+00:14:37,280 --> 00:14:41,240
+ال component في ال X direction قيمتها خمسة و في ال
+
+209
+00:14:41,240 --> 00:14:44,200
+Y مقدرها ماينس تنين و في ال Z مقدرها تلاتة
+
+210
+00:14:44,200 --> 00:14:50,160
+كيلوفورت بالمتر اللي طالب هو الحاجة E2 for Z أقل
+
+211
+00:14:50,160 --> 00:14:53,240
+من Zero عشان اجيب E2 ايش لازم اجيب ال tangential
+
+212
+00:14:53,240 --> 00:14:57,940
+component و ال normal componentطب احنا عرفنا انه
+
+213
+00:14:57,940 --> 00:14:59,840
+بين الـ dielectric و ال dielectric tangential
+
+214
+00:14:59,840 --> 00:15:04,060
+component مالهم continuous يعني E tangential واحد
+
+215
+00:15:04,060 --> 00:15:07,040
+بسوء E tangential تنين مين ال tangential component
+
+216
+00:15:07,040 --> 00:15:10,160
+في هالحالة؟ اللي هي ال X و ال Y مين اللي على ال
+
+217
+00:15:10,160 --> 00:15:13,040
+interface اللي فرجتكميا الدفترين؟ هيكون ال X و ال
+
+218
+00:15:13,040 --> 00:15:17,220
+Y اللي عمودي عليهم مين؟ ال Z component اذا بطلع
+
+219
+00:15:17,220 --> 00:15:20,200
+وين ال X component و ال Y component؟ خمس X minus
+
+220
+00:15:20,200 --> 00:15:27,290
+اتنين Y هي E واحد tangentialE1 norm هي 3AZ hat إذا
+
+221
+00:15:27,290 --> 00:15:31,030
+من ال boundary condition E1 tangential بتسوي E2
+
+222
+00:15:31,030 --> 00:15:35,370
+tangential بتالي E2 tangential ايش قيمتها 5X hat
+
+223
+00:15:35,370 --> 00:15:39,350
+minus 2Y hat واضح؟ طب ال normal component قولنا
+
+224
+00:15:39,350 --> 00:15:46,490
+مين من ال normal اللي هي DN1 بتسوي DN2 أو D1 DN1
+
+225
+00:15:46,490 --> 00:15:50,950
+minus DN2 بتسوي raw free بس هو مجرد نسيرة أي free
+
+226
+00:15:50,950 --> 00:15:55,710
+chargesمعناه raw بتساوي صفر ال surface charge
+
+227
+00:15:55,710 --> 00:16:01,470
+بتساوي zero اذا دي واحد norm بتساوي دي تانين norm
+
+228
+00:16:01,470 --> 00:16:05,210
+طب دي واحد norm مش بتساوي epsilon واحد في E واحد
+
+229
+00:16:05,210 --> 00:16:10,300
+normالتي قيمتها تلاتة اي واحد نورم اي ابسلون ار
+
+230
+00:16:10,300 --> 00:16:14,580
+واحد هي اربعة اربعة في تلاتة هي اللي هي دي واحد
+
+231
+00:16:14,580 --> 00:16:18,180
+نورم هي تساوي دي تانين نورم وبالتالي بقدر اقول اي
+
+232
+00:16:18,180 --> 00:16:21,280
+تانين نورم لان اي تانين نورم مش متساوي دي تانين
+
+233
+00:16:21,280 --> 00:16:25,620
+نورم على ابسلون تانين ار واضح كده شفنا ال
+
+234
+00:16:25,620 --> 00:16:29,460
+components كلهم هي المحلول المحضوطة هي اي واحد
+
+235
+00:16:29,460 --> 00:16:32,920
+نورم متساوي اي واحد dot and hat اللي هي التلاتة
+
+236
+00:16:35,690 --> 00:16:39,190
+والتي هي total E E norm plus E tangential وكذا انا
+
+237
+00:16:39,190 --> 00:16:41,710
+قلت لكم يا tangential component اللي في ال X وY
+
+238
+00:16:41,710 --> 00:16:44,850
+component ال tangential تنين هتسوى E tangential
+
+239
+00:16:44,850 --> 00:16:48,050
+واحد دي تنين norm بتسوى D واحد norm لإن ال free
+
+240
+00:16:48,050 --> 00:16:51,150
+charge على ال surface اللي قلنا بتسوى Zero وD واحد
+
+241
+00:16:51,150 --> 00:16:55,570
+norm ايش بتسوى Y راتب واحد في E واحد N وبنجيب دي
+
+242
+00:16:55,570 --> 00:16:59,040
+تنين N وبالتالي بقدر أجيب E تنين N لإنها هتكوندى
+
+243
+00:16:59,040 --> 00:17:03,780
+تنين N على ي مقار تنين اذا جبنا E تنين tangential
+
+244
+00:17:03,780 --> 00:17:07,200
+او E تنين norm بالتالي بقدر اقول ان E تنين او E
+
+245
+00:17:07,200 --> 00:17:11,480
+tangential زائد E تنين norm و بقدر احسب قيمة ال E
+
+246
+00:17:11,480 --> 00:17:16,800
+تنين واضح كده اذا انا معرفتى المعطيات عن ال field
+
+247
+00:17:16,800 --> 00:17:20,620
+في ال media الأولى عرفت اول شي بال media ال field
+
+248
+00:17:20,620 --> 00:17:23,780
+في ال media التانية لان عارفة ال conditions بتاعة
+
+249
+00:17:23,780 --> 00:17:28,450
+ال boundary بين ال two dielectricsطب الزوايا بين
+
+250
+00:17:28,450 --> 00:17:33,240
+E1 و E2 اللي بيعملوهم على ال interfaceبتوا الزاوية
+
+251
+00:17:33,240 --> 00:17:36,100
+اللي بيعملوها مع ال interface طبعا عندي two
+
+252
+00:17:36,100 --> 00:17:41,020
+components يعني عندي XY component على ال XY plane
+
+253
+00:17:41,020 --> 00:17:44,620
+يعني عندي E1 لو أنا بدأ أفكر في الزاوية اللي بين
+
+254
+00:17:44,620 --> 00:17:49,080
+ال XY plane في ال XY plane هتكون أصعب من إن لو
+
+255
+00:17:49,080 --> 00:17:51,720
+فكرت في ال Z component لإن عندي one component في
+
+256
+00:17:51,720 --> 00:17:55,420
+ال Z component يعني لما طلعت على ال Z component لل
+
+257
+00:17:55,420 --> 00:17:59,380
+electric field بقول إن ال Z component مش متساوي E
+
+258
+00:17:59,380 --> 00:18:04,140
+جبت من ستة واحد صح؟إذا جيبت ال 6 واحد انا هجيب ال
+
+259
+00:18:04,140 --> 00:18:07,420
+alpha واحد بمنتهى البساطة بقدر اقول ان E alpha
+
+260
+00:18:07,420 --> 00:18:11,100
+واحد بالساوي اللى هى ال difference بين ال 90 نقل
+
+261
+00:18:11,100 --> 00:18:16,520
+ال 6 واحد او بدي اجيب قيمة ال E واحد tangential
+
+262
+00:18:16,520 --> 00:18:19,880
+اللى هى ال square root ل X تربيع زى E X تربيع زى E
+
+263
+00:18:19,880 --> 00:18:22,700
+Y تربيع بس هسأل ليه ان اجيب الزاوية ما بين ال Z
+
+264
+00:18:22,700 --> 00:18:29,090
+component و ال norm على ال interfaceالـ E1 والنورم
+
+265
+00:18:29,090 --> 00:18:32,370
+على ال interface وبالتالي بقدر اجيب اللي مع ال
+
+266
+00:18:32,370 --> 00:18:35,670
+interface انا هتكون تسعين ناقص سيتا اللي مع ال
+
+267
+00:18:35,670 --> 00:18:41,270
+norm لذان هذه هي الحطوة التانية بتأجيب سيتا واحد و
+
+268
+00:18:41,270 --> 00:18:44,290
+سيتا اتنين و احنا قولنا انه انا عارفة ال normal
+
+269
+00:18:44,290 --> 00:18:47,710
+component و ال tangential component لل fields بقدر
+
+270
+00:18:47,710 --> 00:18:51,930
+اقول ان سيتا واحد يعني اصلا بعملها بهذه الطريقة ان
+
+271
+00:18:51,930 --> 00:18:57,280
+سيتا واحد بتساوييا سواء اللي هو ال .. بجيب دلالتي
+
+272
+00:18:57,860 --> 00:19:01,460
+الـ tangential component انها cosine او التان ان
+
+273
+00:19:01,460 --> 00:19:05,700
+بقول magnitude تبع ال E1 tangential على اللي هي ال
+
+274
+00:19:05,700 --> 00:19:10,400
+E1Z هى بتكون تان ثتا واحد اذا حسبناها باي طريقة زى
+
+275
+00:19:10,400 --> 00:19:12,860
+ما احنا هنا حاسبينها ان جيبت المتدار تبع ال E1
+
+276
+00:19:12,860 --> 00:19:16,040
+tangential هي ال square root المربع المولى زائد
+
+277
+00:19:16,040 --> 00:19:18,980
+المربع التانية و ال A norm احنا عارفين ان هي في ال
+
+278
+00:19:18,980 --> 00:19:22,280
+Z component بقدر و انت تان ثتا واحد E1 tangential
+
+279
+00:19:22,280 --> 00:19:26,110
+اي واحد norm بجيب ثتا واحدبجيب الفا واحد لان الفا
+
+280
+00:19:26,110 --> 00:19:29,290
+واحد مش هتساوي تسعين minus ستة واحد نفس الحكي
+
+281
+00:19:29,290 --> 00:19:33,390
+بطبقه على اللي هو ال E في ال media التانية و بقدر
+
+282
+00:19:33,390 --> 00:19:38,810
+اجيب اللي هي الفا تنين بعد اشهر بعدهال energy
+
+283
+00:19:38,810 --> 00:19:43,690
+densities in both dielectrics و احنا برضه شوفنا ان
+
+284
+00:19:43,690 --> 00:19:46,750
+ال energy density بتساوي نص ال dielectric فى ال
+
+285
+00:19:46,750 --> 00:19:51,010
+magnitude لفير تربية فزا فى ال media الأولى هتكون
+
+286
+00:19:51,010 --> 00:19:54,830
+ال energy density نص ابسلون واحد اي واحد تربية فى
+
+287
+00:19:54,830 --> 00:19:57,670
+ال media التانية هتكون نص ابسلون اتنين اي
+
+288
+00:19:57,670 --> 00:20:00,230
+magnitude تربية هو ماعطينا ال relative
+
+289
+00:20:00,230 --> 00:20:05,640
+permittivityأبسلون ار واحد ابسلون ار اتنين لكن انا
+
+290
+00:20:05,640 --> 00:20:09,100
+بدي ابسلون فاش بس اذا بضرب هذا ابسلون نوت اذا ربنا
+
+291
+00:20:09,100 --> 00:20:12,280
+ابسلون relative ابسلون نوت بحصل على ابسلون في
+
+292
+00:20:12,280 --> 00:20:15,820
+الميديا فإذا ابسلون واحد ايش هتكون ابسلون نوت اللي
+
+293
+00:20:15,820 --> 00:20:19,000
+هي عشر أقوى نقص تسعة ستة وتلاتين باي في ابسلون
+
+294
+00:20:19,000 --> 00:20:22,120
+relative اللي هي اربع في واحد تربية اللي هي طبعا
+
+295
+00:20:22,120 --> 00:20:27,000
+ال magnitude هو جزر التربية لEX تربية زي ال EY
+
+296
+00:20:27,000 --> 00:20:30,420
+تربية لEZ التربية تربيتها بخلص من الجزر
+
+297
+00:20:34,000 --> 00:20:37,080
+لأنها كانت كل القيانة ميعطينياها بال kilo volt
+
+298
+00:20:37,080 --> 00:20:41,360
+فلما أربعها ايش بتصير عشرة قوة ستة انتبهوا لل
+
+299
+00:20:41,360 --> 00:20:44,520
+units احنا عند ال electric field ميعطينياها ب kilo
+
+300
+00:20:44,520 --> 00:20:48,500
+volt per meter لما اخد ال magnitude ل E تربيه
+
+301
+00:20:48,500 --> 00:20:52,200
+هتصير ايش هكدي K تربيه يعني kilo تربيه يعني عشرة
+
+302
+00:20:52,200 --> 00:20:57,660
+قوة ستةفهذه صارت عندى فى عشرة قوة ستة لو حسبت
+
+303
+00:20:57,660 --> 00:21:00,820
+بيطلع بيضل عندى فى ال micro لإن عشر قوة نقل ستة
+
+304
+00:21:00,820 --> 00:21:05,220
+وفى عندى اللى هي بعض ال .. ال .. حيطلع لنا بعض ال
+
+305
+00:21:05,220 --> 00:21:09,420
+.. برضه ال .. الترمال فهيكون ستمية و اتنين و سبعين
+
+306
+00:21:09,420 --> 00:21:12,300
+micro هي point ستة سبعة تلات .. سبعة اتنين
+
+307
+00:21:12,300 --> 00:21:16,280
+millijoule ده التسهير 672 microjoule per meter
+
+308
+00:21:16,280 --> 00:21:19,270
+cubeنفس الحاجة ال energy density في ال media
+
+309
+00:21:19,270 --> 00:21:22,750
+التانية ما ننساش ال units ان هي كانت بال kilo volt
+
+310
+00:21:22,750 --> 00:21:25,930
+هيطلع عندها عشرة قوة ستة بالنهاية بيطلع مع جواب
+
+311
+00:21:25,930 --> 00:21:29,310
+بال micro joule أخر حاجة هو طالب ال total energy
+
+312
+00:21:31,290 --> 00:21:38,050
+within the cube of side 2m centered at 3,4,-5 بيده
+
+313
+00:21:38,050 --> 00:21:43,430
+ال total energy اللى فى قلب مكعب اللى وين عند 3,4,
+
+314
+00:21:43,550 --> 00:21:45,770
+-5 بتعرف وين هو فى ال media الأولى و لا فى ال
+
+315
+00:21:45,770 --> 00:21:50,270
+media التانية ما أنها سالب z سالب z وين media
+
+316
+00:21:50,270 --> 00:21:57,670
+التانية وهذا ال cube centered عن مين عند x3 و y4 و
+
+317
+00:21:57,670 --> 00:22:02,150
+minus 5 بالنسبة ل ال z componentهذا ال center تبعه
+
+318
+00:22:02,150 --> 00:22:04,870
+عشان انا اعرف اللى هى من و من بدي اخد ال X ل Y و
+
+319
+00:22:04,870 --> 00:22:10,530
+ال Z اذا هو ال center تبع
+
+320
+00:22:10,530 --> 00:22:16,030
+ال X مثلا عند التلاتة اذا قدش هيروح طول الدلع واحد
+
+321
+00:22:16,030 --> 00:22:20,190
+يعني هيروح من وين من من 2 ل 4
+
+322
+00:22:24,560 --> 00:22:28,820
+هيكون بيبدأ ال integration من 1 ل 4 و Y ال center
+
+323
+00:22:28,820 --> 00:22:33,980
+دي عند ال 4 اذا ما هيروح من وين ل 3 ل 5 واضح؟ و
+
+324
+00:22:33,980 --> 00:22:38,040
+هكذا اذا ما هنعمل ال total integral اللي هو X من 2
+
+325
+00:22:38,040 --> 00:22:42,800
+ل 4 و Y من 3 ل 5 زي ما هيكون من minus 6 ل minus 4
+
+326
+00:22:42,800 --> 00:22:47,560
+بعمل ال integration بحصل على ال total energy واضح؟
+
+327
+00:22:47,560 --> 00:22:52,110
+في أسف صح لحد هنا؟طبعا أخدنا هيك واضح ليش لأن قلنا
+
+328
+00:22:52,110 --> 00:22:55,870
+ال X centered عند التلاتة إذا هيكون الطول بروح من
+
+329
+00:22:55,870 --> 00:23:01,390
+2 ل 4 لأن طوله 2 Y centered عند 4 إذا بيكون من 3 ل
+
+330
+00:23:01,390 --> 00:23:05,810
+5 Z centered عند ال minus 5 إذا بروح من minus 6 ل
+
+331
+00:23:05,810 --> 00:23:12,450
+minus 4 طب كده المثال المثال طبعا مهلقة عن
+
+332
+00:23:12,450 --> 00:23:14,770
+conductor و dielectric احنا شوفنا بين dielectric و
+
+333
+00:23:14,770 --> 00:23:16,870
+dielectric نشوف بين conductor و dielectric
+
+334
+00:23:24,290 --> 00:23:27,890
+عند الـ cube الأولاني ال extension في ال XZ
+
+335
+00:23:27,890 --> 00:23:32,970
+والثاني في ال XZ اتقابله عند ال Y equal 0 زى ما
+
+336
+00:23:32,970 --> 00:23:37,590
+تشوفى في الرسمة هى ال Y axis و ال two media اللى
+
+337
+00:23:37,590 --> 00:23:40,430
+هى ال dialectical conductor اتقابل ال interface
+
+338
+00:23:40,430 --> 00:23:45,090
+تبعهم او البلين عند Y equal 0 تبع التقاطه واضح؟
+
+339
+00:23:48,320 --> 00:23:51,440
+for y أقل من أوت ساوة زيرو ال conductor for y أكبر
+
+340
+00:23:51,440 --> 00:23:55,960
+من أوت ساوة زيرو ال نضايلكترك الو ipsim relative
+
+341
+00:23:55,960 --> 00:24:00,500
+بتساوي تنين if there is a surface charge هنا
+
+342
+00:24:00,500 --> 00:24:03,620
+ميعطينا surface charge مقدارها اتنين نانو كولومر
+
+343
+00:24:03,620 --> 00:24:10,040
+متر تربية من دا conductorE and D at اول حاجة بده
+
+344
+00:24:10,040 --> 00:24:14,660
+قيمة E وD عند A اللى موجودة فى الكندكتور ليش
+
+345
+00:24:14,660 --> 00:24:18,600
+موجودة فى الكندكتور عندما Y مالها سالبة قولنا Y
+
+346
+00:24:18,600 --> 00:24:22,580
+سالبة بيكون الكندكتور وY موجباة ده electric طب
+
+347
+00:24:22,580 --> 00:24:24,620
+احنا عارفين ال electric الكندكتور اش ال electric
+
+348
+00:24:24,620 --> 00:24:28,500
+فيه اللى بيكون عنده فى قلبه Zero اذا الجواب
+
+349
+00:24:28,500 --> 00:24:31,760
+الأولانى سهل احنا اول حاجة بيقولوا ايه هذه النقطة
+
+350
+00:24:31,760 --> 00:24:36,580
+اللى تلاتة نقص تنين تنين بتكون فى الكندكتورلأن Y
+
+351
+00:24:36,580 --> 00:24:40,520
+مالها أقل من Zero وبالتالي E و D بيساوة 0 أطول
+
+352
+00:24:40,520 --> 00:24:43,120
+احنا قولنا ال conductor بحتويش على ال electric
+
+353
+00:24:43,120 --> 00:24:45,320
+field لإن ال charges كلها بتروح على ال surfaces
+
+354
+00:24:45,320 --> 00:24:48,360
+بطل فيه عندى enclosed charges جوا بيكون ال
+
+355
+00:24:48,360 --> 00:24:55,800
+electric و ال D بالتالي بيساوة 0النقطة B X-4Y1Z5
+
+356
+00:24:55,800 --> 00:24:58,000
+وين بيكون في Y أكبر من 0
+
+357
+00:25:22,250 --> 00:25:25,170
+واضح؟ لو كانت مافيش free charge، هتكون برضه ال
+
+358
+00:25:25,170 --> 00:25:28,670
+normal component بتساوي zero طب إذا دي norm بتساوي
+
+359
+00:25:28,670 --> 00:25:32,290
+رقص، اللي هي اتنين nano column بالمتر تربية، و دي
+
+360
+00:25:32,290 --> 00:25:37,060
+إيش هتساويأتجاهها as a vector عشان نحددها ال
+
+361
+00:25:37,060 --> 00:25:39,920
+normal اللي هي مالها هتكون اتجاه ال Y component
+
+362
+00:25:39,920 --> 00:25:43,500
+التانجينشال هي في ال XZ component مالها سفر
+
+363
+00:25:43,500 --> 00:25:47,600
+وبالتالي بقدر أقول انه E ايش بتساوي D على ال
+
+364
+00:25:47,600 --> 00:25:49,960
+epsilon اللي هي عبارة عن epsilon note في epsilon
+
+365
+00:25:49,960 --> 00:25:54,440
+relative وبمعطيني ال dialectic ل ال media ال
+
+366
+00:25:54,440 --> 00:25:59,080
+relative dialectic ل ال dialecticيبسون ار
+
+367
+00:25:59,080 --> 00:26:01,400
+لدياليكتريك او ال relative permittivity
+
+368
+00:26:01,400 --> 00:26:04,060
+لدياليكتريك بتساوي تنين تطهي على الرسمة مش في
+
+369
+00:26:04,060 --> 00:26:08,520
+السؤال فإذا انا هقول ان E بسوا D على E not E ر
+
+370
+00:26:08,520 --> 00:26:13,080
+بتساوي المتدرق دمنا اللي هو ستة و تلاتين ب I و I
+
+371
+00:26:13,080 --> 00:26:20,120
+hat في اي سلسلة حد هنا ايه
+
+372
+00:26:20,120 --> 00:26:26,740
+كده احنا بنكون خلصنا شبط درم خمسةشوفنا كيف ال
+
+373
+00:26:26,740 --> 00:26:28,780
+boundary conditions بين ال dialectric و
+
+374
+00:26:28,780 --> 00:26:32,320
+الconductor و ال dialectric و ال dialectric و ال
+
+375
+00:26:32,320 --> 00:26:40,400
+conductor بيجي
+
+376
+00:26:40,400 --> 00:26:42,000
+ال boundary value problem
+
+377
+00:26:45,890 --> 00:26:49,430
+مهمين كتير في حساب الموجات و فهم التصور تبع
+
+378
+00:26:49,430 --> 00:26:52,550
+الموجات في ال medias و برضه بيجوا من Maxwell's
+
+379
+00:26:52,550 --> 00:26:56,650
+equations يعني Maxwell's equations هم الأساس لكل
+
+380
+00:26:56,650 --> 00:27:03,990
+الشغل تبعنانشتغل نفس الحاجة لـ boundary value
+
+381
+00:27:03,990 --> 00:27:08,470
+problems نشتغل نفس الحاجة لـ Passant equations و
+
+382
+00:27:08,470 --> 00:27:11,950
+لـ Plus equations نشتغل نفس الحاجة لـ Passant
+
+383
+00:27:11,950 --> 00:27:14,490
+equations و لـ Plus equations نشتغل نفس الحاجة لـ
+
+384
+00:27:14,490 --> 00:27:15,310
+Passant equations و لـ Plus equations نشتغل نفس
+
+385
+00:27:15,310 --> 00:27:17,230
+الحاجة لـ Passant equations و لـ Plus equations
+
+386
+00:27:17,230 --> 00:27:18,690
+نشتغل نفس الحاجة لـ Passant equations و لـ Plus
+
+387
+00:27:18,690 --> 00:27:18,870
+equations نشتغل نفس الحاجة لـ Passant equations و
+
+388
+00:27:18,870 --> 00:27:18,890
+equations و لـ Plus equations نشتغل نفس الحاجة لـ
+
+389
+00:27:18,890 --> 00:27:19,030
+الحاجة لـ Passant equations و لـ Plus equations
+
+390
+00:27:19,030 --> 00:27:19,390
+نشتغل نفس الحاجة لـ Passant equations و لـ Plus
+
+391
+00:27:19,390 --> 00:27:19,430
+equations نشتغل نفس الحاج
+
+392
+00:27:26,950 --> 00:27:32,550
+لما نقول linear يعني معناه العلاقة بين D و E لها
+
+393
+00:27:32,550 --> 00:27:35,490
+linear فاش علنا اي تربيه و اي cube
+
+394
+00:27:41,870 --> 00:27:47,430
+لكن احنا عرفنا ان E ايش بتساوي minus del V من وين
+
+395
+00:27:47,430 --> 00:27:51,630
+اشتقناها ان اول حاجة كنا بتاكدين ان curl E بيساوي
+
+396
+00:27:51,630 --> 00:27:55,930
+zero ال rotational electric field صح؟ قولنا انه
+
+397
+00:27:55,930 --> 00:28:00,530
+عنده curl E بيساوي zero اذا ال E ماله بيساوي del ل
+
+398
+00:28:00,530 --> 00:28:05,350
+V بعدين شفنا من اشتقاقاتنا ل conservative force
+
+399
+00:28:05,350 --> 00:28:10,370
+انه بتطلع عنا إشارة سالبةبتذكرين صح؟ اذا عندنا E
+
+400
+00:28:10,370 --> 00:28:16,210
+بيسوي minus del V لو عوضت هنا هيكون عندى diverge
+
+401
+00:28:16,210 --> 00:28:22,230
+epsilon minus بدل ا E من E وحطتلها minus del V
+
+402
+00:28:22,230 --> 00:28:27,250
+بيسوي رو V طب احنا ال diverge ال del طبعا ال
+
+403
+00:28:27,250 --> 00:28:31,320
+epsilon اذا أخدتها برضه هموجنسهذه طبعا الحالة اللى
+
+404
+00:28:31,320 --> 00:28:35,840
+عادنا هى المعادلة اللى بصول لل انهمجنس يعنى y ماله
+
+405
+00:28:35,840 --> 00:28:39,240
+بعتمد على x و y و زد اللى انهمجنس معناه ماقدرش
+
+406
+00:28:39,240 --> 00:28:43,120
+اطلعه من ال differential انا بيصيرله تفاضل لو هو
+
+407
+00:28:43,120 --> 00:28:47,180
+انهمجنس معناه y مالها بتعتمد على ال x y z بتعتمد
+
+408
+00:28:47,180 --> 00:28:49,680
+على ال position يعنى برضه نفس ال epsilon function
+
+409
+00:28:49,680 --> 00:28:53,170
+في x y z مش بس potentialلكن لو انا اعتبرتها
+
+410
+00:28:53,170 --> 00:28:56,590
+homogenous، معناه يوماله لا يعتمد على الـX وY، إذا
+
+411
+00:28:56,590 --> 00:28:59,630
+كنت بقدر أطلعه من الـdifferential، بالتالي إذا
+
+412
+00:28:59,630 --> 00:29:01,950
+طلعت الـY من برة الـdifferential، minus يومالي،
+
+413
+00:29:01,950 --> 00:29:04,830
+حسيب عندي الـdivergent دل، و الـdivergent دل احنا
+
+414
+00:29:04,830 --> 00:29:08,550
+شفناها قبل هي كدلتر بيع، إذا هيكون دلتر بيع الـV
+
+415
+00:29:08,550 --> 00:29:11,630
+بتسوء minus rho V على يومالي هي، بس هو equation
+
+416
+00:29:11,630 --> 00:29:17,070
+لمين؟ للـhomogenous mediumتمام؟ إذا المبسطون ال
+
+417
+00:29:17,070 --> 00:29:20,590
+equation لل in homogenous media بتقوللي diverse
+
+418
+00:29:20,590 --> 00:29:25,790
+minus epsilon دل V بتسوي rho V لل homogenous دل
+
+419
+00:29:25,790 --> 00:29:30,170
+تربيع V بتسوي minus rho V على epsilon لو كانت rho
+
+420
+00:29:30,170 --> 00:29:34,250
+V بتسوي zero بحصل على plus equation هيكون عندي
+
+421
+00:29:35,600 --> 00:29:39,040
+diverge minus epsilon دي ال V بالسوء Zero ل ال
+
+422
+00:29:39,040 --> 00:29:42,840
+homogenous و دي ال تربيع V بالسوء Zero ل ال
+
+423
+00:29:42,840 --> 00:29:47,200
+homogenous يعني لما ال free chart بالسوء Zero بحصل
+
+424
+00:29:47,200 --> 00:29:50,900
+على plus equation لما رو V لات سوء Zero بكون بحكي
+
+425
+00:29:50,900 --> 00:29:55,700
+على plus equation واضح؟ طب إيش ال plus equation يا
+
+426
+00:29:55,700 --> 00:29:59,340
+عزيزي؟ طب لما إيش plus equation؟ واحد دلتين، ال
+
+427
+00:29:59,340 --> 00:30:04,630
+homogenous و ال inhomogenous تمامفي ال divergence
+
+428
+00:30:04,630 --> 00:30:08,430
+سالب إبسلون و gradient ال voltage like this و بعد
+
+429
+00:30:08,430 --> 00:30:12,290
+ما عوضنا للخارج، صاروا ستان و نصر تمام، حد ل مين؟
+
+430
+00:30:12,290 --> 00:30:14,910
+للهموجناص و لا للاهموجناص؟ للهموجناص، ايه؟ ليش
+
+431
+00:30:14,910 --> 00:30:17,370
+للهموجناص؟ لأن إبسلون لسه موجودة، ما تقلعوا أنها
+
+432
+00:30:17,370 --> 00:30:20,890
+بجد، ليش؟ لأنها determined على x, y, z، الهموجناص،
+
+433
+00:30:20,890 --> 00:30:24,250
+طب و التعنية إيش بتكون؟لما نضغط على سلب Epsilon
+
+434
+00:30:24,250 --> 00:30:30,030
+مرة اخرى، نعتمد عليه فعلا إلى Δ P بساول رو P على
+
+435
+00:30:30,030 --> 00:30:32,470
+Epsilon مرة أخرى، minus rho V على Epsilon هنا لأن
+
+436
+00:30:32,470 --> 00:30:35,570
+Epsilon تصبح homogenous، مع أنها لا تعتمد على X,
+
+437
+00:30:35,630 --> 00:30:39,350
+Y, Z، في حالة rho V بساول zero، بنحصل على ال plus
+
+438
+00:30:39,350 --> 00:30:43,590
+أسواق اللي هم جناس و لا اللي هم الجناس mediaطب ال
+
+439
+00:30:43,590 --> 00:30:48,090
+Laplace احنا شوفنا قبل هيكى لكن للتذكير اسواء في
+
+440
+00:30:48,090 --> 00:30:50,250
+ال Cartesian او ال cylindrical او ال spherical
+
+441
+00:30:50,250 --> 00:30:54,390
+ماقدروا اشتقوا او يعني اتذكروا او اعرفوا اللى بدى
+
+442
+00:30:54,390 --> 00:30:57,870
+ايه او يعطى ليه فى الامتحان اسهل واحدة فيهم اللى
+
+443
+00:30:57,870 --> 00:31:01,330
+فى ال Cartesian هى D2V بقى DX تربية زى D2V بقى DY
+
+444
+00:31:01,330 --> 00:31:05,010
+تربية زى D2V بقى DZ تربية بساوة Zero طبعا هدى
+
+445
+00:31:05,010 --> 00:31:09,050
+Laplace equation دل تربية V بالساوة Zero لمين؟
+
+446
+00:31:09,050 --> 00:31:12,170
+للهوموجيناص لإن أُس من انا طلعتها برا دل تربية V
+
+447
+00:31:12,170 --> 00:31:17,110
+بالساوة Zeroالهموجينة أصلا plus equation بس هنا في
+
+448
+00:31:17,110 --> 00:31:19,930
+ال cylindrical و هنا في ال spherical coordinate
+
+449
+00:31:19,930 --> 00:31:24,970
+لإن ال plus equation أصلا الهموجينة السيبية طب
+
+450
+00:31:24,970 --> 00:31:27,550
+uniqueness في الريم؟ايش معناه uniqueness يا رم؟
+
+451
+00:31:27,550 --> 00:31:30,950
+انه انا لو انا بدي solution يكون وحداني، يعني انا
+
+452
+00:31:30,950 --> 00:31:34,470
+بحكي عن ال mouse هاي الزرقة، بدي انا اللي احصل
+
+453
+00:31:34,470 --> 00:31:36,470
+عليه في نهاية ال mouse الزرقة، مابديش احصل على ال
+
+454
+00:31:36,470 --> 00:31:39,390
+mouse الحمرة و الخضرة و الصفرة، ماليها الدنيا
+
+455
+00:31:39,390 --> 00:31:43,290
+mouseات، لكن انا بحكي عن mouse معينة، بحكي عن موجة
+
+456
+00:31:43,290 --> 00:31:45,350
+معينة، بدي احصل على هذه الموجة معينة، هاي ال
+
+457
+00:31:45,350 --> 00:31:47,910
+uniquenessمش ال solution تبعاه هذا mathematical
+
+458
+00:31:47,910 --> 00:31:51,510
+هذا ال solution تبعاه mathematical او يعني هذه
+
+459
+00:31:51,510 --> 00:31:54,870
+المعادلات رياضية المعادلات الرياضية هي بتعطيني بس
+
+460
+00:31:54,870 --> 00:31:58,010
+ال solution مليون solution اكملت solution واحد
+
+461
+00:31:58,010 --> 00:32:01,270
+منهم اللي بيخليها uniqueness اللي هي ال boundary
+
+462
+00:32:01,270 --> 00:32:04,590
+conditions بحط ال conditions بتاعت ال problem
+
+463
+00:32:04,590 --> 00:32:07,630
+بتاعتي بتعطيني ال solution تبعاه او بتعطيني ال
+
+464
+00:32:07,630 --> 00:32:10,430
+wave بتاعتي او ال potential تبعاه بدون ال boundary
+
+465
+00:32:10,430 --> 00:32:14,630
+conditions تعوني بيكون عندش solution ماله عامبنفع
+
+466
+00:32:14,630 --> 00:32:22,030
+لأي حد تاني، بنفع لنا و لعبير و لهديل و ل .. و
+
+467
+00:32:22,030 --> 00:32:26,030
+لهبة، بنفع للجميع، لكن أنا بس بدي ال solution تبع
+
+468
+00:32:26,030 --> 00:32:30,190
+مين هديل، بدي بالنهاية يكون بنطبق الحلقة هديل مع
+
+469
+00:32:30,190 --> 00:32:32,790
+نبض أو ال boundary conditions، لبسة جلبة بلونه
+
+470
+00:32:32,790 --> 00:32:39,410
+بالنيباته، حطة إشارب على شكل جلد النمر و هكذابحط
+
+471
+00:32:39,410 --> 00:32:42,970
+ال boundary condition بتاعتي بتطلعلي الموجة اللي
+
+472
+00:32:42,970 --> 00:32:46,050
+أنا بدور عنها هذه هي ال uniqueness اذا انها دي
+
+473
+00:32:46,050 --> 00:32:49,650
+تلتة تربيع V اللي هي ال Laplace equation ل ال
+
+474
+00:32:49,650 --> 00:32:54,850
+homogeneous media بتساوي Zero بتقوللي انه انا عندي
+
+475
+00:32:54,850 --> 00:32:58,930
+solutions متعددة عشان احقق او يعني اوصل ل solution
+
+476
+00:32:58,930 --> 00:33:03,630
+بديها او ال only solution اللي انا بديها فقط بتحقق
+
+477
+00:33:03,630 --> 00:33:06,150
+هذا الحكي اذا طبقت ال right boundary conditions
+
+478
+00:33:09,710 --> 00:33:16,410
+عشان احصل على ال solution تبعي اولا بالدين اختار
+
+479
+00:33:16,410 --> 00:33:22,000
+المعادل المناسبةأنا بدي مين؟ لبلاس و لا بسان؟ إيش
+
+480
+00:33:22,000 --> 00:33:25,460
+بأكمل على إن في عندى free charge و لا لأ؟ هل هي ال
+
+481
+00:33:25,460 --> 00:33:28,680
+homogenous و لا ال homogenous؟ بأكمل هل ال
+
+482
+00:33:28,680 --> 00:33:32,580
+permittivity بتاعك بتاعتك مد على ال XYZ و لا لأ؟
+
+483
+00:33:32,580 --> 00:33:37,160
+إذا أول حاجة بدي أختار المعادلة الصحيحة بعدين بدي
+
+484
+00:33:37,160 --> 00:33:41,900
+أشوف المنطقة اللي بحل فيها عشان أختار اللي هي
+
+485
+00:33:45,560 --> 00:33:48,720
+أول حاجة بختار المعادلة الصحيحة بعدين بشوف ال
+
+486
+00:33:48,720 --> 00:33:52,940
+region بتاعتي و بحل و بختار بعض ال conditions
+
+487
+00:33:52,940 --> 00:33:59,440
+الصحيحة إذا ال zero zero solution كان مرة أول حاجة
+
+488
+00:33:59,440 --> 00:34:03,400
+بنحل ل plus إذا كانت row v بالساوة zero أو بصمم
+
+489
+00:34:03,400 --> 00:34:07,580
+إذا كانت row v لساوة zeroأسواء نستخدم الـ direct
+
+490
+00:34:07,580 --> 00:34:10,560
+integration و لا نستخدم الـ direct integration لو
+
+491
+00:34:10,560 --> 00:34:13,360
+أنا خلينا ناخد أسئلة واحدة اللي هي ال plus
+
+492
+00:34:13,360 --> 00:34:16,820
+equation لل homogenous media اللي هي تقبيع V لو
+
+493
+00:34:16,820 --> 00:34:20,520
+كانت الاعتمادية بتاعة ال potential على Y بتساوي 0
+
+494
+00:34:21,140 --> 00:34:23,080
+الاعتمادية تانية من شاء على z بالساوة زره ايش
+
+495
+00:34:23,080 --> 00:34:25,420
+هيكون عندي فقط الاعتمادية على ال x، عندي تانين v
+
+496
+00:34:25,420 --> 00:34:28,140
+by dx ترويح بساوة زره أزره، مش هيبقى حلها by
+
+497
+00:34:28,140 --> 00:34:31,360
+direct integration بكامل أول مرة و تاني مرة،
+
+498
+00:34:31,360 --> 00:34:34,460
+الحالة تبقى زي هيكون نفس الاشي هنا، لو كان مثلا
+
+499
+00:34:34,460 --> 00:34:36,800
+بعتمدش على ال row و بعتمدش على ال z ده، بسجد ال
+
+500
+00:34:36,800 --> 00:34:41,150
+phi componentباستخدم ال integral نفس الحاجة في ال
+
+501
+00:34:41,150 --> 00:34:43,690
+spherical لو هدولة بقتملش على أعلى و تسيطر عن
+
+502
+00:34:43,690 --> 00:34:47,730
+نفسها على ال five double integral بحل اذا بطلع لو
+
+503
+00:34:47,730 --> 00:34:50,470
+انا ال potential تبعي فقط بعتمد على one variable
+
+504
+00:34:50,470 --> 00:34:53,670
+دايما بسهل علي الحل بكون اني بقدر اعمل بال double
+
+505
+00:34:53,670 --> 00:34:56,730
+integral بجيب ال solution لك لو بعتمد عليهم كلها
+
+506
+00:34:58,750 --> 00:35:02,530
+بنحلل بحاجة بنسميها separation of variables بندق
+
+507
+00:35:02,530 --> 00:35:05,310
+أستخدم ال separation of variables يعني الحل الأول
+
+508
+00:35:05,310 --> 00:35:09,130
+طريقة الأول هي direct integration إذا كانت في فقط
+
+509
+00:35:09,130 --> 00:35:12,590
+فقط content variable واحد أو بستخدم ال separation
+
+510
+00:35:12,590 --> 00:35:15,430
+of variables إذا كانت فيه مالها بتعمل على أكتر من
+
+511
+00:35:15,430 --> 00:35:16,910
+variable واضحة هذه النقطة؟
+
+512
+00:35:19,800 --> 00:35:23,440
+لحدها لقيت الحل اللي حلته أسبوع بالدوبل انتيجرال و
+
+513
+00:35:23,440 --> 00:35:26,260
+لا بال separation of variables الناتج تبعي ماله مش
+
+514
+00:35:26,260 --> 00:35:31,840
+unique لأنه عام لسه ماحفظتش عليه constraints بد
+
+515
+00:35:31,840 --> 00:35:34,540
+أحط ال boundary conditions وبالتالي بحصل على ال
+
+516
+00:35:34,540 --> 00:35:38,770
+unique solutionواضح؟ لما أحط ال boundary
+
+517
+00:35:38,770 --> 00:35:41,250
+conditions أفرضها على ال solution اللي حصلت عليه
+
+518
+00:35:41,250 --> 00:35:45,070
+أسوأ من اللي هي ال double integral و لا من ال
+
+519
+00:35:45,070 --> 00:35:47,550
+separation variable بحصل على ال unique solution
+
+520
+00:35:47,550 --> 00:35:51,350
+إذا حصلت على V بسهولة عليا أجيب E لأن E مش بتساوي
+
+521
+00:35:51,350 --> 00:35:55,830
+minus grade V إذا جبت E بجيب D لأن D مش بتساوي
+
+522
+00:35:55,830 --> 00:36:01,670
+epsilon E واضح؟ كمان بقدر أجيب Q لأن Q مش بتساوي
+
+523
+00:36:01,670 --> 00:36:06,890
+ال integral ل rho S DS و rho S مش بتساوي DNإذا
+
+524
+00:36:06,890 --> 00:36:09,990
+بقدر أجيب أي حاجة إذا عرفت هذا الحكاية قدر أجيب
+
+525
+00:36:09,990 --> 00:36:12,950
+مين is the distance between two media لإن ال C
+
+526
+00:36:12,950 --> 00:36:15,950
+بسوة و Q على V إذا كنت عارفة ال potential already
+
+527
+00:36:15,950 --> 00:36:19,530
+بقدر أجيب اللي هي ال capacitance بالذات لو أنا كنت
+
+528
+00:36:19,530 --> 00:36:24,390
+أحكي على two conductors طبعا خلي الأمثلة القادمة
+
+529
+00:36:24,390 --> 00:36:27,850
+إن شاء الله بس راجعوا اللي حكيناه عشان تكونوا
+
+530
+00:36:27,850 --> 00:36:33,130
+معانا في أحل الأمثلة يعني احنا تقريبا هيك خلصنا ال
+
+531
+00:36:33,130 --> 00:36:37,240
+chapter الباقي أسئلةيعني ان كان اقولكم المقال
+
+532
+00:36:37,240 --> 00:36:41,680
+الجانب ده chapter 7 بس عشان تستفيدوا من حل الأمثلة
+
+533
+00:36:41,680 --> 00:36:45,640
+راجعوا ان تطلعوا عليه، اتطلعوا على اللي حكيناه و
+
+534
+00:36:45,640 --> 00:36:47,860
+اتطلعوا على الأمثلة نفسها عشان لو فينكم اي
+
+535
+00:36:47,860 --> 00:36:50,980
+استفسارات تحصلوا على الإجابات و احنا بنحكيها مع
+
+536
+00:36:50,980 --> 00:36:54,160
+بعض، تسألون ليش هي النقطة هيكي و ليش النقطة هيكي،
+
+537
+00:36:54,160 --> 00:36:57,420
+أما هيكي باعتبار ال chapter خلص، يعطيكم العفو
+
diff --git a/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/-oZSLACDJP8_raw.srt b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/-oZSLACDJP8_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..62bcec13c7ac8dac647baad0042d7924369aea83
--- /dev/null
+++ b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/-oZSLACDJP8_raw.srt
@@ -0,0 +1,2156 @@
+1
+00:00:21,190 --> 00:00:23,730
+بسم الله الرحمن الرحيم السلام عليكم ورحمة الله
+
+2
+00:00:23,730 --> 00:00:26,610
+وبركاته احنا ان شاء الله اليوم هنكمل ال boundary
+
+3
+00:00:26,610 --> 00:00:30,230
+conditions احنا قلنا هناخد boundary conditions بين
+
+4
+00:00:30,230 --> 00:00:33,770
+dielectric و dielectric conductor و dielectric و
+
+5
+00:00:33,770 --> 00:00:38,270
+conductor في space و هنستيين بيه ال y2 max with
+
+6
+00:00:38,270 --> 00:00:42,110
+equations ل ال clause integral دي dot dl بساوة
+
+7
+00:00:42,110 --> 00:00:45,450
+zero هي قلنا conservative force اللي هو ال work و
+
+8
+00:00:45,450 --> 00:00:50,360
+ال clause integral دي dot DS بتساويالخاص هو Gauss
+
+9
+00:00:50,360 --> 00:00:55,440
+law قلنا عشان نفهم إيش بيصير عند ال boundary إنه
+
+10
+00:00:55,440 --> 00:00:57,780
+نكتب ال fields ع شكل tangential و normal
+
+11
+00:00:57,780 --> 00:01:00,720
+components فعندنا اللي كتب field هنكتبه ع شكل
+
+12
+00:01:00,720 --> 00:01:04,200
+tangential زي normal وبالتالي ال fields البقية هم
+
+13
+00:01:04,200 --> 00:01:07,260
+نكتبه بهذه الطريقة بعدين نميز بال dialectric
+
+14
+00:01:07,260 --> 00:01:10,180
+dialectric boundaries قلنا لو كان عندى two
+
+15
+00:01:10,180 --> 00:01:14,670
+dialectrics بينهم هيكون boundaryقلنا بعد نفس
+
+16
+00:01:14,670 --> 00:01:16,330
+الحاجة ال electric field اللي هو في ال media ال
+
+17
+00:01:16,330 --> 00:01:20,670
+1E1 هاسمه ل tangential و normal component و E2
+
+18
+00:01:20,670 --> 00:01:23,430
+اللي هو في ال media التاني هاسمه ل normal و
+
+19
+00:01:23,430 --> 00:01:26,990
+tangential component و هدرس إيش بيصير ل tangential
+
+20
+00:01:26,990 --> 00:01:31,360
+component و إيش بيصير ل normal componentاستفدنا من
+
+21
+00:01:31,360 --> 00:01:34,040
+استخدامنا لل two Maxwell's equation ان ال
+
+22
+00:01:34,040 --> 00:01:36,140
+tangential component للـ electric field على ال
+
+23
+00:01:36,140 --> 00:01:38,680
+boundary between two dielectric مالها continuous
+
+24
+00:01:38,680 --> 00:01:43,720
+يعني E tangential واحد سو E tangential تنين لكن ال
+
+25
+00:01:43,720 --> 00:01:48,680
+intensity اللي هو D بتكون discontinuous هتكون D
+
+26
+00:01:48,680 --> 00:01:52,420
+واحد T على Epsilon واحد سو D تنين T على Epsilon
+
+27
+00:01:52,420 --> 00:01:59,380
+تنينكذلك لما نحكي عن normal components بدنا بال D
+
+28
+00:01:59,380 --> 00:02:03,880
+و أخدنا تنجينشال لل normal components لاقينا ان ال
+
+29
+00:02:03,880 --> 00:02:08,820
+normal component لل D بتكون continuous فقط في حالة
+
+30
+00:02:08,820 --> 00:02:12,820
+ان ال surface charged على ال interface بتساوي 0
+
+31
+00:02:12,820 --> 00:02:17,000
+لكن لو كانت ال surface charged لها تساوي 0 هيكون
+
+32
+00:02:17,000 --> 00:02:19,740
+ال difference بين ال normal components بساوي ال
+
+33
+00:02:19,740 --> 00:02:26,330
+surface charged ال free charged density رؤسمع انه
+
+34
+00:02:26,330 --> 00:02:29,810
+ال normal components continuous لل D هلاحظ انه ال
+
+35
+00:02:29,810 --> 00:02:33,730
+normal component لل E مارها discontinuous انه E1
+
+36
+00:02:33,730 --> 00:02:37,270
+E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1
+
+37
+00:02:37,270 --> 00:02:38,130
+E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1
+
+38
+00:02:38,130 --> 00:02:38,490
+E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1
+
+39
+00:02:38,490 --> 00:02:42,070
+E1 E1 E1 E1 E1 E1 E1 E1 E1 E1
+
+40
+00:02:42,070 --> 00:02:43,610
+E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1
+
+41
+00:02:43,610 --> 00:02:45,690
+E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1 E1
+
+42
+00:02:45,690 --> 00:02:54,050
+E1 E1الـ 2 ده ال electrics فيها E1 و E2 و E1 و D1
+
+43
+00:02:54,050 --> 00:02:58,670
+E1 و D1 زى ما تشايفين هدولة فى ال media الأولى هدا
+
+44
+00:02:58,670 --> 00:03:06,490
+ال norm على ال surface هدا norm على ال surface هده
+
+45
+00:03:06,490 --> 00:03:13,110
+يعنى E1 و D1 برضه هجزقها ل tangential components و
+
+46
+00:03:13,110 --> 00:03:16,790
+normal components نفس الحاجة بالنسبة ل E2 و D2
+
+47
+00:03:17,080 --> 00:03:21,200
+هجزقهم ل tangential components و normal components
+
+48
+00:03:21,200 --> 00:03:25,080
+واضح ال components اللي ماقلتش فيها مشكلة طب احنا
+
+49
+00:03:25,080 --> 00:03:26,960
+بدنا نشوف ايش قانون ال refraction ال refraction
+
+50
+00:03:26,960 --> 00:03:30,560
+بتاعه اللي هو انكسار بين two dielectric medium على
+
+51
+00:03:30,560 --> 00:03:36,480
+اساس ان θ1 و θ2 بمثله θ1 هي الزاوية المابين ال
+
+52
+00:03:36,480 --> 00:03:41,420
+electric field و ال norm على ال surfaceأو θتنين هي
+
+53
+00:03:41,420 --> 00:03:44,840
+الزاور بين ال field و ال norm على ال surface على
+
+54
+00:03:44,840 --> 00:03:47,500
+ال interface يعني وين ال interface بحط normal
+
+55
+00:03:47,500 --> 00:03:51,400
+عليها و الزاور بين ال field و ال norm هي بتكون θتا
+
+56
+00:03:51,400 --> 00:03:54,540
+طب نيجي على ال tangential component ال tangential
+
+57
+00:03:54,540 --> 00:04:00,960
+component لE ايش بتساوي E1 sin θ1 صح و E2
+
+58
+00:04:00,960 --> 00:04:07,150
+tangential ايش هتكون E2 sinثاتنين طب احنا عارفين
+
+59
+00:04:07,150 --> 00:04:09,890
+ان اي واحد tangential بتسوي اتنين tangential اللي
+
+60
+00:04:09,890 --> 00:04:11,730
+اسبقنا اثبتناها في المحاضرة الماضية وارجعناها
+
+61
+00:04:11,730 --> 00:04:14,410
+اليوم ال tangential component لل electric field
+
+62
+00:04:14,410 --> 00:04:17,790
+between two dielectrics مالها continuous اذا اي
+
+63
+00:04:17,790 --> 00:04:21,550
+واحد tangential بتسوي اتنين tangentials لكن احنا
+
+64
+00:04:21,550 --> 00:04:26,430
+عارفنا من الرسمة اللي قمناها ال field وهي ال theta
+
+65
+00:04:26,430 --> 00:04:29,870
+واحد اللي بين ال field و ال non ال tangential
+
+66
+00:04:29,870 --> 00:04:33,690
+بتحدي اشهر كم قيمتها اي واحد sin theta واحدو نفس
+
+67
+00:04:33,690 --> 00:04:37,950
+بقضية بالنسبة ل E2 وهي θتة اتنين هي الزاوية بين ال
+
+68
+00:04:37,950 --> 00:04:40,610
+field و ال norm هتكون ال tangential component
+
+69
+00:04:40,610 --> 00:04:43,790
+بتساوي E2 K sin θتة اتنين اللي هو زي ما احنا
+
+70
+00:04:43,790 --> 00:04:48,710
+شايفين هذا من ال boundary condition ان E1
+
+71
+00:04:48,710 --> 00:04:51,890
+tangential بتساوي E2 tangential E1 tangential
+
+72
+00:04:51,890 --> 00:04:55,570
+بتساوي E1 sin θتة اتنين و E2 tangential بتساوي E2
+
+73
+00:04:55,570 --> 00:04:57,590
+sin θتة اتنين ايش كمان بعض ال condition التاني
+
+74
+00:04:57,590 --> 00:05:02,390
+قالنا ان ال D norm هي ال continuousD1 non بتسوي D2
+
+75
+00:05:02,390 --> 00:05:05,510
+non إذا ماكانش هنا free charge يعني إذا كانت هذه
+
+76
+00:05:05,510 --> 00:05:09,690
+row بتسوي zero ال free charge بتسوي zero إذا D1
+
+77
+00:05:09,690 --> 00:05:13,830
+non بتسوي D2 non D1 non شو هتسوي ال normal
+
+78
+00:05:13,830 --> 00:05:18,090
+component ل D1 هاي دي D1 ال normal اللي هي هاي
+
+79
+00:05:18,090 --> 00:05:25,150
+هتكون D1 cosine theta 1 جيب تمام theta 1
+
+80
+00:05:49,950 --> 00:05:51,960
+D1D1D1D1D1D1D1D1D1D1D1D1D1D1D1D1D1D1D1D1D1D1D1ساين
+
+81
+00:05:51,960 --> 00:05:55,500
+على كوساين اللي هي tan θ1 أقى epsilon 1 بيساوي tan
+
+82
+00:05:55,500 --> 00:06:00,400
+θ2 على epsilon 2 إذا عبضنا عن epsilon 1 و epsilon
+
+83
+00:06:00,400 --> 00:06:04,480
+2 بقيمتهم ده لاتر ال relative permittivity epsilon
+
+84
+00:06:04,480 --> 00:06:06,540
+1 هتكون epsilon not في relative permittivity
+
+85
+00:06:06,540 --> 00:06:09,660
+للmedia الأولى و epsilon 2 هتكون epsilon not في
+
+86
+00:06:09,660 --> 00:06:13,680
+epsilon relative للmedia التانية هيكون الtan θ1
+
+87
+00:06:13,680 --> 00:06:16,480
+على tan θ2 بيساوي relative permittivity للmedia
+
+88
+00:06:16,480 --> 00:06:20,400
+الأولى على relative permittivity للmedia التانية
+
+89
+00:06:29,190 --> 00:06:32,770
+نجي لقى ال conductor dielectric ايش الفرق بين
+
+90
+00:06:32,770 --> 00:06:35,330
+dielectric و dielectric؟ بين dielectric و
+
+91
+00:06:35,330 --> 00:06:38,190
+conductor احنا قلنا ال conductor ايش بيكون ال
+
+92
+00:06:38,190 --> 00:06:41,930
+electric field في قلبه zero يعني خصائص ال
+
+93
+00:06:41,930 --> 00:06:44,210
+conductor ال electric field بيكون بساوة سفر في
+
+94
+00:06:44,210 --> 00:06:47,410
+قلبه لأن ال charges بيروح على ال surface بطل فيه
+
+95
+00:06:47,410 --> 00:06:50,470
+charges in plus في ال conductor وبالتالي بيكون ال
+
+96
+00:06:50,470 --> 00:06:53,310
+electric field بساوة zero قولنا معدى اذا احنا
+
+97
+00:06:53,310 --> 00:06:57,630
+أجبرناه ووصلنا معاه أسلاب، مفذكرين؟ لإن هو في ال
+
+98
+00:06:57,630 --> 00:07:02,090
+free spaceوحطيها electric field هلاقي انه في قلب
+
+99
+00:07:02,090 --> 00:07:06,670
+ال conductor electric field بساوي 0 اذا أنا عندي
+
+100
+00:07:06,670 --> 00:07:10,110
+هاي ال conductor وهي ال electric field ال
+
+101
+00:07:10,110 --> 00:07:12,850
+dielectric وهي ال boundary اللي بين ال two medium
+
+102
+00:07:12,850 --> 00:07:16,170
+اللي هو الخط هذا، هذا هو ال boundary، هذا خط ال
+
+103
+00:07:16,170 --> 00:07:22,630
+boundary لو استخدمنا Maxwell's equations هلاقي نفس
+
+104
+00:07:22,630 --> 00:07:25,870
+القضية ان E tangential لازم تكون continuous اللي
+
+105
+00:07:25,870 --> 00:07:28,890
+هي ال clause انتجرة لE dot dlلكن الـ tangential
+
+106
+00:07:28,890 --> 00:07:32,510
+component في القندكتور أشبه الساوي 0 ال electric
+
+107
+00:07:32,510 --> 00:07:35,810
+field في القندكتور أشبه الساوي 0 فال tangential
+
+108
+00:07:35,810 --> 00:07:41,270
+component 0 إذا E tangential في اللي هو ال media
+
+109
+00:07:41,270 --> 00:07:44,410
+اللي هي الدايليكتريك الساوي 0 لو أخدنا النمر
+
+110
+00:07:44,410 --> 00:07:48,530
+components اللي هي DN هلاحظ أنه مالها احنا قلنا
+
+111
+00:07:48,530 --> 00:07:52,290
+بتكون ال D continuous إذا كانت رقص ساوي 0 لاتوا
+
+112
+00:07:52,290 --> 00:07:58,230
+ساوي 0 هتكون DN أشبه ساوي رقصفال E tangential هي 0
+
+113
+00:07:58,230 --> 00:08:02,330
+لأن E tangential في الconductor هي 0 انتوا باخدين
+
+114
+00:08:02,330 --> 00:08:05,530
+ان احنا بس بحطين E واحدة مش E واحد و E اتنين E
+
+115
+00:08:05,530 --> 00:08:08,390
+اللي هي ال direct trip فال tangential component
+
+116
+00:08:08,390 --> 00:08:12,250
+بتاعتها 0 لأن E tangential في ال conductor هي 0 و
+
+117
+00:08:12,250 --> 00:08:17,830
+ال normal component لD هتكون بالسوء raw D مش هيكون
+
+118
+00:08:17,830 --> 00:08:22,970
+D على 1 نقص D على 2 لأن D على 2 هي 0الكندكتور عنده
+
+119
+00:08:22,970 --> 00:08:26,810
+ال electric field بيساوي 0 إذا A0 إذا D بيساوي 0
+
+120
+00:08:26,810 --> 00:08:31,010
+لو
+
+121
+00:08:31,010 --> 00:08:35,990
+كان ال electric field قلنا بيبقى انه انه مافيش
+
+122
+00:08:35,990 --> 00:08:39,490
+electric field في قلب الكندكتور لو كان Trophy
+
+123
+00:08:39,490 --> 00:08:45,610
+بيساوي 0لأ في قلب ال conductor اللي انا حكيته انه
+
+124
+00:08:45,610 --> 00:08:48,330
+اي charges ايش بتصير اللي هقولنا بتصير على الباندر
+
+125
+00:08:48,330 --> 00:08:50,850
+لو موجودة charges بتروح كلها على الباندر وبالتالي
+
+126
+00:08:50,850 --> 00:08:54,330
+ال electric field لو أخدت gauss law بساوة zeroفهذا
+
+127
+00:08:54,330 --> 00:08:57,990
+اللي بنحكي هنا ان مافيش انا عندى اي field exist فى
+
+128
+00:08:57,990 --> 00:09:00,610
+قلب ال conductor معناه ان رو V بالثاوة زيرو و E
+
+129
+00:09:00,610 --> 00:09:03,210
+بالثاوة زيرو E بالثاوة زيرو ان احنا ال electric
+
+130
+00:09:03,210 --> 00:09:06,290
+field ايش اللي بنعبر عنه برضه ال potential scalar
+
+131
+00:09:06,290 --> 00:09:09,570
+potential انه E بالثاوة minus grade V ايش قولنا
+
+132
+00:09:09,570 --> 00:09:12,250
+echo potential surfaces للكندكتور من الذاكرين
+
+133
+00:09:12,250 --> 00:09:16,710
+قولنا دل V بالثاوة زيرو معناه ان ال conductor
+
+134
+00:09:16,710 --> 00:09:18,770
+بتصرف as echo potential body
+
+135
+00:09:28,080 --> 00:09:31,460
+طبعا اذا احنا قلنا معناه ان ال electric field مانه
+
+136
+00:09:31,460 --> 00:09:34,400
+zero على ال conductor اذا معناه زى ما انتوا شايفين
+
+137
+00:09:34,400 --> 00:09:38,140
+ان E T tangential لنا بالساوة Zero برضه E T
+
+138
+00:09:38,140 --> 00:09:41,320
+بالساوة Zero لان E T ايش علاقتها ب E T بال Epsilon
+
+139
+00:09:41,320 --> 00:09:44,520
+Epsilon ل ال media للكندكتور اذا ماحتكون برضه Zero
+
+140
+00:09:44,520 --> 00:09:48,800
+لكن DN اللى احنا قلناه هتساوي ρو S وين بتكون
+
+141
+00:09:48,800 --> 00:09:53,460
+External للكندكتور و عمودي عليه يعني فقط هى اللى
+
+142
+00:09:53,460 --> 00:09:57,320
+بيكون موجود لو كان عندى conductorهيكون الـ
+
+143
+00:09:57,320 --> 00:10:00,260
+tangential component تسوى 0 دائما، external
+
+144
+00:10:00,260 --> 00:10:05,080
+للكندكتور هتكون ال tangential component 0، وإيش
+
+145
+00:10:05,080 --> 00:10:08,080
+هتكون فقط ال external، اللي هي ال normal component
+
+146
+00:10:08,080 --> 00:10:12,480
+فقط ال non-zero component هي ال normal component،
+
+147
+00:10:12,480 --> 00:10:16,180
+ال tangential تسوى 0، ال normal .. يعني نقدر نقول
+
+148
+00:10:16,180 --> 00:10:20,860
+بساطة إن ال electric field خارج الكندكتور هيكون
+
+149
+00:10:20,860 --> 00:10:23,480
+دائما على ال normal direction لأن ال tangential
+
+150
+00:10:23,480 --> 00:10:25,280
+component دائما بتسوى 0
+
+151
+00:10:36,070 --> 00:10:38,570
+عشان هذا الاشي ان ال electric field في قلب اي
+
+152
+00:10:38,570 --> 00:10:42,350
+conductor بيساوي zero احنا بنسمي ال conductor as a
+
+153
+00:10:42,350 --> 00:10:46,430
+shield يعني مثلا لو احنا اعتبرنا اللي هي ال a هذه
+
+154
+00:10:46,430 --> 00:10:51,950
+هي عبارة عن conductor بحط هنا body اللي هو b في
+
+155
+00:10:51,950 --> 00:10:56,120
+قلب اللي هو ال conductor aال conductor A ايش
+
+156
+00:10:56,120 --> 00:11:00,760
+بيعمل؟ بيمنع اختراق اي electric field ل inside ال
+
+157
+00:11:00,760 --> 00:11:05,460
+A فمعناه ان B مش هتشعر بالمرة في وجود ال C و نفس
+
+158
+00:11:05,460 --> 00:11:08,360
+الشيء ال C مش هتشعر بالمرة في وجود ال B لأن ال
+
+159
+00:11:08,360 --> 00:11:13,660
+conductor A ايش عمل؟ ك shield كدرع واقي هيمنع ان
+
+160
+00:11:13,660 --> 00:11:18,040
+ال body B انه يشعر في وجود ال C و نفس العضية ال
+
+161
+00:11:18,040 --> 00:11:22,140
+body C مش هيعشعر في وجود ال body Bأنه إحنا شرناه
+
+162
+00:11:22,140 --> 00:11:24,920
+بمنع اختراف ال electric field إله فقط هيكون
+
+163
+00:11:24,920 --> 00:11:28,460
+external و normal إله، مش هيكون في قلبه، وبالتالي
+
+164
+00:11:28,460 --> 00:11:33,060
+ال body بيه هيشعر إنه محمي من اللي هو أي تأثير ل
+
+165
+00:11:33,060 --> 00:11:38,460
+ال body تسييه، بنسميه electrostatic screening or
+
+166
+00:11:38,460 --> 00:11:40,920
+shielding، shielding اللي هو حالي و ال screen هو
+
+167
+00:11:40,920 --> 00:11:44,580
+برضه زي إحنا بنحمي حالنا الشبكة من البعض و من
+
+168
+00:11:44,580 --> 00:11:47,160
+الحشبات الدارة
+
+169
+00:11:54,690 --> 00:11:57,090
+أخر حاجة اللي هي conductor of free space احنا قلنا
+
+170
+00:11:57,090 --> 00:11:59,410
+بالـ free space ما هو إلا الـ dielectric و الـ
+
+171
+00:11:59,410 --> 00:12:02,850
+epsilon بتساوي epsilon node يعني اللي حكيناه قبل
+
+172
+00:12:02,850 --> 00:12:06,350
+قليل على conductor dielectric حالة خاصة منه اللي
+
+173
+00:12:06,350 --> 00:12:09,710
+هي الـ free space يعني بقدر أقول إنه ال electric
+
+174
+00:12:09,710 --> 00:12:14,690
+field هيكون external للكندكتور و normal عليه بمعنى
+
+175
+00:12:14,690 --> 00:12:18,710
+إن ال tangential component بتساوي 0 و ال normal
+
+176
+00:12:18,710 --> 00:12:22,390
+component بتساوي ρو S و ال D norm مش بتساوي
+
+177
+00:12:22,390 --> 00:12:28,520
+epsilon node Emواضح؟ لأن Epsilon relative بالنسبة
+
+178
+00:12:28,520 --> 00:12:33,260
+للـ space بالساوي واحد لنشوف بعض الأمثلة بنا
+
+179
+00:12:33,260 --> 00:12:35,920
+نستفيد من power condition احنا في حالتنا عشان نحل
+
+180
+00:12:35,920 --> 00:12:39,200
+الأمثلة ان لو انا كنت عارفة بعض المعلومات عن ال
+
+181
+00:12:39,200 --> 00:12:42,040
+electric field في media كيف اقدر اجيبها في media
+
+182
+00:12:42,040 --> 00:12:46,140
+تانية يعني مثل ان هذا المثل اللي قدامنا الناتو
+
+183
+00:12:46,140 --> 00:12:50,130
+extensive homogeneousisotropic، dielectric،
+
+184
+00:12:50,130 --> 00:12:52,850
+homogenous إيش معناه؟ قلنا إبسلون لتعتمد على X
+
+185
+00:12:52,850 --> 00:12:56,530
+والـ Y إيستروبك إنه الـ D والـ E بيكونوا في اتجاه
+
+186
+00:12:56,530 --> 00:13:02,030
+واحد meet أن بلان Z بالساوة Zero يعني هاي ال two
+
+187
+00:13:02,030 --> 00:13:05,950
+planes هاي الأولاني، هاي المكعب الأولاني أو ال
+
+188
+00:13:05,950 --> 00:13:08,890
+media الأولى وهي ال media التانية وانتقعوا تعاون،
+
+189
+00:13:08,890 --> 00:13:14,730
+قعدوا على بعض يعني Z equal Zero هاي ال Z-axis هاي
+
+190
+00:13:14,730 --> 00:13:22,430
+ال Z-axisوهذه z equals 0 احنا ال two media قاعدة
+
+191
+00:13:22,430 --> 00:13:26,070
+على بعض ال z equals 0 اذا ال interface بيكون ال
+
+192
+00:13:26,070 --> 00:13:29,170
+plan تبع ال interface بيكون ال z equals 0 واضح
+
+193
+00:13:29,170 --> 00:13:33,410
+مبتد في ال x y plan ويكون زي ما قلنا احنا لو
+
+194
+00:13:33,410 --> 00:13:37,350
+دفترين او مكعبين يعني لو قعدتكم دفترين افرجكم ايش
+
+195
+00:13:37,350 --> 00:13:44,030
+اصلا في ال two medias و ال interfaceهذه الميديا
+
+196
+00:13:44,030 --> 00:13:47,810
+الأولى وهذه الميديا الثانية وانطلاقها هذا هو ما
+
+197
+00:13:47,810 --> 00:13:51,370
+نسميه ال interface اللي هو جلد الدفتر بالتمام احنا
+
+198
+00:13:51,370 --> 00:13:55,250
+كنا حاطين جلد الدفتر عن z equal 0 هدوله two plans
+
+199
+00:13:55,250 --> 00:13:59,530
+يعني موجودين في ال XY plan لكن في ال z axis واحدة
+
+200
+00:13:59,530 --> 00:14:06,950
+هتكون في minus z والتانية في plus z شكرا لكم لذا
+
+201
+00:14:06,950 --> 00:14:11,890
+هى انا ال two mediasاللي هي الـ 1 و 2 Epsilon R1
+
+202
+00:14:11,890 --> 00:14:15,850
+للميديا الأولى التي الديالكتريك 1 و الديالكتريك
+
+203
+00:14:15,850 --> 00:14:20,410
+للميديا Epsilon R2 Epsilon R1 قيمتها 4 و Epsilon
+
+204
+00:14:20,410 --> 00:14:24,570
+R2 قيمتها 3 و زى ما قلنا ان ال Epsilon الميديا
+
+205
+00:14:24,570 --> 00:14:28,170
+الأولى في Z أكبر من أو تساوي 0 و الميديا التانية
+
+206
+00:14:28,170 --> 00:14:32,960
+في Z أقل من أو تساوي 0في ال media الأولى كان في
+
+207
+00:14:32,960 --> 00:14:37,280
+عندي electric field E1 انا عارفة كل معلوماته انه
+
+208
+00:14:37,280 --> 00:14:41,240
+ال component في ال X direction قيمتها خمسة و في ال
+
+209
+00:14:41,240 --> 00:14:44,200
+Y مقدرها ماينس تنين و في ال Z مقدرها تلاتة
+
+210
+00:14:44,200 --> 00:14:50,160
+كيلوفورت بالمتر اللي طالب هو الحاجة E2 for Z أقل
+
+211
+00:14:50,160 --> 00:14:53,240
+من Zero عشان اجيب E2 ايش لازم اجيب ال tangential
+
+212
+00:14:53,240 --> 00:14:57,940
+component و ال normal componentطب احنا عرفنا انه
+
+213
+00:14:57,940 --> 00:14:59,840
+بين الـ dielectric و ال dielectric tangential
+
+214
+00:14:59,840 --> 00:15:04,060
+component مالهم continuous يعني E tangential واحد
+
+215
+00:15:04,060 --> 00:15:07,040
+بسوء E tangential تنين مين ال tangential component
+
+216
+00:15:07,040 --> 00:15:10,160
+في هالحالة؟ اللي هي ال X و ال Y مين اللي على ال
+
+217
+00:15:10,160 --> 00:15:13,040
+interface اللي فرجتكميا الدفترين؟ هيكون ال X و ال
+
+218
+00:15:13,040 --> 00:15:17,220
+Y اللي عمودي عليهم مين؟ ال Z component اذا بطلع
+
+219
+00:15:17,220 --> 00:15:20,200
+وين ال X component و ال Y component؟ خمس X minus
+
+220
+00:15:20,200 --> 00:15:27,290
+اتنين Y هي E واحد tangentialE1 norm هي 3AZ hat إذا
+
+221
+00:15:27,290 --> 00:15:31,030
+من ال boundary condition E1 tangential بتسوي E2
+
+222
+00:15:31,030 --> 00:15:35,370
+tangential بتالي E2 tangential ايش قيمتها 5X hat
+
+223
+00:15:35,370 --> 00:15:39,350
+minus 2Y hat واضح؟ طب ال normal component قولنا
+
+224
+00:15:39,350 --> 00:15:46,490
+مين من ال normal اللي هي DN1 بتسوي DN2 أو D1 DN1
+
+225
+00:15:46,490 --> 00:15:50,950
+minus DN2 بتسوي raw free بس هو مجرد نسيرة أي free
+
+226
+00:15:50,950 --> 00:15:55,710
+chargesمعناه raw بتساوي صفر ال surface charge
+
+227
+00:15:55,710 --> 00:16:01,470
+بتساوي zero اذا دي واحد norm بتساوي دي تانين norm
+
+228
+00:16:01,470 --> 00:16:05,210
+طب دي واحد norm مش بتساوي epsilon واحد في E واحد
+
+229
+00:16:05,210 --> 00:16:10,300
+normالتي قيمتها تلاتة اي واحد نورم اي ابسلون ار
+
+230
+00:16:10,300 --> 00:16:14,580
+واحد هي اربعة اربعة في تلاتة هي اللي هي دي واحد
+
+231
+00:16:14,580 --> 00:16:18,180
+نورم هي تساوي دي تانين نورم وبالتالي بقدر اقول اي
+
+232
+00:16:18,180 --> 00:16:21,280
+تانين نورم لان اي تانين نورم مش متساوي دي تانين
+
+233
+00:16:21,280 --> 00:16:25,620
+نورم على ابسلون تانين ار واضح كده شفنا ال
+
+234
+00:16:25,620 --> 00:16:29,460
+components كلهم هي المحلول المحضوطة هي اي واحد
+
+235
+00:16:29,460 --> 00:16:32,920
+نورم متساوي اي واحد dot and hat اللي هي التلاتة
+
+236
+00:16:35,690 --> 00:16:39,190
+والتي هي total E E norm plus E tangential وكذا انا
+
+237
+00:16:39,190 --> 00:16:41,710
+قلت لكم يا tangential component اللي في ال X وY
+
+238
+00:16:41,710 --> 00:16:44,850
+component ال tangential تنين هتسوى E tangential
+
+239
+00:16:44,850 --> 00:16:48,050
+واحد دي تنين norm بتسوى D واحد norm لإن ال free
+
+240
+00:16:48,050 --> 00:16:51,150
+charge على ال surface اللي قلنا بتسوى Zero وD واحد
+
+241
+00:16:51,150 --> 00:16:55,570
+norm ايش بتسوى Y راتب واحد في E واحد N وبنجيب دي
+
+242
+00:16:55,570 --> 00:16:59,040
+تنين N وبالتالي بقدر أجيب E تنين N لإنها هتكوندى
+
+243
+00:16:59,040 --> 00:17:03,780
+تنين N على ي مقار تنين اذا جبنا E تنين tangential
+
+244
+00:17:03,780 --> 00:17:07,200
+او E تنين norm بالتالي بقدر اقول ان E تنين او E
+
+245
+00:17:07,200 --> 00:17:11,480
+tangential زائد E تنين norm و بقدر احسب قيمة ال E
+
+246
+00:17:11,480 --> 00:17:16,800
+تنين واضح كده اذا انا معرفتى المعطيات عن ال field
+
+247
+00:17:16,800 --> 00:17:20,620
+في ال media الأولى عرفت اول شي بال media ال field
+
+248
+00:17:20,620 --> 00:17:23,780
+في ال media التانية لان عارفة ال conditions بتاعة
+
+249
+00:17:23,780 --> 00:17:28,450
+ال boundary بين ال two dielectricsطب الزوايا بين
+
+250
+00:17:28,450 --> 00:17:33,240
+E1 و E2 اللي بيعملوهم على ال interfaceبتوا الزاوية
+
+251
+00:17:33,240 --> 00:17:36,100
+اللي بيعملوها مع ال interface طبعا عندي two
+
+252
+00:17:36,100 --> 00:17:41,020
+components يعني عندي XY component على ال XY plane
+
+253
+00:17:41,020 --> 00:17:44,620
+يعني عندي E1 لو أنا بدأ أفكر في الزاوية اللي بين
+
+254
+00:17:44,620 --> 00:17:49,080
+ال XY plane في ال XY plane هتكون أصعب من إن لو
+
+255
+00:17:49,080 --> 00:17:51,720
+فكرت في ال Z component لإن عندي one component في
+
+256
+00:17:51,720 --> 00:17:55,420
+ال Z component يعني لما طلعت على ال Z component لل
+
+257
+00:17:55,420 --> 00:17:59,380
+electric field بقول إن ال Z component مش متساوي E
+
+258
+00:17:59,380 --> 00:18:04,140
+جبت من ستة واحد صح؟إذا جيبت ال 6 واحد انا هجيب ال
+
+259
+00:18:04,140 --> 00:18:07,420
+alpha واحد بمنتهى البساطة بقدر اقول ان E alpha
+
+260
+00:18:07,420 --> 00:18:11,100
+واحد بالساوي اللى هى ال difference بين ال 90 نقل
+
+261
+00:18:11,100 --> 00:18:16,520
+ال 6 واحد او بدي اجيب قيمة ال E واحد tangential
+
+262
+00:18:16,520 --> 00:18:19,880
+اللى هى ال square root ل X تربيع زى E X تربيع زى E
+
+263
+00:18:19,880 --> 00:18:22,700
+Y تربيع بس هسأل ليه ان اجيب الزاوية ما بين ال Z
+
+264
+00:18:22,700 --> 00:18:29,090
+component و ال norm على ال interfaceالـ E1 والنورم
+
+265
+00:18:29,090 --> 00:18:32,370
+على ال interface وبالتالي بقدر اجيب اللي مع ال
+
+266
+00:18:32,370 --> 00:18:35,670
+interface انا هتكون تسعين ناقص سيتا اللي مع ال
+
+267
+00:18:35,670 --> 00:18:41,270
+norm لذان هذه هي الحطوة التانية بتأجيب سيتا واحد و
+
+268
+00:18:41,270 --> 00:18:44,290
+سيتا اتنين و احنا قولنا انه انا عارفة ال normal
+
+269
+00:18:44,290 --> 00:18:47,710
+component و ال tangential component لل fields بقدر
+
+270
+00:18:47,710 --> 00:18:51,930
+اقول ان سيتا واحد يعني اصلا بعملها بهذه الطريقة ان
+
+271
+00:18:51,930 --> 00:18:57,280
+سيتا واحد بتساوييا سواء اللي هو ال .. بجيب دلالتي
+
+272
+00:18:57,860 --> 00:19:01,460
+الـ tangential component انها cosine او التان ان
+
+273
+00:19:01,460 --> 00:19:05,700
+بقول magnitude تبع ال E1 tangential على اللي هي ال
+
+274
+00:19:05,700 --> 00:19:10,400
+E1Z هى بتكون تان ثتا واحد اذا حسبناها باي طريقة زى
+
+275
+00:19:10,400 --> 00:19:12,860
+ما احنا هنا حاسبينها ان جيبت المتدار تبع ال E1
+
+276
+00:19:12,860 --> 00:19:16,040
+tangential هي ال square root المربع المولى زائد
+
+277
+00:19:16,040 --> 00:19:18,980
+المربع التانية و ال A norm احنا عارفين ان هي في ال
+
+278
+00:19:18,980 --> 00:19:22,280
+Z component بقدر و انت تان ثتا واحد E1 tangential
+
+279
+00:19:22,280 --> 00:19:26,110
+اي واحد norm بجيب ثتا واحدبجيب الفا واحد لان الفا
+
+280
+00:19:26,110 --> 00:19:29,290
+واحد مش هتساوي تسعين minus ستة واحد نفس الحكي
+
+281
+00:19:29,290 --> 00:19:33,390
+بطبقه على اللي هو ال E في ال media التانية و بقدر
+
+282
+00:19:33,390 --> 00:19:38,810
+اجيب اللي هي الفا تنين بعد اشهر بعدهال energy
+
+283
+00:19:38,810 --> 00:19:43,690
+densities in both dielectrics و احنا برضه شوفنا ان
+
+284
+00:19:43,690 --> 00:19:46,750
+ال energy density بتساوي نص ال dielectric فى ال
+
+285
+00:19:46,750 --> 00:19:51,010
+magnitude لفير تربية فزا فى ال media الأولى هتكون
+
+286
+00:19:51,010 --> 00:19:54,830
+ال energy density نص ابسلون واحد اي واحد تربية فى
+
+287
+00:19:54,830 --> 00:19:57,670
+ال media التانية هتكون نص ابسلون اتنين اي
+
+288
+00:19:57,670 --> 00:20:00,230
+magnitude تربية هو ماعطينا ال relative
+
+289
+00:20:00,230 --> 00:20:05,640
+permittivityأبسلون ار واحد ابسلون ار اتنين لكن انا
+
+290
+00:20:05,640 --> 00:20:09,100
+بدي ابسلون فاش بس اذا بضرب هذا ابسلون نوت اذا ربنا
+
+291
+00:20:09,100 --> 00:20:12,280
+ابسلون relative ابسلون نوت بحصل على ابسلون في
+
+292
+00:20:12,280 --> 00:20:15,820
+الميديا فإذا ابسلون واحد ايش هتكون ابسلون نوت اللي
+
+293
+00:20:15,820 --> 00:20:19,000
+هي عشر أقوى نقص تسعة ستة وتلاتين باي في ابسلون
+
+294
+00:20:19,000 --> 00:20:22,120
+relative اللي هي اربع في واحد تربية اللي هي طبعا
+
+295
+00:20:22,120 --> 00:20:27,000
+ال magnitude هو جزر التربية لEX تربية زي ال EY
+
+296
+00:20:27,000 --> 00:20:30,420
+تربية لEZ التربية تربيتها بخلص من الجزر
+
+297
+00:20:34,000 --> 00:20:37,080
+لأنها كانت كل القيانة ميعطينياها بال kilo volt
+
+298
+00:20:37,080 --> 00:20:41,360
+فلما أربعها ايش بتصير عشرة قوة ستة انتبهوا لل
+
+299
+00:20:41,360 --> 00:20:44,520
+units احنا عند ال electric field ميعطينياها ب kilo
+
+300
+00:20:44,520 --> 00:20:48,500
+volt per meter لما اخد ال magnitude ل E تربيه
+
+301
+00:20:48,500 --> 00:20:52,200
+هتصير ايش هكدي K تربيه يعني kilo تربيه يعني عشرة
+
+302
+00:20:52,200 --> 00:20:57,660
+قوة ستةفهذه صارت عندى فى عشرة قوة ستة لو حسبت
+
+303
+00:20:57,660 --> 00:21:00,820
+بيطلع بيضل عندى فى ال micro لإن عشر قوة نقل ستة
+
+304
+00:21:00,820 --> 00:21:05,220
+وفى عندى اللى هي بعض ال .. ال .. حيطلع لنا بعض ال
+
+305
+00:21:05,220 --> 00:21:09,420
+.. برضه ال .. الترمال فهيكون ستمية و اتنين و سبعين
+
+306
+00:21:09,420 --> 00:21:12,300
+micro هي point ستة سبعة تلات .. سبعة اتنين
+
+307
+00:21:12,300 --> 00:21:16,280
+millijoule ده التسهير 672 microjoule per meter
+
+308
+00:21:16,280 --> 00:21:19,270
+cubeنفس الحاجة ال energy density في ال media
+
+309
+00:21:19,270 --> 00:21:22,750
+التانية ما ننساش ال units ان هي كانت بال kilo volt
+
+310
+00:21:22,750 --> 00:21:25,930
+هيطلع عندها عشرة قوة ستة بالنهاية بيطلع مع جواب
+
+311
+00:21:25,930 --> 00:21:29,310
+بال micro joule أخر حاجة هو طالب ال total energy
+
+312
+00:21:31,290 --> 00:21:38,050
+within the cube of side 2m centered at 3,4,-5 بيده
+
+313
+00:21:38,050 --> 00:21:43,430
+ال total energy اللى فى قلب مكعب اللى وين عند 3,4,
+
+314
+00:21:43,550 --> 00:21:45,770
+-5 بتعرف وين هو فى ال media الأولى و لا فى ال
+
+315
+00:21:45,770 --> 00:21:50,270
+media التانية ما أنها سالب z سالب z وين media
+
+316
+00:21:50,270 --> 00:21:57,670
+التانية وهذا ال cube centered عن مين عند x3 و y4 و
+
+317
+00:21:57,670 --> 00:22:02,150
+minus 5 بالنسبة ل ال z componentهذا ال center تبعه
+
+318
+00:22:02,150 --> 00:22:04,870
+عشان انا اعرف اللى هى من و من بدي اخد ال X ل Y و
+
+319
+00:22:04,870 --> 00:22:10,530
+ال Z اذا هو ال center تبع
+
+320
+00:22:10,530 --> 00:22:16,030
+ال X مثلا عند التلاتة اذا قدش هيروح طول الدلع واحد
+
+321
+00:22:16,030 --> 00:22:20,190
+يعني هيروح من وين من من 2 ل 4
+
+322
+00:22:24,560 --> 00:22:28,820
+هيكون بيبدأ ال integration من 1 ل 4 و Y ال center
+
+323
+00:22:28,820 --> 00:22:33,980
+دي عند ال 4 اذا ما هيروح من وين ل 3 ل 5 واضح؟ و
+
+324
+00:22:33,980 --> 00:22:38,040
+هكذا اذا ما هنعمل ال total integral اللي هو X من 2
+
+325
+00:22:38,040 --> 00:22:42,800
+ل 4 و Y من 3 ل 5 زي ما هيكون من minus 6 ل minus 4
+
+326
+00:22:42,800 --> 00:22:47,560
+بعمل ال integration بحصل على ال total energy واضح؟
+
+327
+00:22:47,560 --> 00:22:52,110
+في أسف صح لحد هنا؟طبعا أخدنا هيك واضح ليش لأن قلنا
+
+328
+00:22:52,110 --> 00:22:55,870
+ال X centered عند التلاتة إذا هيكون الطول بروح من
+
+329
+00:22:55,870 --> 00:23:01,390
+2 ل 4 لأن طوله 2 Y centered عند 4 إذا بيكون من 3 ل
+
+330
+00:23:01,390 --> 00:23:05,810
+5 Z centered عند ال minus 5 إذا بروح من minus 6 ل
+
+331
+00:23:05,810 --> 00:23:12,450
+minus 4 طب كده المثال المثال طبعا مهلقة عن
+
+332
+00:23:12,450 --> 00:23:14,770
+conductor و dielectric احنا شوفنا بين dielectric و
+
+333
+00:23:14,770 --> 00:23:16,870
+dielectric نشوف بين conductor و dielectric
+
+334
+00:23:24,290 --> 00:23:27,890
+عند الـ cube الأولاني ال extension في ال XZ
+
+335
+00:23:27,890 --> 00:23:32,970
+والثاني في ال XZ اتقابله عند ال Y equal 0 زى ما
+
+336
+00:23:32,970 --> 00:23:37,590
+تشوفى في الرسمة هى ال Y axis و ال two media اللى
+
+337
+00:23:37,590 --> 00:23:40,430
+هى ال dialectical conductor اتقابل ال interface
+
+338
+00:23:40,430 --> 00:23:45,090
+تبعهم او البلين عند Y equal 0 تبع التقاطه واضح؟
+
+339
+00:23:48,320 --> 00:23:51,440
+for y أقل من أوت ساوة زيرو ال conductor for y أكبر
+
+340
+00:23:51,440 --> 00:23:55,960
+من أوت ساوة زيرو ال نضايلكترك الو ipsim relative
+
+341
+00:23:55,960 --> 00:24:00,500
+بتساوي تنين if there is a surface charge هنا
+
+342
+00:24:00,500 --> 00:24:03,620
+ميعطينا surface charge مقدارها اتنين نانو كولومر
+
+343
+00:24:03,620 --> 00:24:10,040
+متر تربية من دا conductorE and D at اول حاجة بده
+
+344
+00:24:10,040 --> 00:24:14,660
+قيمة E وD عند A اللى موجودة فى الكندكتور ليش
+
+345
+00:24:14,660 --> 00:24:18,600
+موجودة فى الكندكتور عندما Y مالها سالبة قولنا Y
+
+346
+00:24:18,600 --> 00:24:22,580
+سالبة بيكون الكندكتور وY موجباة ده electric طب
+
+347
+00:24:22,580 --> 00:24:24,620
+احنا عارفين ال electric الكندكتور اش ال electric
+
+348
+00:24:24,620 --> 00:24:28,500
+فيه اللى بيكون عنده فى قلبه Zero اذا الجواب
+
+349
+00:24:28,500 --> 00:24:31,760
+الأولانى سهل احنا اول حاجة بيقولوا ايه هذه النقطة
+
+350
+00:24:31,760 --> 00:24:36,580
+اللى تلاتة نقص تنين تنين بتكون فى الكندكتورلأن Y
+
+351
+00:24:36,580 --> 00:24:40,520
+مالها أقل من Zero وبالتالي E و D بيساوة 0 أطول
+
+352
+00:24:40,520 --> 00:24:43,120
+احنا قولنا ال conductor بحتويش على ال electric
+
+353
+00:24:43,120 --> 00:24:45,320
+field لإن ال charges كلها بتروح على ال surfaces
+
+354
+00:24:45,320 --> 00:24:48,360
+بطل فيه عندى enclosed charges جوا بيكون ال
+
+355
+00:24:48,360 --> 00:24:55,800
+electric و ال D بالتالي بيساوة 0النقطة B X-4Y1Z5
+
+356
+00:24:55,800 --> 00:24:58,000
+وين بيكون في Y أكبر من 0
+
+357
+00:25:22,250 --> 00:25:25,170
+واضح؟ لو كانت مافيش free charge، هتكون برضه ال
+
+358
+00:25:25,170 --> 00:25:28,670
+normal component بتساوي zero طب إذا دي norm بتساوي
+
+359
+00:25:28,670 --> 00:25:32,290
+رقص، اللي هي اتنين nano column بالمتر تربية، و دي
+
+360
+00:25:32,290 --> 00:25:37,060
+إيش هتساويأتجاهها as a vector عشان نحددها ال
+
+361
+00:25:37,060 --> 00:25:39,920
+normal اللي هي مالها هتكون اتجاه ال Y component
+
+362
+00:25:39,920 --> 00:25:43,500
+التانجينشال هي في ال XZ component مالها سفر
+
+363
+00:25:43,500 --> 00:25:47,600
+وبالتالي بقدر أقول انه E ايش بتساوي D على ال
+
+364
+00:25:47,600 --> 00:25:49,960
+epsilon اللي هي عبارة عن epsilon note في epsilon
+
+365
+00:25:49,960 --> 00:25:54,440
+relative وبمعطيني ال dialectic ل ال media ال
+
+366
+00:25:54,440 --> 00:25:59,080
+relative dialectic ل ال dialecticيبسون ار
+
+367
+00:25:59,080 --> 00:26:01,400
+لدياليكتريك او ال relative permittivity
+
+368
+00:26:01,400 --> 00:26:04,060
+لدياليكتريك بتساوي تنين تطهي على الرسمة مش في
+
+369
+00:26:04,060 --> 00:26:08,520
+السؤال فإذا انا هقول ان E بسوا D على E not E ر
+
+370
+00:26:08,520 --> 00:26:13,080
+بتساوي المتدرق دمنا اللي هو ستة و تلاتين ب I و I
+
+371
+00:26:13,080 --> 00:26:20,120
+hat في اي سلسلة حد هنا ايه
+
+372
+00:26:20,120 --> 00:26:26,740
+كده احنا بنكون خلصنا شبط درم خمسةشوفنا كيف ال
+
+373
+00:26:26,740 --> 00:26:28,780
+boundary conditions بين ال dialectric و
+
+374
+00:26:28,780 --> 00:26:32,320
+الconductor و ال dialectric و ال dialectric و ال
+
+375
+00:26:32,320 --> 00:26:40,400
+conductor بيجي
+
+376
+00:26:40,400 --> 00:26:42,000
+ال boundary value problem
+
+377
+00:26:45,890 --> 00:26:49,430
+مهمين كتير في حساب الموجات و فهم التصور تبع
+
+378
+00:26:49,430 --> 00:26:52,550
+الموجات في ال medias و برضه بيجوا من Maxwell's
+
+379
+00:26:52,550 --> 00:26:56,650
+equations يعني Maxwell's equations هم الأساس لكل
+
+380
+00:26:56,650 --> 00:27:03,990
+الشغل تبعنانشتغل نفس الحاجة لـ boundary value
+
+381
+00:27:03,990 --> 00:27:08,470
+problems نشتغل نفس الحاجة لـ Passant equations و
+
+382
+00:27:08,470 --> 00:27:11,950
+لـ Plus equations نشتغل نفس الحاجة لـ Passant
+
+383
+00:27:11,950 --> 00:27:14,490
+equations و لـ Plus equations نشتغل نفس الحاجة لـ
+
+384
+00:27:14,490 --> 00:27:15,310
+Passant equations و لـ Plus equations نشتغل نفس
+
+385
+00:27:15,310 --> 00:27:17,230
+الحاجة لـ Passant equations و لـ Plus equations
+
+386
+00:27:17,230 --> 00:27:18,690
+نشتغل نفس الحاجة لـ Passant equations و لـ Plus
+
+387
+00:27:18,690 --> 00:27:18,870
+equations نشتغل نفس الحاجة لـ Passant equations و
+
+388
+00:27:18,870 --> 00:27:18,870
+لـ Plus equations نشتغل نفس الحاجة لـ Passant
+
+389
+00:27:18,870 --> 00:27:18,890
+equations و لـ Plus equations نشتغل نفس الحاجة لـ
+
+390
+00:27:18,890 --> 00:27:18,890
+Passant equations و لـ Plus equations نشتغل نفس
+
+391
+00:27:18,890 --> 00:27:19,030
+الحاجة لـ Passant equations و لـ Plus equations
+
+392
+00:27:19,030 --> 00:27:19,390
+نشتغل نفس الحاجة لـ Passant equations و لـ Plus
+
+393
+00:27:19,390 --> 00:27:19,430
+equations نشتغل نفس الحاج
+
+394
+00:27:26,950 --> 00:27:32,550
+لما نقول linear يعني معناه العلاقة بين D و E لها
+
+395
+00:27:32,550 --> 00:27:35,490
+linear فاش علنا اي تربيه و اي cube
+
+396
+00:27:41,870 --> 00:27:47,430
+لكن احنا عرفنا ان E ايش بتساوي minus del V من وين
+
+397
+00:27:47,430 --> 00:27:51,630
+اشتقناها ان اول حاجة كنا بتاكدين ان curl E بيساوي
+
+398
+00:27:51,630 --> 00:27:55,930
+zero ال rotational electric field صح؟ قولنا انه
+
+399
+00:27:55,930 --> 00:28:00,530
+عنده curl E بيساوي zero اذا ال E ماله بيساوي del ل
+
+400
+00:28:00,530 --> 00:28:05,350
+V بعدين شفنا من اشتقاقاتنا ل conservative force
+
+401
+00:28:05,350 --> 00:28:10,370
+انه بتطلع عنا إشارة سالبةبتذكرين صح؟ اذا عندنا E
+
+402
+00:28:10,370 --> 00:28:16,210
+بيسوي minus del V لو عوضت هنا هيكون عندى diverge
+
+403
+00:28:16,210 --> 00:28:22,230
+epsilon minus بدل ا E من E وحطتلها minus del V
+
+404
+00:28:22,230 --> 00:28:27,250
+بيسوي رو V طب احنا ال diverge ال del طبعا ال
+
+405
+00:28:27,250 --> 00:28:31,320
+epsilon اذا أخدتها برضه هموجنسهذه طبعا الحالة اللى
+
+406
+00:28:31,320 --> 00:28:35,840
+عادنا هى المعادلة اللى بصول لل انهمجنس يعنى y ماله
+
+407
+00:28:35,840 --> 00:28:39,240
+بعتمد على x و y و زد اللى انهمجنس معناه ماقدرش
+
+408
+00:28:39,240 --> 00:28:43,120
+اطلعه من ال differential انا بيصيرله تفاضل لو هو
+
+409
+00:28:43,120 --> 00:28:47,180
+انهمجنس معناه y مالها بتعتمد على ال x y z بتعتمد
+
+410
+00:28:47,180 --> 00:28:49,680
+على ال position يعنى برضه نفس ال epsilon function
+
+411
+00:28:49,680 --> 00:28:53,170
+في x y z مش بس potentialلكن لو انا اعتبرتها
+
+412
+00:28:53,170 --> 00:28:56,590
+homogenous، معناه يوماله لا يعتمد على الـX وY، إذا
+
+413
+00:28:56,590 --> 00:28:59,630
+كنت بقدر أطلعه من الـdifferential، بالتالي إذا
+
+414
+00:28:59,630 --> 00:29:01,950
+طلعت الـY من برة الـdifferential، minus يومالي،
+
+415
+00:29:01,950 --> 00:29:04,830
+حسيب عندي الـdivergent دل، و الـdivergent دل احنا
+
+416
+00:29:04,830 --> 00:29:08,550
+شفناها قبل هي كدلتر بيع، إذا هيكون دلتر بيع الـV
+
+417
+00:29:08,550 --> 00:29:11,630
+بتسوء minus rho V على يومالي هي، بس هو equation
+
+418
+00:29:11,630 --> 00:29:17,070
+لمين؟ للـhomogenous mediumتمام؟ إذا المبسطون ال
+
+419
+00:29:17,070 --> 00:29:20,590
+equation لل in homogenous media بتقوللي diverse
+
+420
+00:29:20,590 --> 00:29:25,790
+minus epsilon دل V بتسوي rho V لل homogenous دل
+
+421
+00:29:25,790 --> 00:29:30,170
+تربيع V بتسوي minus rho V على epsilon لو كانت rho
+
+422
+00:29:30,170 --> 00:29:34,250
+V بتسوي zero بحصل على plus equation هيكون عندي
+
+423
+00:29:35,600 --> 00:29:39,040
+diverge minus epsilon دي ال V بالسوء Zero ل ال
+
+424
+00:29:39,040 --> 00:29:42,840
+homogenous و دي ال تربيع V بالسوء Zero ل ال
+
+425
+00:29:42,840 --> 00:29:47,200
+homogenous يعني لما ال free chart بالسوء Zero بحصل
+
+426
+00:29:47,200 --> 00:29:50,900
+على plus equation لما رو V لات سوء Zero بكون بحكي
+
+427
+00:29:50,900 --> 00:29:55,700
+على plus equation واضح؟ طب إيش ال plus equation يا
+
+428
+00:29:55,700 --> 00:29:59,340
+عزيزي؟ طب لما إيش plus equation؟ واحد دلتين، ال
+
+429
+00:29:59,340 --> 00:30:04,630
+homogenous و ال inhomogenous تمامفي ال divergence
+
+430
+00:30:04,630 --> 00:30:08,430
+سالب إبسلون و gradient ال voltage like this و بعد
+
+431
+00:30:08,430 --> 00:30:12,290
+ما عوضنا للخارج، صاروا ستان و نصر تمام، حد ل مين؟
+
+432
+00:30:12,290 --> 00:30:14,910
+للهموجناص و لا للاهموجناص؟ للهموجناص، ايه؟ ليش
+
+433
+00:30:14,910 --> 00:30:17,370
+للهموجناص؟ لأن إبسلون لسه موجودة، ما تقلعوا أنها
+
+434
+00:30:17,370 --> 00:30:20,890
+بجد، ليش؟ لأنها determined على x, y, z، الهموجناص،
+
+435
+00:30:20,890 --> 00:30:24,250
+طب و التعنية إيش بتكون؟لما نضغط على سلب Epsilon
+
+436
+00:30:24,250 --> 00:30:30,030
+مرة اخرى، نعتمد عليه فعلا إلى Δ P بساول رو P على
+
+437
+00:30:30,030 --> 00:30:32,470
+Epsilon مرة أخرى، minus rho V على Epsilon هنا لأن
+
+438
+00:30:32,470 --> 00:30:35,570
+Epsilon تصبح homogenous، مع أنها لا تعتمد على X,
+
+439
+00:30:35,630 --> 00:30:39,350
+Y, Z، في حالة rho V بساول zero، بنحصل على ال plus
+
+440
+00:30:39,350 --> 00:30:43,590
+أسواق اللي هم جناس و لا اللي هم الجناس mediaطب ال
+
+441
+00:30:43,590 --> 00:30:48,090
+Laplace احنا شوفنا قبل هيكى لكن للتذكير اسواء في
+
+442
+00:30:48,090 --> 00:30:50,250
+ال Cartesian او ال cylindrical او ال spherical
+
+443
+00:30:50,250 --> 00:30:54,390
+ماقدروا اشتقوا او يعني اتذكروا او اعرفوا اللى بدى
+
+444
+00:30:54,390 --> 00:30:57,870
+ايه او يعطى ليه فى الامتحان اسهل واحدة فيهم اللى
+
+445
+00:30:57,870 --> 00:31:01,330
+فى ال Cartesian هى D2V بقى DX تربية زى D2V بقى DY
+
+446
+00:31:01,330 --> 00:31:05,010
+تربية زى D2V بقى DZ تربية بساوة Zero طبعا هدى
+
+447
+00:31:05,010 --> 00:31:09,050
+Laplace equation دل تربية V بالساوة Zero لمين؟
+
+448
+00:31:09,050 --> 00:31:12,170
+للهوموجيناص لإن أُس من انا طلعتها برا دل تربية V
+
+449
+00:31:12,170 --> 00:31:17,110
+بالساوة Zeroالهموجينة أصلا plus equation بس هنا في
+
+450
+00:31:17,110 --> 00:31:19,930
+ال cylindrical و هنا في ال spherical coordinate
+
+451
+00:31:19,930 --> 00:31:24,970
+لإن ال plus equation أصلا الهموجينة السيبية طب
+
+452
+00:31:24,970 --> 00:31:27,550
+uniqueness في الريم؟ايش معناه uniqueness يا رم؟
+
+453
+00:31:27,550 --> 00:31:30,950
+انه انا لو انا بدي solution يكون وحداني، يعني انا
+
+454
+00:31:30,950 --> 00:31:34,470
+بحكي عن ال mouse هاي الزرقة، بدي انا اللي احصل
+
+455
+00:31:34,470 --> 00:31:36,470
+عليه في نهاية ال mouse الزرقة، مابديش احصل على ال
+
+456
+00:31:36,470 --> 00:31:39,390
+mouse الحمرة و الخضرة و الصفرة، ماليها الدنيا
+
+457
+00:31:39,390 --> 00:31:43,290
+mouseات، لكن انا بحكي عن mouse معينة، بحكي عن موجة
+
+458
+00:31:43,290 --> 00:31:45,350
+معينة، بدي احصل على هذه الموجة معينة، هاي ال
+
+459
+00:31:45,350 --> 00:31:47,910
+uniquenessمش ال solution تبعاه هذا mathematical
+
+460
+00:31:47,910 --> 00:31:51,510
+هذا ال solution تبعاه mathematical او يعني هذه
+
+461
+00:31:51,510 --> 00:31:54,870
+المعادلات رياضية المعادلات الرياضية هي بتعطيني بس
+
+462
+00:31:54,870 --> 00:31:58,010
+ال solution مليون solution اكملت solution واحد
+
+463
+00:31:58,010 --> 00:32:01,270
+منهم اللي بيخليها uniqueness اللي هي ال boundary
+
+464
+00:32:01,270 --> 00:32:04,590
+conditions بحط ال conditions بتاعت ال problem
+
+465
+00:32:04,590 --> 00:32:07,630
+بتاعتي بتعطيني ال solution تبعاه او بتعطيني ال
+
+466
+00:32:07,630 --> 00:32:10,430
+wave بتاعتي او ال potential تبعاه بدون ال boundary
+
+467
+00:32:10,430 --> 00:32:14,630
+conditions تعوني بيكون عندش solution ماله عامبنفع
+
+468
+00:32:14,630 --> 00:32:22,030
+لأي حد تاني، بنفع لنا و لعبير و لهديل و ل .. و
+
+469
+00:32:22,030 --> 00:32:26,030
+لهبة، بنفع للجميع، لكن أنا بس بدي ال solution تبع
+
+470
+00:32:26,030 --> 00:32:30,190
+مين هديل، بدي بالنهاية يكون بنطبق الحلقة هديل مع
+
+471
+00:32:30,190 --> 00:32:32,790
+نبض أو ال boundary conditions، لبسة جلبة بلونه
+
+472
+00:32:32,790 --> 00:32:39,410
+بالنيباته، حطة إشارب على شكل جلد النمر و هكذابحط
+
+473
+00:32:39,410 --> 00:32:42,970
+ال boundary condition بتاعتي بتطلعلي الموجة اللي
+
+474
+00:32:42,970 --> 00:32:46,050
+أنا بدور عنها هذه هي ال uniqueness اذا انها دي
+
+475
+00:32:46,050 --> 00:32:49,650
+تلتة تربيع V اللي هي ال Laplace equation ل ال
+
+476
+00:32:49,650 --> 00:32:54,850
+homogeneous media بتساوي Zero بتقوللي انه انا عندي
+
+477
+00:32:54,850 --> 00:32:58,930
+solutions متعددة عشان احقق او يعني اوصل ل solution
+
+478
+00:32:58,930 --> 00:33:03,630
+بديها او ال only solution اللي انا بديها فقط بتحقق
+
+479
+00:33:03,630 --> 00:33:06,150
+هذا الحكي اذا طبقت ال right boundary conditions
+
+480
+00:33:09,710 --> 00:33:16,410
+عشان احصل على ال solution تبعي اولا بالدين اختار
+
+481
+00:33:16,410 --> 00:33:22,000
+المعادل المناسبةأنا بدي مين؟ لبلاس و لا بسان؟ إيش
+
+482
+00:33:22,000 --> 00:33:25,460
+بأكمل على إن في عندى free charge و لا لأ؟ هل هي ال
+
+483
+00:33:25,460 --> 00:33:28,680
+homogenous و لا ال homogenous؟ بأكمل هل ال
+
+484
+00:33:28,680 --> 00:33:32,580
+permittivity بتاعك بتاعتك مد على ال XYZ و لا لأ؟
+
+485
+00:33:32,580 --> 00:33:37,160
+إذا أول حاجة بدي أختار المعادلة الصحيحة بعدين بدي
+
+486
+00:33:37,160 --> 00:33:41,900
+أشوف المنطقة اللي بحل فيها عشان أختار اللي هي
+
+487
+00:33:45,560 --> 00:33:48,720
+أول حاجة بختار المعادلة الصحيحة بعدين بشوف ال
+
+488
+00:33:48,720 --> 00:33:52,940
+region بتاعتي و بحل و بختار بعض ال conditions
+
+489
+00:33:52,940 --> 00:33:59,440
+الصحيحة إذا ال zero zero solution كان مرة أول حاجة
+
+490
+00:33:59,440 --> 00:34:03,400
+بنحل ل plus إذا كانت row v بالساوة zero أو بصمم
+
+491
+00:34:03,400 --> 00:34:07,580
+إذا كانت row v لساوة zeroأسواء نستخدم الـ direct
+
+492
+00:34:07,580 --> 00:34:10,560
+integration و لا نستخدم الـ direct integration لو
+
+493
+00:34:10,560 --> 00:34:13,360
+أنا خلينا ناخد أسئلة واحدة اللي هي ال plus
+
+494
+00:34:13,360 --> 00:34:16,820
+equation لل homogenous media اللي هي تقبيع V لو
+
+495
+00:34:16,820 --> 00:34:20,520
+كانت الاعتمادية بتاعة ال potential على Y بتساوي 0
+
+496
+00:34:21,140 --> 00:34:23,080
+الاعتمادية تانية من شاء على z بالساوة زره ايش
+
+497
+00:34:23,080 --> 00:34:25,420
+هيكون عندي فقط الاعتمادية على ال x، عندي تانين v
+
+498
+00:34:25,420 --> 00:34:28,140
+by dx ترويح بساوة زره أزره، مش هيبقى حلها by
+
+499
+00:34:28,140 --> 00:34:31,360
+direct integration بكامل أول مرة و تاني مرة،
+
+500
+00:34:31,360 --> 00:34:34,460
+الحالة تبقى زي هيكون نفس الاشي هنا، لو كان مثلا
+
+501
+00:34:34,460 --> 00:34:36,800
+بعتمدش على ال row و بعتمدش على ال z ده، بسجد ال
+
+502
+00:34:36,800 --> 00:34:41,150
+phi componentباستخدم ال integral نفس الحاجة في ال
+
+503
+00:34:41,150 --> 00:34:43,690
+spherical لو هدولة بقتملش على أعلى و تسيطر عن
+
+504
+00:34:43,690 --> 00:34:47,730
+نفسها على ال five double integral بحل اذا بطلع لو
+
+505
+00:34:47,730 --> 00:34:50,470
+انا ال potential تبعي فقط بعتمد على one variable
+
+506
+00:34:50,470 --> 00:34:53,670
+دايما بسهل علي الحل بكون اني بقدر اعمل بال double
+
+507
+00:34:53,670 --> 00:34:56,730
+integral بجيب ال solution لك لو بعتمد عليهم كلها
+
+508
+00:34:58,750 --> 00:35:02,530
+بنحلل بحاجة بنسميها separation of variables بندق
+
+509
+00:35:02,530 --> 00:35:05,310
+أستخدم ال separation of variables يعني الحل الأول
+
+510
+00:35:05,310 --> 00:35:09,130
+طريقة الأول هي direct integration إذا كانت في فقط
+
+511
+00:35:09,130 --> 00:35:12,590
+فقط content variable واحد أو بستخدم ال separation
+
+512
+00:35:12,590 --> 00:35:15,430
+of variables إذا كانت فيه مالها بتعمل على أكتر من
+
+513
+00:35:15,430 --> 00:35:16,910
+variable واضحة هذه النقطة؟
+
+514
+00:35:19,800 --> 00:35:23,440
+لحدها لقيت الحل اللي حلته أسبوع بالدوبل انتيجرال و
+
+515
+00:35:23,440 --> 00:35:26,260
+لا بال separation of variables الناتج تبعي ماله مش
+
+516
+00:35:26,260 --> 00:35:31,840
+unique لأنه عام لسه ماحفظتش عليه constraints بد
+
+517
+00:35:31,840 --> 00:35:34,540
+أحط ال boundary conditions وبالتالي بحصل على ال
+
+518
+00:35:34,540 --> 00:35:38,770
+unique solutionواضح؟ لما أحط ال boundary
+
+519
+00:35:38,770 --> 00:35:41,250
+conditions أفرضها على ال solution اللي حصلت عليه
+
+520
+00:35:41,250 --> 00:35:45,070
+أسوأ من اللي هي ال double integral و لا من ال
+
+521
+00:35:45,070 --> 00:35:47,550
+separation variable بحصل على ال unique solution
+
+522
+00:35:47,550 --> 00:35:51,350
+إذا حصلت على V بسهولة عليا أجيب E لأن E مش بتساوي
+
+523
+00:35:51,350 --> 00:35:55,830
+minus grade V إذا جبت E بجيب D لأن D مش بتساوي
+
+524
+00:35:55,830 --> 00:36:01,670
+epsilon E واضح؟ كمان بقدر أجيب Q لأن Q مش بتساوي
+
+525
+00:36:01,670 --> 00:36:06,890
+ال integral ل rho S DS و rho S مش بتساوي DNإذا
+
+526
+00:36:06,890 --> 00:36:09,990
+بقدر أجيب أي حاجة إذا عرفت هذا الحكاية قدر أجيب
+
+527
+00:36:09,990 --> 00:36:12,950
+مين is the distance between two media لإن ال C
+
+528
+00:36:12,950 --> 00:36:15,950
+بسوة و Q على V إذا كنت عارفة ال potential already
+
+529
+00:36:15,950 --> 00:36:19,530
+بقدر أجيب اللي هي ال capacitance بالذات لو أنا كنت
+
+530
+00:36:19,530 --> 00:36:24,390
+أحكي على two conductors طبعا خلي الأمثلة القادمة
+
+531
+00:36:24,390 --> 00:36:27,850
+إن شاء الله بس راجعوا اللي حكيناه عشان تكونوا
+
+532
+00:36:27,850 --> 00:36:33,130
+معانا في أحل الأمثلة يعني احنا تقريبا هيك خلصنا ال
+
+533
+00:36:33,130 --> 00:36:37,240
+chapter الباقي أسئلةيعني ان كان اقولكم المقال
+
+534
+00:36:37,240 --> 00:36:41,680
+الجانب ده chapter 7 بس عشان تستفيدوا من حل الأمثلة
+
+535
+00:36:41,680 --> 00:36:45,640
+راجعوا ان تطلعوا عليه، اتطلعوا على اللي حكيناه و
+
+536
+00:36:45,640 --> 00:36:47,860
+اتطلعوا على الأمثلة نفسها عشان لو فينكم اي
+
+537
+00:36:47,860 --> 00:36:50,980
+استفسارات تحصلوا على الإجابات و احنا بنحكيها مع
+
+538
+00:36:50,980 --> 00:36:54,160
+بعض، تسألون ليش هي النقطة هيكي و ليش النقطة هيكي،
+
+539
+00:36:54,160 --> 00:36:57,420
+أما هيكي باعتبار ال chapter خلص، يعطيكم العفو
+
diff --git a/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/5STYzhKVl6A_postprocess.srt b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/5STYzhKVl6A_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..f8f8f950d2f801793444c903576a7bc7d28d80f5
--- /dev/null
+++ b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/5STYzhKVl6A_postprocess.srt
@@ -0,0 +1,2032 @@
+1
+00:00:20,570 --> 00:00:24,090
+بسم الله الرحمن الرحيم السلام عليكم ورحمة الله
+
+2
+00:00:24,090 --> 00:00:29,630
+وبركاته احنا اليوم هنكمل موضوع ال vector analysis
+
+3
+00:00:29,630 --> 00:00:33,070
+و هنكمل هو ال second derivative احنا المحاضرة
+
+4
+00:00:33,070 --> 00:00:36,750
+الماضية شوفنا ال second derivative لل scalar كمان
+
+5
+00:00:36,750 --> 00:00:41,730
+شوفنا ال second derivative لل vector شوفنا كمان لل
+
+6
+00:00:41,730 --> 00:00:44,910
+scalar ان اقدر اكتب ال second derivative ب
+
+7
+00:00:44,910 --> 00:00:45,750
+Cartesian
+
+8
+00:00:48,900 --> 00:00:53,260
+و طبعا قلنا انها scalar لانها diverse الدل تبتد
+
+9
+00:00:53,260 --> 00:00:57,980
+بردك دايما scalar فاحنا في ال cartesian شفناه وفي
+
+10
+00:00:57,980 --> 00:01:01,360
+ال cylindrical وفي ال spherical وعرفنا ال harmonic
+
+11
+00:01:01,360 --> 00:01:07,020
+field اللي بتكون الدل بتاعته بالساوة زير بعدين
+
+12
+00:01:07,020 --> 00:01:10,860
+شفنا ال vector field الدل او second derivative لل
+
+13
+00:01:10,860 --> 00:01:14,900
+vector field قلنا بنعبر عنها في المعادلة قدامنا دل
+
+14
+00:01:14,900 --> 00:01:21,680
+التربيه ايه؟ بتساويدل تايفرج a مانوس كيركل a و
+
+15
+00:01:21,680 --> 00:01:27,060
+برضه تلتر بي ا م بتساوي تلتر بي ا x اكسات ذات تلتر
+
+16
+00:01:27,060 --> 00:01:30,920
+بي ا y و اكسات تلتر بي ا زد زد اكسات و قد حكينا ان
+
+17
+00:01:30,920 --> 00:01:36,880
+المحاضرة تمامة وقفنا عن المثال احنا قلنا اواني
+
+18
+00:01:36,880 --> 00:01:42,360
+scalar here زي اللي امشي هنا طلب مننا ان نجلب اللي
+
+19
+00:01:42,360 --> 00:01:43,360
+هو ال second derivative
+
+20
+00:01:58,040 --> 00:02:02,420
+محضان كارتيجين يقولون ان تذكروا دل تربية هو عبارة
+
+21
+00:02:02,420 --> 00:02:09,160
+عن second derivative بالنسبة ل X اتساور
+
+22
+00:02:09,160 --> 00:02:15,120
+second derivative تربيه بالنسبة ل X تربيه X3 تربيه
+
+23
+00:02:15,120 --> 00:02:22,940
+تربيه Y تربيه
+
+24
+00:02:24,990 --> 00:02:28,210
+بعنوان انا ابقى فاضل اول مرة ال B بالنسبة ل X كلمة
+
+25
+00:02:28,210 --> 00:02:36,230
+مرة اتنين
+
+26
+00:02:36,230 --> 00:02:41,730
+نقطة و اتنين كوصين اتنين X اكس هات زائد B by BY
+
+27
+00:02:41,730 --> 00:02:47,830
+وفاضل بالنسبة ل Y هتكون E3-E3Z E3-E3Z E3-E3Z E3
+
+28
+00:02:47,830 --> 00:02:48,850
+-E3Z E3-E3-E3Z E3-E3-E3-E3-E3-E3-E3-E3-E3-E3-E3-E3
+
+29
+00:02:48,850 --> 00:02:52,290
+-E3-E3-E3-E3-E3-E3-E3-E3-E3-E3-E3-E3-E3-E3-E3-E3
+
+30
+00:02:52,290 --> 00:02:57,520
+-E3-E3-E3-E3-E3-E3-E3-E3-E3-E3-E3بعض الاختصارات
+
+31
+00:03:08,310 --> 00:03:11,230
+يعني إتفاض بسيط يعني مش أكتر بقى بحاجة بس الواحد
+
+32
+00:03:11,230 --> 00:03:15,750
+يكون فيه إيش الأشياء اللي مطلوبينها فمش هترجع قاضل
+
+33
+00:03:15,750 --> 00:03:20,210
+ال 10 بالأعلى بالأسفل X هتجيب Minus 4 E to the
+
+34
+00:03:20,210 --> 00:03:32,750
+minus 6 Cos Inverted Y Sin Inverted X X hat Cos
+
+35
+00:03:32,750 --> 00:03:35,030
+Inverted Y Y hat
+
+36
+00:03:49,790 --> 00:03:53,970
+في حد عنده أي استفسار ما اسمه special course
+
+37
+00:03:53,970 --> 00:03:56,610
+ماكانش بالدولة اصلا في حد بدويا في كهبة اللي عادة
+
+38
+00:03:56,610 --> 00:03:59,970
+يسوقه ان هي فكرة التفاضل زي ما اتفقنا هي second
+
+39
+00:03:59,970 --> 00:04:04,850
+derivative التفاضل مرتين ل V و مرتين ل Y و مرتين ل
+
+40
+00:04:04,850 --> 00:04:10,340
+Z هشوف ان انا X و Y تتنفسد او تسكيل على الكمة Dبس
+
+41
+00:04:10,340 --> 00:04:13,880
+فعلا هذا scalar quantity هي دل ال V انها دل ال
+
+42
+00:04:13,880 --> 00:04:17,220
+diver دل ال diver يعني scalar quantity D2V by DX
+
+43
+00:04:17,220 --> 00:04:21,740
+تربيه زي D2V by DY تربيه زي D2V by DZ تربيه كمرة
+
+44
+00:04:21,740 --> 00:04:25,800
+باكد انه عملت هذا الخطأ لما ان هي خلته vector هي
+
+45
+00:04:25,800 --> 00:04:29,980
+scalar quantity زي ما احنا شفنا كمان مرة ان هي
+
+46
+00:04:29,980 --> 00:04:36,540
+عبارة عن دل diver جدد product عبارة عن scalar
+
+47
+00:04:36,540 --> 00:04:46,230
+quantityو V أصلا هي scalar quantity هذا هو
+
+48
+00:04:46,230 --> 00:04:52,060
+المثال الأولفي بعض ال quantity يعني بشكل عام ال
+
+49
+00:04:52,060 --> 00:04:54,700
+classification تبع ال fields لان بينا نيجي نصنف ال
+
+50
+00:04:54,700 --> 00:04:58,320
+fields لما نقدر ناخد ع ال fields نفترض ان ايه هو
+
+51
+00:04:58,320 --> 00:05:01,960
+بشكل عام هو اي field electric field magnetic field
+
+52
+00:05:01,960 --> 00:05:05,440
+اي تصنيف في اي field بتمن خلال تصنيف ال divergence
+
+53
+00:05:05,440 --> 00:05:08,980
+و ال curve تبعه يعني بحسب ال divergence و ال curve
+
+54
+00:05:08,980 --> 00:05:14,070
+تبعه و قداش كام و ببدأ اصنف ال fieldهل هما
+
+55
+00:05:14,070 --> 00:05:17,590
+vanishing و لا vanishing؟ هل هو يساوي سفر و لا
+
+56
+00:05:17,590 --> 00:05:20,970
+يساوي سفر؟ وبناء عليهم بقرر إيش طبيعة ال field
+
+57
+00:05:20,970 --> 00:05:24,010
+بحناخدهم شوية شوية إيش معنى لما يكونوا تانين zero
+
+58
+00:05:24,010 --> 00:05:28,110
+لما واحد منهم zero والتاني لأ واحد zero والتاني لأ
+
+59
+00:05:28,110 --> 00:05:32,630
+التانين لا يساوي zero يعني هنعرف ال fields بناء
+
+60
+00:05:32,630 --> 00:05:37,230
+على طبيعة ال divergence و ال care تبعهم حتى أعطيهم
+
+61
+00:05:37,230 --> 00:05:41,960
+مسميات و تعريفاتبس ده ايه؟ بشكل عام .. بشكل عام لأ
+
+62
+00:05:41,960 --> 00:05:45,020
+يوصلنا في ال field على واحدة منهم لحالة، يوصلنا
+
+63
+00:05:45,020 --> 00:05:48,360
+نقعد تلتين مع بعض، يعني لازم اجيب ال divergence و
+
+64
+00:05:48,360 --> 00:05:53,320
+ال curl عشان اقول ايش طبيعي في ال fieldمثلًا إن هى
+
+65
+00:05:53,320 --> 00:05:58,080
+نوع من أنواع ال field A بساوى K X hat يعني بهذا
+
+66
+00:05:58,080 --> 00:06:02,960
+الشكل هى ال field اتجاهه قيمته constant K اتجاه X
+
+67
+00:06:02,960 --> 00:06:06,380
+hat لو حسبنا ال divergence تبعه هنلاقيه بساوة صفر
+
+68
+00:06:06,380 --> 00:06:10,560
+لو حسبنا ال curve تبعه برضه بساوة صفر هده نوع من
+
+69
+00:06:10,560 --> 00:06:13,120
+أنواع ال field إله التنين بساوة zero هده مجرد
+
+70
+00:06:13,120 --> 00:06:16,520
+أمثلة لهاي الحلقة و لحلقة A لما يكون ال field ال
+
+71
+00:06:16,520 --> 00:06:19,970
+divergence وال curve بساوة zeroلايلو divergence
+
+72
+00:06:19,970 --> 00:06:23,670
+ولايلو curve يعني لايلو source ولايلو circulation
+
+73
+00:06:23,670 --> 00:06:31,580
+حوالين اللي هو axisهنا ال field مثلا لو كان a
+
+74
+00:06:31,580 --> 00:06:37,980
+بيساوي k r vector يعني x x hat زي y y hat زي z z
+
+75
+00:06:37,980 --> 00:06:42,380
+hat k برضه constant لو جبنا ال divergence تبعه
+
+76
+00:06:42,380 --> 00:06:46,220
+هلاقيها بتساوي تلاتة كيلات تساوي zero إذا ما هي
+
+77
+00:06:46,220 --> 00:06:50,840
+شايفين إذن هي إلها source موجب إذن طالع من ال
+
+78
+00:06:50,840 --> 00:06:55,200
+source واضح؟ لكن ال curve تبعه لو حسبنا ال curve
+
+79
+00:06:55,200 --> 00:07:00,400
+هلاقيه بيساوي zero إذا هذا ال fieldبيمثل لي قيمته
+
+80
+00:07:00,400 --> 00:07:04,980
+k r vector و ال divergence تبعه له سوى zero زى ما
+
+81
+00:07:04,980 --> 00:07:08,220
+أشرحتلكم حتى لو نطلع على الصورة أطول بقول أنه له
+
+82
+00:07:08,220 --> 00:07:11,120
+divergence لكن ال curve تبعه zero مش اللي هو curve
+
+83
+00:07:11,120 --> 00:07:16,700
+فال curve تبعه zero لو جينا على هذا المثال اللي هو
+
+84
+00:07:16,700 --> 00:07:23,220
+عندى a بساوة k cross r اتنين ال vectorsالـ A هو
+
+85
+00:07:23,220 --> 00:07:27,040
+عبارة عن plus product ل K مع R لو حسبت ال
+
+86
+00:07:27,040 --> 00:07:29,100
+divergence على A هو Zero فالشيء عند ال divergence
+
+87
+00:07:29,100 --> 00:07:32,780
+لا بيطلع من ال source ولا بيدخل على ولا sinking
+
+88
+00:07:32,780 --> 00:07:36,100
+ولا emerging لكن الكيرل تبعه بلا إيه اللي بيساوي
+
+89
+00:07:36,100 --> 00:07:39,240
+ال ticket فهو إله curling إله قيمة curl موجة يعني
+
+90
+00:07:39,240 --> 00:07:42,580
+بيكون clockwise سالف بيكون counter clockwise
+
+91
+00:07:42,580 --> 00:07:47,170
+فالقيمة curl ال A موجة بقىفهذا ال field اللي هو
+
+92
+00:07:47,170 --> 00:07:50,470
+curling لكي بلغه share diversions دعونا نشوف field
+
+93
+00:07:50,470 --> 00:07:56,730
+زي هذا A بيساوي k cross R زي CR هذا ال field لو
+
+94
+00:07:56,730 --> 00:07:59,930
+جبت ال diversions تبعه بيطلع له يساوي 0 وال curl
+
+95
+00:07:59,930 --> 00:08:04,510
+يساوي 0هو طالع من source من المقطة و في نفس الوقت
+
+96
+00:08:04,510 --> 00:08:08,510
+ماله بعمل curling يعني هو emerging طالع لبره ال
+
+97
+00:08:08,510 --> 00:08:12,190
+divergence تبعه موجة و في نفس الوقت اش ماله بعمل
+
+98
+00:08:12,190 --> 00:08:16,510
+curling فهذا ال field ماله له both ال divergence و
+
+99
+00:08:16,510 --> 00:08:19,710
+ال curl يسوا zero هذه أسئلة بتيجي في الامتحانة
+
+100
+00:08:19,710 --> 00:08:22,770
+يجيكي field يقولك حسب ال divergence و يحسبيه ال
+
+101
+00:08:22,770 --> 00:08:26,090
+curl عايزاكم اعرفوا كيف تحسب ال divergence و كيف
+
+102
+00:08:26,090 --> 00:08:27,110
+تحسبيه ال curl
+
+103
+00:08:30,840 --> 00:08:33,920
+أول حاجة التصنيفات احنا قلنا حسب ايش طبيعة ال
+
+104
+00:08:33,920 --> 00:08:37,300
+field احنا بنبدأ نصنفه يعني لما يكون عند ال
+
+105
+00:08:37,300 --> 00:08:40,800
+divergence تبع ال field بساوة zero ماله و احنا
+
+106
+00:08:40,800 --> 00:08:43,020
+قلنا ال divergence تبعه ماله zero ال divergence
+
+107
+00:08:43,020 --> 00:08:46,880
+لسه دهمالوش divergence يعني لأ له source ال source
+
+108
+00:08:46,880 --> 00:08:50,400
+تبعه zero مالروحش على نقطة ولا بيطلع من نقطة هاي
+
+109
+00:08:50,400 --> 00:08:53,500
+معناه divergence بيسوا zero دل أو ال divergence
+
+110
+00:08:53,500 --> 00:08:59,000
+تبع ايه بيسوا zero معناه divergence less مالوش
+
+111
+00:08:59,000 --> 00:09:02,000
+divergence او باختصار بيقولوا عنه solenoidal
+
+112
+00:09:02,870 --> 00:09:07,370
+Solenoidal أو Divergence لسه فبكوا تحفظوها لأن هاي
+
+113
+00:09:07,370 --> 00:09:10,450
+الأسئلة بتيجي في الانتحار بعطيك ال field بقولك إيش
+
+114
+00:09:10,450 --> 00:09:13,430
+طبيعي في هذا ال field بتجيب ال divergence تبعه
+
+115
+00:09:13,430 --> 00:09:19,730
+بساوي zero بتقولي Solenoidal هذا ال field معناه لا
+
+116
+00:09:19,730 --> 00:09:23,130
+sinking ولا إيش مالله لا إله source ولا إله sink
+
+117
+00:09:23,130 --> 00:09:26,610
+لا إله source بتطلع منه ولا إله sink اللي بنزل في
+
+118
+00:09:26,610 --> 00:09:29,920
+قلبهامن ال divergence theorem احنا متذكرين ايش هو
+
+119
+00:09:29,920 --> 00:09:31,920
+ال divergence theorem؟ ال clause انتجرال على ال
+
+120
+00:09:31,920 --> 00:09:35,840
+surface دقاقه ال DS ايش بيساوي ال volume انتجرال ل
+
+121
+00:09:35,840 --> 00:09:40,040
+divergence ADVمتذكرين هال divergence of sphere؟
+
+122
+00:09:40,040 --> 00:09:42,880
+قولنا ال class integral على ال surface بساوي a dot
+
+123
+00:09:42,880 --> 00:09:46,740
+ds بتساوي ال volume integral بس divergence a بساوي
+
+124
+00:09:46,740 --> 00:09:52,020
+zero إذا ماله ال surface integral بساوي zero هذا
+
+125
+00:09:52,020 --> 00:09:55,840
+معناه إن مجموعة ال flux اللي داخل بساوي اللي خارج
+
+126
+00:09:55,840 --> 00:09:58,820
+لما يكون ليه، احنا قولنا هذا ال class surface
+
+127
+00:09:58,820 --> 00:10:02,080
+integral بسميه ال flux متذكرين؟ سمينا ب Psi، ال
+
+128
+00:10:02,080 --> 00:10:05,980
+fluxمعنى ان يكون ال flux بيساوي zero معناه ان
+
+129
+00:10:05,980 --> 00:10:08,480
+الحطوط اللى دخلت بساوي الحطوط اللى خرجت من ال
+
+130
+00:10:08,480 --> 00:10:12,720
+surface كمان مفهوم اوصله منه اذا ان هو solenoidal
+
+131
+00:10:12,720 --> 00:10:17,340
+معناه ان ال divage بيساوي zero كمان ال flux بتاعه
+
+132
+00:10:17,340 --> 00:10:21,680
+بيساوي zero لان ال closed surface integral لهذا ال
+
+133
+00:10:21,680 --> 00:10:25,700
+vector field بيساوي zero معناه عدد الحطوط اللى
+
+134
+00:10:25,700 --> 00:10:29,940
+بتدخل ال surface لازم تساوي عدد اللى تخرج منهامن
+
+135
+00:10:29,940 --> 00:10:32,900
+أمثلة الـ fields اللي هي أسنانويدال، ال
+
+136
+00:10:32,900 --> 00:10:36,360
+incompressible في fluids اللي هي السواق اللي غير
+
+137
+00:10:36,360 --> 00:10:40,060
+مضغوطة، magnetic fields، هي الأمثلة برضه يازم
+
+138
+00:10:40,060 --> 00:10:43,120
+تكونوا حافظينها في امتحان النصفي، conduction
+
+139
+00:10:43,120 --> 00:10:47,560
+current densityunder steady state conditions مش اي
+
+140
+00:10:47,560 --> 00:10:49,900
+conduction current لكن conduction current density
+
+141
+00:10:49,900 --> 00:10:54,520
+under steady state conditions بشكل عام هذا ال
+
+142
+00:10:54,520 --> 00:10:59,200
+field اللي له ال divergence بسوة zero بقدر اعبر
+
+143
+00:10:59,200 --> 00:11:03,600
+عنه هذا ال field ايه ب care field التالي لان احنا
+
+144
+00:11:03,600 --> 00:11:08,300
+اتعلمنا ان diverge ال care بسوة zero واضح؟ احنا
+
+145
+00:11:08,300 --> 00:11:13,200
+قلنا ان diverge ال care بشكل عام قلنا diverge
+
+146
+00:11:15,150 --> 00:11:18,950
+الـKern مثلا ال field up is diverged الـKern
+
+147
+00:11:18,950 --> 00:11:23,690
+بيساوي 0 و احنا بنقول السنونويدل field diverged
+
+148
+00:11:23,690 --> 00:11:27,190
+تبعه 0 مع أنها بشكل عام أي field ال divergence
+
+149
+00:11:27,190 --> 00:11:31,410
+تبعه ساوي 0 بقدر أعبر عنه لإنه بيساوي K و field
+
+150
+00:11:31,410 --> 00:11:36,730
+داني اذا لما يكون عندى
+
+151
+00:11:40,680 --> 00:11:45,960
+بقدر اقول ان دفع دفع دفع دفع دفع دفع دفع دفع
+
+152
+00:11:49,170 --> 00:11:53,170
+إذاً هيك معناه إنه بقدر أعبّل عن ال A field دلالة
+
+153
+00:11:53,170 --> 00:11:58,150
+ال F أو مثلا هذا ال F بيه C بس ال curve تبعه معروف
+
+154
+00:11:58,150 --> 00:12:02,250
+لأنه A بتساوت .. إذا ساوت curve ال field تاني،
+
+155
+00:12:02,250 --> 00:12:05,530
+divergence هذا ال curve بساوة Zero إذا أكمل سنتجة
+
+156
+00:12:05,530 --> 00:12:08,050
+سنتجنا، قولنا إذا هذا ال field كان Solenoidal، إيش
+
+157
+00:12:08,050 --> 00:12:11,230
+معناه؟ أو ال divergence لس، إن ال divergence تبعه
+
+158
+00:12:11,230 --> 00:12:15,340
+بساوة Zeroهذه اسمها ال divergence تبعه صوه zero
+
+159
+00:12:15,340 --> 00:12:18,640
+معناه ال flux برضه صوه zero يعني ال flow of
+
+160
+00:12:18,640 --> 00:12:21,660
+surface integral لهذا ال field صوه zero معناه عدد
+
+161
+00:12:21,660 --> 00:12:24,120
+خطوط الفيض اللي داخل على ال surface بالساعة الخطوط
+
+162
+00:12:24,120 --> 00:12:27,240
+اللي طالعة من ال surface كمان لإن احنا عارفين ال
+
+163
+00:12:27,240 --> 00:12:30,140
+divergence الكيار بصوه zero إذا هذا ال field تبعه
+
+164
+00:12:30,140 --> 00:12:35,190
+مادر أكتر بدلالة كيار في ال field تانيهذه
+
+165
+00:12:35,190 --> 00:12:39,310
+الاستنتاجات اذا كان دايفرج ايه بيساوي 0 اذا ال
+
+166
+00:12:39,310 --> 00:12:43,770
+surface integral لدى ال DS بيساوي 0 وكمان ال field
+
+167
+00:12:43,770 --> 00:12:49,630
+تبع ايه بيساوي k ال field تاني ال vector a ال
+
+168
+00:12:49,630 --> 00:12:54,610
+rotational يعني لا يلوف ال rotational بلوف ال
+
+169
+00:12:54,610 --> 00:12:59,580
+rotational لايلوفاو potential بقول عن ال field ال
+
+170
+00:12:59,580 --> 00:13:03,660
+rotational او potential اذا كان ال curve تبعه بسوء
+
+171
+00:13:03,660 --> 00:13:07,520
+0 هاي كمان تصنيف اذا نقولنا divergence less اذا
+
+172
+00:13:07,520 --> 00:13:10,880
+كان divergence تبعه بسوء 0 ال rotational او
+
+173
+00:13:10,880 --> 00:13:14,360
+potential اذا كان ال curve بسوء 0 طب احنا نذاكرين
+
+174
+00:13:14,360 --> 00:13:17,380
+stock theory مش اهلة لان ال surface integral اللي
+
+175
+00:13:17,380 --> 00:13:20,160
+كان ل a dot ds بتسوء ال closed line او ال
+
+176
+00:13:20,160 --> 00:13:23,480
+circulation ل a dot dl بسوء 0 هذا ال integral
+
+177
+00:13:23,480 --> 00:13:26,860
+يسميها ال circulationالـ A بيساوي 0 إذاً ال
+
+178
+00:13:26,860 --> 00:13:30,100
+circulation بيساوي 0 وانت خدت في رياضيات
+
+179
+00:13:30,100 --> 00:13:32,180
+الcirculation بيساوي 0 إيش بيسمي ال field
+
+180
+00:13:32,180 --> 00:13:37,260
+conservative field معناه إن ال field من أي boss
+
+181
+00:13:37,260 --> 00:13:42,740
+أخده بين نقطتين لازم يعطيه نفس الجواب ممكن أخدته ب
+
+182
+00:13:42,740 --> 00:13:44,500
+6-2 أو أخدته بال
+
+183
+00:13:47,550 --> 00:13:53,130
+لأفض الـDR يساوي 0 إذا كان الـ integral لأفض الـDR
+
+184
+00:13:53,130 --> 00:13:56,630
+ما اعتمدش على ال bus ما بين نقطتين لإن احنا بنعمل
+
+185
+00:13:56,630 --> 00:14:00,610
+integral line integral أفض الـDR بين نقطتين A وB
+
+186
+00:14:00,610 --> 00:14:03,730
+مافرقش أخد هذا ال bus ولا هذا ال bus ولا هذا ال
+
+187
+00:14:03,730 --> 00:14:07,670
+bus أعطان نفس الجواب بنقول إن هاي ال force منها
+
+188
+00:14:07,670 --> 00:14:11,960
+conservative أخدوا قبل هيكهذا مثال مباشر على هذا
+
+189
+00:14:11,960 --> 00:14:15,360
+ال .. احنا بشكل عام هذا field دعم لسه بنحكي عنه اي
+
+190
+00:14:15,360 --> 00:14:18,660
+field اذا ال curl تبعه بصوة zero اذا ال
+
+191
+00:14:18,660 --> 00:14:21,480
+circulation تبعه بصوة zero يعني ال line integral
+
+192
+00:14:21,480 --> 00:14:26,200
+تبعه بصوة zero يعني لو انا بتعمل integral هي plus
+
+193
+00:14:26,200 --> 00:14:32,880
+plus ل a dot dl بصوة zero اش معناه انه انا هيعندي
+
+194
+00:14:32,880 --> 00:14:38,020
+مطبطين مثلا a و b و روحت اخدت هي plus وكملت وقولت
+
+195
+00:14:38,020 --> 00:14:41,860
+مجموع ال integral هيبقى بصوة zeroيعني معناه لو أنا
+
+196
+00:14:41,860 --> 00:14:47,340
+قلت التتابه من A لB زي التتابه من B لA بساوسي تبقى
+
+197
+00:14:47,340 --> 00:14:50,660
+معناه أنه مابعتمدش على البعض بس هو أحد من هنا لهنا
+
+198
+00:14:50,660 --> 00:14:54,920
+و أنا من هنا لهنا ال feel تكون لا يعتمد على البعض
+
+199
+00:14:54,920 --> 00:14:58,260
+أو النتيجة لا تعتمد على البعض وهذا بسميه
+
+200
+00:14:58,260 --> 00:14:59,840
+conservative feel
+
+201
+00:15:06,830 --> 00:15:09,750
+this implies that the line integral is independent
+
+202
+00:15:09,750 --> 00:15:18,530
+of the chosen path لا يعتمد على ال path اللي تم
+
+203
+00:15:18,530 --> 00:15:22,250
+اختياره field is also known as conservative يعني
+
+204
+00:15:22,250 --> 00:15:26,510
+أكمل تعريف صرنا معلفينه ال rotational potential
+
+205
+00:15:26,510 --> 00:15:30,430
+conservative ليش انه conservative؟ لأنه لا يعتمد
+
+206
+00:15:30,430 --> 00:15:34,370
+على ال path لا يعتمد على المصاد لأنه لعين ال
+
+207
+00:15:34,370 --> 00:15:38,540
+circulation تبعه بساوة صفرالأمثلة على هيك ال
+
+208
+00:15:38,540 --> 00:15:40,980
+electrostatic fields و ال gravitational fields
+
+209
+00:15:40,980 --> 00:15:45,140
+هدولة كلهم conservative fields اللي هتبقوا لازم
+
+210
+00:15:45,140 --> 00:15:50,120
+عارفينه عارفين إيش تعريف ال curve سواء zero إيش
+
+211
+00:15:50,120 --> 00:15:53,480
+الأمثلة تعطيهم بالتمام زي هنا قولنا ال divergence
+
+212
+00:15:53,480 --> 00:15:54,400
+و أمثلة عليه
+
+213
+00:15:58,920 --> 00:16:01,360
+دائما احنا لما عرفنا ال kill قولنا kill ال
+
+214
+00:16:01,360 --> 00:16:06,380
+gradient بيساوي 0 و احنا
+
+215
+00:16:06,380 --> 00:16:09,140
+عاملا بنقول kill ال field تبعنا اللي هو ال
+
+216
+00:16:09,140 --> 00:16:17,480
+rotational kill أي field kill ال gradient بالfield
+
+217
+00:16:17,480 --> 00:16:21,140
+بيساوي 0 و معناه بقدر اقول ان ايه بتاعتي بتساوي
+
+218
+00:16:21,140 --> 00:16:25,430
+gradient scalar fieldأيه ال vector بتاعي؟ بيسوي
+
+219
+00:16:25,430 --> 00:16:29,210
+gradient scalar field يعني بقدر احصر اللي حكيناها
+
+220
+00:16:29,210 --> 00:16:33,110
+كله لو كان عندي irrotational field إيش معناها؟ إنه
+
+221
+00:16:33,110 --> 00:16:37,730
+هذا ال field الكيلوب تبعته سواء zero مع أنها برضه
+
+222
+00:16:37,730 --> 00:16:41,130
+ال circulation تبعته بالسواء zero و بقدر أقول إنه
+
+223
+00:16:41,130 --> 00:16:46,020
+ايه بالسواء minus grad Vعشان هيك احنا بنسميه
+
+224
+00:16:46,020 --> 00:16:50,060
+potential field لان بقدر اعبر عن ايه بدلالة scalar
+
+225
+00:16:50,060 --> 00:16:55,020
+potential يعني امثل اقولنا مين ال electrostatic
+
+226
+00:16:55,020 --> 00:16:59,560
+field E ايه بنقدر نكتب دلالة minus grade Phi Phi
+
+227
+00:16:59,560 --> 00:17:03,040
+potential field اقولنا امثلة هذا ال field اللي هو
+
+228
+00:17:03,040 --> 00:17:05,720
+ال field تبعه سوى Zero اللي هو ال electrostatic
+
+229
+00:17:05,720 --> 00:17:10,980
+field E ايه بقدر اعبر عنه minus grade Phi فPhi هذا
+
+230
+00:17:10,980 --> 00:17:12,860
+هو عبارة عن potential scalar
+
+231
+00:17:17,210 --> 00:17:20,570
+عشان هيك بالثاني هدولة ال fields و ال killer تبعهم
+
+232
+00:17:20,570 --> 00:17:24,610
+بيساوي zero potential لإن بقدر أعبر عنهم دلارة
+
+233
+00:17:24,610 --> 00:17:25,970
+scalar potential
+
+234
+00:17:29,340 --> 00:17:32,200
+طبعا ال minus sign ممكن تقول ما هو الجواب صحيح لو
+
+235
+00:17:32,200 --> 00:17:35,840
+أخدت ال minus ولا ما أخدتش ال minus يعني E لو قلت
+
+236
+00:17:35,840 --> 00:17:39,680
+بتساوي grade 5 او E بتساوي minus grade 5 الجواب
+
+237
+00:17:39,680 --> 00:17:44,260
+صحيح لكن ال minus sign هتقلها أسباب فيزيائية يعني
+
+238
+00:17:44,260 --> 00:17:48,620
+عشان ما تكونش تخالف طبيعة ال .. الطبيعة بتاعة ال
+
+239
+00:17:48,620 --> 00:17:52,240
+problem بتاعة ال ecrostatic problem ال minus بتفرق
+
+240
+00:17:52,240 --> 00:17:57,380
+في طبيعة ال .. ال .. ال fieldبس هاي الهدف فيزيائي
+
+241
+00:17:57,380 --> 00:18:03,520
+يعني مش .. مش هيهدف رياضي a vector A is uniquely
+
+242
+00:18:03,520 --> 00:18:07,000
+described within a region by its divergence S
+
+243
+00:18:07,000 --> 00:18:10,660
+-chair هذا الحكي حكينا قولنا أي field بقدر عبر عنه
+
+244
+00:18:10,660 --> 00:18:16,120
+بشكل أكيد يعني unique بتلالة divergence و الchair
+
+245
+00:18:16,120 --> 00:18:18,740
+تبعه لو كان divergence A بيساوره V اللي هو ال
+
+246
+00:18:18,740 --> 00:18:25,250
+sourceوالـ curl A بيساوي رو S يعني إله curl رو V
+
+247
+00:18:25,250 --> 00:18:28,270
+can be regarded as a source دي بنسميها ال source
+
+248
+00:18:28,270 --> 00:18:32,230
+رو S برضه بنسميها ال circulation density هي بنعبر
+
+249
+00:18:32,230 --> 00:18:35,350
+عنها ال source density لإن هذا ال source في ال
+
+250
+00:18:35,350 --> 00:18:38,850
+divergence عند نقطة بتطلع منها أو تدخل عليها
+
+251
+00:18:38,850 --> 00:18:41,870
+فبنسميها ال source density لكن هنا ال circulation
+
+252
+00:18:41,870 --> 00:18:45,890
+فإيش بسميها ال circulation density إذا رو V في هذه
+
+253
+00:18:45,890 --> 00:18:48,890
+الحالة ال V هنا عشان سميناها ال source density
+
+254
+00:18:54,320 --> 00:18:59,840
+لأي vector اللي رو S رو V بروحه للصفر بقدر أعبر عن
+
+255
+00:18:59,840 --> 00:19:02,980
+ال field بقدر أقول طبعا لو اتنين و اتنين صفر معناه
+
+256
+00:19:02,980 --> 00:19:05,020
+انه ماله ال divergence ايه قلنا ماله بيساوي الصفر
+
+257
+00:19:05,020 --> 00:19:10,900
+ال rotational اسمه ال divergence أسرنويدل و ال
+
+258
+00:19:10,900 --> 00:19:14,200
+field بيساوي ال zero ال rotational فأي field اتنين
+
+259
+00:19:14,200 --> 00:19:16,780
+له zero بيكون ماله ال solenoidal و ال rotational
+
+260
+00:19:17,960 --> 00:19:21,320
+لما يكونوا اتنين زيرو لأي field هيكون A بقدر أوع
+
+261
+00:19:21,320 --> 00:19:26,060
+انه ماله solenoidal زاد ال rotational هذا ال field
+
+262
+00:19:26,060 --> 00:19:30,740
+له ال divergence بيساوي زيرو و ال curl بيساوي زيرو
+
+263
+00:19:30,740 --> 00:19:35,320
+بنسميه Helmholtz field و بيطبق ال helmholtz
+
+264
+00:19:35,320 --> 00:19:41,080
+theorem ان A بيساوي minus ال scalar field زاد curl
+
+265
+00:19:41,080 --> 00:19:47,090
+Bهذا نسميها الـ Helmholtz theorem واضح؟ هذا ال
+
+266
+00:19:47,090 --> 00:19:50,630
+field ماله؟ هذا ال field له ال divergence بتساوي
+
+267
+00:19:50,630 --> 00:19:56,350
+zero و ال curve بساوي zero واضح؟ في أي سؤال لحد
+
+268
+00:19:56,350 --> 00:20:00,910
+هنا؟ بنسمي هذا ال field أو يعني المعادلة اللى
+
+269
+00:20:00,910 --> 00:20:04,070
+بتعبر عن ال field اللى له دوس ال divergence و ال
+
+270
+00:20:04,070 --> 00:20:06,350
+curve بتساوي zero Helmholtz theorem
+
+271
+00:20:11,780 --> 00:20:15,780
+مثلًا، لو قلنا احنا خلّينا AOI بالساوية minus للـV
+
+272
+00:20:15,780 --> 00:20:19,560
+زي الـElectric field وAS بالساوية curl الـV زي
+
+273
+00:20:19,560 --> 00:20:22,420
+الـMagnetic field، هيكون عندنا curl الـAOI
+
+274
+00:20:22,420 --> 00:20:26,480
+بالساوية zero و divergence الـAS بالساوية zero، أي
+
+275
+00:20:26,480 --> 00:20:29,500
+vector اللي له divergence A بالساوية رؤس
+
+276
+00:20:34,800 --> 00:20:39,780
+DEL A Diverge
+
+277
+00:20:39,780 --> 00:20:45,780
+A Diverge A Diverge A Diverge
+
+278
+00:20:45,780 --> 00:20:50,080
+Aبشكل عام، اذا اي vector اللي ال divergence تبعه
+
+279
+00:20:50,080 --> 00:20:53,440
+لا تسوى zero ولا ال curl تبعه تسوى zero، بقدر اقول
+
+280
+00:20:53,440 --> 00:20:57,540
+ان دلتر بيه ال a ببعبر عنها بدلالة ال theorem اللي
+
+281
+00:20:57,540 --> 00:21:00,380
+شفناها بالـA اللي هي gradient divergence A minus
+
+282
+00:21:00,380 --> 00:21:04,280
+curl curl A، بقدر اعبر عن divergence A برا V و
+
+283
+00:21:04,280 --> 00:21:08,260
+curl A برا S، هاي طريقة تانية لكتابة اللي هو ال
+
+284
+00:21:08,260 --> 00:21:15,180
+field اللي مالهسولانويدال وليس الـ rotational يعني
+
+285
+00:21:15,180 --> 00:21:18,520
+rotational و divergence مادام الـ divergence تبعه
+
+286
+00:21:18,520 --> 00:21:21,060
+لها يسوى zero إذا ان هو divergence ومادام ال
+
+287
+00:21:21,060 --> 00:21:23,540
+character تبعه لها يسوى zero إذا ان هو rotational
+
+288
+00:21:23,540 --> 00:21:30,160
+واضح فهذا ال field divergence و rotational هذه
+
+289
+00:21:30,160 --> 00:21:33,160
+أسئلة عامة على كل الأشياء اللي حدناها في هذا الشطر
+
+290
+00:21:33,160 --> 00:21:38,860
+نشوف السؤال هذا اللي قولناهذا الـ differential
+
+291
+00:21:38,860 --> 00:21:44,540
+volume هذا جزء من الـ space اذا اعتبرت الصفحة هذا
+
+292
+00:21:44,540 --> 00:21:49,780
+كارتيش الكواردينية الـ XYZ و اخدت مكعب في الفضاء
+
+293
+00:21:49,780 --> 00:21:53,540
+هذا الـ differential volume نعمل matching بين ال
+
+294
+00:21:53,540 --> 00:22:00,100
+items من column A و column B يعني مثلا DL from A
+
+295
+00:22:00,100 --> 00:22:04,690
+to Bهي a to b طبعا هاي ال coordinate صنع x hat y
+
+296
+00:22:04,690 --> 00:22:09,570
+hat z hat يعني هذا الاتجاه هو ال x هذا ال y و اللي
+
+297
+00:22:09,570 --> 00:22:13,930
+طالع هو ال z فبده dl على هذا ال line ايش dl؟ مين
+
+298
+00:22:13,930 --> 00:22:17,070
+اللي بتغير في هذا ال line ال y ال y برافو عليك يا
+
+299
+00:22:17,070 --> 00:22:21,030
+لما مالها بس لما اللي معايا يعني ما شاء الله عليها
+
+300
+00:22:21,030 --> 00:22:24,550
+لما يعني هنا ياهوا كلكوا تكونوا معايا اذا هذا الحط
+
+301
+00:22:24,550 --> 00:22:29,950
+او هذا المصار اللي بتغير في مين ال yفبيكون عندى dy
+
+302
+00:22:29,950 --> 00:22:34,210
+y hat اذا مين هو يا لما الجواب انك انت الجواب ده
+
+303
+00:22:34,210 --> 00:22:43,950
+اللي هي ستة صح ستة اللي بعده dl من a ل d من a ل d
+
+304
+00:22:43,950 --> 00:22:48,930
+ايش اللي بتغير هنا z bravo عليكم d z اذا على a d
+
+305
+00:22:48,930 --> 00:22:55,930
+هو d z z hat اذا هو مين سبع ممتازين dl from a to e
+
+306
+00:22:56,830 --> 00:23:02,470
+from A to E مين اللي بتغير هنا ال X ال X ليش ال Y؟
+
+307
+00:23:02,470 --> 00:23:05,510
+ال Y ثابتة على Zero يعني إذا فرقتنا إن هو ده على
+
+308
+00:23:05,510 --> 00:23:09,390
+Zero قعدت بتمام أو على قيمة Y ثابتة هنا اللي بتغير
+
+309
+00:23:09,390 --> 00:23:14,510
+هو ال X A to E اللي بتغير هو DX X hat اللي هو رقم
+
+310
+00:23:14,510 --> 00:23:21,650
+5 طب DS على الفاس A B C D مين السابت هنا و مين
+
+311
+00:23:21,650 --> 00:23:27,110
+اللي بتغير؟ مين السابت؟الـ X اللي ثابتة و اللي
+
+312
+00:23:27,110 --> 00:23:31,050
+بتغير ال Y أصلا هو ال Y و ال Z I D X لأنها
+
+313
+00:23:31,050 --> 00:23:34,950
+differential volume DY DX DZ هذا ال surface mean
+
+314
+00:23:34,950 --> 00:23:39,110
+اللي ثابت فيه اللي هو ال X و اللي بتغير فيه ال Y و
+
+315
+00:23:39,110 --> 00:23:43,090
+ال Z طب ال .. ال .. هذا vector ال DS إيش اتجاهه دي
+
+316
+00:23:43,090 --> 00:23:47,870
+و إيش اتجاهه؟ إذا حيكون اتجاهه في اتجاه ال X hat
+
+317
+00:23:47,870 --> 00:23:52,710
+برا ال volumeبدي دايما احط ال unit vector بحيث انه
+
+318
+00:23:52,710 --> 00:23:56,130
+يكون برا ال volume فهو ال volume تبعي ف ال surface
+
+319
+00:23:56,130 --> 00:23:59,910
+hat هيكون عمودي عليه و بره عشان هيك هيكون x hat
+
+320
+00:23:59,910 --> 00:24:06,090
+اذا اي واحد فيهم ال اولاني رقم واحد dy dz x hat
+
+321
+00:24:06,090 --> 00:24:16,290
+طيب اللي بعده ال surface element ds للفاس a e hD
+
+322
+00:24:16,290 --> 00:24:23,150
+لو هذا A, E, H, D مين اللي بتغير فيه؟ دي Z و دي X
+
+323
+00:24:23,150 --> 00:24:28,740
+صح؟Y ثابتة عند مثلا السفر و لا عند .. يعني هاد
+
+324
+00:24:28,740 --> 00:24:31,840
+خلنا نقول Y ثابتة عند السفر هاد يقول مثلا عند خمسة
+
+325
+00:24:31,840 --> 00:24:36,900
+مثلا اذا هاد مين بتغير فيه اللي هو DZ و DX طب ايش
+
+326
+00:24:36,900 --> 00:24:42,580
+قيمة ال unit vector سالب Y hat لأن هيك من الاتجاه
+
+327
+00:24:42,580 --> 00:24:45,040
+لبرا ال volume احنا دفعنا الدنيا اللي بيكون برا
+
+328
+00:24:45,040 --> 00:24:49,360
+اذا هو عبارة عن مين قلنا DY DZ و سالب اللي هو اذا
+
+329
+00:24:49,360 --> 00:24:53,720
+هيكون اتنين قلنا ايش هو DX
+
+330
+00:25:06,700 --> 00:25:12,040
+ممتاز هذا التغير XY و X اتجاهه سالب Z ممتازين يعني
+
+331
+00:25:12,040 --> 00:25:15,680
+واضحة لكل فكرة يعني بناخد اللي هو المتغيرين هم
+
+332
+00:25:15,680 --> 00:25:19,380
+بيعطوني قيمة ال surface المجلة اللي تبعها والاتجاه
+
+333
+00:25:19,380 --> 00:25:23,120
+ده من برا ال volume عشان هيقول اللي هو ال minusطب
+
+334
+00:25:23,120 --> 00:25:29,940
+أخر واحد اللي هو ال case A B F E مين المتغيرات؟ D
+
+335
+00:25:29,940 --> 00:25:38,480
+Y D X والاتجاه إيش هيكون؟ Z نعم مجب Z اللي هو إيش
+
+336
+00:25:38,480 --> 00:25:46,420
+هيكون أي واحد فيهم؟ اللي هو تلاتة، bravoكمان في
+
+337
+00:25:46,420 --> 00:25:49,640
+أين؟ في الـ cylindrical coordinate هنعمل مثال و
+
+338
+00:25:49,640 --> 00:25:52,980
+أشرك مثال على ال line و مثال على ال surface ناخد
+
+339
+00:25:52,980 --> 00:26:01,500
+مثلا هو DL من D to L D to L مين اللي بتغير هنا؟
+
+340
+00:26:01,500 --> 00:26:05,920
+مين بتغير هنا؟ هو أصلا مرسوم الرسلة هذا إيش بتغير
+
+341
+00:26:05,920 --> 00:26:10,600
+أين؟ دي رو صح؟ و هذا اللي هو ال curve D Phi رو D
+
+342
+00:26:10,600 --> 00:26:16,240
+Phi و هذا مين؟ ال DZ هاي ال coordinates روفاي زد
+
+343
+00:26:16,240 --> 00:26:23,980
+اذا هنا مين بتغير الى دي زد دي زد دي زد خلنا نشوف
+
+344
+00:26:23,980 --> 00:26:29,020
+ان هو فيه هون هيكون دي زد زد هاتأمام؟ ناخد ال
+
+345
+00:26:29,020 --> 00:26:37,240
+surface مثلا a,b,f,e a,b,f,e هذا ال surface هذا ال
+
+346
+00:26:37,240 --> 00:26:42,260
+links ايش بيساوي؟ رو دي فاي و هذا دي ال؟ دي رو،
+
+347
+00:26:42,260 --> 00:26:47,360
+اذا دي رو، رو، دي رو، دي فاي و ايش العمودي علينيه؟
+
+348
+00:26:47,360 --> 00:26:52,380
+ز هات، اذا احنا بيكون رو، دي رو، دي فاي، ز هات،
+
+349
+00:26:52,380 --> 00:26:58,500
+مفتاحطب نشوف هذا ال surface معطينا شكل source او
+
+350
+00:26:58,500 --> 00:27:03,200
+شكل field هدفيه و بقولنا ايش طبيعته هو current
+
+351
+00:27:03,200 --> 00:27:07,140
+density J هذا ال current density J بمثلنى current
+
+352
+00:27:07,140 --> 00:27:11,920
+density J و بقولنا قوليلي ايش طبيعته هل طبيعته
+
+353
+00:27:11,920 --> 00:27:16,620
+صحيحة ان هو على ال surface على ال top surface
+
+354
+00:27:16,620 --> 00:27:21,420
+divergence بينما على الجوانب divergence lessهل هذا
+
+355
+00:27:21,420 --> 00:27:26,860
+صحي ولا لأ؟ هل هنا divergence؟ فهذا ال topsurface
+
+356
+00:27:26,860 --> 00:27:30,660
+و هنا divergence less صحيح احنا مش تعرفنا
+
+357
+00:27:30,660 --> 00:27:33,960
+divergence less زي ال kx hat مالهوش divergence
+
+358
+00:27:33,960 --> 00:27:38,020
+divergence سبقه هيكون zero مش طالع ولا داخل مالهوش
+
+359
+00:27:38,020 --> 00:27:41,640
+source لكن على ال top في source هيه طالع طالع و
+
+360
+00:27:41,640 --> 00:27:44,560
+داخل كمان يعني طالع من هذه النقطة و داخل هذه
+
+361
+00:27:44,560 --> 00:27:47,740
+النقطة اذا هو بالفعل على ال top surface هو
+
+362
+00:27:47,740 --> 00:27:51,300
+divergence بطلع من نقطة من source و بروح على
+
+363
+00:27:51,300 --> 00:27:56,080
+source تاني لكن عندي جواند مال وخطوط مستقيمةخطوط
+
+364
+00:27:56,080 --> 00:27:59,680
+مستقيمة معناها لا sinking ولا sourcing ولا حتى
+
+365
+00:27:59,680 --> 00:28:02,400
+curling فإذا اللي بيحكي إن هو فقط على ال top
+
+366
+00:28:02,400 --> 00:28:06,160
+surface divergence بينما على جوانب divergence لسه
+
+367
+00:28:06,160 --> 00:28:12,720
+صحيح إذا إن هو أتروج أهو قبل إتر هم يعطينا field A
+
+368
+00:28:13,860 --> 00:28:18,360
+وقت كان بيست AS هنا انا حاطبتكم براجع على كل
+
+369
+00:28:18,360 --> 00:28:21,580
+الأشياء انه معناه harmonic انه ال delta V على
+
+370
+00:28:21,580 --> 00:28:25,380
+scalar field بساوة zero ال divergence بتاعه بساوة
+
+371
+00:28:25,380 --> 00:28:29,120
+zero معناه divergence less سلوندويدل هي نفسها
+
+372
+00:28:29,120 --> 00:28:33,310
+divergence lessrotational معناه ان ال care تبعه
+
+373
+00:28:33,310 --> 00:28:36,830
+لايه سوا زيرو conservative ال care تبعه بسوا سفره
+
+374
+00:28:36,830 --> 00:28:40,470
+بدي اخد هذا ال field و اطبق عليه كل هذه الأشياء
+
+375
+00:28:40,470 --> 00:28:44,570
+اجيب الدلتر بيه اللي هو vector field بقى انا بس
+
+376
+00:28:44,570 --> 00:28:49,070
+يعني كمثال حتى هو برضه بقدر احط الدلتر بيه ايه اذا
+
+377
+00:28:49,070 --> 00:28:52,390
+كان الدلتر بيه ايه بسوا زيرو كل harmony ال
+
+378
+00:28:52,390 --> 00:28:55,170
+divergence تبعه بسوا زيرو معناه divergence less
+
+379
+00:28:57,160 --> 00:28:59,880
+الـKey اللي بتبعه لو يسوي Zero معناه Rotational
+
+380
+00:28:59,880 --> 00:29:03,240
+الـKey اللي بيسوي Zero معناه Conservative إذا نبدأ
+
+381
+00:29:03,240 --> 00:29:06,180
+أخد هذا ال Metrophed و أطبق كل هذه الأشياء عليه
+
+382
+00:29:06,180 --> 00:29:14,820
+نبدأ، حد بيحب يطلع؟ حد بيحب يطلع؟ حاجة حاجة، حد
+
+383
+00:29:14,820 --> 00:29:23,660
+بيحب يطلع؟ كده مرة لنا؟ يلّا أطلعهي اسمها الهجرة
+
+384
+00:29:23,660 --> 00:29:26,060
+نيجي لل harmonic احنا اشي قولنا ال harmonic اللي
+
+385
+00:29:26,060 --> 00:29:29,880
+هو بده اقيس الدل تربيع تبعه لل vector field اللي
+
+386
+00:29:29,880 --> 00:29:32,340
+هو تقريبا السؤال اللي عملته طولها معاكش رايب تمسح
+
+387
+00:29:32,340 --> 00:29:36,180
+اللعجنة هو في وسع معاك بس تمسحين اللعجنة
+
+388
+00:29:43,910 --> 00:29:46,710
+الدل تربيع طب عميلنا برضه ال field ناله في ال
+
+389
+00:29:46,710 --> 00:29:49,390
+Cartesian Coordinate اذا معناها بعضنا نستخدم دي
+
+390
+00:29:49,390 --> 00:29:58,270
+تربيع by دي X تربيع Xها زي F by دي X تربيع او اول
+
+391
+00:29:58,270 --> 00:30:03,990
+اول اول نعمل دل تربيع AX Xها زي الدل تربيع AYY ها
+
+392
+00:30:03,990 --> 00:30:10,170
+عشان نشوف اسكالة اه بس هو هذا هي الدل اسكالة الدل
+
+393
+00:30:10,170 --> 00:30:15,630
+اسكالةبس اعمل من تربيرانها اشي بيساوي دل ضد دل لكن
+
+394
+00:30:15,630 --> 00:30:20,510
+هدم قام جي عمين على vector field عشان خطبناها انها
+
+395
+00:30:20,510 --> 00:30:27,910
+عبارة عن دل تربية ax x hat ذأت دل تربية ay y hat
+
+396
+00:30:27,910 --> 00:30:33,710
+ذأت دل تربية az z يعني اش هعمل second derivative ل
+
+397
+00:30:33,710 --> 00:30:39,150
+ال x component ذأت second y derivative ل ال x
+
+398
+00:30:39,150 --> 00:30:44,480
+componentزائد second derivative of z component هو
+
+399
+00:30:44,480 --> 00:30:49,460
+x hat لو
+
+400
+00:30:49,460 --> 00:30:52,780
+كان scalar field هتكون مفيش يعني هيكون بس بالتربيه
+
+401
+00:30:52,780 --> 00:30:54,100
+على scalar field
+
+402
+00:31:14,760 --> 00:31:20,560
+أو لحد ال second derivative ل X ل مين؟ ل X كله طيب
+
+403
+00:31:20,560 --> 00:31:26,320
+و ال Y derivative ل مين؟ Y كله هو بتطلع هاي جزء من
+
+404
+00:31:26,320 --> 00:31:29,600
+الحلقة بس احنا قاعدت بيهم على انهم Δ V زي ما انا
+
+405
+00:31:29,600 --> 00:31:36,400
+كتبتها دي التربيه A XX hat capital A هو ال field A
+
+406
+00:31:36,400 --> 00:31:37,520
+XX hat
+
+407
+00:31:40,700 --> 00:31:49,600
+اي واي هات زائد دلتر بيه از زت هات يعني انا بدي
+
+408
+00:31:49,600 --> 00:31:55,340
+اجيب الدلتر بيه ده ال vector فيه ال x component و
+
+409
+00:31:55,340 --> 00:32:00,240
+ال y component و ال z component ده دي معناه هال
+
+410
+00:32:00,240 --> 00:32:05,620
+second derivative لax بالنسبة لxزائد اعوض عن ال
+
+411
+00:32:05,620 --> 00:32:09,480
+del بس لحظة x تربيع زائد ال second derivative d
+
+412
+00:32:09,480 --> 00:32:18,580
+تربيع by dy تربيع زائد del تربيع by z تربيع لمين
+
+413
+00:32:18,580 --> 00:32:28,220
+separate للax ax x زائد second derivative عرفت ايش
+
+414
+00:32:28,220 --> 00:32:32,380
+المحقق تبعي dx تربيع مبسوط هو اودي تنقليه بس لمين
+
+415
+00:32:32,380 --> 00:32:40,700
+هلقيتهابال Y كم هو ناقص اي
+
+416
+00:32:40,700 --> 00:32:42,380
+حاجة
+
+417
+00:32:58,100 --> 00:33:00,560
+بتذكر سكريات الاخرين، بحي حاجة بس احنا كمان
+
+418
+00:33:00,560 --> 00:33:03,640
+بتذكرين كمان يعني عشان نحط يعني طريقة تانية وممكن
+
+419
+00:33:03,640 --> 00:33:07,960
+توفر علينا شغل كتير مش احنا بقلنا دل تنبيه ا
+
+420
+00:33:07,960 --> 00:33:17,500
+متساوي اجرم دايدر ا minus curl curl ال a برضه انا
+
+421
+00:33:17,500 --> 00:33:21,140
+ممكن استغل هذه، يا بعمل هاي، يا بعمل هاي، ليش؟ انا
+
+422
+00:33:21,140 --> 00:33:26,000
+في النهاية بدي أحسب الدايدر، مش لازمني، بدي أحسب
+
+423
+00:33:26,000 --> 00:33:27,500
+ال curl، لازمني
+
+424
+00:33:45,400 --> 00:33:50,420
+مش plus minus عشان ماكنش كتبلكم حاجة
+
+425
+00:33:55,440 --> 00:34:00,240
+طبعا يعني انا بعمل الدمانية و بعمل الدانية حسب ايش
+
+426
+00:34:00,240 --> 00:34:03,700
+انا بفضل لو بدنا نعمل ال divergence كيف بجيب ال
+
+427
+00:34:03,700 --> 00:34:09,240
+divergence ال divergence ايه اللي عملتيه في الأول
+
+428
+00:34:09,240 --> 00:34:16,580
+هاين dot product اللي هي dAx by dx هاي dot product
+
+429
+00:34:16,580 --> 00:34:23,500
+زي dAy by dy زي dAz
+
+430
+00:34:26,740 --> 00:34:30,200
+تلاحظين ان ال divergence ملبوطة على سكالة لإن بقاش
+
+431
+00:34:30,200 --> 00:34:32,660
+بتعمل في عمرها application للدل هادر بتطلع
+
+432
+00:34:32,660 --> 00:34:39,230
+للvector لإن لأ لما بقاش بتحط الدل عشان تدفعمش
+
+433
+00:34:39,230 --> 00:34:41,650
+عامل الدل على الـ divergence اللي هو القرن اللي
+
+434
+00:34:41,650 --> 00:34:48,070
+بتظهرلكم، إيش هيعطينا الدل؟ d by dx إكسها، زائد d
+
+435
+00:34:48,070 --> 00:34:54,750
+by dy، yها، زائد d by dz، zها، تعني ال application
+
+436
+00:34:54,750 --> 00:35:01,310
+على اللي هو القرن اللي بتظهرلكم، dx by dy, x زائد
+
+437
+00:35:01,310 --> 00:35:05,350
+dy by dy
+
+438
+00:35:09,400 --> 00:35:14,140
+هيطلع معنا ناتج vector مش scalar واضح انه هاد اصلا
+
+439
+00:35:14,140 --> 00:35:19,800
+vector دل تربيع اه vector دل ال diverse صحيح هي
+
+440
+00:35:19,800 --> 00:35:23,100
+scalar لكن applied على vector P فهو ناتج vector
+
+441
+00:35:23,100 --> 00:35:26,640
+واضح؟
+
+442
+00:35:26,640 --> 00:35:35,900
+في مجال تروح غير طالبة ولا تكمل هنا تكمل
+
+443
+00:35:35,900 --> 00:35:36,760
+هنا تعالى
+
+444
+00:35:43,660 --> 00:35:47,920
+أول حاجة بتفاضل هذه الكمبونات بالنسبة ل X هتعطينا
+
+445
+00:35:47,920 --> 00:35:54,480
+6
+
+446
+00:35:54,480 --> 00:36:04,880
+X 6 X زائد التفاضل هاي بالنسبة ل Y هو Zero التفاضل
+
+447
+00:36:04,880 --> 00:36:10,710
+هاي بالنسبة ل Z هيكون هذاخلاص، إذا النتج ماله لا
+
+448
+00:36:10,710 --> 00:36:13,890
+يساوي zero ديري فالي، صح؟ ال divergence لا يساوي
+
+449
+00:36:13,890 --> 00:36:18,050
+zero، خط هذا لا يساوي zero طبعا بيكفيني جزء إنه لا
+
+450
+00:36:18,050 --> 00:36:21,150
+يساوي zero، بس ده حلينا اختياطها، لحظة يكون
+
+451
+00:36:21,150 --> 00:36:24,870
+بالنهاية لما أقعد أدله، أجيب دليل كير بكير، نجيب
+
+452
+00:36:24,870 --> 00:36:28,130
+كير للآخر، كير للآخر، طبعا هي أسهل أنتم شايفين
+
+453
+00:36:28,130 --> 00:36:31,980
+حاجة جميلة بالسرعةفانا هجيبكوا ال divergence
+
+454
+00:36:31,980 --> 00:36:35,960
+فهجيبوا ال kill و ايه؟ اذا ال divergence تبعه لا
+
+455
+00:36:35,960 --> 00:36:40,760
+يساوي zero اذا ان هو ماله هي احد قصائصه ماله ال
+
+456
+00:36:40,760 --> 00:36:43,620
+divergence لا يساوي zero اذا ان هو لا divergence
+
+457
+00:36:43,620 --> 00:36:47,240
+ولا sinusoidal انا لازم يكون zero عشان اقول ده اذا
+
+458
+00:36:47,240 --> 00:36:53,740
+هدول هتبقى ببقى بس تبعدهم من احتماليتها فسألنا ع
+
+459
+00:36:53,740 --> 00:36:55,820
+كيم يتأكد ان هو لا B ولا هو C
+
+460
+00:37:00,460 --> 00:37:06,400
+خلّيني أقول لك تلاتة X ترمية Y زت ويئة تمتن X
+
+461
+00:37:06,400 --> 00:37:17,240
+cubed زت ويئة تالتة X cubed Y minus اتنين زت انا
+
+462
+00:37:17,240 --> 00:37:24,860
+X hat بس اكتر هدوله هيكون تفاضل هده تفاضل هده
+
+463
+00:37:24,860 --> 00:37:30,600
+تفاضل هده تفاضل هده اتنين Xتفاضل بالنسبة ل X
+
+464
+00:37:30,600 --> 00:37:31,220
+ماهيكون؟ تفاضل بالنسبة ل X ماهيكون؟ تفاضل بالنسبة
+
+465
+00:37:31,220 --> 00:37:32,540
+ل X ماهيكون؟ تفاضل بالنسبة ل X ماهيكون؟ تفاضل
+
+466
+00:37:32,540 --> 00:37:33,700
+بالنسبة ل X ماهيكون؟ تفاضل بالنسبة ل X ماهيكون؟
+
+467
+00:37:33,700 --> 00:37:33,860
+تفاضل بالنسبة ل X ماهيكون؟ تفاضل بالنسبة ل X
+
+468
+00:37:33,860 --> 00:37:34,020
+ماهيكون؟ تفاضل بالنسبة ل X ماهيكون؟ تفاضل بالنسبة
+
+469
+00:37:34,020 --> 00:37:34,960
+ل X ماهيكون؟ تفاضل بالنسبة ل X ماهيكون؟ تفاضل
+
+470
+00:37:34,960 --> 00:37:36,920
+بالنسبة ل X ماهيكون؟ تفاضل بالنسبة ل X ماهيكون؟
+
+471
+00:37:36,920 --> 00:37:40,600
+تفاضل
+
+472
+00:37:40,600 --> 00:37:51,340
+بالنسبة ل X ماهيكون؟ تفاضل
+
+473
+00:37:51,340 --> 00:37:56,460
+بالنسبة
+
+474
+00:37:56,460 --> 00:38:07,350
+ل X ماهيكون-3X³Y-3X³Y
+
+475
+00:38:07,350 --> 00:38:10,690
+-3X³Y
+
+476
+00:38:10,690 --> 00:38:16,730
+-3X³Y-3X³Y
+
+477
+00:38:16,730 --> 00:38:21,210
+-3X³Y-3X³Y
+
+478
+00:38:21,210 --> 00:38:23,230
+-3X³Y
+
+479
+00:38:26,440 --> 00:38:29,880
+الكلب بيساوي Zero الكلب بيساوي Zero إذا هو ماله
+
+480
+00:38:29,880 --> 00:38:34,520
+Conservative هاي واحد منهم أخدناه هاي عامة حد هو
+
+481
+00:38:34,520 --> 00:38:37,940
+Conservative إيش طلع علينا نفحص ليه ادتنا البيع؟
+
+482
+00:38:37,940 --> 00:38:40,660
+هدول أحنا متأكدين مش هنختارهم اللي هو ال
+
+483
+00:38:40,660 --> 00:38:44,260
+divergence وسنون دول ده و rotational لإن طلعنا
+
+484
+00:38:44,260 --> 00:38:49,020
+الكلب بيساوي Zero إذا هو Conservative وسنون دول ده
+
+485
+00:38:49,020 --> 00:38:52,920
+مش صحيح لإن ال divergence لها سوا Zero لإذن هدول
+
+486
+00:38:52,920 --> 00:38:57,400
+اللي اتحققوه تظهر نكمل هايأحنا طبعا هدا و هدا،
+
+487
+00:38:57,400 --> 00:39:01,620
+تمام هذا طبعا كل كل zero خلاص، هذا zero، ضال علينا
+
+488
+00:39:01,620 --> 00:39:05,860
+أجيب دل ال divergence مثلا أنا اكتب ده هنا، بس
+
+489
+00:39:05,860 --> 00:39:11,740
+عاوزة بدنا ناخد دي x by دي y، وين ال divergence
+
+490
+00:39:11,740 --> 00:39:16,020
+تبعك؟ دي x by دي y، دي a x by دي x
+
+491
+00:39:24,030 --> 00:39:31,410
+D2AXYDX D2AXYDX D2AXYDX
+
+492
+00:39:31,410 --> 00:39:39,530
+D2AXYDX D2AXYDX D2AXYDX
+
+493
+00:39:39,530 --> 00:39:50,570
+D2AXYDX
+
+494
+00:39:51,450 --> 00:40:01,290
+بدّل هذا هو عبارة عن 6xyz-2 أي
+
+495
+00:40:01,290 --> 00:40:08,430
+تفاضل مش هيفاضل عن نقصين صح؟ بنفضل
+
+496
+00:40:08,430 --> 00:40:14,370
+بالأول يعني لx يعني بقى 6 بسلامة أجل بس حلي نكتب
+
+497
+00:40:14,370 --> 00:40:16,290
+احنا مين هو اللي بنقوله اللي هو الدل
+
+498
+00:40:20,140 --> 00:40:25,820
+ماذا سيحصل؟ ستة وزد
+
+499
+00:40:25,820 --> 00:40:38,520
+اكس هات ايوة
+
+500
+00:40:38,520 --> 00:40:45,230
+وزدها سمّالها دل دعي فرج A لتسوى Zeroفإذا دي
+
+501
+00:40:45,230 --> 00:40:49,330
+الترميع قالة تساوي zero، إذا هو مش هامل، إذا هو بس
+
+502
+00:40:49,330 --> 00:40:52,550
+conservative، واضح؟ هذه الأسئلة برضه تواجه في
+
+503
+00:40:52,550 --> 00:40:57,130
+الامتحان، فينكم أسئلة كتير في الكتاب، يعني بدكم
+
+504
+00:40:57,130 --> 00:41:00,850
+تشوفوا هدول ال kids، أسئلة عليهم، تحلوهم، جيبوا
+
+505
+00:41:00,850 --> 00:41:04,610
+line integral, surface integral, volume integral،
+
+506
+00:41:04,610 --> 00:41:06,610
+هدولها كلهم أسئلة من الكتاب
+
+507
+00:41:13,280 --> 00:41:16,780
+النقاء القادم ان شاء الله يبدو شكر جديد واتفقنا ان
+
+508
+00:41:16,780 --> 00:41:18,900
+امتحانكم يوم تلاتين احد عشر
+
diff --git a/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/5STYzhKVl6A_raw.json b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/5STYzhKVl6A_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..1558132b055dcd8cb0aec72b42415c994ad59f0f
--- /dev/null
+++ b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/5STYzhKVl6A_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 4575, "start": 20.57, "end": 45.75, "text": "بسم الله الرحمن الرحيم السلام عليكم ورحمة الله وبركاته احنا اليوم هنكمل موضوع ال vector analysis و هنكمل هو ال second derivative احنا المحاضرة الماضية شوفنا ال second derivative لل scalar كمان شوفنا ال second derivative لل vector شوفنا كمان لل scalar ان اقدر اكتب ال second derivative ب Cartesian", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 21136, 37440, 25894, 24793, 4032, 2288, 35571, 3660, 21984, 4032, 26890, 4117, 9307, 3224, 1975, 5016, 8315, 45595, 20498, 8032, 1863, 24793, 1211, 3714, 2407, 11242, 45367, 2423, 8062, 5215, 4032, 8032, 1863, 24793, 1211, 31439, 2423, 1150, 13760, 1975, 5016, 8315, 9673, 5016, 46958, 25720, 9673, 46958, 10632, 13412, 38688, 8315, 2423, 1150, 13760, 24976, 39684, 9122, 2304, 7649, 13412, 38688, 8315, 2423, 1150, 13760, 24976, 8062, 13412, 38688, 8315, 9122, 2304, 7649, 24976, 39684, 16472, 1975, 28543, 2288, 1975, 4117, 2655, 3555, 2423, 1150, 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1.0}, {"id": 30, "seek": 70596, "start": 700.68, "end": 705.96, "text": "بقدر اقول ان دفع دفع دفع دفع دفع دفع دفع دفع", "tokens": [3555, 28543, 2288, 1975, 39648, 16472, 11778, 5172, 3615, 11778, 5172, 3615, 11778, 5172, 3615, 11778, 5172, 3615, 11778, 5172, 3615, 11778, 5172, 3615, 11778, 5172, 3615, 11778, 5172, 3615], "avg_logprob": -0.7212701728267055, "compression_ratio": 2.0, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 700.68, "end": 701.16, "word": "بقدر", "probability": 0.4179484049479167}, {"start": 701.16, "end": 701.4, "word": " اقول", "probability": 0.746826171875}, {"start": 701.4, "end": 701.58, "word": " ان", "probability": 0.80908203125}, {"start": 701.58, "end": 704.48, "word": " دفع", "probability": 0.36712646484375}, {"start": 704.48, "end": 704.8, "word": " دفع", "probability": 0.4849039713541667}, {"start": 704.8, "end": 704.92, "word": " دفع", "probability": 0.6162516276041666}, {"start": 704.92, "end": 704.92, "word": " دفع", "probability": 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732.78, "end": 753.38, "text": "هذه اسمها ال divergence تبعه صوه zero معناه ال flux برضه صوه zero يعني ال flow of surface integral لهذا ال field صوه zero معناه عدد خطوط الفيض اللي داخل على ال surface بالساعة الخطوط اللي طالعة من ال surface كمان لإن احنا عارفين ال divergence الكيار بصوه zero إذا هذا ال field تبعه مادر أكتر بدلالة كيار في ال field تاني", "tokens": [3224, 24192, 24525, 2304, 11296, 2423, 47387, 6055, 3555, 3615, 3224, 20328, 2407, 3224, 4018, 20449, 8315, 3224, 2423, 19298, 4724, 43042, 3224, 20328, 2407, 3224, 4018, 37495, 22653, 2423, 3095, 295, 3753, 11573, 46740, 15730, 2423, 2519, 20328, 2407, 3224, 4018, 20449, 8315, 3224, 6225, 3215, 3215, 16490, 9566, 2407, 9566, 27188, 1829, 11242, 13672, 1829, 11778, 47283, 1211, 15844, 2423, 3753, 20666, 3794, 995, 27884, 33962, 9566, 2407, 9566, 13672, 1829, 23032, 6027, 27884, 9154, 2423, 3753, 9122, 2304, 7649, 5296, 28814, 1863, 1975, 5016, 8315, 6225, 9640, 5172, 9957, 2423, 47387, 33251, 1829, 9640, 4724, 9381, 2407, 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"end": 1181.42, "word": " B", "probability": 0.83544921875}], "temperature": 1.0}, {"id": 50, "seek": 120634, "start": 1182.43, "end": 1206.35, "text": "هذا نسميها الـ Helmholtz theorem واضح؟ هذا ال field ماله؟ هذا ال field له ال divergence بتساوي zero و ال curve بساوي zero واضح؟ في أي سؤال لحد هنا؟ بنسمي هذا ال field أو يعني المعادلة اللى بتعبر عن ال field اللى له دوس ال divergence و ال curve بتساوي zero Helmholtz theorem", "tokens": [3224, 15730, 8717, 38251, 1829, 11296, 2423, 39184, 6128, 76, 71, 4837, 89, 20904, 4032, 46958, 5016, 22807, 23758, 2423, 2519, 3714, 6027, 3224, 22807, 23758, 2423, 2519, 46740, 2423, 47387, 39894, 3794, 995, 45865, 4018, 4032, 2423, 7605, 4724, 3794, 995, 45865, 4018, 4032, 46958, 5016, 22807, 8978, 36632, 8608, 33604, 6027, 5296, 24401, 34105, 22807, 44945, 38251, 1829, 23758, 2423, 2519, 34051, 37495, 22653, 9673, 3615, 18513, 37977, 13672, 7578, 39894, 3615, 3555, 2288, 18871, 2423, 2519, 13672, 7578, 46740, 11778, 41779, 2423, 47387, 4032, 2423, 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0.73583984375}, {"start": 1199.07, "end": 1199.31, "word": " يعني", "probability": 0.830810546875}, {"start": 1199.31, "end": 1200.69, "word": " المعادلة", "probability": 0.98779296875}, {"start": 1200.69, "end": 1200.91, "word": " اللى", "probability": 0.833740234375}, {"start": 1200.91, "end": 1201.49, "word": " بتعبر", "probability": 0.77001953125}, {"start": 1201.49, "end": 1201.67, "word": " عن", "probability": 0.96142578125}, {"start": 1201.67, "end": 1201.83, "word": " ال", "probability": 0.9228515625}, {"start": 1201.83, "end": 1202.13, "word": " field", "probability": 0.96142578125}, {"start": 1202.13, "end": 1202.65, "word": " اللى", "probability": 0.962158203125}, {"start": 1202.65, "end": 1202.83, "word": " له", "probability": 0.72705078125}, {"start": 1202.83, "end": 1203.11, "word": " دوس", "probability": 0.3253173828125}, {"start": 1203.11, "end": 1203.27, "word": " ال", "probability": 0.65185546875}, {"start": 1203.27, "end": 1203.75, "word": " divergence", "probability": 0.9794921875}, {"start": 1203.75, "end": 1204.01, "word": " و", "probability": 0.9404296875}, {"start": 1204.01, "end": 1204.07, "word": " ال", "probability": 0.697265625}, {"start": 1204.07, "end": 1204.25, "word": " curve", "probability": 0.96826171875}, {"start": 1204.25, "end": 1204.53, "word": " بتساوي", "probability": 0.930908203125}, {"start": 1204.53, "end": 1204.85, "word": " zero", "probability": 0.8671875}, {"start": 1204.85, "end": 1205.85, "word": " Helmholtz", "probability": 0.8490234375}, {"start": 1205.85, "end": 1206.35, "word": " theorem", "probability": 0.82666015625}], "temperature": 1.0}, {"id": 51, "seek": 122950, "start": 1211.78, "end": 1229.5, "text": "مثلًا، لو قلنا احنا خلّينا AOI بالساوية minus للـV زي الـElectric field وAS بالساوية curl الـV زي الـMagnetic field، هيكون عندنا curl الـAOI بالساوية zero و divergence الـAS بالساوية zero، أي vector اللي له divergence A بالساوية رؤس", "tokens": [2304, 12984, 1211, 14111, 995, 12399, 45164, 12174, 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Diverge A Diverge A Diverge A Diverge A", "tokens": [35, 3158, 316, 413, 1837, 432, 316, 413, 1837, 432, 316, 413, 1837, 432, 316, 413, 1837, 432, 316], "avg_logprob": -0.6882812291383743, "compression_ratio": 1.9565217391304348, "no_speech_prob": 0.0, "words": [{"start": 1234.8, "end": 1235.94, "word": "DEL", "probability": 0.124237060546875}, {"start": 1235.94, "end": 1236.7, "word": " A", "probability": 0.494384765625}, {"start": 1236.7, "end": 1239.78, "word": " Diverge", "probability": 0.4780680338541667}, {"start": 1239.78, "end": 1240.08, "word": " A", "probability": 0.82177734375}, {"start": 1240.08, "end": 1240.7, "word": " Diverge", "probability": 0.5826822916666666}, {"start": 1240.7, "end": 1240.82, "word": " A", "probability": 0.79345703125}, {"start": 1240.82, "end": 1241.16, "word": " Diverge", "probability": 0.6608072916666666}, {"start": 1241.16, "end": 1241.68, "word": " A", "probability": 0.84326171875}, {"start": 1241.68, "end": 1245.78, "word": " Diverge", 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divergence ومادام ال character تبعه لها يسوى zero إذا ان هو rotational واضح فهذا ال field divergence و rotational هذه أسئلة عامة على كل الأشياء اللي حدناها في هذا الشطر نشوف السؤال هذا اللي قولنا", "tokens": [3794, 12610, 7649, 2407, 25708, 6027, 4032, 20292, 3794, 2423, 39184, 45420, 37495, 22653, 45420, 4032, 47387, 3714, 18513, 10943, 2423, 39184, 47387, 6055, 3555, 3615, 3224, 5296, 11296, 7251, 3794, 2407, 7578, 4018, 11933, 15730, 16472, 31439, 47387, 4032, 2304, 18513, 10943, 2423, 2517, 6055, 3555, 3615, 3224, 5296, 11296, 7251, 3794, 2407, 7578, 4018, 11933, 15730, 16472, 31439, 45420, 4032, 46958, 5016, 6156, 3224, 15730, 2423, 2519, 47387, 4032, 45420, 29538, 5551, 3794, 19986, 37977, 6225, 10943, 3660, 15844, 28242, 16247, 8592, 1829, 16606, 13672, 1829, 11331, 3215, 8315, 11296, 8978, 23758, 25124, 9566, 2288, 8717, 8592, 38688, 21136, 33604, 6027, 23758, 13672, 1829, 12174, 12610, 8315], "avg_logprob": -0.40142045021057127, "compression_ratio": 1.982608695652174, 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{"start": 2460.59, "end": 2460.85, "word": " جيبوا", "probability": 0.9844970703125}, {"start": 2460.85, "end": 2461.05, "word": " line", "probability": 0.97802734375}, {"start": 2461.05, "end": 2461.55, "word": " integral,", "probability": 0.8076171875}, {"start": 2461.75, "end": 2462.05, "word": " surface", "probability": 0.7548828125}, {"start": 2462.05, "end": 2462.69, "word": " integral,", "probability": 0.833984375}, {"start": 2463.15, "end": 2463.41, "word": " volume", "probability": 0.97607421875}, {"start": 2463.41, "end": 2464.61, "word": " integral،", "probability": 0.850830078125}, {"start": 2464.61, "end": 2464.95, "word": " هدولها", "probability": 0.87353515625}, {"start": 2464.95, "end": 2465.29, "word": " كلهم", "probability": 0.9404296875}, {"start": 2465.29, "end": 2465.69, "word": " أسئلة", "probability": 0.9942626953125}, {"start": 2465.69, "end": 2465.99, "word": " من", "probability": 0.99560546875}, {"start": 2465.99, "end": 2466.61, "word": " الكتاب", "probability": 0.9921875}], "temperature": 1.0}, {"id": 101, "seek": 247890, "start": 2473.28, "end": 2478.9, "text": "النقاء القادم ان شاء الله يبدو شكر جديد واتفقنا ان امتحانكم يوم تلاتين احد عشر", "tokens": [6027, 1863, 4587, 16606, 25062, 18513, 2304, 16472, 13412, 16606, 21984, 7251, 44510, 2407, 13412, 37983, 10874, 16254, 3215, 4032, 9307, 5172, 4587, 8315, 16472, 1975, 2304, 2655, 5016, 7649, 24793, 7251, 20498, 6055, 1211, 9307, 9957, 1975, 24401, 6225, 46309], "avg_logprob": -0.2905505945285161, "compression_ratio": 1.42, "no_speech_prob": 0.0, "words": [{"start": 2473.28, "end": 2473.62, "word": "النقاء", "probability": 0.6824951171875}, {"start": 2473.62, "end": 2474.0, "word": " القادم", "probability": 0.9812825520833334}, {"start": 2474.0, "end": 2474.1, "word": " ان", "probability": 0.61083984375}, {"start": 2474.1, "end": 2474.24, "word": " شاء", "probability": 0.960693359375}, {"start": 2474.24, "end": 2474.28, "word": " الله", "probability": 0.96337890625}, {"start": 2474.28, "end": 2474.48, "word": " يبدو", "probability": 0.3892822265625}, {"start": 2474.48, "end": 2474.9, "word": " شكر", "probability": 0.54931640625}, {"start": 2474.9, "end": 2475.54, "word": " جديد", "probability": 0.99169921875}, {"start": 2475.54, "end": 2476.68, "word": " واتفقنا", "probability": 0.86416015625}, {"start": 2476.68, "end": 2476.78, "word": " ان", "probability": 0.3623046875}, {"start": 2476.78, "end": 2477.34, "word": " امتحانكم", "probability": 0.9441731770833334}, {"start": 2477.34, "end": 2477.56, "word": " يوم", "probability": 0.99072265625}, {"start": 2477.56, "end": 2478.2, "word": " تلاتين", "probability": 0.81121826171875}, {"start": 2478.2, "end": 2478.6, "word": " احد", "probability": 0.663818359375}, {"start": 2478.6, "end": 2478.9, "word": " عشر", "probability": 0.763916015625}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2479.75175, "duration_after_vad": 2330.5224999999928}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/9d9AlY75ruU.srt b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/9d9AlY75ruU.srt
new file mode 100644
index 0000000000000000000000000000000000000000..f2a8971043ec4e090839d9740e021cb548ab3b25
--- /dev/null
+++ b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/9d9AlY75ruU.srt
@@ -0,0 +1,2090 @@
+1
+00:00:21,060 --> 00:00:23,380
+بسم الله الرحمن الرحيم السلام عليكم ورحمة الله 
+
+2
+00:00:23,380 --> 00:00:27,320
+وبركاته قبل ما نتبع موضوعنا اللي هو ال coordinate
+
+3
+00:00:27,320 --> 00:00:29,160
+system وال transformation من coordinate ل
+
+4
+00:00:29,160 --> 00:00:31,800
+coordinate ثاني بحب أسألكم إذا في حد عنده أي سؤال 
+
+5
+00:00:31,800 --> 00:00:35,920
+ماضي اللي حكيناها، في حد عنده أي سؤال واضحة كل 
+
+6
+00:00:35,920 --> 00:00:38,700
+الأمور قدامكم إن شاء الله، احنا المحاضرة الماضية
+
+7
+00:00:39,400 --> 00:00:41,820
+شوفنا كيف العلاقة بين اللي هو الـ Cartesian
+
+8
+00:00:41,820 --> 00:00:44,520
+coordinate وال cylindrical coordinate قلنا
+
+9
+00:00:44,520 --> 00:00:47,600
+الاثنين ما بهم orthogonal coordinate يعني بتبعوا ال
+
+10
+00:00:47,600 --> 00:00:51,440
+right hand rule يعني x hat وy hat وz hat متعامدين
+
+11
+00:00:51,440 --> 00:00:55,720
+rho hat وphi hat وz hat متعامدين x hat وy hat وz 
+
+12
+00:00:55,720 --> 00:00:59,580
+hat قلنا بالتمام زي ال corner تبع ال class ال y
+
+13
+00:00:59,580 --> 00:01:02,300
+hat والrho hat والz hat بالتمام زي ال cylinder
+
+14
+00:01:02,300 --> 00:01:06,780
+منظر لل cylinder أنه ال radius تبع الدائرة تاعت
+
+15
+00:01:06,780 --> 00:01:11,120
+القاعدة أو يعني تاعت دائرة السيلندر بشكل عام rho هو
+
+16
+00:01:11,120 --> 00:01:16,600
+اتجاه ال radius وrho هو اتجاه ال radius ف phi هو
+
+17
+00:01:16,600 --> 00:01:20,880
+العمودي عليه المماس لميه للدائرة في اتجاه ال
+
+18
+00:01:20,880 --> 00:01:24,740
+counter clockwise عكس عقارب الساعة والz hat هو
+
+19
+00:01:24,740 --> 00:01:28,660
+نفس ال z hat في اتجاه ال axis الطويل تبع السيلندر
+
+20
+00:01:28,660 --> 00:01:32,020
+لحظة من المحاضرة الماضية أن احنا نقدر نحول من ال Cartesian
+
+21
+00:01:33,670 --> 00:01:37,110
+ل cylindrical أو non-cylindrical ل
+
+22
+00:01:37,110 --> 00:01:41,770
+Cartesian فشوفنا اللي هي العلاقة بين ال x hat وال
+
+23
+00:01:41,770 --> 00:01:44,870
+y hat والz hat والrho hat والphi hat وشوفنا 
+
+24
+00:01:44,870 --> 00:01:49,390
+كمان العلاقة بين الrho hat والphi hat والz 
+
+25
+00:01:49,390 --> 00:01:53,840
+hat العكس يعني احنا كتبناها ال rho hat والphi hat
+
+26
+00:01:53,840 --> 00:01:57,260
+والz hat مع الx hat والy hat والz hat إذا 
+
+27
+00:01:57,260 --> 00:02:00,460
+صرنا عارفين ال transformation من ال Cartesian
+
+28
+00:02:00,460 --> 00:02:03,920
+ل cylindrical وال cylindrical لل Cartesian فبشكل عام
+
+29
+00:02:03,920 --> 00:02:08,140
+أي vector a في ال Cartesian اللي هو ax x hat ال x
+
+30
+00:02:08,140 --> 00:02:11,800
+component ay y hat az z hat  
+
+31
+00:02:11,800 --> 00:02:14,660
+ay y hat az z hat
+
+32
+00:02:14,660 --> 00:02:20,880
+az z hat ax x hat ay y hat
+
+33
+00:02:20,880 --> 00:02:21,540
+az z hat 
+
+34
+00:02:21,540 --> 00:02:21,640
+ax x hat
+
+35
+00:02:21,640 --> 00:02:26,200
+ay y hat
+
+36
+00:02:26,200 --> 00:02:37,660
+az z hat 
+
+37
+00:02:37,660 --> 00:02:43,210
+والـ first component cos phi sin phi 0 وال vector ايش 
+
+38
+00:02:43,210 --> 00:02:47,490
+هيكون ax ay az ونفس الشيء ال rho ثاني هيكون a
+
+39
+00:02:47,490 --> 00:02:53,250
+phi بيساوي سالب sin phi cos phi 0 ax وطبعا نفس ال vector ax 
+
+40
+00:02:53,250 --> 00:02:59,900
+ay az  0 0 1 لو أنا بدي اخذ اللي هو الـ Cartesian 
+
+41
+00:02:59,900 --> 00:03:02,180
+coordinate إذا كنت عارف اللي هو الاسلاندركال 
+
+42
+00:03:02,180 --> 00:03:04,320
+coordinate ببساطة باخد ال inverse بتاعة ال
+
+43
+00:03:04,320 --> 00:03:07,420
+transformation matrix لو جبت ال inverse تبعها
+
+44
+00:03:07,420 --> 00:03:09,860
+بالتمام بيطلع عليه اللي هي ال matrix اللي احنا 
+
+45
+00:03:09,860 --> 00:03:14,520
+شفناها العلاقة بين ال x ax وال arrow وال ay وال
+
+46
+00:03:14,520 --> 00:03:22,000
+fy وال az وال azبشكل عام أنا عشان أجيب مثلًا ax بدلالة 
+
+47
+00:03:22,000 --> 00:03:25,760
+ال a rho وال a phi وال a z أول rho في ال component
+
+48
+00:03:25,760 --> 00:03:30,530
+في ال matrix هيكون ax hat أو x hat . rho hatيكون
+
+49
+00:03:30,530 --> 00:03:35,850
+ax . phi hat ax . z hat وال arrow الثاني اللي هو ay هيكون
+
+50
+00:03:35,850 --> 00:03:42,550
+ay . rho hat y hat . phi hat y hat . z hat وال z 
+
+51
+00:03:42,550 --> 00:03:46,430
+component هتكون z hat . rho hat z hat . phi hat z hat
+
+52
+00:03:46,430 --> 00:03:52,550
+. z hat مضروبين في ال vector arrow a phi a z
+53
+00:03:52,550 --> 00:03:54,490
+الـ spherical coordinates الـ spherical
+
+54
+00:03:54,490 --> 00:03:57,330
+coordinates بتميز أن هو صفير يعني هنا بنحكي احنا
+
+55
+00:03:57,330 --> 00:04:00,970
+عصرنا على ال coordinates بتشكّلوا على شكل أشباه بطيخة
+
+56
+00:04:00,970 --> 00:04:04,390
+هالبطيخة أحد ال coordinates بتاعتها اللي هو ال r
+
+57
+00:04:04,390 --> 00:04:08,230
+ال r اللي هو ال radius تبع البطيخة ال surface
+
+58
+00:04:08,230 --> 00:04:13,130
+تبعنا بطيخة أو اللي هو كرة محيطة في ال r بتاعتنا
+
+59
+00:04:13,600 --> 00:04:17,660
+كرة إذا ال radius تبعنا بيجي من ال origin وفي 
+
+60
+00:04:17,660 --> 00:04:20,440
+اتجاه ال radius تبع ال sphere اللي هو ال r hat
+
+61
+00:04:20,440 --> 00:04:24,780
+اتجاهه هذا ال r طوله r واتجاهه في اتجاه اللي هو
+
+62
+00:04:24,780 --> 00:04:28,700
+ال radius تبع ال sphere r hat الثانية اللي هي ثيتا 
+
+63
+00:04:28,700 --> 00:04:32,620
+ثيتا اللي هي الزاوية بين ال radius وال z axis ثيتا
+
+64
+00:04:32,620 --> 00:04:37,280
+اللي هي بين ال radius وال z axis هي الثيتا بتروح
+
+65
+00:04:37,280 --> 00:04:45,110
+من zero ل π من zero ل π إذا عندي r اللي هي من
+
+66
+00:04:45,110 --> 00:04:49,710
+zero ل infinity ال radius ثيتا بتروح من zero ل π و
+
+67
+00:04:49,710 --> 00:04:53,130
+phi عندي اللي هي إذا طلعت على ال cross المقطع
+
+68
+00:04:55,040 --> 00:04:59,040
+البطيخة تاعتي أو ال sphere تاعتي هيكون في دائرة phi 
+
+69
+00:04:59,040 --> 00:05:04,960
+هي الزاوية ما بين مسقط r على ال cross section على
+
+70
+00:05:04,960 --> 00:05:10,480
+الدائرة مسقطها و x axis يعني phi هي ما بين ال x
+
+71
+00:05:10,480 --> 00:05:16,660
+axis ومسقط ال r على الدائرة اللي هي cross section
+
+72
+00:05:16,660 --> 00:05:21,430
+تبع ال sphere فنقول لو بتروح حالة ال x-axis بتبدأ من
+
+73
+00:05:21,430 --> 00:05:25,470
+ال 0 وبتلف لفة كاملة يعني لها من 0 ل 2π يعني
+
+74
+00:05:25,470 --> 00:05:29,790
+إذا تخيلناها كويس فبتروح من 0 ل 2π ثيتا بتروح من 0
+
+75
+00:05:29,790 --> 00:05:33,070
+ل π وr من 0 ل infinity هلاقي أن أنا غطيت كل ال
+
+76
+00:05:33,070 --> 00:05:36,790
+space زي ما ال x وال y, x بتروح ل ∞ لباس ∞, y بتروح ل ∞ 
+
+77
+00:05:36,790 --> 00:05:38,970
+لباس ∞, z بتروح ل ∞ لباس ∞ أنا غطيت كل ال
+
+78
+00:05:38,970 --> 00:05:42,070
+space
+
+79
+00:05:42,070 --> 00:05:42,410
+ 
+80
+00:05:46,370 --> 00:05:49,290
+هنا كمان نفس الحاجة لأن orthogonal coordinate
+
+81
+00:05:49,290 --> 00:05:53,170
+معناه أن r hat . r hat بتساوي theta hat .
+
+82
+00:05:53,170 --> 00:05:57,650
+theta hat ف i hat . i hat بيساوي واحد يعني ال 
+
+83
+00:05:57,650 --> 00:06:00,450
+unit vector في نفسه بيعطيني واحد بينما أي unit
+
+84
+00:06:00,450 --> 00:06:04,130
+vector dotted مع unit vector ثاني هيكون zero لأنهم 
+
+85
+00:06:04,130 --> 00:06:07,730
+احنا قلنا orthogonal coordinate كمان تطبق عليهم
+
+86
+00:06:07,730 --> 00:06:09,910
+الدائرة اللي هي ال r hat
+
+87
+00:06:28,940 --> 00:06:32,600
+العكس هتعطي إشارة سالبة 
+
+88
+00:06:38,750 --> 00:06:42,410
+إذا أنا الوثيشن فيكتور أو الفيكتور لأي نقطة في ال 
+
+89
+00:06:42,410 --> 00:06:45,090
+space اللي احنا عشان اللي بنسميه الوثيشن فيكتور
+
+90
+00:06:45,090 --> 00:06:49,630
+برضه هو عبارة عن ar اللي هو component في اتجاه
+
+91
+00:06:49,630 --> 00:06:54,570
+ال r hat a theta a phi أو ar r hat زي a theta
+
+92
+00:06:54,570 --> 00:06:57,870
+theta hat زي a phi phi hat الماجنتود التبعه ايش 
+
+93
+00:06:57,870 --> 00:07:01,210
+اتفاقًا نحن الماجنتود بتاعنا؟ الماجنتود هو just vector
+
+94
+00:07:01,210 --> 00:07:08,390
+a . a ايه بط ايه ايش بظل معنا هاي component
+
+95
+00:07:08,390 --> 00:07:12,890
+دت مع نفسها هاي دت مع نفسها هاي دت مع نفسها لأن ال
+
+96
+00:07:12,890 --> 00:07:16,670
+dot ما بين هاي وهاي ايش بيساوي zero r hat . theta 
+
+97
+00:07:16,670 --> 00:07:19,370
+hat zero r hat . phi hat zero theta hat . phi
+
+98
+00:07:19,370 --> 00:07:24,610
+hat zero بظل معنا بس ar تربيع زائد a theta تربيع زائد a
+
+99
+00:07:24,610 --> 00:07:26,050
+phi تربيع 
+
+100
+00:07:37,290 --> 00:07:40,190
+طب احنا كمان نقدر نروح من ال cylindrical
+
+101
+00:07:40,190 --> 00:07:42,850
+coordinate من ال spherical coordinate لكارتيشن و
+
+102
+00:07:42,850 --> 00:07:45,990
+لعكس من أني بدي أطلع على ال coordinate system و
+
+103
+00:07:45,990 --> 00:07:49,350
+أشوف العلاقة بين ال r وال θ وال phi وال x وال y
+
+104
+00:07:49,350 --> 00:07:53,110
+وال z طبعًا العلاقة هتكون بسيطة بالنسبة لنا وواضحة 
+
+105
+00:07:53,110 --> 00:07:58,230
+إذا طلعنا كويس على الرسم اللي قدامنا إذا طلعنا على
+
+106
+00:07:58,230 --> 00:08:00,510
+الرسم اللي قدامنا هي r اللي هو ال radius على
+
+107
+00:08:00,510 --> 00:08:04,280
+ال sphere ده هتجيب نقطة إنطلاقة في ال space هي θ اللي 
+
+108
+00:08:04,280 --> 00:08:10,080
+قلنا الزاوية بين z axis و r و phi اللي بتحدد له
+
+109
+00:08:10,080 --> 00:08:14,400
+الزاوية بين نقطة قطعة r على الدائرة و x axis
+
+110
+00:08:14,400 --> 00:08:17,560
+فال cartesian
+
+111
+00:08:17,560 --> 00:08:22,840
+coordinate  لنا ال x وال y وال z نجيب العلاقة مباري اللي هي
+
+112
+00:08:22,840 --> 00:08:27,140
+ال Gaussian عند نقطة xyz وrθφ وأكيد هنجيبها
+
+113
+00:08:27,140 --> 00:08:31,580
+بدلالة السنة اللي كانت coordinate لأن السنة عارفين احنا 
+
+114
+00:08:31,580 --> 00:08:34,820
+قبل هيك حكينا أن ال position بتأثرش في أي
+
+115
+00:08:34,820 --> 00:08:37,980
+coordinate بحكي عنه أنا عندي هذا ال atom محطوط في ال 
+
+116
+00:08:37,980 --> 00:08:41,720
+space أسوأ عبرت عن موقع بالنسبة لل origin بال
+
+117
+00:08:41,720 --> 00:08:43,900
+Cartesian coordinate أو بال spherical أو
+
+118
+00:08:43,900 --> 00:08:47,300
+بال cylindrical بتغير مكانه؟ المفروض ما يتغيرش عشان 
+
+119
+00:08:47,300 --> 00:08:50,820
+هيك احنا دائمًا نقول أن ال position عند ال xyz لازم
+
+120
+00:08:50,820 --> 00:08:52,640
+يساوي position في ال spherical coordinate اللي هو
+
+121
+00:08:52,640 --> 00:08:58,130
+rθφ أو في ال cylindrical اللي هو rθz نعمل الرصنة
+
+122
+00:08:58,130 --> 00:09:01,850
+بيحقق لها ال x,y,z r اللي هو ال radius تبع ال sphere 
+
+123
+00:09:01,850 --> 00:09:06,830
+بيحدد لي مواقع النقطة عامل زاوية θ مع z axis و φ 
+
+124
+00:09:06,830 --> 00:09:10,970
+اللي هي زاوية ما بين مسقط r على الدائرة اللي هي ال
+
+125
+00:09:10,970 --> 00:09:14,510
+cross section لل spherical coordinate و x axis اللي
+
+126
+00:09:14,510 --> 00:09:19,350
+هي ال r كيف العلاقة بينهم؟ هنجيبها بمحدد شعرنا في 
+
+127
+00:09:19,350 --> 00:09:23,170
+الرصنة اللي أمامنا r اللي هو ال radius تبع
+
+128
+00:09:23,170 --> 00:09:28,400
+ال spherical ايش هيكون؟ هيكون هو عبارة عن الجذر 
+
+129
+00:09:28,400 --> 00:09:32,700
+التربيعي لقيم ال x تربيع إذا طلعنا احنا هذا بصراحه
+
+130
+00:09:32,700 --> 00:09:36,720
+متكتر اللي
+
+131
+00:09:36,720 --> 00:09:43,200
+هو موقع في ال x-axis وهي ال y-axis وهي z-axis ف ايش
+
+132
+00:09:43,200 --> 00:09:49,200
+هيكون x تربيع زي y تربيع زي z تربيع وحياتي تحت
+
+133
+00:09:49,200 --> 00:09:53,320
+الجذر طبعًا حياتي r لأن r vector بضربته في بدلالة xx
+
+134
+00:09:53,320 --> 00:09:55,960
+hat yy hat zz hat 
+
+135
+00:10:07,100 --> 00:10:10,660
+هذا r ميجي لزاوية θ 
+
+136
+00:10:14,010 --> 00:10:18,290
+ممكن أعمل له إسقاط على z-axis، ايش بيساوي الإسقاط
+
+137
+00:10:18,290 --> 00:10:21,230
+طبعًا على z-axis؟ أو ال component بتاعته على z-axis
+
+138
+00:10:21,230 --> 00:10:28,930
+هي r cos θ، r cos θ وال component الثانية اللي
+
+139
+00:10:28,930 --> 00:10:34,860
+متعامدة عليها هتكون r sin θ، صحيح؟ طب احنا عندنا هي
+
+140
+00:10:34,860 --> 00:10:39,060
+اللي هي r cos θ وهذا ال r فال θ باخد الضلع 
+
+141
+00:10:39,060 --> 00:10:42,900
+باخد ال cos باخد ال component هي على هي أو هي على
+
+142
+00:10:42,900 --> 00:10:46,960
+هي هذا اللي هي ال z component وهذا المقابل وهذا
+
+143
+00:10:46,960 --> 00:10:52,260
+اللي هو الوتر الثاني هيكون المقابل على المجاور هي 
+
+144
+00:10:52,260 --> 00:10:56,360
+sin لل θ يعني هذه على هي ايش هتكون لو قسمناها 
+
+145
+00:10:56,360 --> 00:10:58,880
+هيكون sin θ على cos θ اللي هي tan لل θ
+
+146
+00:11:13,260 --> 00:11:19,360
+طب مين هي ال rho ال rho اللي هي هذا اللي هو
+
+147
+00:11:19,360 --> 00:11:24,960
+الإسقاط تبع ال r على ال x y plane اللي هي ال
+
+148
+00:11:24,960 --> 00:11:31,260
+component هي موازية لهذه هذا المستطيل وهذا الطول 
+
+149
+00:11:31,260 --> 00:11:35,560
+هو نفسه هذا الطول اللي هو عبارة عن مين؟ r sin θ 
+
+150
+00:11:35,560 --> 00:11:39,680
+إذا أنا هي اللي بقدر أعمل له component r cos θ وr sin θ
+
+151
+00:11:39,680 --> 00:11:44,120
+ف rho هي r sin θ إذا طلعت في عملية الجمهور زي ما احنا 
+
+152
+00:11:44,120 --> 00:11:48,440
+اتعلمنا كجمهور ال vector ايه أخذت هذا ال component 
+
+153
+00:11:48,440 --> 00:11:51,760
+وهذا ال component وهذا ال x component وهذا ال y
+
+154
+00:11:51,760 --> 00:11:53,900
+component وهذا ال rho rho مش بيساوي
+
+155
+00:12:14,890 --> 00:12:22,210
+موضح لحدنا؟ ميجي
+
+156
+00:12:22,210 --> 00:12:29,840
+للِفعل إذا طلعت احنا عندنا ال rho لأن دي it's ال phi
+
+157
+00:12:29,840 --> 00:12:34,740
+المجاور لها والمقابل لها المجاور لها هو عبارة عن
+
+158
+00:12:34,740 --> 00:12:41,000
+rho cos φ والمقابل اللي هو rho sin φ 
+
+159
+00:12:41,000 --> 00:12:45,060
+إذا نوجد ال tan هيكون المقابل هو rho sin φ 
+
+160
+00:12:45,310 --> 00:12:51,290
+على المجاور هو rho cos φ إذا نوجد rho cos 
+
+161
+00:12:51,290 --> 00:12:57,350
+φ على rho cos φ تتساوي tan φ هي 
+
+162
+00:12:57,350 --> 00:13:03,730
+بتساوي tan مين؟ هذه عبارة عن y على مين؟ على x إذا 
+
+163
+00:13:03,730 --> 00:13:10,100
+ال phi هي عبارة عن tan inverse y على x هيك أنا كتبت
+
+164
+00:13:10,100 --> 00:13:14,100
+ال r وال θ وال phi لما أكون عارف ال x وال y وال 
+
+165
+00:13:14,100 --> 00:13:16,840
+z إذا كنت عارف ال x وال y وال z ال question تبع
+
+166
+00:13:16,840 --> 00:13:19,920
+النقطة بتاعتي تقول أن r اللي هي ال radius تبع
+
+167
+00:13:19,920 --> 00:13:23,620
+ال sphere هيكون جذر التربيعي ل x تربيع زي y تربيع زي 
+
+168
+00:13:23,620 --> 00:13:28,620
+z تربيع θ هتكون tan inverse rho على z rho اللي هي
+
+169
+00:13:28,620 --> 00:13:32,500
+جذر التربيعي ل x تربيع زي y تربيع وفي هتكون tan 
+
+170
+00:13:32,500 --> 00:13:34,400
+inverse y على x
+
+171
+00:13:41,490 --> 00:13:47,050
+هي أي سؤال أحد منكم؟ طب نشوف ايش هي ال x component 
+
+172
+00:13:47,050 --> 00:13:52,150
+لدالة ال r وال θ وال φ احنا قلنا الإسقاط تبع ال r على
+
+173
+00:13:52,150 --> 00:13:57,890
+الدائرة على ال circle اللي هي ال cross section تبع 
+
+174
+00:13:57,890 --> 00:14:03,630
+ال sphere فابع عن r sin θ r sin θ اللي هي rho 
+
+175
+00:14:03,630 --> 00:14:06,370
+احنا قلنا rho أنها ابع عن r sin θ
+
+176
+00:14:12,130 --> 00:14:15,630
+ال r sin θ أو ال rho لها x component و y component و
+
+177
+00:14:15,630 --> 00:14:20,130
+لا.. ايش ال x component هتكون؟ ال x عبارة عن 
+
+178
+00:14:20,130 --> 00:14:31,210
+r sin θ cos φ.. ريسينا ال r sin θ
+
+179
+00:14:31,210 --> 00:14:36,410
+cos φ إذا ال x component لا قصش ال vector يعني
+
+180
+00:14:36,410 --> 00:14:41,160
+عبارة عن مين؟ r sin θ cos φ طب ال y component ايش
+
+181
+00:14:41,16
+
+201
+00:16:17,880 --> 00:16:21,860
+cos θ الـ  theta hat نفس الحاجة الـ theta hat
+
+202
+00:16:21,860 --> 00:16:24,440
+احنا قلنا ايش اتجاه الـ theta hat عشان ارجع لقسم
+
+203
+00:16:24,440 --> 00:16:30,580
+السابق عموديات على بعض كل مرة أنا
+
+204
+00:16:30,580 --> 00:16:35,020
+حكيت الـ theta بتروح من zero لـ π  إذا اتجاه ال
+
+205
+00:16:35,020 --> 00:16:38,700
+theta لو أنا خيلت هاي الـ sphere المنطقة هيكنك
+
+206
+00:16:38,700 --> 00:16:45,080
+اتجاه المثل الـ sphere و اتجاه الـ theta بتروح من هاي
+
+207
+00:16:45,080 --> 00:16:49,140
+الـ X Axis بتروح من Zero لـ Two Pi فاتجاه الـ Phi hat
+
+208
+00:16:49,140 --> 00:16:55,440
+والمناسب لقى الدائرة تمام
+
+209
+00:16:55,440 --> 00:17:04,500
+سنة ده هو اتجاه الـ X الـ R hat و الـ R hat أخرى R
+
+210
+00:17:04,500 --> 00:17:10,480
+hat طالع من بسفير ستة hat مناسبة لسفيربنقل الـ 0
+
+211
+00:17:10,480 --> 00:17:14,320
+إلى الـ I و الـ Phi هات مماس للدائرة اللي هي cross
+
+212
+00:17:14,320 --> 00:17:18,980
+section لاسفير و بعدين نقل الـ Phi Zero رفح الكم
+
+213
+00:17:18,980 --> 00:17:24,140
+هنا فاكر ان الناس تجاه الـ X hat و بروف مع الدائرة
+
+214
+00:17:24,140 --> 00:17:27,220
+من Zero لـ Phi
+
+215
+00:17:37,100 --> 00:17:40,420
+إذا العلاقة بين هدول الـ unit vectors هلاقي ان R
+
+216
+00:17:40,420 --> 00:17:45,700
+هتقولنا sin θ cos في x hat sin θ sin في y hat ذات
+
+217
+00:17:45,700 --> 00:17:49,880
+cos θ z hat بينما الـ z hat ايش هنلاقيها cos θ cos
+
+218
+00:17:49,880 --> 00:17:57,200
+في cos θ sin في minus sin θ z hat الفي هت هتكون
+
+219
+00:17:57,200 --> 00:18:04,990
+minus في x hat ذات cos في y hatبالنسبة للـ X في
+
+220
+00:18:04,990 --> 00:18:07,870
+درجة الارهات والثيتاهات والفايهات هتكون الـ X هتبع
+
+221
+00:18:07,870 --> 00:18:11,510
+عن Sine Theta Cosine Phi Arhat زائد Cosine Theta
+
+222
+00:18:11,510 --> 00:18:15,190
+Cosine Phi Theta Hat minus Sine Phi Phi Hat الـ Y
+
+223
+00:18:15,190 --> 00:18:18,850
+hat هتكون Sine Theta Sine Phi Arhat زائد Cosine
+
+224
+00:18:18,850 --> 00:18:23,010
+Theta Sine Phi Theta Hat زائد Cosine Phi Phi Hat
+
+225
+00:18:23,010 --> 00:18:26,270
+وAZ هتكون Cosine Theta Arhat minus Sine Theta
+
+226
+00:18:26,270 --> 00:18:31,970
+Theta Hatعشان اكتب اي vector في الـ Cartesian
+
+227
+00:18:31,970 --> 00:18:34,550
+coordinate للسيفريكال coordinate هنعمل نفس الطريقة
+
+228
+00:18:34,550 --> 00:18:37,430
+اللي تبعناها لما كان عندها Cartesian position و
+
+229
+00:18:37,430 --> 00:18:40,370
+كتبناها بدلها الـ cylindrical coordinate ان ال
+
+230
+00:18:40,370 --> 00:18:44,730
+vector في الـ Cartesian coordinate هو ax x hat ذات
+
+231
+00:18:44,730 --> 00:18:48,560
+ay y hat ذات a z z hatعشان اكتبوا في الـ spherical
+
+232
+00:18:48,560 --> 00:18:52,540
+coordinate ايش بسويه بروح معاوضة عن الـ a hat و ال
+
+233
+00:18:52,540 --> 00:18:58,920
+y hat و الـ z hat تلات مين الـ a phi و الـ r phi و ال
+
+234
+00:18:58,920 --> 00:19:06,620
+theta phi و الـ phi hat انا x hat بستبدلها بهاي ال
+
+235
+00:19:06,620 --> 00:19:10,000
+component كلها و الـ y component بستبدلها بهاي و ال
+
+236
+00:19:10,000 --> 00:19:11,020
+theta في هاي الـ component
+
+237
+00:19:13,770 --> 00:19:18,010
+AX مضروبة في sinus طبعا أول حاجة بعود عن X hat و
+
+238
+00:19:18,010 --> 00:19:22,270
+بعدين بلم لن الـ R hat و Y hat و θ hat و فيهات
+
+239
+00:19:22,270 --> 00:19:27,590
+نعملها و لا واضحة نعملها مع بعض و لا واضحة واضحة
+
+240
+00:19:27,590 --> 00:19:31,870
+إذا إحنا إيش بنسوي بنقيم الـ X hat اللي فيها تلاتة
+
+241
+00:19:31,870 --> 00:19:35,890
+componentsوحدة في الـ R hat وحدة في الـ theta hat
+
+242
+00:19:35,890 --> 00:19:39,050
+وحدة في الـ phi hat بقية من الـ Y hat و بعوض عنها
+
+243
+00:19:39,050 --> 00:19:41,870
+لإيه برضه لها تلاتة component و الـ Z hat اللي لها
+
+244
+00:19:41,870 --> 00:19:44,330
+two components دلت الـ R hat و الـ theta hat اذا
+
+245
+00:19:44,330 --> 00:19:49,550
+بتوقع الـ R hat اكم component لها تلاتة و الـ theta
+
+246
+00:19:49,550 --> 00:19:54,850
+hat اكم واحدة تلاتة و الـ phi hat تنتيةزي ما بتطلع
+
+247
+00:19:54,850 --> 00:19:59,490
+هنا بالفعل عندي ax cos θ cos فى ذات ay sin θ sin
+
+248
+00:19:59,490 --> 00:20:05,430
+فى ذات a z cos θ r hat و الـ theta hat عندي ax cos
+
+249
+00:20:05,430 --> 00:20:11,010
+θ cos فى ذات ay cos θ sin فى minus a z sin θ بتجاه
+
+250
+00:20:11,010 --> 00:20:15,750
+الـ theta hatوالـ Phi hat عند ماينوس Ax sin Phi زي
+
+251
+00:20:15,750 --> 00:20:19,670
+Ay cos Phi Phi hat بالتالي بقدر اقول ان الـ R
+
+252
+00:20:19,670 --> 00:20:22,210
+component اللي بوش في دلالة الـ spherical
+
+253
+00:20:22,210 --> 00:20:27,570
+coordinate هي برعى Ax sin θ cos Phi زي Ay sin θ
+
+254
+00:20:27,570 --> 00:20:32,510
+sin Phi زي Az cos Phi الـ theta component هي Ax cos
+
+255
+00:20:32,510 --> 00:20:37,820
+θ cos Phiزي a y cos θ sin فاي minus a z sin θ
+
+256
+00:20:37,820 --> 00:20:41,960
+ويظهر ان الفاي component يبقى على minus a x sin
+
+257
+00:20:41,960 --> 00:20:47,560
+فاي زي a y cos فاي نقدر نكتبها على دلالة أشكل ال
+
+258
+00:20:47,560 --> 00:20:52,000
+matrix هذا الـ vector a r a θ a فاي وهنا ال
+
+259
+00:20:52,000 --> 00:20:56,940
+components بقدر اكتبهم على دلالة الـ matrixهيكون
+
+260
+00:20:56,940 --> 00:21:01,540
+عند الـ sin θ cos φ cos θ cos φ minus sin فى دلالة
+
+261
+00:21:01,540 --> 00:21:06,520
+اللى هي ar a θ a فى الـ equation التانية اللى هي ay
+
+262
+00:21:06,520 --> 00:21:13,020
+تسوى sin θ sin فى ar cos θ sin فى a θ cos فى a فى
+
+263
+00:21:13,020 --> 00:21:18,320
+واخر المعادلة هي az تسوى cos θ ar minus sin θ a θ
+
+264
+00:21:19,780 --> 00:21:23,120
+عشان اجيب لو كنت انا عارفة الـ Cartesian coordinate
+
+265
+00:21:23,120 --> 00:21:26,100
+او بدي اجيب الـ spherical coordinate ايش بقي اعمل
+
+266
+00:21:26,100 --> 00:21:30,040
+بروحه انا محدد الـ inverse ل الـ matrix اللي هي
+
+267
+00:21:30,040 --> 00:21:33,460
+بالصفة بهذا الشكل اللي هي sin theta cos phi sin
+
+268
+00:21:33,460 --> 00:21:38,340
+theta sin phi cos phi minus cos theta cos phi sin
+
+269
+00:21:38,340 --> 00:21:42,460
+theta sin phi minus sin theta minus sin phi cos
+
+270
+00:21:42,460 --> 00:21:47,180
+phi اذا لو انا بدي اكون او كنت عارف ال ax ay ez و
+
+271
+00:21:47,180 --> 00:21:50,890
+بدي اكتب ar a theta a phiهتكون طبعا dot product من
+
+272
+00:21:50,890 --> 00:21:55,590
+R hat و X hat, R hat و Y hat, R hat و Z hat هدول
+
+273
+00:21:55,590 --> 00:22:00,890
+المحتوى تبع الـ matrix A theta hat dot X hat, theta
+
+274
+00:22:00,890 --> 00:22:04,190
+hat dot Y hat, theta hat dot Z hat, phi hat dot X
+
+275
+00:22:04,190 --> 00:22:06,910
+hat, phi hat dot Y hat, phi hat dot Z hat
+
+276
+00:22:12,570 --> 00:22:14,590
+الاخر حاجة اللى هو الـ transformation بين ال
+
+277
+00:22:14,590 --> 00:22:17,590
+cylindrical و الـ spherical coordinate انا هتركه
+
+278
+00:22:17,590 --> 00:22:22,050
+لكم إياه as a task جيبوه اللقاء القادر تستعينوا
+
+279
+00:22:22,050 --> 00:22:24,990
+باللي احنا اتعلمناه مش هيكون اي حاجة جديدة ان ال
+
+280
+00:22:24,990 --> 00:22:29,330
+spherical هي الـ theta hat و الـ r hat و الـ phi hat
+
+281
+00:22:29,330 --> 00:22:33,830
+الـ cylindrical يعني الـ raw hat يعني هتلاقوا كمان
+
+282
+00:22:33,830 --> 00:22:40,310
+نقاط أسهل بكتير ان الـ raw hat و الـ phi hat و الـ z
+
+283
+00:22:40,310 --> 00:22:45,230
+hatأنه في علاقة واضحة الـ Phi hat و الـ Z hat و ال
+
+284
+00:22:45,230 --> 00:22:48,610
+Raw hat تقريبا بتشابهوا في بين الـ cylindrical و
+
+285
+00:22:48,610 --> 00:22:53,410
+الـ spherical الاختلاف اللى هى الـ theta و الـ R ال
+
+286
+00:22:53,410 --> 00:22:57,450
+Raw hat اللى هى الإسقاط تبع الـ R في اللى هى المقطع
+
+287
+00:22:57,450 --> 00:23:01,310
+أو الـ growth section تبع الاسفيرفان شاء الله يعني
+
+288
+00:23:01,310 --> 00:23:05,570
+متغلبوش بتعملوه بسهولة المطالب القادر يعني عمره
+
+289
+00:23:05,570 --> 00:23:08,730
+بنتذكر ان الـ magnitude بتاع الـ vector بس شينه له
+
+290
+00:23:08,730 --> 00:23:12,130
+ان الـ magnitude بتاعه مالهوش علاقة بأي coordinate
+
+291
+00:23:12,130 --> 00:23:16,610
+بستخدمه يعني انا هيحطه زي ما قلنا قلم تبعيه بده
+
+292
+00:23:16,610 --> 00:23:20,250
+أجيب الموقع بتاعه بالنسبة لل originأنا و أقدر أكتب
+
+293
+00:23:20,250 --> 00:23:23,470
+بالـ Cartesian هذا البسجن الـ vector الـ vector اللي
+
+294
+00:23:23,470 --> 00:23:26,650
+هو سميناه R ده الـ Cartesian ده السفريكا ده
+
+295
+00:23:26,650 --> 00:23:30,330
+السمينريكا لما أجيب الـ magnitude تبع هذه مسافة أي
+
+296
+00:23:30,330 --> 00:23:34,330
+سبسافرة بتتأثر بحاجة من هدولة الـ magnitude هتقول
+
+297
+00:23:34,330 --> 00:23:38,950
+هي R dot R تحت الجزر نفس المقدار إذا هي 5 متر
+
+298
+00:23:38,950 --> 00:23:42,200
+هتبقى 5 متر مش هتتغيرلأ في الـ spherical ولا في ال
+
+299
+00:23:42,200 --> 00:23:45,000
+cylindrical ولا في الـ Cartesian فهي نقطة مهمة ان
+
+300
+00:23:45,000 --> 00:23:48,060
+انت لو انك بتحسبيه وطلعلك ان المجدد اللي بيخلف
+
+301
+00:23:48,060 --> 00:23:54,240
+يعرف انك انت عاملة عاملة حاجة خاطئة طبالة
+
+302
+00:23:54,240 --> 00:23:57,380
+الـ distance الـ distance احنا اشتغلنا الـ distance
+
+303
+00:23:57,380 --> 00:24:02,400
+من الـ two points هي عبارة عن موقع نقطة R2 minus R1
+
+304
+00:24:02,400 --> 00:24:08,500
+يعني عندي انا two vectors هذه
+
+305
+00:24:08,500 --> 00:24:15,440
+نقطة R1فهي نقطة R2 فهي قسش مفتولة كل واحدة منهم و
+
+306
+00:24:15,440 --> 00:24:22,380
+بدي انا الـ distance بين R2 وR1 هتكون R2 ناقص R1 ال
+
+307
+00:24:22,380 --> 00:24:27,700
+magnitude هتكون هاي دي اللي هي الـ magnitude الجزر
+
+308
+00:24:27,700 --> 00:24:39,160
+التربيه لR2 minus R1 او الجزر التربيهالجزء التربيه
+
+309
+00:24:39,160 --> 00:24:41,080
+دخل في الـ Magnitude بس أنا كنت عاملة dot
+
+310
+00:24:41,080 --> 00:24:50,860
+البرودرات ر هي جزء التربيه لR8-R1
+
+311
+00:24:53,650 --> 00:24:57,630
+R2-R1 زى ما اتفقنا لأى vector قولنا المجلد التابع
+
+312
+00:24:57,630 --> 00:25:01,610
+هو جزر التربية لA.A قلت احنا بنحكي على الـ distance
+
+313
+00:25:01,610 --> 00:25:05,010
+vector distance vector هو between two points هى
+
+314
+00:25:05,010 --> 00:25:08,190
+يكون المجلد التابع نفس الحاجة جزر التربية لهذا ال
+
+315
+00:25:08,190 --> 00:25:13,070
+vector doted في نفسه هى
+
+316
+00:25:13,070 --> 00:25:15,030
+الـ distance vector فى الـ Cartesian إيش هتكون؟ عنا
+
+317
+00:25:15,030 --> 00:25:20,110
+الـ component لR1 وR2 فالتالي في الـ Cartesian R1 هي
+
+318
+00:25:20,110 --> 00:25:33,180
+X1Y1 Z1 R2 X2 Y2 Z2 اذا طلعنا عليها بالكارتيجين
+
+319
+00:25:33,180 --> 00:25:40,500
+هتكون ببساطة هي عبارة عن R2-R1 ب X2-X1 X3 اذا
+
+320
+00:25:40,500 --> 00:25:46,000
+كتبناها بشكل vector اولا هي D vector هتكون من X2
+
+321
+00:25:46,000 --> 00:26:00,300
+-X1 X3زائد y تنين minus y واحد y واحد y hat زائد
+
+322
+00:26:00,300 --> 00:26:06,100
+زي التنين minus z واحد z hat هدا في الـ Cartesian
+
+323
+00:26:06,100 --> 00:26:09,610
+coordinatesلما أجيب الماجنسة تبعها احنا لشمنها
+
+324
+00:26:09,610 --> 00:26:13,930
+نفسه بعمله ضد الـ product مع نفسه و تحت الجزر، بدي
+
+325
+00:26:13,930 --> 00:26:17,150
+التربيه تبعها باقيم الجزر، فبصير دي تربيه زى ما
+
+326
+00:26:17,150 --> 00:26:20,430
+احنا محقرها خلالنا بدون الجزر، بدون ما أعمل بقى
+
+327
+00:26:20,430 --> 00:26:27,710
+ايه، يعني هاد الـ D دي تربيهاش هاتبون بيه R2-R1 دو
+
+328
+00:26:27,710 --> 00:26:30,530
+تت فR2-R1
+
+329
+00:26:32,480 --> 00:26:36,040
+غالبا في الكهرة المناطسية الـ EMAG حلق انه يا ابن
+
+330
+00:26:36,040 --> 00:26:39,660
+تتعامل معادي دي تربيةT تربيعي بدون ما أخد جزء
+
+331
+00:26:39,660 --> 00:26:43,180
+تربيعي فإذا أخدت dot الـ product تبعهم طبعا الـ X
+
+332
+00:26:43,180 --> 00:26:46,020
+component مع الـ X component هي اللي هتتبقى الـ Y
+
+333
+00:26:46,020 --> 00:26:48,100
+component مع الـ Y component هي اللي هتتبقى و Z
+
+334
+00:26:48,100 --> 00:26:50,580
+component مع الـ Z component هي اللي هتتبقى الباقي
+
+335
+00:26:50,580 --> 00:26:55,260
+هيكون أصفر لأن X hat مع Y hat dot Y hat Zero X hat
+
+336
+00:26:55,260 --> 00:26:58,560
+dot Z hat Zero و هكذا فماش هيكون في الـ Cartesian
+
+337
+00:26:58,560 --> 00:27:04,840
+coordinate X2-X1 لكل تربيع زي Y2-Y1 لكل تربيع زي
+
+338
+00:27:04,840 --> 00:27:09,530
+Z2-Z1 لكل تربيعفي الـ cylindrical احنا مين عيلنا ال
+
+339
+00:27:09,530 --> 00:27:14,970
+components؟ رو واحد فاى واحد زد واحد وبتانى رو
+
+340
+00:27:14,970 --> 00:27:21,710
+تنين فاى تنين وزد تنين عشان احنا مش هتكون رو رو
+
+341
+00:27:21,710 --> 00:27:25,750
+هات زاد فاى فاى هات لأ مش بهذا الشكل ببساطة احنا
+
+342
+00:27:25,750 --> 00:27:28,790
+هنعمل الـ transformation عشان هيك تطلع معنا رو
+
+343
+00:27:28,790 --> 00:27:33,570
+تربيع زاد رو واحد تربيعحتى لو طلعتوا انتوا على هذه
+
+344
+00:27:33,570 --> 00:27:39,530
+الدائرة البساطة ايش رو تنين؟ رو تنين هي X تنين
+
+345
+00:27:39,530 --> 00:27:44,390
+تربية زاد Y تنين تربية رو واحد تربية اللي هي X
+
+346
+00:27:44,390 --> 00:27:48,770
+واحد تربية زاد Y واحد تربية اذا انتوا ربعتوا
+
+347
+00:27:48,770 --> 00:27:52,570
+هتشوفوها هتطلع هاي الـ components مباشرة من هنا او
+
+348
+00:27:52,570 --> 00:27:55,150
+اذا كتبتوه مباشرة في الـ cylindrical coordinate
+
+349
+00:27:55,150 --> 00:27:58,370
+اللي هي D كتبت اول R تنين اللي طلعت الـ cylindrical
+
+350
+00:27:58,370 --> 00:28:01,250
+coordinate حولنا ليه الـ X تنين
+
+351
+00:28:06,440 --> 00:28:10,200
+أو من التربيع إذا طلعتوا على التربيع هذا هتلاقي X
+
+352
+00:28:10,200 --> 00:28:14,480
+تربيه زائد Y واحد تربيه زائد الزاوية اللي بينهم
+
+353
+00:28:19,660 --> 00:28:24,380
+و Y2-Y1 هتلاقي انه بيطلع معنا X Y X التربية و Y
+
+354
+00:28:24,380 --> 00:28:28,780
+تربية تانية تربية و X1 تربية Y1 تربية و بعدين
+
+355
+00:28:28,780 --> 00:28:32,040
+هتطلع الحدود الوسطى بس مش بالسهولة ان احولها
+
+356
+00:28:32,040 --> 00:28:34,280
+سليندركال بس انا بفرجيكوا انها هتوضح انها هتبدأ
+
+357
+00:28:34,280 --> 00:28:38,360
+الصورة توضح اولا بكتبهم بسليندركال coordinate و
+
+358
+00:28:38,360 --> 00:28:43,840
+بربع فبتطلع ليه ليه الصورة الواضحة معناه واضح؟نفس
+
+359
+00:28:43,840 --> 00:28:48,560
+الشيء في الـ spherical coordinates هيكون عندي R2
+
+360
+00:28:48,560 --> 00:28:52,620
+تربية اللي هي بسهولة ممكن اشوفها ليه X تربية و Y
+
+361
+00:28:52,620 --> 00:28:57,760
+تربية و Z تربية و X1 تربية و Y1 تربية و Z1 تربية
+
+362
+00:28:57,760 --> 00:29:01,220
+اظهروا معنا بظل الترمات اللي بين نصها دول هشتغل
+
+363
+00:29:01,220 --> 00:29:04,160
+عليهم لكن بدل ما اشتغل عليهم الـ Cartesian ابدأ ان
+
+364
+00:29:04,160 --> 00:29:07,420
+اكتب R2 و R1 من البداية ابدلها من الـ spherical
+
+365
+00:29:07,420 --> 00:29:11,990
+coordinates زي ما احنا شوفناها في الـ slideأخد
+
+366
+00:29:11,990 --> 00:29:16,790
+الفرق ما بين R2-R1 وعمل التربية تظهر معايا D تربية
+
+367
+00:29:16,790 --> 00:29:22,350
+تسوى R2 تربية زاد R1 تربية minus 2R1R2 cos 6R2 cos
+
+368
+00:29:22,350 --> 00:29:30,430
+6R1 minus 2R1R2 sin 6R2 sin 6R1 cos 5R2-1تمام هاي
+
+369
+00:29:30,430 --> 00:29:33,230
+كمان task اذا الـ task الأولى بدنا نعمل
+
+370
+00:29:33,230 --> 00:29:36,170
+transformation matrix بين الـ spherical و ال
+
+371
+00:29:36,170 --> 00:29:39,
+
+401
+00:31:44,080 --> 00:31:47,580
+البعنى آخر نعم تقلب دوة cylindrical
+
+402
+00:31:55,700 --> 00:32:01,260
+بس الواحدة زي اللي ممكن تتساوي زي التلاتة
+
+403
+00:32:05,080 --> 00:32:08,300
+ممتازة يعني إذا احنا بنحكي عن ال point B أنا بدي
+
+404
+00:32:08,300 --> 00:32:11,560
+أروح من ال Cartesian لـ ال cylindrical معناه أني
+
+405
+00:32:11,560 --> 00:32:15,940
+بدي أروح من ال XYZ لـ raw of Y و Z raw هي جزر ال X
+
+406
+00:32:15,940 --> 00:32:21,960
+تربيع زي Y تربيع يبقى سوى جزر 4 زي 36 جزر الأرمين
+
+407
+00:32:21,960 --> 00:32:26,500
+اللي هي جزر الأرمين ممتازة، و الفارق تنقل ال Y على 
+408
+00:32:26,500 --> 00:32:28,140
+X
+
+409
+00:32:38,390 --> 00:32:45,570
+بصارت اللي هي حطيها بالكارتيجين minus 2 و 6 و 3
+
+410
+00:32:45,570 --> 00:32:49,310
+بتساوي
+
+411
+00:32:49,310 --> 00:32:54,290
+اللي هي جزر الأربعين و 5 اعتبارها لقيت من طول
+
+412
+00:32:54,290 --> 00:33:01,990
+رقمها ثاني inverse ثاني inverse سالب تلاتة و Z
+
+413
+00:33:01,990 --> 00:33:07,490
+تلاتة هنا وين فيه cylindrical coordinate؟ بدنا في 
+
+414
+00:33:07,490 --> 00:33:09,330
+ال spherical coordinate احنا أول شهرة ال spherical
+
+415
+00:33:09,330 --> 00:33:13,070
+coordinate اللي هي R, R بتساوي التربية زي ات واي
+
+416
+00:33:13,070 --> 00:33:18,610
+تربيع زي التربية تربيع تربيع تربيع تربيع تربيع تربيع 
+
+417
+00:33:18,610 --> 00:33:20,210
+تربيع تربيع تربيع تربيع تربيع تربيع تربيع تربيع
+
+418
+00:33:20,210 --> 00:33:21,090
+تربيع تربيع تربيع تربيع تربيع تربيع تربيع تربيع
+
+419
+00:33:21,090 --> 00:33:21,230
+تربيع تربيع تربيع تربيع تربيع تربيع تربيع تربيع
+
+420
+00:33:21,230 --> 00:33:23,390
+تربيع تربيع تربيع تربيع تربيع تربيع تربيع تربيع
+
+421
+00:33:23,390 --> 00:33:23,410
+تربيع تربيع تربيع تربيع تربيع تربيع تربيع تربيع
+
+422
+00:33:23,410 --> 00:33:32,390
+تربيع تربيع تربيع ترب
+
+423
+00:33:32,700 --> 00:33:35,980
+وSETA تقريباً تقريباً تقريباً تقريباً تقريباً تقريباً
+
+424
+00:33:35,980 --> 00:33:40,620
+تقريباً تقريباً تقريباً تقريباً تقريباً تقريباً تقريباً
+
+425
+00:33:40,620 --> 00:33:43,560
+تقريباً تقريباً تقريباً تقريباً تقريباً تقريباً تقريباً
+
+426
+00:33:43,560 --> 00:33:46,160
+تقريباً تقريباً تقريباً 
+
+427
+00:33:52,760 --> 00:33:56,400
+هذا إذا لل point B قدرنا نعبر عنها من ال Cartesian
+
+428
+00:33:56,400 --> 00:33:59,080
+coordinate أن أحولها لـ ال cylindrical و ال
+
+429
+00:33:59,080 --> 00:34:01,660
+spherical coordinate طب هو بده كمان ال A النقطة A
+
+430
+00:34:01,660 --> 00:34:04,300
+النقطة A احنا عارفين ال X component و ال K
+
+431
+00:34:04,300 --> 00:34:07,900
+component قم بلها بدي أحولها و أجيب اللي هي ال R
+
+432
+00:34:07,900 --> 00:34:11,220
+hat component و ال theta hat و ال phi hat و كم بده
+
+433
+00:34:11,220 --> 00:34:15,560
+أجيب اللي هي ال R hat و ال .. اعمل هي اللي تفضل
+
+434
+00:34:21,180 --> 00:34:24,080
+طبعاً زي ما عملت زميلتنا قولنا في الـ cylindrical
+
+435
+00:34:24,080 --> 00:34:26,500
+coordinate ال role هي جزر تربيع ل X تربيع Z وY
+
+436
+00:34:26,500 --> 00:34:31,600
+تربيع تطلع 6.32 أن الفاي اللي هي tan inverse Y على
+
+437
+00:34:31,600 --> 00:34:36,980
+X تطلع 108 و 43 درجة وإن ال Z بدها تساوي 3 طب تمام
+
+438
+00:34:36,980 --> 00:34:39,400
+زي ما عملت زميلتنا نجي لها اللي هو the spherical
+
+439
+00:34:39,400 --> 00:34:43,340
+قولنا R هي جزر تربيع ل X تربيع Z وY تربيع Z تطلع 7
+
+440
+00:34:43,340 --> 00:34:47,340
+طبعاً زي ما حسبتها الـ set هي 10 inverse rho على z
+
+441
+00:34:47,340 --> 00:34:52,400
+اللي هي 64 مبتدأ 60 مية صراحة أنا مش عارفة كيف هي
+
+442
+00:34:52,400 --> 00:34:56,440
+انهيأت ال vector عن ال point يعني برضه هنا في نفس
+
+443
+00:34:56,440 --> 00:34:58,560
+القوانين المفروض تستخدمها ما هي ال point بتعبلني 
+
+444
+00:34:58,560 --> 00:35:04,080
+vector احنا في نقطة ايش نقطة في ال space موقعها هو
+
+445
+00:35:04,080 --> 00:35:07,380
+عبارة عن vector اللي هو قيمة ال X وY وZ هاي ال
+
+446
+00:35:07,380 --> 00:35:11,940
+point هو يعطيني نقطة اللي هي لها position vector و
+
+447
+00:35:11,940 --> 00:35:15,160
+vector ثاني E اللي ما فيه شلقة فيه بنقوله what's
+
+448
+00:35:15,160 --> 00:35:40,320
+component احنا 
+
+449
+00:35:40,320 --> 00:35:43,800
+أسهل حاجة أنّه متذكره احنا مشينا لهذه ال matrix
+
+450
+00:35:46,280 --> 00:35:51,440
+احنا قولنا أي vector بواطر أكتبه بدلالة اللي هو ال
+
+451
+00:35:51,440 --> 00:35:55,880
+vector اللي بت X, Y, Z ال matrix بتاعة اللي بتربط
+
+452
+00:35:55,880 --> 00:36:00,360
+ال X component بال raw component بال X component و
+
+453
+00:36:00,360 --> 00:36:03,940
+ال Phi component بال Y component و Z component وهي
+
+454
+00:36:03,940 --> 00:36:12,380
+عبارة عن كمبونات ال matrix رو hat dot x hat رو hat
+
+455
+00:36:12,380 --> 00:36:16,780
+dot y hat رو hat dot z hat وهكذا فهذه أسهل حاجة
+
+456
+00:36:16,780 --> 00:36:20,140
+لأنك أنت هتلاقي حاجة بالاخر وسط في مداها وأنت بدك
+
+457
+00:36:20,140 --> 00:36:24,080
+تجيب هذا ال vector من اللي هو ال Cartesian لاسم
+
+458
+00:36:24,080 --> 00:36:27,780
+المركز فهذه الفرق بين النقطة و ال vector
+
+459
+00:36:32,360 --> 00:36:36,760
+عشان أنا مقصودة 
+
+460
+00:36:36,760 --> 00:36:40,300
+لنفسه عشان إذا عندي أنا ال vector a اللي هو ال x
+
+461
+00:36:40,300 --> 00:36:43,620
+component قولنا قيمتها y ال y component قيمتها x
+
+462
+00:36:43,620 --> 00:36:46,180
+زات زت و ال z component بالزا و zero قولنا ايش
+
+463
+00:36:46,180 --> 00:36:49,820
+نستخدم عشان أنا أحول vector من one coordinate لـ
+
+464
+00:36:49,820 --> 00:36:54,020
+another coordinate أني بستخدم ال matrix طب إذا A رو
+
+465
+00:36:54,020 --> 00:36:59,780
+عبارة عن Y Cos Phi زات X زات Z Sin Phi و A Phi
+
+466
+00:36:59,780 --> 00:37:03,780
+عبارة عن Minus Y Sin Phi زات X زات Z Cos Phi و A Z
+
+467
+00:37:03,780 --> 00:37:07,960
+بتساوي Zero أنا عشان أكمل ايش بدأ أسوي و أجيب 
+
+468
+00:37:07,960 --> 00:37:13,340
+القيام بتاعة ال Y و X و Z بدلالة ال Phi و ال Rho
+
+469
+00:37:14,530 --> 00:37:17,910
+معين؟ إذا ماقشف ده أكمل السؤال، ده أجيب قيمة هدول
+
+470
+00:37:17,910 --> 00:37:22,430
+ال components، يعني ال X ايش بتساوي رو كسين الفاية،
+
+471
+00:37:22,430 --> 00:37:26,830
+وال Y رو سين الفاية، وإلّا بيكون في حل ناقص، إلّا
+
+472
+00:37:26,830 --> 00:37:31,420
+بيكون mixture ما بين Cartesian وCylindrical عشان
+
+473
+00:37:31,420 --> 00:37:34,720
+أنا أكمل الحالة ال Y و X و Z لازم أقيمها من هنا
+
+474
+00:37:34,720 --> 00:37:38,960
+طبعاً ال Z دلت Z لكن ال X و Y فعند ال X مش هتساوي
+
+475
+00:37:38,960 --> 00:37:42,560
+Rho Cos Phi و Y Rho Sin Phi بنعوض عنهم مش باعطيني
+
+476
+00:37:42,560 --> 00:37:45,980
+أنّ ال A اللي اللي لها A Rho و A Phi و A Z
+
+477
+00:37:45,980 --> 00:37:49,750
+component هتساوي Rho Cos Phi Sin Phi زاد رو كسين
+
+478
+00:37:49,750 --> 00:37:54,730
+الفي زاد زد سين الفي رو هات زاد ماينس رو سين تربيه
+
+479
+00:37:54,730 --> 00:37:58,770
+في زاد رو كسين الفي زاد زد كسين الفي في هات وطبعاً
+
+480
+00:37:58,770 --> 00:38:01,310
+ماطلعش معنا z component لإن ال z component مالها
+
+481
+00:38:01,310 --> 00:38:06,610
+من الأساس zero a z zero zero zero ففقط هيدلع عندي
+
+482
+00:38:06,610 --> 00:38:09,470
+ال raw component و ال phi component بعد ما أخلص من 
+
+483
+00:38:09,470 --> 00:38:12,210
+قلم القيام اللي هي ال y و ال x 
+
+484
+00:38:15,680 --> 00:38:20,040
+Exactly ولا ايه؟ طبعاً كلا زميلتكم متذكرين قيمة ال raw
+
+485
+00:38:20,040 --> 00:38:23,260
+اللي هي جزر الأربعين و phi هي tan inverse minus
+
+486
+00:38:23,260 --> 00:38:28,000
+تلاتة بعود عنهم في اللي هي ال components اللي
+
+487
+00:38:28,000 --> 00:38:30,180
+عندنا طبعاً احنا قلنا cosine ال phi بقدر أجيب sin
+
+488
+00:38:30,180 --> 00:38:35,220
+ال phi إذا عرفت ال cosine بقدر أجيب ال sin صحيح؟
+
+489
+00:38:35,220 --> 00:38:39,340
+tan بجيب ال cosine و بجيب ال sin انتهى البساطة بحط
+
+490
+00:38:39,340 --> 00:38:42,810
+القيم في قلب ال component بتاعتي بتاعة ال vector
+
+491
+00:38:42,810 --> 00:38:46,250
+بقدر أحصل على ال vector اللي هو بيعطيني ال two
+
+492
+00:38:46,250 --> 00:38:48,230
+components اللي هي واحدة في الرواحات وواحدة في ال
+
+493
+00:38:48,230 --> 00:38:51,430
+file هات لإن اتفقنا كلنا أنّه بيظهر ما لها zero لو
+
+494
+00:38:51,430 --> 00:38:55,030
+بيبقى لها zero ليه بس المعادلات؟ لأ بس عشان أنا
+
+495
+00:38:55,030 --> 00:38:58,630
+مكبرة الحط أن عشان تشوف الأرقام ما هي اليرة يعني
+
+496
+00:38:58,630 --> 00:39:03,980
+ما بتاخدش سطرين السطر الأول هي ال matrix وبدي أنتبه 
+
+497
+00:39:03,980 --> 00:39:09,000
+أن في دلالتي Y و X و Z فبالتالي بدي أعرف ايش كيام
+
+498
+00:39:09,000 --> 00:39:13,080
+ال Y و X و Z طبعاً هو بقيت السؤال هو بدويا نكتبها
+
+499
+00:39:13,080 --> 00:39:16,220
+في دلالة ال cosine و ال phi ال cylindrical و ال
+
+500
+00:39:16,220 --> 00:39:20,360
+spherical و بدويا نحسبها عند النقطة P عشان هي أدت 
+
+501
+00:39:20,360 --> 00:39:22,840
+النقطة P أما هنا احنا خلصنا الجزء الأول كتبتها في 
+
+502
+00:39:22,840 --> 00:39:26,560
+دلالة ال cylindrical coordinate انتهى يعني أنا
+
+503
+00:39:26,560 --> 00:39:29,800
+باستخدام ال matrix انتهى الحل عشان اقولك أنه صغير
+
+504
+00:39:29,800 --> 00:39:36,380
+الحل هو بده نكتب هي نرجع للسؤال بدو يانا ال P نكتب
+
+505
+00:39:36,380 --> 00:39:39,780
+ال components تعونها بدلالة ال cylindrical و ال
+
+506
+00:39:39,780 --> 00:39:44,100
+spherical و ال vector A بدي أكتبه بدلالة برضه ال
+
+507
+00:39:44,100 --> 00:39:47,580
+cylindrical و ال spherical و احسبه evaluate A at P
+
+508
+00:39:47,580 --> 00:39:50,240
+في ال Cartesian و في ال cylindrical و في ال
+
+509
+00:39:50,240 --> 00:39:53,560
+spherical في ال Cartesian عطول بعوض عن Y اللي هي
+
+510
+00:39:53,560 --> 00:40:00,280
+ال 6 و X ذات Z ماقص ثلاثة و نقص ثانية ذات تلاتة هدف
+
+511
+00:40:00,280 --> 00:40:03,520
+ال kartesian في ال cylindrical احنا حسبنا القيم
+
+512
+00:40:03,520 --> 00:40:07,220
+طبعاً
+
+513
+00:40:07,220 --> 00:40:09,680
+احنا عملنا هده ال matrix transformation من ال
+
+514
+00:40:09,680 --> 00:40:13,140
+kartesian لـ ال cylindrical وبعد ما أنا حصفت على
+
+515
+00:40:13,140 --> 00:40:16,260
+ال vector A في ال cylindrical بدي اروح على النقطة
+
+516
+00:40:16,260 --> 00:40:19,700
+B و اعوض على القيم بتاعة ال Phi و ال rho
+
+517
+00:40:22,520 --> 00:40:25,320
+بظهر على الـ Cepherical مارجع كلمة مرة على ال 
+
+518
+00:40:25,320 --> 00:40:27,820
+matrix قال لي ال ar و ال a theta و ال a phi
+
+519
+00:40:27,820 --> 00:40:32,340
+فقدرتهم دلالات ال a x و ال a y و ال a z ال x دي y
+
+520
+00:40:32,340 --> 00:40:37,660
+ال a y هي x ذات z و ال a z zero هو بساخدم اللي هي
+
+521
+00:40:37,660 --> 00:40:41,500
+ال transformation matrix بعرف قيمة ar و a theta و
+
+522
+00:40:41,500 --> 00:40:47,200
+a phi بظهر علي نفس القضية جيب قيمة y وقيم X و Z و θ
+
+523
+00:40:47,200 --> 00:40:52,080
+و ف يعني أولاً بدون اللي هي عند النقطة P بدي أقيم
+
+524
+00:40:52,080 --> 00:40:56,120
+ال Y و X و بعود عنهم الدلالة ال R و ال θ و ال ف
+
+525
+00:40:56,120 --> 00:41:00,000
+احنا عارفين أن X هي عبارة عن R sin θ cos ف و Y هي 
+
+526
+00:41:00,000 --> 00:41:03,740
+عبارة عن R sin θ sin ف و Z هي عبارة عن R cos θ
+
+527
+00:41:03,740 --> 00:41:09,570
+بعود عنهم بطلع معايا ال vector الصحيح في البدون 
+
+528
+00:41:09,570 --> 00:41:12,390
+هيك بيكون حل ناقص أنا بيصير mixture ما بين
+
+529
+00:41:12,390 --> 00:41:16,250
+cartesian و spherical السؤال هذا يعني فيه هاي ال
+
+530
+00:41:16,250 --> 00:41:18,810
+trick أنّه اتقعد بفكر حل عملت transformation matrix
+
+531
+00:41:18,810 --> 00:41:23,130
+وانتهى الحل لأ أنا هو ال trick أنّه كمان عندي ال x
+
+532
+00:41:23,130 --> 00:41:25,930
+component و ال y component بدلة ال y و ال x و ال z
+
+533
+00:41:25,930 --> 00:41:29,730
+فبالتالي هدولة بدي أعوض عنهم بدلة ال R و ال θ بحصل
+
+534
+00:41:29,730 --> 00:41:32,750
+على ال vector في ال spherical coordinate بجي عند
+
+535
+00:41:32,750 --> 00:41:38,970
+النقطة B بدي أحسب قيمة R و Phi و Theta R هي حسابات
+
+536
+00:41:38,970 --> 00:41:44,330
+اللي هيها emblema 7 و Phi هي 10 inverse-3 و Theta
+
+537
+00:41:44,330 --> 00:41:49,630
+هي 10 inverse-شزر الأربعين على 3 بجيب كل الحاجة 
+
+538
+00:41:49,630 --> 00:41:52,750
+لزماني و بعود عنها يعني لازم ال cos Phi cos Phi
+
+539
+00:41:52,750 --> 00:41:56,550
+cos Theta sin Theta و بعود في قيمة ال A و بطلع
+
+540
+00:41:56,550 --> 00:41:59,690
+معايا اللي هي هاي ال vector في ال spherical
+
+541
+00:41:59,690 --> 00:42:03,020
+coordinate لو أنا بدي أعمل فحص أن أحل صح ولا غلط
+
+542
+00:42:03,020 --> 00:42:07,040
+ايش بسويه بجيب ال magneto بتبع ايه في ال Cartesian
+
+543
+00:42:07,040 --> 00:42:10,060
+و ال magneto بتبع ايه في ال cylindrical و ال 
+
+544
+00:42:10,060 --> 00:42:13,680
+magneto بتبع ايه في ال spherical إذا طلع معايا لا
+
+545
+00:42:13,680 --> 00:42:17,320
+أي تساوى معناه اعملها غلط طلعوا بتساوى معناها أن
+
+546
+00:42:17,320 --> 00:42:20,920
+أنا الحمد لله ما عملتش أي mathematical mistakes
+
+547
+00:42:23,530 --> 00:42:27,010
+هذا هو هذا ال check ال magnitude تبع a ال function
+
+548
+00:42:27,010 --> 00:42:29,810
+x,y,z لازم يساوي ال magnitude في ال raw of y,z
+
+549
+00:42:29,810 --> 00:42:35,370
+بيساوي ال magnitude في r,θ,y تمام احنا هيكد 
+
+550
+00:42:35,370 --> 00:42:39,770
+المفروض ننهي المحاضرة بس هشطبها بإني أشرح حاجة
+
+551
+00:42:39,770 --> 00:42:44,810
+اسمها ال constant coordinate يعني مثلاً إذا روحنا
+
+552
+00:42:44,810 --> 00:42:45,830
+على ال Cartesian coordinate
+
+553
+00:42:48,390 --> 00:42:51,650
+إذا روحت على ال Cartesian coordinate XYZ عشان اللي
+
+554
+00:42:51,650 --> 00:42:55,070
+القادم هعملها ال cylindrical و ال spherical ايش 
+
+555
+00:42:55,070 --> 00:42:58,410
+معنى constant coordinate؟ يعني إذا قلت أنا عندي في
+
+556
+00:42:58,410 --> 00:43:03,590
+ال XYZ coordinate عندي Z دايماً ثابتة، قيمة ثابتة،
+
+557
+00:43:03,590 --> 00:43:08,670
+تلاتة فهده بتمثلي ال plan بتمثلي ال plan اللي ال
+
+558
+00:43:08,670 --> 00:43:12,790
+X و ال Y بتغيروا على طول و Z ثابتة اللي هو هذا ال
+
+559
+00:43:12,790 --> 00:43:16,280
+plan شايفين هو هذا ال plan؟ هذا ماله constant
+
+560
+00:43:16,280 --> 00:43:20,380
+coordinate يعني قيمة الـ z component ثابتة لو كانت 
+
+561
+00:43:20,380 --> 00:43:24,220
+x هي اللي ثابتة حيكون عند الـ z بتتغير منصة
+
+562
+00:43:24,220 --> 00:43:26,120
+infinity للواصلة infinity و ال y بتتغير منصة
+
+563
+00:43:26,120 --> 00:43:30,780
+infinity للواصلة infinity هذا اللي بيعمل هذا اللي
+
+564
+00:43:30,780 --> 00:43:38,780
+هي قيمة ال y ثابتة ال x ثابتة الـ X قيمة ثابتة و
+
+565
+00:43:38,780 --> 00:43:42,000
+الـ Y و الـ Z بتغيروا في هذا الـ plan و أعطي
+
+566
+00:43:42,000 --> 00:43:44,060
+الحيالي constant coordinate يعني تكون واحدة من
+
+567
+00:43:44,060 --> 00:43:47,800
+القيم ثابتة مهما تغيرت القيم التانية و هيك
+
+568
+00:43:47,800 --> 00:43:50,400
+يعطيكم العافية و لقاء قادم إن شاء الله هشوف ال
+
+569
+00:43:50,400 --> 00:43:53,960
+constant coordinate
+
+570
+00:43:53,960 --> 00:43:57,180
+أو يعني أن أخلي واحد القوانين ثابت في سفر الكلب
+
+571
+00:43:57,180 --> 00:44:00,700
+و السندر الكلب يشوف القيامة يعطيكم العافية إن شاء
+
+572
+00:44:00,700 --> 00:44:00,780
+الله
diff --git a/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/9d9AlY75ruU_raw.json b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/9d9AlY75ruU_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..0c8b11db424e552961f4ec783ad141a852e60d90
--- /dev/null
+++ b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/9d9AlY75ruU_raw.json
@@ -0,0 +1 @@
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0.5478515625}, {"start": 64.14, "end": 64.4, "word": " ال", "probability": 0.96484375}, {"start": 64.4, "end": 64.84, "word": " radius", "probability": 0.96142578125}, {"start": 64.84, "end": 65.28, "word": " تبع", "probability": 0.9453125}], "temperature": 1.0}, {"id": 3, "seek": 9202, "start": 65.68, "end": 92.02, "text": "الدائرة تاعت القاعدة أو يعني تاعت دائرة السيلندر بشكل عام رو هو اتجاه ال radius و رو هو اتجاه ال radius ففاي هو العمودي عليه المماس لميه للدائرة في اتجاه ال counter clockwise عكس عقارب الساعة و ال z hat هو نفس ال z hat في اتجاه ال axis الطويل تبع السيلندر لحظة من المحاضرة الماضية ان احنا نقدر نحول اسواق", "tokens": [6027, 3215, 16373, 25720, 6055, 995, 34268, 25062, 995, 22488, 3660, 34051, 37495, 22653, 6055, 995, 34268, 11778, 16373, 25720, 21136, 1829, 1211, 41260, 2288, 4724, 8592, 28820, 6225, 10943, 12602, 2407, 31439, 1975, 2655, 7435, 40294, 2423, 2843, 4872, 4032, 12602, 2407, 31439, 1975, 2655, 7435, 40294, 2423, 2843, 4872, 6156, 5172, 47302, 31439, 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{"start": 85.04, "end": 85.18, "word": " ال", "probability": 0.955078125}, {"start": 85.18, "end": 85.36, "word": " z", "probability": 0.82763671875}, {"start": 85.36, "end": 85.64, "word": " hat", "probability": 0.94775390625}, {"start": 85.64, "end": 85.78, "word": " في", "probability": 0.78173828125}, {"start": 85.78, "end": 86.18, "word": " اتجاه", "probability": 0.9776611328125}, {"start": 86.18, "end": 86.66, "word": " ال", "probability": 0.8759765625}, {"start": 86.66, "end": 87.04, "word": " axis", "probability": 0.76708984375}, {"start": 87.04, "end": 87.58, "word": " الطويل", "probability": 0.8416341145833334}, {"start": 87.58, "end": 87.9, "word": " تبع", "probability": 0.6781412760416666}, {"start": 87.9, "end": 88.66, "word": " السيلندر", "probability": 0.827392578125}, {"start": 88.66, "end": 89.66, "word": " لحظة", "probability": 0.8946533203125}, {"start": 89.66, "end": 89.78, "word": " من", "probability": 0.96533203125}, {"start": 89.78, "end": 90.16, "word": " 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0.873046875}, {"start": 166.91, "end": 167.29, "word": " هيكون", "probability": 0.940185546875}, {"start": 167.29, "end": 167.49, "word": " a", "probability": 0.459716796875}, {"start": 167.49, "end": 167.85, "word": " phi", "probability": 0.6357421875}, {"start": 167.85, "end": 168.47, "word": " بيسوي", "probability": 0.6214599609375}, {"start": 168.47, "end": 168.83, "word": " سلب", "probability": 0.803955078125}, {"start": 168.83, "end": 169.25, "word": " sin", "probability": 0.72900390625}, {"start": 169.25, "end": 169.97, "word": " cos", "probability": 0.31103515625}, {"start": 169.97, "end": 171.11, "word": " 0", "probability": 0.736328125}, {"start": 171.11, "end": 171.93, "word": " ax", "probability": 0.810546875}, {"start": 171.93, "end": 172.11, "word": " و", "probability": 0.390625}, {"start": 172.11, "end": 172.35, "word": " طبعا", "probability": 0.8330078125}, {"start": 172.35, "end": 172.57, "word": " نفس", "probability": 0.987548828125}, {"start": 172.57, "end": 172.71, "word": " ال", "probability": 0.978515625}, {"start": 172.71, "end": 172.91, "word": " vector", "probability": 0.98779296875}, {"start": 172.91, "end": 173.25, "word": " ax", "probability": 0.70166015625}, {"start": 173.25, "end": 173.67, "word": " ay", "probability": 0.80126953125}, {"start": 173.67, "end": 174.09, "word": " و", "probability": 0.85205078125}, {"start": 174.09, "end": 174.49, "word": " 0", "probability": 0.11962890625}, {"start": 174.49, "end": 175.73, "word": " 0", "probability": 0.4658203125}, {"start": 175.73, "end": 176.23, "word": " 1", "probability": 0.9306640625}], "temperature": 1.0}, {"id": 8, "seek": 19602, "start": 177.3, "end": 196.02, "text": "لو انا بدى اخد اللى هو الـ Cartesian coordinate اذا كنت عارفة اللى هو الاسلاندركال coordinate ببساطة باخد ال inverse بتاعة ال transformation matrix لو جبت ال inverse تبعها بالتمام بيطلع عليه اللى هى ال matrix اللى احنا شفناها العلاقة بين ال X AX و ال Arrow و ال AY و ال FY و AZ و AZ", "tokens": [1211, 2407, 1975, 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0.97119140625}, {"start": 190.5, "end": 191.26, "word": " العلاقة", "probability": 0.7991536458333334}, {"start": 191.26, "end": 191.46, "word": " بين", "probability": 0.82470703125}, {"start": 191.46, "end": 191.6, "word": " ال", "probability": 0.69921875}, {"start": 191.6, "end": 191.86, "word": " X", "probability": 0.658203125}, {"start": 191.86, "end": 192.6, "word": " AX", "probability": 0.4232177734375}, {"start": 192.6, "end": 192.88, "word": " و", "probability": 0.5302734375}, {"start": 192.88, "end": 193.08, "word": " ال", "probability": 0.366455078125}, {"start": 193.08, "end": 193.48, "word": " Arrow", "probability": 0.358642578125}, {"start": 193.48, "end": 193.76, "word": " و", "probability": 0.7919921875}, {"start": 193.76, "end": 193.86, "word": " ال", "probability": 0.69091796875}, {"start": 193.86, "end": 194.26, "word": " AY", "probability": 0.5103759765625}, {"start": 194.26, "end": 194.42, "word": " و", "probability": 0.97216796875}, {"start": 194.42, "end": 194.52, "word": " ال", "probability": 0.75390625}, {"start": 194.52, "end": 194.96, "word": " FY", "probability": 0.512451171875}, {"start": 194.96, "end": 195.12, "word": " و", "probability": 0.9658203125}, {"start": 195.12, "end": 195.4, "word": " AZ", "probability": 0.560546875}, {"start": 195.4, "end": 195.82, "word": " و", "probability": 0.693359375}, {"start": 195.82, "end": 196.02, "word": " AZ", "probability": 0.86376953125}], "temperature": 1.0}, {"id": 9, "seek": 20984, "start": 198.28, "end": 209.84, "text": "بشكل عام انا عشان اجيب مثلا ax دلالة ال a rho وال a phi وال a z اول rho في ال component في ال matrix هيكون ax hat او x hat dot rho hat", "tokens": [3555, 8592, 28820, 6225, 10943, 1975, 8315, 6225, 8592, 7649, 1975, 7435, 1829, 3555, 50113, 15040, 6360, 11778, 1211, 6027, 3660, 2423, 257, 20293, 16070, 257, 13107, 16070, 257, 710, 1975, 12610, 20293, 8978, 2423, 6542, 8978, 2423, 8141, 39896, 30544, 6360, 2385, 1975, 2407, 2031, 2385, 5893, 20293, 2385], "avg_logprob": 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{"start": 202.88, "end": 203.02, "word": " وال", "probability": 0.395751953125}, {"start": 203.02, "end": 203.14, "word": " a", "probability": 0.54345703125}, {"start": 203.14, "end": 203.34, "word": " phi", "probability": 0.308349609375}, {"start": 203.34, "end": 203.5, "word": " وال", "probability": 0.95751953125}, {"start": 203.5, "end": 203.62, "word": " a", "probability": 0.7177734375}, {"start": 203.62, "end": 203.86, "word": " z", "probability": 0.88427734375}, {"start": 203.86, "end": 204.62, "word": " اول", "probability": 0.82275390625}, {"start": 204.62, "end": 204.98, "word": " rho", "probability": 0.67724609375}, {"start": 204.98, "end": 205.12, "word": " في", "probability": 0.91259765625}, {"start": 205.12, "end": 205.24, "word": " ال", "probability": 0.9013671875}, {"start": 205.24, "end": 205.76, "word": " component", "probability": 0.408935546875}, {"start": 205.76, "end": 206.14, "word": " في", "probability": 0.63134765625}, {"start": 206.14, "end": 206.36, "word": " ال", "probability": 0.94921875}, {"start": 206.36, "end": 206.76, "word": " matrix", "probability": 0.966796875}, {"start": 206.76, "end": 207.34, "word": " هيكون", "probability": 0.849365234375}, {"start": 207.34, "end": 208.06, "word": " ax", "probability": 0.9345703125}, {"start": 208.06, "end": 208.44, "word": " hat", "probability": 0.89404296875}, {"start": 208.44, "end": 208.6, "word": " او", "probability": 0.891845703125}, {"start": 208.6, "end": 208.8, "word": " x", "probability": 0.9423828125}, {"start": 208.8, "end": 209.04, "word": " hat", "probability": 0.9453125}, {"start": 209.04, "end": 209.24, "word": " dot", "probability": 0.90283203125}, {"start": 209.24, "end": 209.44, "word": " rho", "probability": 0.9130859375}, {"start": 209.44, "end": 209.84, "word": " hat", "probability": 0.9873046875}], "temperature": 1.0}, {"id": 10, "seek": 23007, "start": 210.11, "end": 230.07, "text": "يكون ax.phi hat ax.z hat و الاروه التانى الهو ay هيكون ny.rho hat y hat.phi hat y hat.z hat و ال z component هتكون z hat.rho hat z hat.phi hat z hat.z hat مضربين فى ال vector arrow a phi a z", "tokens": [1829, 30544, 6360, 13, 950, 72, 2385, 6360, 13, 89, 2385, 4032, 2423, 9640, 2407, 3224, 16712, 7649, 7578, 2423, 3224, 2407, 7494, 8032, 1829, 30544, 18052, 13, 81, 1289, 2385, 288, 2385, 13, 950, 72, 2385, 288, 2385, 13, 89, 2385, 4032, 2423, 710, 6542, 8032, 2655, 30544, 710, 2385, 13, 81, 1289, 2385, 710, 2385, 13, 950, 72, 2385, 710, 2385, 13, 89, 2385, 3714, 11242, 25513, 9957, 6156, 7578, 2423, 8062, 11610, 257, 13107, 257, 710], "avg_logprob": -0.414843750372529, "compression_ratio": 1.625, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 210.11, "end": 210.53, "word": "يكون", "probability": 0.31683349609375}, {"start": 210.53, "end": 210.57, "word": " ax", "probability": 0.08917236328125}, {"start": 210.57, "end": 211.69, "word": ".phi", "probability": 0.635986328125}, {"start": 211.69, "end": 212.05, "word": " hat", "probability": 0.6669921875}, 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283.63, "end": 293.13, "text": "أذا عندي R اللي هي من Zero ل Infinity ال Radius ثتا بتروح من Zero ل Pi و Phi عندي اللي هي إذا طلعت على ال cross المقطع", "tokens": [10721, 15730, 18871, 16254, 497, 13672, 1829, 39896, 9154, 17182, 5296, 34762, 2423, 9654, 4872, 38637, 2655, 995, 39894, 32887, 5016, 9154, 17182, 5296, 17741, 4032, 41435, 18871, 16254, 13672, 1829, 39896, 11933, 15730, 23032, 1211, 34268, 15844, 2423, 3278, 9673, 47432, 3615], "avg_logprob": -0.4723011431368915, "compression_ratio": 1.3333333333333333, "no_speech_prob": 2.3245811462402344e-06, "words": [{"start": 283.63, "end": 283.91, "word": "أذا", "probability": 0.41436767578125}, {"start": 283.91, "end": 284.23, "word": " عندي", "probability": 0.691162109375}, {"start": 284.23, "end": 284.59, "word": " R", "probability": 0.495361328125}, {"start": 284.59, "end": 284.87, "word": " اللي", "probability": 0.36029052734375}, {"start": 284.87, "end": 284.97, "word": " هي", "probability": 0.83837890625}, {"start": 284.97, 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{"start": 946.08, "end": 946.46, "word": " مجنته", "probability": 0.670166015625}, {"start": 946.46, "end": 946.66, "word": " تبع", "probability": 0.8291015625}, {"start": 946.66, "end": 946.86, "word": " R", "probability": 0.787109375}, {"start": 946.86, "end": 947.32, "word": " hat", "probability": 0.958984375}, {"start": 947.32, "end": 947.6, "word": " في", "probability": 0.8994140625}, {"start": 947.6, "end": 948.28, "word": " cos", "probability": 0.41015625}, {"start": 948.28, "end": 949.32, "word": " θ،", "probability": 0.581787109375}, {"start": 949.32, "end": 949.74, "word": " فإذا", "probability": 0.8404947916666666}, {"start": 949.74, "end": 950.26, "word": " الإسقاط", "probability": 0.9830322265625}, {"start": 950.26, "end": 950.68, "word": " تبعها", "probability": 0.8822021484375}, {"start": 950.68, "end": 950.96, "word": " على", "probability": 0.896484375}, {"start": 950.96, "end": 951.74, "word": " الدائرة", "probability": 0.99462890625}, {"start": 951.74, "end": 952.0, 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العلاقة بين هدول ال unit vectors هلاقي ان R هتقولنا sin θ cos في x hat sin θ sin في y hat ذات cos θ z hat بينما ال z hat ايش هنلاقيها cos θ cos في cos θ sin في minus sin θ z hat الفي هت هتكون minus في x hat ذات cos في y hat", "tokens": [28814, 15730, 18863, 15040, 28671, 49374, 8032, 3215, 12610, 2423, 4985, 18875, 8032, 15040, 38436, 16472, 497, 8032, 2655, 39648, 8315, 3343, 12622, 3792, 8978, 2031, 2385, 3343, 12622, 3343, 8978, 288, 2385, 29910, 9307, 3792, 12622, 710, 2385, 49374, 15042, 2423, 710, 2385, 1975, 1829, 8592, 8032, 1863, 15040, 38436, 11296, 3792, 12622, 3792, 8978, 3792, 12622, 3343, 8978, 3175, 3343, 12622, 710, 2385, 27188, 1829, 8032, 2655, 8032, 2655, 30544, 3175, 8978, 2031, 2385, 29910, 9307, 3792, 8978, 288, 2385], "avg_logprob": -0.3484563389456416, "compression_ratio": 1.819767441860465, "no_speech_prob": 0.0, "words": [{"start": 1057.1, "end": 1057.34, "word": "إذا", "probability": 0.421661376953125}, {"start": 1057.34, "end": 1057.98, "word": " العلاقة", 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Sine Phi Theta Hat زائد Cosine Phi Phi Hat وAZ هتكون Cosine Theta Arhat minus Sine Theta Theta Hat", "tokens": [3555, 6027, 1863, 35457, 3660, 24976, 1783, 8978, 11778, 47341, 3660, 2423, 9640, 3224, 9307, 16070, 12984, 36081, 40294, 9307, 16070, 5172, 47302, 3224, 9307, 8032, 2655, 30544, 2423, 1783, 8032, 2655, 3555, 3615, 18871, 318, 533, 334, 7664, 15855, 533, 41435, 1587, 15178, 30767, 16373, 3215, 15855, 533, 334, 7664, 15855, 533, 41435, 334, 7664, 15867, 3175, 318, 533, 41435, 41435, 15867, 2423, 398, 2385, 8032, 2655, 30544, 318, 533, 334, 7664, 318, 533, 41435, 1587, 15178, 30767, 16373, 3215, 15855, 533, 334, 7664, 318, 533, 41435, 334, 7664, 15867, 30767, 16373, 3215, 15855, 533, 41435, 41435, 15867, 4032, 32, 57, 8032, 2655, 30544, 15855, 533, 334, 7664, 1587, 15178, 3175, 318, 533, 334, 7664, 334, 7664, 15867], "avg_logprob": -0.2389322894314925, "compression_ratio": 2.1467391304347827, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 1083.83, "end": 1084.37, 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"probability": 0.9921875}, {"start": 1254.12, "end": 1254.28, "word": " ال", "probability": 0.93798828125}, {"start": 1254.28, "end": 1254.68, "word": " matrix", "probability": 0.9755859375}], "temperature": 1.0}, {"id": 52, "seek": 127832, "start": 1256.54, "end": 1278.32, "text": "هيكون عند الـ sin θ cos φ cos θ cos φ minus sin فى دلالة اللى هي ar a θ a فى ال equation التانية اللى هي ay تسوى sin θ sin فى ar cos θ sin فى a θ cos فى a فى واخر المعادلة هي az تسوى cos θ ar minus sin θ a θ", "tokens": [3224, 1829, 30544, 43242, 2423, 39184, 3343, 12622, 3792, 17579, 3792, 12622, 3792, 17579, 3175, 3343, 6156, 7578, 11778, 1211, 6027, 3660, 13672, 7578, 39896, 594, 257, 12622, 257, 6156, 7578, 2423, 5367, 16712, 7649, 10632, 13672, 7578, 39896, 7494, 6055, 3794, 2407, 7578, 3343, 12622, 3343, 6156, 7578, 594, 3792, 12622, 3343, 6156, 7578, 257, 12622, 3792, 6156, 7578, 257, 6156, 7578, 4032, 47283, 2288, 9673, 3615, 18513, 37977, 39896, 7883, 6055, 3794, 2407, 7578, 3792, 12622, 594, 3175, 3343, 12622, 257, 12622], "avg_logprob": -0.3801470518112183, "compression_ratio": 1.7839506172839505, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1256.54, "end": 1256.94, "word": "هيكون", "probability": 0.6702473958333334}, {"start": 1256.94, "end": 1257.14, "word": " عند", "probability": 0.9384765625}, {"start": 1257.14, "end": 1257.34, "word": " الـ", "probability": 0.23834228515625}, {"start": 1257.34, "end": 1257.46, "word": " sin", "probability": 0.4423828125}, {"start": 1257.46, "end": 1257.8, "word": " θ", "probability": 0.55810546875}, {"start": 1257.8, "end": 1258.06, "word": " cos", "probability": 0.87353515625}, {"start": 1258.06, "end": 1258.66, "word": " φ", "probability": 0.322998046875}, {"start": 1258.66, "end": 1259.06, "word": " cos", "probability": 0.68115234375}, {"start": 1259.06, "end": 1259.68, "word": " θ", "probability": 0.9599609375}, {"start": 1259.68, "end": 1259.92, "word": " cos", "probability": 0.841796875}, {"start": 1259.92, "end": 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inverse ل ال matrix اللي هي بالصفة بهذا الشكل اللي هي sin theta cos phi sin theta sin phi cos phi minus cos theta cos phi sin theta sin phi minus sin theta minus sin phi cos phi اذا لو انا بدي اكون او كنت عارف ال ax ay ez و بدي اكتب ar a theta a phi", "tokens": [3615, 8592, 7649, 1975, 7435, 1829, 3555, 45164, 9122, 29399, 1975, 8315, 6225, 9640, 5172, 3660, 2423, 22478, 42434, 15670, 1975, 2407, 4724, 16254, 1975, 7435, 1829, 3555, 2423, 37300, 15670, 1975, 1829, 8592, 4724, 38436, 1975, 25957, 1211, 4724, 32887, 5016, 3224, 1975, 8315, 3714, 24401, 3215, 2423, 17340, 5296, 2423, 8141, 13672, 1829, 39896, 20666, 9381, 5172, 3660, 39627, 15730, 25124, 28820, 13672, 1829, 39896, 3343, 9725, 3792, 13107, 3343, 9725, 3343, 13107, 3792, 13107, 3175, 3792, 9725, 3792, 13107, 3343, 9725, 3343, 13107, 3175, 3343, 9725, 3175, 3343, 13107, 3792, 13107, 1975, 15730, 45164, 1975, 8315, 4724, 16254, 1975, 30544, 1975, 2407, 9122, 29399, 6225, 9640, 5172, 2423, 6360, 7494, 25220, 4032, 4724, 16254, 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hat, phi hat dot Y hat, phi hat dot Z hat", "tokens": [3224, 2655, 30544, 23032, 3555, 3615, 995, 5893, 1674, 9154, 497, 2385, 4032, 1783, 2385, 11, 497, 2385, 4032, 398, 2385, 11, 497, 2385, 4032, 1176, 2385, 8032, 3215, 12610, 9673, 33753, 2407, 7578, 6055, 3555, 3615, 2423, 8141, 316, 9725, 2385, 5893, 1783, 2385, 11, 9725, 2385, 5893, 398, 2385, 11, 9725, 2385, 5893, 1176, 2385, 11, 13107, 2385, 5893, 1783, 2385, 11, 13107, 2385, 5893, 398, 2385, 11, 13107, 2385, 5893, 1176, 2385], "avg_logprob": -0.246916132930078, "compression_ratio": 1.8432835820895523, "no_speech_prob": 0.0, "words": [{"start": 1309.33, "end": 1309.79, "word": "هتكون", "probability": 0.6558430989583334}, {"start": 1309.79, "end": 1310.13, "word": " طبعا", "probability": 0.7738037109375}, {"start": 1310.13, "end": 1310.35, "word": " dot", "probability": 0.31298828125}, {"start": 1310.35, "end": 1310.73, "word": " product", "probability": 0.892578125}, {"start": 1310.73, "end": 1310.89, "word": " من", 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{"start": 1314.35, "end": 1314.43, "word": " و", "probability": 0.67919921875}, {"start": 1314.43, "end": 1314.53, "word": " Z", "probability": 0.80859375}, {"start": 1314.53, "end": 1315.07, "word": " hat", "probability": 0.9794921875}, {"start": 1315.07, "end": 1315.59, "word": " هدول", "probability": 0.8680013020833334}, {"start": 1315.59, "end": 1316.29, "word": " المحتوى", "probability": 0.90283203125}, {"start": 1316.29, "end": 1316.51, "word": " تبع", "probability": 0.84033203125}, {"start": 1316.51, "end": 1316.65, "word": " ال", "probability": 0.91015625}, {"start": 1316.65, "end": 1317.09, "word": " matrix", "probability": 0.86083984375}, {"start": 1317.09, "end": 1317.79, "word": " A", "probability": 0.2186279296875}, {"start": 1317.79, "end": 1318.31, "word": " theta", "probability": 0.5830078125}, {"start": 1318.31, "end": 1318.73, "word": " hat", "probability": 0.92578125}, {"start": 1318.73, "end": 1319.01, "word": " dot", "probability": 0.892578125}, {"start": 1319.01, 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phi", "probability": 0.459228515625}, {"start": 1323.51, "end": 1323.73, "word": " hat", "probability": 0.9814453125}, {"start": 1323.73, "end": 1323.93, "word": " dot", "probability": 0.92822265625}, {"start": 1323.93, "end": 1324.19, "word": " X", "probability": 0.9619140625}, {"start": 1324.19, "end": 1324.41, "word": " hat,", "probability": 0.98779296875}, {"start": 1324.51, "end": 1324.63, "word": " phi", "probability": 0.89404296875}, {"start": 1324.63, "end": 1324.83, "word": " hat", "probability": 0.98193359375}, {"start": 1324.83, "end": 1324.99, "word": " dot", "probability": 0.94580078125}, {"start": 1324.99, "end": 1325.19, "word": " Y", "probability": 0.990234375}, {"start": 1325.19, "end": 1325.45, "word": " hat,", "probability": 0.9873046875}, {"start": 1325.53, "end": 1325.69, "word": " phi", "probability": 0.88623046875}, {"start": 1325.69, "end": 1325.87, "word": " hat", "probability": 0.9833984375}, {"start": 1325.87, "end": 1326.05, "word": " dot", "probability": 0.9560546875}, {"start": 1326.05, "end": 1326.31, "word": " Z", "probability": 0.96875}, {"start": 1326.31, "end": 1326.91, "word": " hat", "probability": 0.98779296875}], "temperature": 1.0}, {"id": 55, "seek": 136059, "start": 1332.57, "end": 1360.59, "text": "الاخر حاجة اللى هو ال transformation بين ال cylindrical و ال spherical coordinate انا هتركه لكم إياه as a task جيبوه اللقاء القادر تستعينوا باللي احنا اتعلمناه مش هيكون اي حاجة جديدة ان ال spherical هي ال theta hat و ال r hat و ال phi hat ال cylindrical يعني ال raw hat يعني هتلاقوا كمان نقاط أسهل بكتير ان ال raw hat و ال phi hat و ال z hat", "tokens": [6027, 47283, 2288, 11331, 26108, 3660, 13672, 7578, 31439, 2423, 9887, 49374, 2423, 28044, 15888, 4032, 2423, 37300, 15670, 1975, 8315, 8032, 2655, 31747, 3224, 5296, 24793, 11933, 25528, 3224, 382, 257, 5633, 10874, 1829, 3555, 2407, 3224, 13672, 4587, 16606, 25062, 18513, 2288, 6055, 14851, 3615, 9957, 14407, 20666, 20292, 1975, 5016, 8315, 1975, 2655, 3615, 19528, 8315, 3224, 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"probability": 0.8486328125}, {"start": 1347.91, "end": 1348.27, "word": " r", "probability": 0.45361328125}, {"start": 1348.27, "end": 1348.53, "word": " hat", "probability": 0.95166015625}, {"start": 1348.53, "end": 1348.69, "word": " و", "probability": 0.978515625}, {"start": 1348.69, "end": 1348.77, "word": " ال", "probability": 0.8154296875}, {"start": 1348.77, "end": 1348.95, "word": " phi", "probability": 0.58544921875}, {"start": 1348.95, "end": 1349.33, "word": " hat", "probability": 0.98583984375}, {"start": 1349.33, "end": 1350.07, "word": " ال", "probability": 0.78955078125}, {"start": 1350.07, "end": 1350.65, "word": " cylindrical", "probability": 0.91015625}, {"start": 1350.65, "end": 1350.97, "word": " يعني", "probability": 0.718505859375}, {"start": 1350.97, "end": 1351.75, "word": " ال", "probability": 0.496337890625}, {"start": 1351.75, "end": 1352.05, "word": " raw", "probability": 0.59912109375}, {"start": 1352.05, "end": 1352.53, "word": " hat", "probability": 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{"start": 1358.31, "end": 1359.57, "word": " phi", "probability": 0.75927734375}, {"start": 1359.57, "end": 1359.95, "word": " hat", "probability": 0.984375}, {"start": 1359.95, "end": 1360.11, "word": " و", "probability": 0.98046875}, {"start": 1360.11, "end": 1360.19, "word": " ال", "probability": 0.73974609375}, {"start": 1360.19, "end": 1360.31, "word": " z", "probability": 0.96435546875}, {"start": 1360.31, "end": 1360.59, "word": " hat", "probability": 0.97900390625}], "temperature": 1.0}, {"id": 56, "seek": 137945, "start": 1362.15, "end": 1379.45, "text": "أنه في علاقة واضحة الـ Phi hat و ال Z hat و ال Raw hat تقريبا بتشابهوا في بين الـ cylindrical و ال spherical الاختلاف اللى هى ال theta و ال R ال Raw hat اللى هى الإسقاط تبع ال R في اللى هى المقطع أو ال growth section تبع الاسفير", "tokens": [33456, 3224, 8978, 11203, 995, 28671, 4032, 46958, 5016, 3660, 2423, 39184, 41435, 2385, 4032, 2423, 1176, 2385, 4032, 2423, 23732, 2385, 6055, 4587, 16572, 3555, 995, 39894, 8592, 16758, 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{"start": 1363.85, "end": 1364.13, "word": " hat", "probability": 0.83837890625}, {"start": 1364.13, "end": 1364.29, "word": " و", "probability": 0.521484375}, {"start": 1364.29, "end": 1364.37, "word": " ال", "probability": 0.41748046875}, {"start": 1364.37, "end": 1364.55, "word": " Z", "probability": 0.3701171875}, {"start": 1364.55, "end": 1364.99, "word": " hat", "probability": 0.96337890625}, {"start": 1364.99, "end": 1365.15, "word": " و", "probability": 0.9150390625}, {"start": 1365.15, "end": 1365.23, "word": " ال", "probability": 0.9609375}, {"start": 1365.23, "end": 1365.35, "word": " Raw", "probability": 0.217041015625}, {"start": 1365.35, "end": 1365.75, "word": " hat", "probability": 0.962890625}, {"start": 1365.75, "end": 1366.69, "word": " تقريبا", "probability": 0.9611328125}, {"start": 1366.69, "end": 1367.45, "word": " بتشابهوا", "probability": 0.746923828125}, {"start": 1367.45, "end": 1367.57, "word": " في", "probability": 0.6689453125}, {"start": 1367.57, "end": 1367.89, "word": " بين", "probability": 0.87255859375}, {"start": 1367.89, "end": 1368.19, "word": " الـ", "probability": 0.379150390625}, {"start": 1368.19, "end": 1368.45, "word": " cylindrical", "probability": 0.75244140625}, {"start": 1368.45, "end": 1368.61, "word": " و", "probability": 0.94140625}, {"start": 1368.61, "end": 1368.67, "word": " ال", "probability": 0.92236328125}, {"start": 1368.67, "end": 1369.03, "word": " spherical", "probability": 0.261962890625}, {"start": 1369.03, "end": 1370.05, "word": " الاختلاف", "probability": 0.72943115234375}, {"start": 1370.05, "end": 1370.23, "word": " اللى", "probability": 0.628662109375}, {"start": 1370.23, "end": 1370.33, "word": " هى", "probability": 0.813232421875}, {"start": 1370.33, "end": 1370.51, "word": " ال", "probability": 0.76416015625}, {"start": 1370.51, "end": 1370.83, "word": " theta", "probability": 0.21337890625}, {"start": 1370.83, "end": 1371.35, "word": " و", "probability": 0.97021484375}, {"start": 1371.35, 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"probability": 0.80517578125}, {"start": 1748.32, "end": 1748.82, "word": " زي", "probability": 0.787109375}, {"start": 1748.82, "end": 1748.86, "word": " ما", "probability": 0.9482421875}, {"start": 1748.86, "end": 1749.02, "word": " احنا", "probability": 0.95654296875}, {"start": 1749.02, "end": 1749.5, "word": " شوفناها", "probability": 0.8511962890625}, {"start": 1749.5, "end": 1749.62, "word": " في", "probability": 0.8857421875}, {"start": 1749.62, "end": 1749.7, "word": " ال", "probability": 0.484619140625}, {"start": 1749.7, "end": 1749.9, "word": " slide", "probability": 0.55029296875}], "temperature": 1.0}, {"id": 73, "seek": 176849, "start": 1751.61, "end": 1768.49, "text": "أخد الفرق ما بين R2-R1 وعمل التربية تظهر معايا D تربية تسوى R2 تربية زاد R1 تربية minus 2R1R2 cos 6R2 cos 6R1 minus 2R1R2 sin 6R2 sin 6R1 cos 5R2-1", "tokens": [10721, 9778, 3215, 27188, 2288, 4587, 19446, 49374, 497, 17, 12, 49, 16, 4032, 25957, 1211, 16712, 25513, 10632, 6055, 19913, 3224, 2288, 20449, 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minus", "probability": 0.5546875}, {"start": 1760.27, "end": 1761.31, "word": " 2R1R2", "probability": 0.81943359375}, {"start": 1761.31, "end": 1761.53, "word": " cos", "probability": 0.1912841796875}, {"start": 1761.53, "end": 1762.13, "word": " 6R2", "probability": 0.6959635416666666}, {"start": 1762.13, "end": 1762.35, "word": " cos", "probability": 0.7138671875}, {"start": 1762.35, "end": 1763.11, "word": " 6R1", "probability": 0.9251302083333334}, {"start": 1763.11, "end": 1763.79, "word": " minus", "probability": 0.91015625}, {"start": 1763.79, "end": 1765.15, "word": " 2R1R2", "probability": 0.963671875}, {"start": 1765.15, "end": 1765.41, "word": " sin", "probability": 0.68701171875}, {"start": 1765.41, "end": 1765.91, "word": " 6R2", "probability": 0.98046875}, {"start": 1765.91, "end": 1766.11, "word": " sin", "probability": 0.873046875}, {"start": 1766.11, "end": 1766.79, "word": " 6R1", "probability": 0.9635416666666666}, {"start": 1766.79, "end": 1767.31, "word": " cos", 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اكتبه بكل ال components وبالتالي بقدر اعمل ليه ال distance vector منتهى البساطة لذا انها لقيتها two tasks بدنا نسلمهم اللقاء القادم في اي استفسار لحد هنا؟", "tokens": [2655, 15042, 2304, 22807, 5296, 15730, 1975, 5016, 8315, 6225, 9640, 5172, 9957, 2423, 1168, 8062, 1975, 4117, 2655, 3555, 3224, 4724, 28820, 2423, 6677, 46599, 6027, 2655, 6027, 1829, 4724, 28543, 2288, 1975, 25957, 1211, 32239, 3224, 2423, 4560, 8062, 9154, 47395, 7578, 29739, 3794, 41193, 3660, 5296, 15730, 16472, 11296, 5296, 4587, 36081, 11296, 732, 9608, 47525, 8315, 8717, 3794, 19528, 16095, 13672, 4587, 16606, 25062, 18513, 2304, 8978, 1975, 1829, 44713, 36178, 9640, 5296, 24401, 34105, 22807], "avg_logprob": -0.28935185185185186, "compression_ratio": 1.5396039603960396, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 1800.92, "end": 1801.72, "word": "تمام؟", "probability": 0.4755859375}, {"start": 1801.72, "end": 1801.96, "word": " لذا", "probability": 0.520751953125}, {"start": 1801.96, "end": 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2104.82, "end": 2105.04, "word": " اللي", "probability": 0.873779296875}, {"start": 2105.04, "end": 2105.18, "word": " هو", "probability": 0.982421875}, {"start": 2105.18, "end": 2105.58, "word": " قيمة", "probability": 0.9921875}, {"start": 2105.58, "end": 2105.76, "word": " ال", "probability": 0.90869140625}, {"start": 2105.76, "end": 2106.0, "word": " X", "probability": 0.5927734375}, {"start": 2106.0, "end": 2106.6, "word": " وY", "probability": 0.5733642578125}, {"start": 2106.6, "end": 2106.98, "word": " وZ", "probability": 0.81591796875}, {"start": 2106.98, "end": 2107.26, "word": " هاي", "probability": 0.6181640625}, {"start": 2107.26, "end": 2107.38, "word": " ال", "probability": 0.9794921875}, {"start": 2107.38, "end": 2107.72, "word": " point", "probability": 0.986328125}, {"start": 2107.72, "end": 2108.96, "word": " هو", "probability": 0.6142578125}, {"start": 2108.96, "end": 2109.38, "word": " يعطيني", "probability": 0.695556640625}, {"start": 2109.38, "end": 2109.92, "word": " نقطة", "probability": 0.9908854166666666}, {"start": 2109.92, "end": 2110.12, "word": " اللي", "probability": 0.93017578125}, {"start": 2110.12, "end": 2110.26, "word": " هي", "probability": 0.5458984375}, {"start": 2110.26, "end": 2110.52, "word": " لها", "probability": 0.56353759765625}, {"start": 2110.52, "end": 2110.88, "word": " position", "probability": 0.70068359375}, {"start": 2110.88, "end": 2111.4, "word": " vector", "probability": 0.9697265625}, {"start": 2111.4, "end": 2111.94, "word": " و", "probability": 0.93408203125}, {"start": 2111.94, "end": 2112.18, "word": " vector", "probability": 0.962890625}, {"start": 2112.18, "end": 2112.68, "word": " تاني", "probability": 0.9427083333333334}, {"start": 2112.68, "end": 2112.9, "word": " E", "probability": 0.275634765625}, {"start": 2112.9, "end": 2113.02, "word": " اللي", "probability": 0.749755859375}, {"start": 2113.02, "end": 2113.18, "word": " مافيه", "probability": 0.552490234375}, {"start": 2113.18, "end": 2113.58, "word": " شلقة", "probability": 0.6292317708333334}, {"start": 2113.58, "end": 2113.98, "word": " فيه", "probability": 0.70849609375}], "temperature": 1.0}, {"id": 88, "seek": 214380, "start": 2114.44, "end": 2143.8, "text": "بنقوله what's component احنا أسهل الحاجة انه متذكره احنا مشينا لهذه ال matrix", "tokens": [3555, 1863, 39648, 3224, 437, 311, 6542, 1975, 5016, 8315, 5551, 3794, 3224, 1211, 21542, 26108, 3660, 16472, 3224, 44650, 8848, 37983, 3224, 1975, 5016, 8315, 37893, 1829, 8315, 46740, 24192, 2423, 8141], "avg_logprob": -0.48851101188098683, "compression_ratio": 1.110091743119266, "no_speech_prob": 4.172325134277344e-07, "words": [{"start": 2114.44, "end": 2114.88, "word": "بنقوله", "probability": 0.5340118408203125}, {"start": 2114.88, "end": 2115.16, "word": " what's", "probability": 0.6007080078125}, {"start": 2115.16, "end": 2115.64, "word": " component", "probability": 0.37890625}, {"start": 2115.64, "end": 2140.32, "word": " احنا", "probability": 0.4899088541666667}, {"start": 2140.32, "end": 2140.64, "word": " أسهل", "probability": 0.819091796875}, {"start": 2140.64, "end": 2140.94, "word": " الحاجة", "probability": 0.8416341145833334}, {"start": 2140.94, "end": 2141.36, "word": " انه", "probability": 0.4005126953125}, {"start": 2141.36, "end": 2142.3, "word": " متذكره", "probability": 0.65313720703125}, {"start": 2142.3, "end": 2142.56, "word": " احنا", "probability": 0.7799479166666666}, {"start": 2142.56, "end": 2143.08, "word": " مشينا", "probability": 0.8746744791666666}, {"start": 2143.08, "end": 2143.4, "word": " لهذه", "probability": 0.833984375}, {"start": 2143.4, "end": 2143.5, "word": " ال", "probability": 0.88134765625}, {"start": 2143.5, "end": 2143.8, "word": " matrix", "probability": 0.83154296875}], "temperature": 1.0}, {"id": 89, "seek": 216340, "start": 2146.28, "end": 2163.4, "text": "أحنا قولنا أي vector بواطر أكتبه بدلالة اللي هو ال vector اللي بت X, Y, Z ال matrix بتاعة اللي بتربط ال X component بال raw component بال X component و ال Phi component بال Y component و Z component", "tokens": [10721, 5016, 8315, 12174, 12610, 8315, 36632, 8062, 4724, 2407, 41193, 2288, 5551, 4117, 2655, 3555, 3224, 47525, 1211, 6027, 3660, 13672, 1829, 31439, 2423, 8062, 13672, 1829, 39894, 1783, 11, 398, 11, 1176, 2423, 8141, 39894, 995, 27884, 13672, 1829, 39894, 25513, 9566, 2423, 1783, 6542, 20666, 8936, 6542, 20666, 1783, 6542, 4032, 2423, 41435, 6542, 20666, 398, 6542, 4032, 1176, 6542], "avg_logprob": -0.2607421902939677, "compression_ratio": 1.7532467532467533, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 2146.28, "end": 2146.5, "word": "أحنا", "probability": 0.7154947916666666}, {"start": 2146.5, "end": 2146.82, "word": " قولنا", "probability": 0.8196614583333334}, {"start": 2146.82, "end": 2147.14, "word": " أي", "probability": 0.583984375}, {"start": 2147.14, "end": 2147.68, "word": " vector", "probability": 0.83056640625}, {"start": 2147.68, "end": 2148.1, "word": " بواطر", 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0.58837890625}, {"start": 2154.6, "end": 2154.98, "word": " matrix", "probability": 0.5263671875}, {"start": 2154.98, "end": 2155.32, "word": " بتاعة", "probability": 0.7701822916666666}, {"start": 2155.32, "end": 2155.46, "word": " اللي", "probability": 0.9794921875}, {"start": 2155.46, "end": 2155.88, "word": " بتربط", "probability": 0.9571940104166666}, {"start": 2155.88, "end": 2156.02, "word": " ال", "probability": 0.82373046875}, {"start": 2156.02, "end": 2156.22, "word": " X", "probability": 0.92626953125}, {"start": 2156.22, "end": 2156.9, "word": " component", "probability": 0.94091796875}, {"start": 2156.9, "end": 2157.98, "word": " بال", "probability": 0.61865234375}, {"start": 2157.98, "end": 2158.52, "word": " raw", "probability": 0.38134765625}, {"start": 2158.52, "end": 2159.0, "word": " component", "probability": 0.9775390625}, {"start": 2159.0, "end": 2159.2, "word": " بال", "probability": 0.95947265625}, {"start": 2159.2, "end": 2159.44, "word": " X", "probability": 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2187.78, "text": "وهي عبارة عن كمبونات ال matrix رو hat dot x hat رو hat dot y hat رو hat dot z hat وهكذا فهذه أسهل حاجة لأنك انت هتلاقي حاجة بالاخر وسط في مداها وانت بدك تجيبي هذا ال vector من اللي هو ال Cartesian لاسم المركز فهذه الفرق بين النقطة و ال vector", "tokens": [2407, 3224, 1829, 6225, 3555, 9640, 3660, 18871, 9122, 2304, 3555, 2407, 8315, 2655, 2423, 8141, 12602, 2407, 2385, 5893, 2031, 2385, 12602, 2407, 2385, 5893, 288, 2385, 12602, 2407, 2385, 5893, 710, 2385, 37037, 4117, 15730, 6156, 3224, 24192, 5551, 3794, 3224, 1211, 11331, 26108, 3660, 5296, 33456, 4117, 16472, 2655, 8032, 2655, 15040, 38436, 11331, 26108, 3660, 20666, 47283, 2288, 46952, 9566, 8978, 3714, 28259, 11296, 4032, 7649, 2655, 47525, 4117, 6055, 7435, 1829, 21292, 23758, 2423, 8062, 9154, 13672, 1829, 31439, 2423, 22478, 42434, 5296, 32277, 2304, 9673, 31747, 11622, 6156, 3224, 24192, 27188, 2288, 4587, 49374, 28239, 47432, 3660, 4032, 2423, 8062], "avg_logprob": -0.42114484532971247, 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"word": " coordinate", "probability": 0.76318359375}], "temperature": 1.0}, {"id": 107, "seek": 259423, "start": 2568.39, "end": 2594.23, "text": "إذا روحت على ال Cartesian coordinate XYZ عشان اللي القادم هعملها ال cylindrical و ال spherical إيش معنى constant coordinate؟ يعني إذا قلت أنا عندي في ال XYZ coordinate عندي Z دايما ثابتة، قيمة ثابتة، تلاتة فهداش بتمثلي ال plan بتمثلي ال plan اللي ال X و ال Y بتغيروا على طول و Z ثابتة اللي هو هذا ال plan شايفين هو هذا ال plan؟", "tokens": [28814, 15730, 12602, 2407, 33753, 15844, 2423, 22478, 42434, 15670, 48826, 57, 6225, 8592, 7649, 13672, 1829, 25062, 18513, 2304, 8032, 25957, 1211, 11296, 2423, 28044, 15888, 4032, 2423, 37300, 11933, 1829, 8592, 20449, 1863, 7578, 5754, 15670, 22807, 37495, 22653, 11933, 15730, 12174, 1211, 2655, 41850, 18871, 16254, 8978, 2423, 48826, 57, 15670, 18871, 16254, 1176, 11778, 47302, 15042, 38637, 16758, 2655, 3660, 12399, 12174, 32640, 3660, 38637, 16758, 2655, 3660, 12399, 6055, 1211, 9307, 3660, 6156, 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constant coordinate يعني قيمة الـ z component سابطة لو كانت x هي اللي سابطة حيكون عند الـ z بتتغير منصة infinity للواصلة infinity و ال y بتتغير منصة infinity للواصلة infinity هذا اللي بيعمل هذا اللي هي قيمة ال y سابطة ال x سابطة", "tokens": [3224, 15730, 3714, 6027, 3224, 5754, 15670, 37495, 22653, 12174, 32640, 3660, 2423, 39184, 710, 6542, 8608, 16758, 9566, 3660, 45164, 25961, 2655, 2031, 39896, 13672, 1829, 8608, 16758, 9566, 3660, 11331, 1829, 30544, 43242, 2423, 39184, 710, 39894, 2655, 17082, 13546, 9154, 9381, 3660, 13202, 24976, 2407, 33546, 37977, 13202, 4032, 2423, 288, 39894, 2655, 17082, 13546, 9154, 9381, 3660, 13202, 24976, 2407, 33546, 37977, 13202, 23758, 13672, 1829, 4724, 1829, 25957, 1211, 23758, 13672, 1829, 39896, 12174, 32640, 3660, 2423, 288, 8608, 16758, 9566, 3660, 2423, 2031, 8608, 16758, 9566, 3660], "avg_logprob": -0.3749999961954482, "compression_ratio": 2.0, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2594.9, "end": 2595.24, "word": 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يعني تكون واحدة من القيم ثابتة مهما تغيرت القنطين التانية و هيك يعطيكوا العافية و لقاء القدم ان شاء الله هشوف ال constant coordinate او يعني ان اخلي واحد القوانين ثابت في السفر الكلب و السندر الكلب يشوف القيامة يعطيكوا العافية ان شاء الله", "tokens": [6027, 39184, 1783, 12174, 32640, 3660, 38637, 16758, 2655, 3660, 4032, 2423, 39184, 398, 4032, 2423, 39184, 1176, 39894, 17082, 13546, 14407, 8978, 23758, 2423, 39184, 1393, 4032, 1975, 3615, 9566, 1829, 21542, 1829, 6027, 1829, 5754, 15670, 37495, 22653, 6055, 30544, 36764, 24401, 3660, 9154, 25062, 32640, 38637, 16758, 2655, 3660, 3714, 3224, 15042, 6055, 17082, 13546, 2655, 25062, 1863, 9566, 9957, 16712, 7649, 10632, 4032, 39896, 4117, 37495, 9566, 1829, 4117, 14407, 18863, 31845, 10632, 4032, 5296, 4587, 16606, 25062, 40448, 16472, 13412, 16606, 21984, 8032, 8592, 38688, 2423, 5754, 15670, 1975, 2407, 37495, 22653, 16472, 1975, 9778, 20292, 36764, 24401, 25062, 2407, 7649, 9957, 38637, 16758, 2655, 8978, 21136, 5172, 2288, 2423, 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او", "probability": 0.822265625}, {"start": 2634.46, "end": 2634.66, "word": " يعني", "probability": 0.952880859375}, {"start": 2634.66, "end": 2634.82, "word": " ان", "probability": 0.7783203125}, {"start": 2634.82, "end": 2635.16, "word": " اخلي", "probability": 0.923828125}, {"start": 2635.16, "end": 2635.48, "word": " واحد", "probability": 0.991455078125}, {"start": 2635.48, "end": 2635.94, "word": " القوانين", "probability": 0.531982421875}, {"start": 2635.94, "end": 2636.38, "word": " ثابت", "probability": 0.96142578125}, {"start": 2636.38, "end": 2636.5, "word": " في", "probability": 0.9111328125}, {"start": 2636.5, "end": 2636.8, "word": " السفر", "probability": 0.7591145833333334}, {"start": 2636.8, "end": 2637.18, "word": " الكلب", "probability": 0.6078287760416666}, {"start": 2637.18, "end": 2637.42, "word": " و", "probability": 0.8564453125}, {"start": 2637.42, "end": 2637.82, "word": " السندر", "probability": 0.736328125}, {"start": 2637.82, "end": 2638.08, "word": " 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/9u_8vIOnPD0.srt b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/9u_8vIOnPD0.srt
new file mode 100644
index 0000000000000000000000000000000000000000..3cd9190a4aa6a8ee73d0306da441508ea9d8d7e2
--- /dev/null
+++ b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/9u_8vIOnPD0.srt
@@ -0,0 +1,2015 @@
+1
+00:00:20,670 --> 00:00:22,930
+بسم الله الرحمن الرحيم السلام عليكم ورحمة الله
+
+2
+00:00:22,930 --> 00:00:27,650
+وبركاته إحنا في الاتحادات الماضية أو شابتر الأربع كان
+
+3
+00:00:27,650 --> 00:00:31,790
+متخصص  في الـ electric field في الـ space  الشبتر هذا 
+
+4
+00:00:31,790 --> 00:00:34,550
+هنتحكي عن الـ electric field في الـ material space،
+
+5
+00:00:34,550 --> 00:00:36,530
+يعني إيش بيصير لما الـ electric field يكون في قلب
+
+6
+00:00:36,530 --> 00:00:40,790
+material، بيمشي في قلب metal، في مواد electric،
+
+7
+00:00:40,790 --> 00:00:43,090
+صحيح الـ space إحنا بنعتبره حالة خاصة من ال
+
+8
+00:00:43,090 --> 00:00:47,050
+dielectric، الفرق في معامل الـ permittivity، ال
+
+9
+00:00:47,050 --> 00:00:49,330
+permittivity بتاعة الـ space هي epsilon node و
+
+10
+00:00:49,330 --> 00:00:52,870
+هنشوف كيف إنه بس الفرق إنه هتكون في عندنا معامل
+
+11
+00:00:52,870 --> 00:00:58,380
+خاص لـ dielectric materials، فإذا هنبدأ اليوم
+
+12
+00:00:58,380 --> 00:01:04,140
+electric field في الـ material space أولا بالنسبة 
+
+13
+00:01:04,140 --> 00:01:08,060
+لوضعية الـ material و علاقتها بالـ electric field
+
+14
+00:01:08,060 --> 00:01:12,620
+إحنا بنربطهم وسط خاصية الـ conductivity اللي هي 
+
+15
+00:01:12,620 --> 00:01:17,120
+التوصيلية sigma أخذناها حتى في الدوائر sigma 1 على
+
+16
+00:01:17,120 --> 00:01:22,240
+روح resistivity، فإذا إحنا بنصنف الـ material تبعا
+
+17
+00:01:22,240 --> 00:01:26,260
+للتوصيلية بتاعتها اللي هي sigma فبنصنفهم ل
+
+18
+00:01:26,260 --> 00:01:32,180
+conductors و non conductors موصلات و غير موصلات
+
+19
+00:01:32,180 --> 00:01:38,950
+أو بمعنى آخر بنسميهم metals و insulators، الـ metals
+
+20
+00:01:38,950 --> 00:01:42,230
+غالبا بتكون الـ conductive بتاعتهم عالية زي النحاس
+
+21
+00:01:42,230 --> 00:01:46,210
+يعني بتكون sigma مالها أكبر بكثير من واحد عالية ال
+
+22
+00:01:46,210 --> 00:01:49,910
+conductive بتاعتها، الـ insulators اللي زي الخشب و
+
+23
+00:01:49,910 --> 00:01:53,330
+الورق بيكون sigma مالها أقل بكثير من واحد و
+
+24
+00:01:53,330 --> 00:01:56,940
+المايكا و كل أنواع الـ insulators، طبعا في عندنا
+
+25
+00:01:56,940 --> 00:01:59,620
+materials تانية اللي هي زي الـ semiconductors اللي
+
+26
+00:01:59,620 --> 00:02:01,860
+هي ما بين الـ metal و الـ insulator و ال
+
+27
+00:02:01,860 --> 00:02:06,880
+superconductors اللي هي عبارة عن سبائك تم اكتشافها
+
+28
+00:02:06,880 --> 00:02:10,660
+خلال القرن الماضي اللي توصيليتها عالية جدا يعني ال
+
+29
+00:02:10,660 --> 00:02:15,640
+resistivity بتاعتها تقريبا 0، هذه تصنيف الـ materials
+
+30
+00:02:15,640 --> 00:02:19,760
+تبعا لـ الـ conductivity إحنا هنقود غالبا ما بين الـ
+
+31
+00:02:19,760 --> 00:02:20,720
+metals و الـ insulators
+
+32
+00:02:23,760 --> 00:02:26,860
+إحنا عرفنا kinds of currents واحد بنسميه الـ
+
+33
+00:02:26,860 --> 00:02:29,480
+convection current واحد بنسميه conduction current
+
+34
+00:02:29,480 --> 00:02:33,740
+الـ current بشكل عام قبل ما نميز بين الـ convection
+
+35
+00:02:33,740 --> 00:02:37,640
+و الـ conduction الـ current ممكن أخذتوها في الدوائر
+
+36
+00:02:37,640 --> 00:02:42,040
+برضه هو عبارة عن إيه كمية الـ charges اللي بتقطع
+
+37
+00:02:42,040 --> 00:02:46,820
+مساحة معينة فترة زمنية per unit time اللي ال
+
+38
+00:02:46,820 --> 00:02:50,260
+electric charging passing through the area per
+
+39
+00:02:50,260 --> 00:02:55,700
+unit time، يعني إن I هي DQ بDT إذا بتذكروا قلنا ال
+
+40
+00:02:55,700 --> 00:02:58,540
+current اللي علاقته بالـ charges و الـ voltage اللي
+
+41
+00:02:58,540 --> 00:03:02,160
+علاقته بالـ charges واحد اللي علاقته بالـ rate بتاعة ال
+
+42
+00:03:02,160 --> 00:03:06,220
+charge DQ بDT والتاني بقدرش بفصل الـ charges اللي
+
+43
+00:03:06,220 --> 00:03:13,420
+هي الـ voltage DW بDQ إذا التيار هو DQ بDT إذا كانت
+
+44
+00:03:13,420 --> 00:03:17,180
+الـ charge بال column و الـ time بال second بيكون ال
+
+45
+00:03:17,180 --> 00:03:21,320
+current بلقاس بالامبير، كمان إحنا لن نقدر نعرف اللي
+
+46
+00:03:21,320 --> 00:03:25,260
+هي current density J، current density معناه density
+
+47
+00:03:25,260 --> 00:03:29,580
+عن حاجة بالنسبة لـ area أو بالنسبة لـ volume إحنا
+
+48
+00:03:29,580 --> 00:03:33,160
+بنحكي عن current density بالنسبة لـ area ف J هي
+
+49
+00:03:33,160 --> 00:03:37,580
+عبارة عن delta I by delta S أو delta I إيش بتساوي J
+
+50
+00:03:37,580 --> 00:03:43,250
+في delta S، غالبا الـ current إحنا قلنا هي الـ current
+
+51
+00:03:43,250 --> 00:03:47,630
+هو عبارة عن الشحنات اللي بتمرق من الـ area الشحنات
+
+52
+00:03:47,630 --> 00:03:50,050
+اللي بتقطع واحدة الـ area لو أنا مثلا عندي الـ
+
+53
+00:03:50,050 --> 00:03:53,230
+circular الـ area بتاعتي زي هذا القلم وهي الـ
+
+54
+00:03:53,230 --> 00:03:56,610
+current ماشي في قلبه هلاحظ إنه دائما عمودي ماله
+
+55
+00:03:56,610 --> 00:04:01,190
+على اتجاهه و عمودي على cross section فالـ current
+
+56
+00:04:01,190 --> 00:04:06,150
+density ماله دائما عمودي على الـ surface، واضح شيء
+
+57
+00:04:06,150 --> 00:04:10,000
+بيصير تدفق الـ charges بيكون في هذا الاتجاه، هي
+
+58
+00:04:10,000 --> 00:04:13,180
+تخيلوا هذا الـ metal أو الـ dielectric و الـ charges
+
+59
+00:04:13,180 --> 00:04:16,980
+بتمر في هيك أو يعني هيك أو هيك مش فارق أنا بس
+
+60
+00:04:16,980 --> 00:04:19,600
+تخيلوا الـ charges كمية الـ charges اللي بتقطع ال
+
+61
+00:04:19,600 --> 00:04:24,780
+unit area اللي هي الدائرة بالزمن هي اتجاه ال
+
+62
+00:04:24,780 --> 00:04:26,800
+current أو الـ current density هنلاقي دائما الـ
+
+63
+00:04:26,800 --> 00:04:30,400
+current density اللي ماله عمودي على اتجاه الـ area
+
+64
+00:04:32,070 --> 00:04:36,050
+إذا عندي delta I إيش بتساوي J delta S لأن J هي
+
+65
+00:04:36,050 --> 00:04:38,890
+عبارة عن الـ mean للـ current density يعني delta I
+
+66
+00:04:38,890 --> 00:04:44,250
+على delta S، إذا اتفقنا إن J هي vector عمودي على ال
+
+67
+00:04:44,250 --> 00:04:49,850
+area إذا هيكون delta I إيش بتساوي J dot DS، J dot
+
+68
+00:04:49,850 --> 00:04:54,110
+DS وإحنا أصلا أخذنا إن الـ S ماله الـ unit vector
+
+69
+00:04:54,110 --> 00:04:57,870
+تبعها عمودي عليها برضه، عشان هيك إحنا قلنا dot
+
+70
+00:04:57,870 --> 00:05:01,410
+product إذا الـ DS الـ unit vector العمودي عليها و
+
+71
+00:05:01,410 --> 00:05:05,890
+الـ J عمودي على الـ area إذا الـ J في delta S و عبارة
+
+72
+00:05:05,890 --> 00:05:12,810
+عن J dot DS واضح؟ as vectors، طيب
+
+73
+00:05:12,810 --> 00:05:19,490
+الـ total current I هذا الـ delta الـ total current
+
+74
+00:05:19,490 --> 00:05:24,570
+اللي هيكون التكامل على الـ surface J dot DS، واضح؟
+
+75
+00:05:28,740 --> 00:05:31,880
+طب إحنا قلنا إنه في فرق ما بين two currents
+
+76
+00:05:31,880 --> 00:05:36,060
+إحنا هنا عرفنا الـ current و current density و إحنا
+
+77
+00:05:36,060 --> 00:05:39,240
+بدنا نعرف اللي هو الـ current إنه ثلاثة أنواع من الـ
+
+78
+00:05:39,240 --> 00:05:42,500
+currents اللي هيمروا عليكم في مغناطيسية الكهرومغناطيسية
+
+79
+00:05:42,500 --> 00:05:46,280
+أهم واحد الأول أو الأول والثاني هم ال
+
+80
+00:05:46,280 --> 00:05:49,380
+convection الـ conduction و الـ displacement، فهذا
+
+81
+00:05:49,380 --> 00:05:51,800
+الشابتر إحنا بس هنحكي عن convection أو الفرق ما
+
+82
+00:05:51,800 --> 00:05:55,490
+بين convection و conduction، this placement هتكون في
+
+83
+00:05:55,490 --> 00:06:06,930
+شباتر لاحقة في شابتر 9 اللي هتاخذوه في كهرباء 2 طبعا
+
+84
+00:06:06,930 --> 00:06:09,290
+إيش الفرق بين convection و conduction؟ الـ
+
+85
+00:06:09,290 --> 00:06:13,950
+convection مالوش علاقة بـ conductor مالوش علاقة بإنه
+
+86
+00:06:13,950 --> 00:06:18,130
+تيار بيمر في conductor ولا بيحقق ohms law، ال
+
+87
+00:06:18,130 --> 00:06:19,610
+convection لا مربوط
+
+88
+00:06:30,030 --> 00:06:36,070
+هو عبارة عن مجموعات، هو عبارة عن التيار اللي بيتدفق
+
+89
+00:06:36,070 --> 00:06:40,470
+في المادة العازلة، بسخن مية بتدفق convection
+
+90
+00:06:40,470 --> 00:06:44,350
+current يعني مش heat دي، بس يعني إنه لو مثلا بدي
+
+91
+00:06:44,350 --> 00:06:49,210
+insulators على المية، بمر فيها تيار، هذا بنسميه
+
+92
+00:06:49,210 --> 00:06:54,100
+convection current، إذن هو عبارة عن التيار اللي بيمر
+
+93
+00:06:54,100 --> 00:06:57,500
+في مين؟ في الـ insulating media، إحنا قلنا طبيعة
+
+94
+00:06:57,500 --> 00:07:01,740
+المواد حسب الـ conductivity بنقسمها لـ metal وإيش؟
+
+95
+00:07:01,740 --> 00:07:05,920
+insulator، التيار بيمر في الـ insulators زي الـ liquid
+
+96
+00:07:05,920 --> 00:07:10,020
+الـ red gases، الـ vacuum هدول ماله اللي التيار
+
+97
+00:07:10,020 --> 00:07:15,900
+بيمروا فيهم بنسميه convection current لكن
+
+98
+00:07:16,760 --> 00:07:21,020
+حتى مثال عليها يعني قبل ما نروح للـ conduction مثال
+
+99
+00:07:21,020 --> 00:07:24,680
+عليها إذا بتذكروا الـ cathode ray tube أخذتوها يمكن
+
+100
+00:07:24,680 --> 00:07:28,500
+شفتوا الـ oscilloscope التلفزيونات بتاعة زمان، beam
+
+101
+00:07:28,500 --> 00:07:32,760
+الإلكترونات اللي كان بسقط على الشاشة عشان يحدد لنا
+
+102
+00:07:32,760 --> 00:07:37,820
+موقع الصورة، هذا بنسميه convection current لأنه مش
+
+103
+00:07:37,820 --> 00:07:41,020
+مربوط في الـ conductor و عبارة عن beam الإلكترونات
+
+104
+00:07:41,020 --> 00:07:46,520
+بتنطلق من اللي هو الـ cathode و بتتدفق لحين ما توصل
+
+105
+00:07:46,520 --> 00:07:50,520
+للشاشة بتاعة الـ cathode ray tube و بتحدد موقع
+
+106
+00:07:50,520 --> 00:07:53,260
+الصورة، هدول كلهم أمثلة على convection current
+
+107
+00:07:53,260 --> 00:07:59,960
+Electro net بلعشان قلناها قبل مرة فبنطلقها من cathode
+
+108
+00:07:59,960 --> 00:08:03,040
+بطريقة معينة اللي بفرض voltage حواليها هذا ال
+
+109
+00:08:03,040 --> 00:08:06,780
+cathode تطلق منه Electro net ممكن تنطلق في الهواء
+
+110
+00:08:06,780 --> 00:08:11,860
+في dielectric media، مهم إنها مادة عازلة هذا
+
+111
+00:08:11,860 --> 00:08:15,800
+بنسميه convection conduction، واضح إنه له علاقة
+
+112
+00:08:15,800 --> 00:08:22,700
+ماله بالكوندكتور عشان الموجودة علاقات ما بين ال
+
+113
+00:08:22,700 --> 00:08:27,120
+conduction current و current density و ohms law
+
+114
+00:08:27,120 --> 00:08:31,080
+بتبدا نبدأ نعرف الـ current المار في filament
+
+115
+00:08:31,080 --> 00:08:37,460
+هاي filament هي قطعة من metal و بتدفق عندها 
+
+116
+00:08:37,460 --> 00:08:44,770
+تيار بسرعة U، التيار تجاه الحط المتقطع بيمشي بسرعة U
+
+117
+00:08:44,770 --> 00:08:49,690
+U هي الـ velocity بتاعة الإلكترونات اللي بتمثل
+
+118
+00:08:49,690 --> 00:08:57,570
+الكورنت، إحنا عرفنا إن دلتا I إيش بتساوي أو يعني DI
+
+119
+00:08:57,570 --> 00:09:01,810
+بس إحنا بداخل دلتا I شوية أكبر من DI هي دلتا Q على
+
+120
+00:09:01,810 --> 00:09:07,380
+دلتا T، إذا عرفنا إن الـ charge density في هذا ال
+
+121
+00:09:07,380 --> 00:09:12,460
+filament، في هذا القطع من الـ metal، هي عبارة عن ρ و V،
+
+122
+00:09:12,460 --> 00:09:15,280
+فهذا الـ charge density رو V، إذا الـ total charge
+
+123
+00:09:15,280 --> 00:09:21,600
+هي رو V في الـ volume، صحيح؟ لو أخذنا element من ال
+
+124
+00:09:21,600 --> 00:09:25,120
+volume، هذا الـ element، هذا اللي محصور بين اللوحين
+
+125
+00:09:25,120 --> 00:09:30,170
+المقطعين، هذا الـ element أخذناه، هذا الـ volume هيكون
+
+126
+00:09:30,170 --> 00:09:32,970
+إيش الـ volume بيساوي؟ الـ area اللي هو مسميها delta
+
+127
+00:09:32,970 --> 00:09:38,030
+S اللي هو المربع ده في الطول، طول بيساوي ال
+
+128
+00:09:38,030 --> 00:09:41,430
+velocity في الزمن اللي هو delta Y مسميها أو delta
+
+129
+00:09:41,430 --> 00:09:48,620
+L هتكون سوا الـ velocity اللي هي U في T، معايا؟ إذا
+
+130
+00:09:48,620 --> 00:09:52,560
+إحنا خدنا هذا الـ delta volume اللي هو ما بين ال
+
+131
+00:09:52,560 --> 00:09:56,520
+two surfaces، هذا delta volume which charges to rho
+
+132
+00:09:56,520 --> 00:09:59,920
+V إذا total charge delta V ماهي ساوية؟ rho V في
+
+133
+00:09:59,920 --> 00:10:04,200
+delta V، delta V إيش هتكون؟ delta S اللي هي هذا ال
+
+134
+00:10:04,200 --> 00:10:10,120
+surface area في الطول متوازي الأضلاع أو يعني المكعب
+
+135
+00:10:10,120 --> 00:10:15,690
+هذا الطول ده إيش بيساوي؟ الـ Velocity في Delta T، لو
+
+136
+00:10:15,690 --> 00:10:18,710
+عملنا هيك Delta T بتروح من الطرفين من فوق و تحت
+
+137
+00:10:18,710 --> 00:10:24,230
+هيضل عند مين؟ رو V Delta S في U واضح؟ في S في ساعة
+
+138
+00:10:24,230 --> 00:10:28,410
+اللي حد هنا؟ إذا Delta I تتساوي رو V اللي هي ال
+
+139
+00:10:28,410 --> 00:10:31,890
+charge density في Delta S اللي هي الـ cross section
+
+140
+00:10:31,890 --> 00:10:35,070
+تبع الـ filament في U اللي هي Velocity بتاعتي
+
+141
+00:10:35,070 --> 00:10:38,090
+الإلكترونات اللي بتدفق عبر الـ filament
+
+142
+00:10:40,320 --> 00:10:43,100
+إحنا عرفنا الـ current density إنها delta I على
+
+143
+00:10:43,100 --> 00:10:46,120
+delta S، إذا الـ current density إيش بساويها، لو
+
+144
+00:10:46,120 --> 00:10:49,340
+قسمنا delta I على delta S، هتساوي charge density
+
+145
+00:10:49,340 --> 00:10:55,090
+في الـ volume state هتكون ρو V في U، إذا J بشكل عام
+
+146
+00:10:55,090 --> 00:10:57,410
+هدي J اللي هي في اتجاه الـ Y يعني هو أنا ماخذ
+
+147
+00:10:57,410 --> 00:11:00,730
+واحدة منهم مفترض إن كله في اتجاه الـ Y تدفق، فـ J
+
+148
+00:11:00,730 --> 00:11:04,490
+بشكل عام as a vector هي سوا رو في U اللي هي vector
+
+149
+00:11:04,490 --> 00:11:08,450
+رو الـ charge density مالها scalar، U ممكن تكون UX,
+
+150
+00:11:08,590 --> 00:11:14,990
+UI و Z فبشكل عام هتكون الـ charge density عبارة عن
+
+151
+00:11:14,990 --> 00:11:20,640
+رو V في UI، لو إحنا قلنا I هي الـ convection current
+
+152
+00:11:20,640 --> 00:11:24,320
+هيكون J هي الـ convection current density، لو قلنا
+
+153
+00:11:24,320 --> 00:11:27,720
+I هي الـ conduction current هتكون J هي الـ
+
+154
+00:11:27,720 --> 00:11:31,680
+conduction current per unit density، إذا كانت I
+
+155
+00:11:31,680 --> 00:11:36,320
+بالامبير J هتكون امبير بمتر تربيع لأن هي عبارة عن
+
+156
+00:11:36,320 --> 00:11:40,860
+current على area، إذا J بقدر أخدها دائما أربطها بأنها
+
+157
+00:11:40,860 --> 00:11:44,220
+current density بالـ velocity أو هي عبارة عن delta
+
+158
+00:11:44,220 --> 00:11:47,060
+I على delta S، تمام؟
+
+159
+00:11:51,920 --> 00:11:55,080
+نكمل تعريفنا لـ Ohm's law يعني إحنا قلنا الـ
+
+160
+00:11:55,080 --> 00:11:58,820
+conduction له علاقة بـ Ohm's law كمان مرة الـ
+
+161
+00:11:58,820 --> 00:12:02,540
+conductor conduction current بده conductor مابيمشيش
+
+162
+00:12:02,540 --> 00:12:03,260
+إلا في conductor
+
+163
+00:12:06,450 --> 00:12:10,150
+وبعبر عن الـ current بإن هو عبارة عن كمية هائلة من
+
+164
+00:12:10,150 --> 00:12:13,290
+الإلكترونات اللي بتتدفق عبر الـ cross-section
+
+165
+00:12:13,290 --> 00:12:17,910
+للكوندكتور في وحدة الزمن، فبتذكرين حتى قلنا إن ال
+
+166
+00:12:17,910 --> 00:12:21,350
+charges مالها discrete، إذا بتذكروا في الدوائر،
+
+167
+00:12:21,350 --> 00:12:25,670
+بينما الـ current ماله continuous، إذا الـ conductor
+
+168
+00:12:25,670 --> 00:12:28,030
+is characterized by a large amount of free
+
+169
+00:12:28,030 --> 00:12:30,350
+electrons that provide conduction current due to and
+
+170
+00:12:30,350 --> 00:12:31,290
+impressed electrically 
+
+171
+00:12:33,790 --> 00:12:37,690
+العلاقة لو كان عند الـ conductor في وجود electric
+
+172
+00:12:37,690 --> 00:12:41,270
+field هدول الإلكترونات الموجودة في القندكتور إيش
+
+173
+00:12:41,270 --> 00:12:44,670
+هيصير لها؟ هتأثر الـ electric field هيتولد عليها قوة
+
+174
+00:12:44,670 --> 00:12:48,130
+إحنا عرفنا الـ force إيش بتساوي؟ minus E في E، minus
+
+175
+00:12:48,130 --> 00:12:51,690
+الشحنة في الـ electric field يعني لو أنا حطيت
+
+176
+00:12:51,690 --> 00:12:55,690
+القندكتور في وجود المجال الـ electric field ساعتها
+
+177
+00:12:55,690 --> 00:12:59,070
+هو في الـ free space بس حطيت في طريقه الـ electric
+
+178
+00:12:59,070 --> 00:13:03,370
+field، الإلكترونات هتتأثر في وجود ال
+
+201
+00:14:21,820 --> 00:14:25,780
+انتقاله من زرع لزرع ثانية أو اصطدامه من زرع لزرع
+
+202
+00:14:25,780 --> 00:14:29,680
+ثانية طب إذا أنا كان عندي electron  الـ mass بتاعته
+
+203
+00:14:29,680 --> 00:14:35,040
+سميتها M طبعًا هو بيصطدم قاعد يدريفت بلغّة مقدارها هيوم
+
+204
+00:14:35,040 --> 00:14:39,180
+القانون بيقول لي قوانين نيوتن بتقول لي تغير في كمية
+
+205
+00:14:39,180 --> 00:14:44,080
+الحركة إيش لازم تساوي القوة على الجسم؟ صح بالنسبة
+
+206
+00:14:44,080 --> 00:14:46,560
+للإلكترونات إيش القوة اللي هتعملها؟ هو قاعد في
+
+207
+00:14:46,560 --> 00:14:49,940
+electric field minus E في E؟ صح هذا إيش لازم يساوي
+
+208
+00:14:49,940 --> 00:14:52,840
+تغير في كمية التحرك التغير في كمية التحرك اللي هو 
+
+209
+00:14:52,840 --> 00:14:57,300
+عبارة عن M في V على Ta اللي هي DMV على DT
+
+210
+00:15:01,110 --> 00:15:05,110
+إذن الـvelocity بتاعته، الـvelocity هتساوي minus E
+
+211
+00:15:05,110 --> 00:15:10,650
+في TAU على M في E  TAU اللي هي الـaverage time ما
+
+212
+00:15:10,650 --> 00:15:16,290
+بين الـcollision والـcollision الثاني، واضح؟ إذن
+
+213
+00:15:16,290 --> 00:15:23,550
+velocity عبّرنا عنها minus E TAU على M في E لو
+
+214
+00:15:23,550 --> 00:15:27,070
+إحنا عبّرنا عن ناقص M في E بإنها الـ charge density
+
+215
+00:15:27,070 --> 00:15:30,710
+بحيث إنه M هذه هي عبارة عن M كابيتال على V
+
+216
+00:15:36,780 --> 00:15:44,820
+بتاعته ما هي بتساوي أو
+
+217
+00:15:44,820 --> 00:15:49,980
+رتبهم من هي كده بيدينا أنا
+
+218
+00:15:49,980 --> 00:15:53,800
+كمان
+
+219
+00:15:53,800 --> 00:16:00,380
+عندي الـ charge density رو في V  إيش بتساوي الـ total 
+
+220
+00:16:00,380 --> 00:16:04,600
+charge إيش بيقول الـ total charge بيساوي عددهم في
+
+221
+00:16:04,600 --> 00:16:11,060
+شحنة الإلكترون هذه في V في Q 
+
+222
+00:16:11,060 --> 00:16:18,460
+total تساوي رو في V فإذا رو في V تساوي minus N في E 
+
+223
+00:16:18,460 --> 00:16:22,760
+ليه N مين؟ N capital على V number of charges per
+
+224
+00:16:22,760 --> 00:16:27,180
+unit volume الـ total charge تساوي Q في V اللي هو 
+
+225
+00:16:27,180 --> 00:16:32,140
+هذا الـ volume بتساوي الـ total N في E الـ total
+
+226
+00:16:32,140 --> 00:16:37,980
+charges في E Row في V هي Charge بين Volume وDensity هي
+
+227
+00:16:37,980 --> 00:16:44,440
+Charge بين Volume تساوي نقل
+
+228
+00:16:44,440 --> 00:16:48,120
+نقل نقل
+
+229
+00:16:48,120 --> 00:16:51,640
+نقل
+
+230
+00:16:51,640 --> 00:16:59,080
+نقل
+
+231
+00:16:59,080 --> 00:17:05,730
+نقل نقل نقل نقل نقل نقل نقل نقل نقلRow في V منعوض
+
+232
+00:17:05,730 --> 00:17:14,330
+عنها هي minus M E متعود عن V يعني كمان minus تصير
+
+233
+00:17:14,330 --> 00:17:22,650
+plus E تربيع تو على M في E  جيه
+
+234
+00:17:22,650 --> 00:17:28,070
+اللي هو current density بيساوي constant value في E
+
+235
+00:17:28,070 --> 00:17:31,190
+إيش هالـ constant؟ إن E تربيع إن احنا عارفين إن الـ
+
+236
+00:17:31,190 --> 00:17:35,640
+charge بتاعة الالكترون تربيع Tau average time
+
+237
+00:17:35,640 --> 00:17:41,240
+between two intervals رقم إن عددهم رقم على N رقم
+
+238
+00:17:41,240 --> 00:17:47,680
+فإذا هنكون العلاقة بين J و E هي عبارة عن some value
+
+239
+00:17:47,680 --> 00:17:56,560
+بنسميها سيجما sigma اللي هي conductivity سيجما الـ
+
+240
+00:17:56,560 --> 00:18:02,020
+conductivity اللي هي بنعبر عنها واحد على رو تمام؟ 
+
+241
+00:18:11,120 --> 00:18:14,800
+في S فصرحت هنا هذا كمان بنعبر عن جيه اللي بتساوي
+
+242
+00:18:14,800 --> 00:18:21,000
+sigma E اللي هو point form of Ohm's law شكل من
+
+243
+00:18:21,000 --> 00:18:25,220
+أشكال Ohm's law هو point form of Ohm's law اللي
+
+244
+00:18:25,220 --> 00:18:29,080
+برمّط لي current density جيه بالـ electric field
+
+245
+00:18:29,080 --> 00:18:34,420
+بواسطه sigma اللي هي conductivity وبعدين هنشوف كيف
+
+246
+00:18:34,420 --> 00:18:37,380
+هذا من إنه بنطلع بـ Ohm's law لإنه E بتساوي V على L 
+
+247
+00:18:37,380 --> 00:18:43,160
+وجيه بتساوي I P على S اللي هي current buoyant area
+
+248
+00:18:43,160 --> 00:18:50,860
+وبنستنتج منها Ohms law برضه إذا
+
+249
+00:18:50,860 --> 00:18:55,740
+كمان مرة جيه اللي هي current density مربوطة في الـ
+
+250
+00:18:55,740 --> 00:19:01,160
+electric field بواسطة سيجما الـ
+
+251
+00:19:01,160 --> 00:19:06,890
+conductors الـ conductor غالبًا هو عبارة عن element
+
+252
+00:19:06,890 --> 00:19:10,690
+اللي فيه إلكترونات بتتحرك يعني نسبيًا بالنسبة لي الـ
+
+253
+00:19:10,690 --> 00:19:16,390
+insulators بحرية هاي عند أنا perfect conductor هذا
+
+254
+00:19:16,390 --> 00:19:19,910
+الـ perfect conductor مرّ فيه electric field بهذا
+
+255
+00:19:19,910 --> 00:19:24,350
+الشكل هاي مجال كهربائي إيش هي من مجال الكهربائي
+
+256
+00:19:24,350 --> 00:19:27,750
+الإلكترونات الشحنات الموجودة هتجذب في طريقة
+
+257
+00:19:27,750 --> 00:19:31,390
+الشحنات الموجبة وتتزاحم على هذا الطرف من الـ
+
+258
+00:19:31,390 --> 00:19:35,040
+conductor هذا تخيلوا لي على كوندكتور طويل هيك المادة
+
+259
+00:19:35,040 --> 00:19:40,360
+لحالها وعلى الطرف الثاني هيكون في عندي الـ
+
+260
+00:19:40,360 --> 00:19:44,460
+negative charges اتكومت هنا إيش بيصير عندي؟ بيصير
+
+261
+00:19:44,460 --> 00:19:48,680
+الطرف من الكوندكتور عليه شحنات موجبة والطرف الثاني 
+
+262
+00:19:48,680 --> 00:19:52,220
+عليه شحنات سالبة إيش هيتولد؟ هيتولد عندي internal
+
+263
+00:19:52,220 --> 00:19:55,220
+electric field هذا الـ internal electric field
+
+264
+00:19:55,220 --> 00:19:57,960
+بالتمام بيساوي الـ electric field اللي هو الـ
+
+265
+00:19:57,960 --> 00:20:03,380
+external أنا اللي ابتعدت ترتيب الشحنات نتج عن وجود 
+
+266
+00:20:03,380 --> 00:20:06,360
+الـ External Electric Field. بالتالي الـ Internal
+
+267
+00:20:06,360 --> 00:20:10,160
+Electric Field اتجاهه عكس للـ External وبساويه في
+
+268
+00:20:10,160 --> 00:20:15,320
+المقدار ففي داخل الـ conductor لو جمعنا الـ Total
+
+269
+00:20:15,320 --> 00:20:19,040
+Electric Field هيكون الـ External زائد الـ Internal،
+
+270
+00:20:19,040 --> 00:20:23,600
+مش هيكون بساوة Zero إذا الـ Electric Field بساوة
+
+271
+00:20:23,600 --> 00:20:27,410
+Zero في قلب الـ conductor وإحنا بنعرف من Gauss law
+
+272
+00:20:27,410 --> 00:20:32,190
+إن الـ close integral لـ EWS بيساوي raw في V على
+
+273
+00:20:32,190 --> 00:20:36,230
+epsilon نقطة صح؟ طب إذا E بيساوي 0 معناه إن الـ
+
+274
+00:20:36,230 --> 00:20:38,830
+charge هو ما له صفر وهذا واضح لأن كل الـ charges
+
+275
+00:20:38,830 --> 00:20:43,110
+و أنا إيش صار لها charges؟ اتزاحمت عند الأطراف فصار
+
+276
+00:20:43,110 --> 00:20:47,070
+الـ charge density ما له بيساوي صفر هذا الحكاية
+
+277
+00:20:47,070 --> 00:20:52,230
+بيعنى ما له منطقي بالنسبة لي E صفر معناه الـ charge
+
+278
+00:20:52,230 --> 00:20:55,590
+enclosed ما له Zero وطبعًا أكيد الـ charge enclosed
+
+279
+00:20:55,590 --> 00:20:59,830
+Zero لأن كل الـ charges ما له تراكمت عند الأطراف إحنا
+
+280
+00:20:59,830 --> 00:21:04,230
+بنسمي الـ conductor في وجود electric field إنه
+
+281
+00:21:04,230 --> 00:21:06,730
+equipotential body طب ليش بنسميه equipotential
+
+282
+00:21:06,730 --> 00:21:10,990
+body إيش
+
+283
+00:21:10,990 --> 00:21:13,530
+معناه equipotential بتتذكرين إيش احنا بقولوا معناه
+
+284
+00:21:13,530 --> 00:21:19,480
+equipotential إيش معنى equipotential تتذكرين؟
+
+285
+00:21:19,480 --> 00:21:23,360
+أخدناها لسه المحاضرة الماضية، إيش معنى
+
+286
+00:21:23,360 --> 00:21:28,360
+equipotential؟ equipotential surface، إيش معنى
+
+287
+00:21:28,360 --> 00:21:32,300
+equipotential surface؟
+
+288
+00:21:32,300 --> 00:21:34,600
+يا ده تخيلوا الله شويه إنجليزي بلاش تكونوا بتعرفوا 
+
+289
+00:21:34,600 --> 00:21:39,260
+كهرباء شويه إنجليزي، equi-potential equi من equal
+
+290
+00:21:39,260 --> 00:21:42,200
+و potential potential، equipotential يعني إيه الـ
+
+291
+00:21:42,200 --> 00:21:46,400
+potential بقى له متساوي يعني الـ potential عند أي 
+
+292
+00:21:46,400 --> 00:21:50,380
+نقطة ما له متساوي طب ليش هذا الحكي؟ إيش اللي خلاه
+
+293
+00:21:50,380 --> 00:21:52,640
+بساويه؟ مذاكرين إيش علاقة الـ electric field بالـ
+
+294
+00:21:52,640 --> 00:21:56,840
+potential؟ electric field بساوي minus del V ولا
+
+295
+00:21:56,840 --> 00:22:00,820
+لأ؟ مش قلنا E وأثبتناها المحاضرة الماضية E بالساوة
+
+296
+00:22:00,820 --> 00:22:04,240
+و minus del V E بالساوة 0 إذا الـ differential تبع V
+
+297
+00:22:04,240 --> 00:22:06,440
+إيش بساوة 0؟ إيش مع الـ differential تبع V
+
+298
+00:22:06,440 --> 00:22:09,420
+بساوي 0؟ يعني الـ voltage عند أي نقطة وأي نقطة 
+
+299
+00:22:09,420 --> 00:22:12,460
+لازم يكون متساوي إذا الـ differential تبعه بساوي
+
+300
+00:22:12,460 --> 00:22:16,140
+0 عشان هيك إحنا بنسمي الـ conductor أو الـ perfect 
+
+301
+00:22:16,140 --> 00:22:19,480
+conductor الـ equipotential body يعني الـ voltage عند
+
+302
+00:22:19,480 --> 00:22:22,720
+أي نقطة عند أي نقطة لازم يكون متساوي
+
+303
+00:22:26,880 --> 00:22:29,280
+طيب إحنا لو رجعنا لـ Ohm's law وقلنا J بالثانية و
+
+304
+00:22:29,280 --> 00:22:34,360
+ثانية إيه؟ إيه بتروح للصفر في inside الـ conductor 
+
+305
+00:22:34,360 --> 00:22:39,200
+عشان J تتظل حاصلة current density يعني تكون finite
+
+306
+00:22:39,940 --> 00:22:43,760
+مش تروح لقيمة غير معينة لأن فيه اندي طيار أنا 
+
+307
+00:22:43,760 --> 00:22:46,400
+بأمره sigma إيش لازم تكون؟ Infinity هذا perfect
+
+308
+00:22:46,400 --> 00:22:49,480
+conductor perfect conductor إيش معناه إنه ما فيش
+
+309
+00:22:49,480 --> 00:22:52,740
+عنده أي resistivity إحنا بنحكي عن perfect conductor
+
+310
+00:22:52,740 --> 00:22:55,400
+perfect conductors ما بيحتويش عنده في قلبه أي
+
+311
+00:22:55,400 --> 00:22:59,930
+electrostatic electric field بمنع اللي خطوط المجال
+
+312
+00:22:59,930 --> 00:23:02,730
+الكهربائي اللي هتكون جوه وأثبتنا ليش الـ electric
+
+313
+00:23:02,730 --> 00:23:06,130
+field إيش بيكون Zero جوه بيصير زي الـ equipotential
+
+314
+00:23:06,130 --> 00:23:09,630
+surfaces إذا إذا E بساوي Zero معناه إنه Sigma 
+
+315
+00:23:09,630 --> 00:23:14,630
+بتروح لـ Infinity و هذا الحكي أنا حكيته E بساوي
+
+316
+00:23:14,630 --> 00:23:18,150
+Zero معناه رو في V بساوي Zero من جاسله وبرضه من تعريف
+
+317
+00:23:18,150 --> 00:23:20,610
+الـ electric field إنه برضه الـ potential هيكون Zero
+
+318
+00:23:20,610 --> 00:23:23,210
+لأنه الـ electric field هي بساوة ناقص للـ V
+
+319
+00:23:29,720 --> 00:23:32,880
+فبنيجي لـ electric fields in material space، احنا
+
+320
+00:23:32,880 --> 00:23:34,880
+لازمنا في الـ material space بس في هذه الحالة أنا 
+
+321
+00:23:34,880 --> 00:23:39,000
+بعمل حاجة ثانية، ما بديش اخلي زي ما أنا طوالي شفنا إن
+
+322
+00:23:39,000 --> 00:23:41,700
+الـ conductor هيك في الـ free space وحطينا في 
+
+323
+00:23:41,700 --> 00:23:49,220
+الاتجاه فرضنا electric field في طريقة أما هنا
+
+324
+00:23:49,220 --> 00:23:52,320
+أنا بالعكس بدأت أوصله مع أسلاك ما بديش اخليه في الـ
+
+325
+00:23:52,320 --> 00:23:56,340
+space بطل الـ free space أنا وصلتها بـ conductors هذا
+
+326
+00:23:56,340 --> 00:24:00,460
+الـ element تبعي أو المادة بتاعتي الـ perfect
+
+327
+00:24:00,460 --> 00:24:04,160
+conductor أو الـ material space وصلته بأسلاك عبر
+
+328
+00:24:04,160 --> 00:24:09,280
+بطارية الفرق بين ده الشكل وده الشكل إن هناك 
+
+329
+00:24:12,090 --> 00:24:15,310
+ما فيش أي connections في الـ conductor هذا، مش وصلها 
+
+330
+00:24:15,310 --> 00:24:19,430
+بأي حاجة، في مجال كهربائي أنا حاطه في وجود المجال 
+
+331
+00:24:19,430 --> 00:24:23,330
+الكهربائي، لكن هنا أنا وصلته بواسطة أسلاك مع 
+
+332
+00:24:23,330 --> 00:24:27,760
+بطارية هذه البطارية عملت فرق جهد بين الطرفين
+
+333
+00:24:27,760 --> 00:24:31,500
+وبالتالي هيمر electric field في قلب الـ conductor
+
+334
+00:24:31,500 --> 00:24:35,880
+هذا electric field هيقدر إلى إيش؟ تدفق الشحنات
+
+335
+00:24:35,880 --> 00:24:40,140
+اللي هذا اللي هو كرسي الدوائر هيصير إن دي طيار
+
+336
+00:24:40,140 --> 00:24:43,600
+بيمر في الدائرة الكهربائية في هذه الحالة ما أقدرش 
+
+337
+00:24:43,600 --> 00:24:45,820
+أقول إن الـ electric field inside الـ conductor 
+
+338
+00:24:45,820 --> 00:24:51,390
+بيساوي Zero هنا فيه قوة بتجبر الإلكترونات ما أنا 
+
+339
+00:24:51,390 --> 00:24:56,390
+تتضّفق من طرف لطرف ثاني في حركة مستمرة وبالتالي
+
+340
+00:24:56,390 --> 00:24:59,770
+هيكون في عندي electric field inside الـ conductor
+
+341
+00:24:59,770 --> 00:25:10,170
+إحنا
+
+342
+00:25:10,170 --> 00:25:15,880
+قلنا إن E إيش بساوي؟ V على L أو V بتساوي إذا كان 
+
+343
+00:25:15,880 --> 00:25:19,100
+الـ close integral أو الـ integral over L E ضد DL 
+
+344
+00:25:19,100 --> 00:25:27,260
+أو بساطة إذا عندي أقل يعني معروف الطول فإذا كان E
+
+345
+00:25:27,260 --> 00:25:31,200
+constant هيكون E في L هذا الـ general الشكل تبعه V
+
+346
+00:25:31,200 --> 00:25:36,680
+بتساوي الـ integral E ضد DLE constant وقال طول معين
+
+347
+00:25:36,680 --> 00:25:40,460
+من 0 لـ L حصل V بيساوي E في L فهذا الـ electric field 
+
+348
+00:25:40,460 --> 00:25:44,540
+لـ conductor اللي له form cross section S وقال طول L 
+
+349
+00:25:44,540 --> 00:25:51,550
+هيكون بيساوي E بيساوي V على L تمام؟ فإحنا عرفنا الـ
+
+350
+00:25:51,550 --> 00:25:54,850
+current density إيش بتساوي؟ I على S جيه الـ current
+
+351
+00:25:54,850 --> 00:25:59,590
+density إيش بتساوي؟ I على S وجيه إيش بتساوي؟ سيجما في 
+
+352
+00:25:59,590 --> 00:26:04,530
+E و E إيش بتساوي؟ V على L إذا I على S إيش بتساوي
+
+353
+00:26:04,530 --> 00:26:09,710
+سيجما V على L طب أنا بدي أعرف الـ resistance علناها
+
+354
+00:26:09,710 --> 00:26:14,110
+V على I بدي اخذ هذا الشكل وهذا الشكل V على I إيش
+
+355
+00:26:14,110 --> 00:26:15,610
+هتساوي؟ L
+
+356
+00:26:27,990 --> 00:26:31,470
+القانون اللي كلنا بنعرفه من وين جبناه؟ من الـ point
+
+357
+00:26:31,470 --> 00:26:37,730
+form تبع Ohm's law معرفتنا علاقة الـ current 
+
+358
+00:26:37,730 --> 00:26:40,750
+density بالـ current إن هي I على S والـ electric
+
+359
+00:26:40,750 --> 00:26:45,220
+field علاقته بالـ potential هو V على L وبالتالي بقدر أقول 
+
+360
+00:26:45,220 --> 00:26:53,280
+إن R بتساوي رو L على S رو اللي هي واحد على سيجما بشكل 
+
+361
+00:26:53,280 --> 00:26:56,740
+عام لو كان عندي non uniform conductor هذا لو حكينا 
+
+362
+00:26:56,740 --> 00:26:59,900
+إنه uniform أخدنا ببساطة إن لو uniform cross
+
+363
+00:26:59,900 --> 00:27:03,120
+section هذا اللي بتاع المقاومات الدوائر عشان هي كده
+
+364
+00:27:03,120 --> 00:27:07,240
+بنعرف إن R بساوي rho L على S لو non uniform بدي
+
+365
+00:27:07,240 --> 00:27:11,040
+استخدم الـ integrals هيكون R بيساوي V على I بيساوي 
+
+366
+00:27:11,040 --> 00:27:15,740
+integral E ضد L على I اللي هي الـ integral لـ J ضد S 
+
+367
+00:27:15,740 --> 00:27:22,760
+و J اللي هي mean sigma E ضد S إذا هي المقاومة الـ
+
+368
+00:27:22,760 --> 00:27:25,580
+power لو بدها حسب الـ power اللي جايه على هذا 
+
+369
+00:27:25,580 --> 00:27:30,280
+المقاومة بنعرفها هي عبارة عن التغير في إيش في الـ
+
+370
+00:27:30,280 --> 00:27:35,680
+energy and joules أو الـ force times velocity الـ
+
+371
+00:27:35,680 --> 00:27:38,860
+power بتساوي الـ force times velocity هيها الـ force
+
+372
+00:27:38,860 --> 00:27:43,680
+اللي رو أو يعني Q في E هي الـ force و V الـ velocity
+
+373
+00:27:43,680 --> 00:27:48,400
+الـ Q بقدر أعبر عنها بإيش رو في V دي في V إذا الـ total 
+
+374
+00:27:48,400 --> 00:27:51,140
+power أو الـ .. الـ .. الـ ..
+
+375
+00:28:01,720 --> 00:28:05,200
+عادة الترتيب بسيط بس
+
+401
+00:30:01,830 --> 00:30:07,730
+أي تربية في R هذا اللي نطلع نكون دكتور، واضح؟ احنا
+
+402
+00:30:07,730 --> 00:30:12,250
+متذكرين قولنا التوائر هي حالة خاصة من الكهرومغناطيسية
+
+403
+00:30:12,250 --> 00:30:18,290
+الصينية، نرجعلها لما بيكون عندي lumped، linear
+
+404
+00:30:18,750 --> 00:30:23,990
+circuits صح؟ الذاكرين أمبيرمتر linear circuits
+
+405
+00:30:23,990 --> 00:30:27,430
+وكل ال conductors اللي موجودين عندنا لهم uniform
+
+406
+00:30:27,430 --> 00:30:32,410
+فاحنا بنقدر نستخدم الدوائر، otherwise لازم نستخدم 
+
+407
+00:30:32,410 --> 00:30:34,550
+ال electromagnetic يعني لو فش عندي uniform
+
+408
+00:30:34,550 --> 00:30:38,730
+conductor لازم أرجع لهذه المعادلات، لهذه المعادلات
+
+409
+00:30:38,730 --> 00:30:42,990
+بشكل عام، لكن يوفور بقدر أقول على طول أن ال B هي بساوية
+
+410
+00:30:42,990 --> 00:30:47,150
+ال BFR اللي تعلمناها في الدوائر واللي اصلا جاية
+
+411
+00:30:47,150 --> 00:30:53,870
+من قوانين الكهرومغناطيسية، واضح؟
+
+412
+00:30:53,870 --> 00:30:59,190
+طب ناخد مثال، مثال بقول لو كانت عارفة أنا ال 
+
+413
+00:30:59,190 --> 00:31:04,490
+current density J انها 1 على R<sup>3</sup> × 2 cos θ تجاه
+
+414
+00:31:04,490 --> 00:31:09,300
+ال R hat، وعندي theta component مقدرها 1 على R
+
+415
+00:31:09,300 --> 00:31:13,480
+cubed sin θ ال unit بتاعة current density بما
+
+416
+00:31:13,480 --> 00:31:16,340
+أن current per unit area هو أمبير/متر تربيع
+
+417
+00:31:17,980 --> 00:31:21,060
+بدنا نحسب ال current passing through أول حاجة
+
+418
+00:31:21,060 --> 00:31:25,360
+hemisphere shell of radius 20 cm، hemisphere shell
+
+419
+00:31:25,360 --> 00:31:30,480
+يعني نص بطيخة، و shell مش مليانة، يعني مش حاجة
+
+420
+00:31:30,480 --> 00:31:34,620
+مليانة اللي هي R بتروح من zero لـ، لأ عند R ثابتة،
+
+421
+00:31:34,620 --> 00:31:38,500
+shell لأنها، ال current بيمر في ال shell بس، يعني
+
+422
+00:31:38,500 --> 00:31:41,380
+قيمة ال radius ثابتة على عشرين centimeter أو point
+
+423
+00:31:41,380 --> 00:31:44,890
+نين متر، عشان أجيب ال I إيش
+
+424
+00:31:44,890 --> 00:31:48,610
+بتساوي ال integral ل J dot DS، و DS بالنسبة
+
+425
+00:31:48,610 --> 00:31:52,450
+للهمسفير، بشكل عام للسفير هو عبارة عن R تربيع
+
+426
+00:31:52,450 --> 00:31:57,630
+sin θ dθ dφ R تربيع، بالكل سبته، وانتجاه ال 
+
+427
+00:31:57,630 --> 00:32:01,570
+sin ده ال S دايما عمودي، عمودي على ال surface إذا
+
+428
+00:32:01,570 --> 00:32:04,530
+أنا عندي هاي همسفير إيش العمودي عليها بيكون اللي
+
+429
+00:32:04,530 --> 00:32:10,910
+في اتجاه ال R hat، تخيلوا طبعا حاجة عمودية على ال
+
+430
+00:32:10,910 --> 00:32:14,110
+surface اللي هو عمودية على ال مماس مين هو ال
+
+431
+00:32:14,110 --> 00:32:18,810
+radius فهيكون تماما في اتجاه ال R hat، ف then DS
+
+432
+00:32:18,810 --> 00:32:25,150
+عبارة عن R تربيع sin θ dθ dφ R hat، نعود طبعا أن هي
+
+433
+00:32:25,150 --> 00:32:29,410
+hemisphere θ و φ بتوقف من ال zero فهي hemisphere
+
+434
+00:32:29,410 --> 00:32:34,680
+يعني هيك بس هيدا هي هتوقف ستة من zero ل π على
+
+435
+00:32:34,680 --> 00:32:38,820
+اتنين، مش هتكمل ل π لو هتكمل ل π إيش بيصير يعني
+
+436
+00:32:38,820 --> 00:32:43,080
+دي طبقة كاملة، و φ ده بتعمل لي كل الدوارة يعني
+
+437
+00:32:43,080 --> 00:32:46,860
+هتروح φ من zero ل 2π، شايفين كل كه يعني عند
+
+438
+00:32:46,860 --> 00:32:50,980
+أنا هاي ال hemisphere نص بطيخة، ستة بتروح من zero ل
+
+439
+00:32:50,980 --> 00:32:56,130
+π على اتنين، و φ من zero ل 2π، R سابق يقدر
+
+440
+00:32:56,130 --> 00:33:01,010
+عشرين سنتمتر، إذا أنا هكامل ستة من زيرو ل π ع
+
+441
+00:33:01,010 --> 00:33:06,590
+اتنين، φ من زيرو ل 2π، واحدة ع ال R cube طبعا
+
+442
+00:33:06,590 --> 00:33:11,290
+اللي هي هدى، طبعا ال J dot DS من هيظل بال R hat
+
+443
+00:33:11,290 --> 00:33:15,270
+هذا هيروح للصفر، θ hat dot R hat zero، بس ال
+
+444
+00:33:15,270 --> 00:33:18,330
+term الأول انه هيظل 1 على R<sup>3</sup> × 2 cosine
+
+445
+00:33:18,330 --> 00:33:22,790
+θ في ds اللي هي R تربيع sin θ dφ dθ
+
+446
+00:33:22,790 --> 00:33:26,870
+بعوض عن R طبعا، R تربيع بتروح مع اثنتين من هدول، تصير
+
+447
+00:33:26,870 --> 00:33:32,370
+واحد على R، بعوض عنها ب point اثنين، تطلع 2 على R
+
+448
+00:33:32,370 --> 00:33:37,950
+الفاي تكملها 2π أنا من zero ل 2π، sin θ dθ
+
+449
+00:33:37,950 --> 00:33:44,330
+في، يعني cos θ sin θ dθ، لعبارة عن sin θ dθ، لأن ال cos
+
+450
+00:33:44,330 --> 00:33:53,070
+له d cos θ، هو d sin θ هو cos θ dθ، فبتصير sin تربيع
+
+451
+00:33:53,070 --> 00:33:58,890
+على اتنين، مواضحش هذا، يعني دي cos θ sin θ dθ، دي sin
+
+452
+00:33:58,890 --> 00:34:05,070
+θ هي ال cos θ dθ، فإذا عندي sin تربيع على اثنين من
+
+453
+00:34:05,070 --> 00:34:08,270
+zero أضعها اثنين بيطلع معايا انها 1 أمبير التيار
+
+454
+00:34:08,270 --> 00:34:12,930
+بالأخص هذا بالنسبة للهمسفير، نجي لـ ال spherical
+
+455
+00:34:12,930 --> 00:34:16,450
+shell، ال radius عشرة برضه shell يعني بس الطبقة
+
+456
+00:34:16,450 --> 00:34:23,600
+السطحية، مش مليانة، بس θ بتسير من zero ل π، φ
+
+457
+00:34:23,600 --> 00:34:27,080
+بتظلها من zero ل 2π، و R هنا ثابتة على عشرة
+
+458
+00:34:27,080 --> 00:34:32,180
+centimeter يعني بدي أكامل نفسي، وطبعا R hat dot R
+
+459
+00:34:32,180 --> 00:34:36,560
+hat هي اللي هتبقى، والجزء هذا هيكون بساوة صفر لو
+
+460
+00:34:36,560 --> 00:34:41,460
+أنا عملتها كيه بتطلع معايا الجواب بساوة zero، الجواب
+
+461
+00:34:41,460 --> 00:34:45,120
+هيطلع معايا بيساوي Zero، التيار قيمته بيساوي Zero
+
+462
+00:34:45,120 --> 00:34:49,400
+السبب لو أنا طلعت على القصة هذه، أنا بعمل Close
+
+463
+00:34:49,400 --> 00:34:53,280
+Integral على السطح كله، مش معروف صح؟ إذا صار
+
+464
+00:34:53,280 --> 00:34:57,920
+هدمله Close Integral لجرد ال DS، صار عندي الفرنسي
+
+465
+00:34:57,920 --> 00:35:02,880
+سوى Close Integral لجرد ال DS وهذه احنا اخذنا
+
+466
+00:35:02,880 --> 00:35:06,500
+عبارة عن مين؟ فقدر أستخدم ال divergence theorem 
+
+467
+00:35:06,500 --> 00:35:10,520
+ساكنين سوى التكامل ل diverge 
+
+468
+00:35:14,040 --> 00:35:17,420
+لو شوفنا ال divergence ده شي حلاقيها في السوقية
+
+469
+00:35:27,870 --> 00:35:31,290
+فأنا كفلتكم طبعا اعملوها في البيت جيبوا ال 
+
+470
+00:35:31,290 --> 00:35:34,230
+divergence لو حسبنا ال divergence هلاقيه بال Zero
+
+471
+00:35:34,230 --> 00:35:36,910
+طبعا احنا لو عملنا أول حاجة التكامل عادي هلاقيه بال 
+
+472
+00:35:36,910 --> 00:35:40,770
+zero، أو ممكن على طول أقول أن هذا Close Integral
+
+473
+00:35:40,770 --> 00:35:44,270
+line integral، Close surface integral بستخدم ال 
+
+474
+00:35:44,270 --> 00:35:47,050
+divergence theorem بربطه ب divergence J اللي
+
+475
+00:35:47,050 --> 00:35:51,450
+هيعطيني zero، المثال
+
+476
+00:35:51,450 --> 00:35:52,050
+اللي بعده
+
+477
+00:35:57,700 --> 00:36:01,940
+هذا convective charge transport، طبعا هذا اللي
+
+478
+00:36:01,940 --> 00:36:05,300
+ما أعرفش إذا بتعرفوا Van de Graaf generator، سمعتوا 
+
+479
+00:36:05,300 --> 00:36:12,560
+عنه؟ Van de Graaf في physics هو بمرق الشحنات وكلها
+
+480
+00:36:12,560 --> 00:36:21,620
+بتتجمع على السطح، فإن احنا هي الشكل تبعه ل Van de 
+
+481
+00:36:21,620 --> 00:36:26,860
+Graaf، وعندي الشحنات بتنطلق بحد اللي هي ال charge 
+
+482
+00:36:26,860 --> 00:36:32,640
+removal أو اللي ال dome بتاعك ال conducting dome
+
+483
+00:36:32,640 --> 00:36:36,640
+ال charges
+
+484
+00:36:36,640 --> 00:36:39,920
+إيش بيصيرلها transported بيصيرلها عملية نقل عبر
+
+485
+00:36:39,920 --> 00:36:43,340
+moving belt، هذا ال belt شايفينه ال belt اللي بالمص
+
+486
+00:36:43,340 --> 00:36:50,540
+هذا اللي بالوصف، وهذا ونقول عماله charges من القاعدة
+
+487
+00:36:50,540 --> 00:36:55,160
+للدوم، لدوم هذه الدوارة نسميها الدوم، القبة، القبة
+
+488
+00:36:55,160 --> 00:37:00,700
+بتاعة الجهاز، إذا كانت ال charge density هي اللي 
+
+489
+00:37:00,700 --> 00:37:04,540
+أنا بنقلها، مقدار ال charges الها charge density 
+
+490
+00:37:04,540 --> 00:37:10,400
+عشرة قوة سبعة كولوم/متر تربيع، بتنقلها الفولوستي
+
+491
+00:37:10,400 --> 00:37:15,920
+مقدارها اثنين متر لكل second، calculate the charge
+
+492
+00:37:15,920 --> 00:37:19,880
+collected in five seconds، إذا اعتبرنا ان ال width
+
+493
+00:37:19,880 --> 00:37:23,460
+تبع ال belt عشرة centimeter، ال width تبع ال belt
+
+494
+00:37:23,460 --> 00:37:26,080
+يعني هذا ال belt هو مرسوم كخط بس هو في الواقع 
+
+495
+00:37:26,080 --> 00:37:31,420
+belt، فلقد حزام ولف وبلقوا ال charges يعني لو
+
+496
+00:37:31,420 --> 00:37:37,300
+أنا طلعت على جزء منه وهيك الحزام هذا
+
+497
+00:37:37,300 --> 00:37:41,820
+اللي احنا شايفينه، الطول تبعه وال width تبعه كده
+
+498
+00:37:41,820 --> 00:37:48,200
+مافيه، قيمة ال width عشرة سنتمتر و
+
+499
+00:37:48,200 --> 00:37:53,680
+ال velocity اللي بنقل فيها عمالة ال charges اثنين
+
+500
+00:37:53,680 --> 00:38:01,160
+متر/هي second وهطلب مني ان احسب ال surface ال
+
+501
+00:38:01,160 --> 00:38:07,560
+total charge، اتشارج ال total charge اللي في زمن 
+
+502
+00:38:07,560 --> 00:38:13,500
+مقداره خمسة second، ال charge اللي بيحسبها إذا عرفنا 
+
+503
+00:38:13,500 --> 00:38:17,740
+ان رو بي أو رو<sub>s</sub> في هذه الحالة surface charge
+
+504
+00:38:17,740 --> 00:38:26,460
+density surface عشرة هو سبعة كولوم/متر كيوب
+
+505
+00:38:26,460 --> 00:38:31,480
+احنا إيش اللي قولنا بتساوي رو<sub>s</sub> كمية في ال area ولا
+
+506
+00:38:31,480 --> 00:38:36,100
+لأ لأ، لأن هنا بال area، لو بال volume هتكون في
+
+507
+00:38:36,100 --> 00:38:40,960
+volume، ال area إيش بتساوي؟ الطول في العرض هتكون رو<sub>s</sub>
+
+508
+00:38:41,840 --> 00:38:47,000
+العرض، خليني أسميه W، في الطول، إيش الطول بيساوي؟
+
+509
+00:38:47,000 --> 00:38:53,560
+الطول بيساوي فرصة في الزمن، هيكون U × T، هو بدوياها
+
+510
+00:38:53,560 --> 00:38:57,720
+بعد خمس ثواني، فهيكون رو<sub>s</sub> اللي هي عشرة قوة سبعة 
+
+511
+00:38:57,720 --> 00:39:01,860
+كولوم/متر تربيع في ال width اللي هو معطيناياه 
+
+512
+00:39:01,860 --> 00:39:07,260
+أداش عشرة سنتيمتر اللي هو 0.1 متر في ال فرصة
+
+513
+00:39:07,260 --> 00:39:11,670
+اللي هي 2 متر/second فقدرش الزمن 5، هذا 
+
+514
+00:39:11,670 --> 00:39:18,030
+هتعطينا قيمة ال total charge اللي تم جمعها في خمس
+
+515
+00:39:18,030 --> 00:39:26,850
+ثواني، واضح؟ كمان 
+
+516
+00:39:26,850 --> 00:39:31,770
+مثال، أنا عندي LED bar يعني من الرصاص قطعة من
+
+517
+00:39:31,770 --> 00:39:34,230
+الرصاص برضه، هدا طويل يعني بس هدا ال cross section
+
+518
+00:39:34,230 --> 00:39:40,770
+تبعه وممتد، cross section تبعه مربع وطويل يعني زي
+
+519
+00:39:40,770 --> 00:39:41,350
+القلم هدا
+
+520
+00:39:44,570 --> 00:39:52,190
+هذا ال bar أو هذا القضيب عملوا فيه خرق Hall طول
+
+521
+00:39:52,190 --> 00:39:55,670
+الطول يعني مش بس من هنا على طوله زي هذا، تخيلوا على
+
+522
+00:39:55,670 --> 00:40:01,170
+طول القضيب اللي هو الهادي، its length القضيب طوله
+
+523
+00:40:01,170 --> 00:40:05,290
+أربع متر، وال cross section تبعه زي ما هذا الشكل
+
+524
+00:40:05,290 --> 00:40:09,250
+شفناه ع طوله اللي هو أربع متر، عملنا الخرق مش بس
+
+525
+00:40:09,250 --> 00:40:13,270
+مثلا نصه، طوله كله أربع، والخرق من أول لآخر عملناه
+
+526
+00:40:18,290 --> 00:40:22,510
+الـ sigma بتاعته اللي هي ال conductive بتاعته خمسة
+
+527
+00:40:22,510 --> 00:40:27,490
+في عشر قوة ستة Siemens/meter، طوله أربع، عملنا 
+
+528
+00:40:27,490 --> 00:40:30,930
+فيه الخروج اللي انتوا شايفينه، طوله وعرضه ثلاثة في
+
+529
+00:40:30,930 --> 00:40:34,410
+ثلاثة اللي هو ال cross section تبعه، المربع تبعه
+
+530
+00:40:34,410 --> 00:40:39,690
+الطول تاعته ثلاثة يعني مربعة، وهي ال radius أو ال 
+
+531
+00:40:39,690 --> 00:40:43,330
+diameter تبع الدائرة اللي عملناها في نصه 1
+
+532
+00:40:43,330 --> 00:40:47,160
+centimeter، ال radius تبعها قداش؟ نص centimeter، بدوا
+
+533
+00:40:47,160 --> 00:40:51,520
+resistance between equal square ends، يعني بدوا 
+
+534
+00:40:51,520 --> 00:40:54,340
+resistance بين هدول الطرفين، إذا اتخيلنا إنه هذا 
+
+535
+00:40:54,340 --> 00:40:58,540
+القضيب وهذا القضيب، بدوا المقاومة بين هدول الطرفين، 
+
+536
+00:40:58,540 --> 00:41:03,160
+إيش عرفنا المقاومة؟ احنا شقناها مع بعض، L على 
+
+537
+00:41:03,160 --> 00:41:09,300
+sigma في S، L يعطينا طوله، من هنا لهنا قديش؟ 4 متر
+
+538
+00:41:11,400 --> 00:41:16,580
+طوله للقضيب أربعة متر، sigma ناطيناه خمسة في عشر 
+
+539
+00:41:16,580 --> 00:41:20,380
+قوى ستة، إيش ضال عليه ال area؟ ال area .. ال
+
+540
+00:41:20,380 --> 00:41:23,260
+cross section area مش مربع، لو ما عملش الخرق 
+
+541
+00:41:23,260 --> 00:41:26,940
+فنقولنا ثلاثة في ثلاثة، لكن هي عمل فيها الخرق،
+
+542
+00:41:26,940 --> 00:41:29,960
+فإيش هجيب؟ ال area بتاعة المربع ناقص ال area بتاعة 
+
+543
+00:41:29,960 --> 00:41:34,210
+الدائرة، بالتلاتة يعني رياضيات فاديالي، d تربيع
+
+544
+00:41:34,210 --> 00:41:39,210
+minus π r تربيع، d تربيع ليه؟ ثلاثة تربيع minus π 
+
+545
+00:41:39,210 --> 00:41:42,410
+في نص الكل تربيع، حد ال unit أنها جا centimeter
+
+546
+00:41:42,410 --> 00:41:45,970
+تربيع، فإذا أنا بدي أحسب كل بالأم بدي انتبه ان 
+
+547
+00:41:45,970 --> 00:41:49,470
+أحول كل حاجة بالمتر يا كل حاجة لإن عند ال sigma ما
+
+548
+00:41:49,470 --> 00:41:56,010
+لها c means/متر فبرجع بحول بحول هاي ل متر، بطلع
+
+549
+00:41:56,010 --> 00:41:59,850
+معايا أن المقاومة بتاعة هذا القضيب ما بين طرفين
+
+550
+00:41:59,850 --> 00:42:05,010
+هذا القضيب المقاومة بين هدول النقطتين هي 974 micro
+
+551
+00:42:05,010 --> 00:42:05,750
+ohm
diff --git a/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/9u_8vIOnPD0_raw.json b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/9u_8vIOnPD0_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..3ede2d84f1c331f8131244edc62e02127da739f0
--- /dev/null
+++ b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/9u_8vIOnPD0_raw.json
@@ -0,0 +1 @@
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diff --git a/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/9u_8vIOnPD0_raw.srt b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/9u_8vIOnPD0_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..54857ec6bab6a4f4e3d958d8613b657db4ed3aa1
--- /dev/null
+++ b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/9u_8vIOnPD0_raw.srt
@@ -0,0 +1,2204 @@
+1
+00:00:20,670 --> 00:00:22,930
+بسم الله الرحمن الرحيم السلام عليكم ورحمة الله
+
+2
+00:00:22,930 --> 00:00:27,650
+وبركاته احنا الاتحادرات الماضية أو شبط الأربع كان
+
+3
+00:00:27,650 --> 00:00:31,790
+متخصصة ال electric field في ال spaceالشبتر هذا
+
+4
+00:00:31,790 --> 00:00:34,550
+هنتحكي عن ال electric field في ال material space،
+
+5
+00:00:34,550 --> 00:00:36,530
+يعني إيش بيصير لما ال electric field يكون في قلب
+
+6
+00:00:36,530 --> 00:00:40,790
+material، بيمشي في قلب metal، في عضايا electric،
+
+7
+00:00:40,790 --> 00:00:43,090
+صحيح ال space إحنا بنعتبره حالة خاصة من ال
+
+8
+00:00:43,090 --> 00:00:47,050
+dielectric، الفرقية في معامل ال permittivity، ال
+
+9
+00:00:47,050 --> 00:00:49,330
+permittivity بتاعة ال space هي epsilon node و
+
+10
+00:00:49,330 --> 00:00:52,870
+هنشوف كيف إنه بس الفرقية إنه هتكون في عنا معامل
+
+11
+00:00:52,870 --> 00:00:58,380
+خاص ل ال dielectric materialsفإذا هنبدأ اليوم
+
+12
+00:00:58,380 --> 00:01:04,140
+electric field في ال material space أولا بالنسبة
+
+13
+00:01:04,140 --> 00:01:08,060
+لوضعية ال material و علاقتها بال electric field
+
+14
+00:01:08,060 --> 00:01:12,620
+احنا بنربطهم وسط تخاصية ال conductivity اللي هي
+
+15
+00:01:12,620 --> 00:01:17,120
+التوصيلية sigma أخدناها حتى في الدوائر sigma 1 على
+
+16
+00:01:17,120 --> 00:01:22,240
+روح resistivityفإذا إحنا بنصنف ال material تبعا
+
+17
+00:01:22,240 --> 00:01:26,260
+للتوصيلية بتاعتها اللي هي sigma فبنصنفهم ل
+
+18
+00:01:26,260 --> 00:01:32,180
+conductors و non conductors مواصلات و غير مواصلات
+
+19
+00:01:32,180 --> 00:01:38,950
+أو بمعنى آخر بنسميهم metals و insulatorsال metals
+
+20
+00:01:38,950 --> 00:01:42,230
+غالبا بتكون ال conductive بتاعتهم عالية زي الكبر
+
+21
+00:01:42,230 --> 00:01:46,210
+يعني بتكون sigma مالها أكبر بكتير من واحد عالية ال
+
+22
+00:01:46,210 --> 00:01:49,910
+conductive بتاعتها ال insulators اللي زي الخشب و
+
+23
+00:01:49,910 --> 00:01:53,330
+الورق بيكون sigma مالها أقل بكتير من واحد و
+
+24
+00:01:53,330 --> 00:01:56,940
+المايكا و كل أنواع ال insulatorsطبعا فينا
+
+25
+00:01:56,940 --> 00:01:59,620
+materials تانين اللي هي زي ال semiconductors اللي
+
+26
+00:01:59,620 --> 00:02:01,860
+هي ما بين ال metal و ال insulator و ال
+
+27
+00:02:01,860 --> 00:02:06,880
+superconductors اللي هي عبارة عن سبائك تم اكتشافها
+
+28
+00:02:06,880 --> 00:02:10,660
+خلال القرن الماضي اللي توصليت هو عالية جدا يعني ال
+
+29
+00:02:10,660 --> 00:02:15,640
+receipt بتاعتها تقريبا 0 هذه تصنيف ال materials
+
+30
+00:02:15,640 --> 00:02:19,760
+تبعا ل ال conductivity احنا هنقود غالبا ما بين ال
+
+31
+00:02:19,760 --> 00:02:20,720
+metals و ال insulators
+
+32
+00:02:23,760 --> 00:02:26,860
+حنا عرفتون kinds of currents واحد بنسميه ال
+
+33
+00:02:26,860 --> 00:02:29,480
+convection current واحد بنسميه conduction current
+
+34
+00:02:29,480 --> 00:02:33,740
+ال current بشكل عام قبل ما مميز بين ال convection
+
+35
+00:02:33,740 --> 00:02:37,640
+و ال conduction ال current ممكن أخدته في الدوائر
+
+36
+00:02:37,640 --> 00:02:42,040
+برضه هو عبارة عن ايه كمية ال charges اللي بتقطع
+
+37
+00:02:42,040 --> 00:02:46,820
+مساحة معينة فترة زمنية per unit time اللي ال
+
+38
+00:02:46,820 --> 00:02:50,260
+electric charging passing through the area per
+
+39
+00:02:50,260 --> 00:02:55,700
+unit timeيعني أن I هي DQ بDT إذا بتذكروا قلنا ال
+
+40
+00:02:55,700 --> 00:02:58,540
+current اللي علاقة بالcharges و ال voltage اللي
+
+41
+00:02:58,540 --> 00:03:02,160
+علاقة بالcharges واحد اللي علاقة بال rate بتاعة ال
+
+42
+00:03:02,160 --> 00:03:06,220
+charge DQ بDT والتاني بقدرش بفصل ال charges اللي
+
+43
+00:03:06,220 --> 00:03:13,420
+هي ال voltage DW بDQ إذا التيار هو DQ بDT إذا كانت
+
+44
+00:03:13,420 --> 00:03:17,180
+ال charge بال column و ال time بال second بيكون ال
+
+45
+00:03:17,180 --> 00:03:21,320
+current بلقاش بالامبيركمان احنا لن نقدر نعرف اللي
+
+46
+00:03:21,320 --> 00:03:25,260
+هي current density J current density معناه density
+
+47
+00:03:25,260 --> 00:03:29,580
+عن حاجة بالنسبة ل area او بالنسبة ل volume احنا
+
+48
+00:03:29,580 --> 00:03:33,160
+بنحكي عن current density بالنسبة ل area ف J هي
+
+49
+00:03:33,160 --> 00:03:37,580
+عبارة عن delta I by delta S او delta I اش بتساوي J
+
+50
+00:03:37,580 --> 00:03:43,250
+في delta Sغالبا ال current احنا قلنا هي ال current
+
+51
+00:03:43,250 --> 00:03:47,630
+هو عبارة عن الشحنات اللى بتمرق من ال area الشحنات
+
+52
+00:03:47,630 --> 00:03:50,050
+اللى بتقطع واحدة ال area لو انا مثلا عندى ال
+
+53
+00:03:50,050 --> 00:03:53,230
+circular ال area بتاعتى زى هذا القلم وهي ال
+
+54
+00:03:53,230 --> 00:03:56,610
+current ماشي في قلبه هلاحظ انه دايما عمودي ماله
+
+55
+00:03:56,610 --> 00:04:01,190
+على اتجاه و عمودي على cross section فال current
+
+56
+00:04:01,190 --> 00:04:06,150
+density ماله دايما عمودي على ال surface واضح شىء
+
+57
+00:04:06,150 --> 00:04:10,000
+بيصير تدفق ال charges بيكون في هذا الاتجاههي
+
+58
+00:04:10,000 --> 00:04:13,180
+تخيلوا هذا ال metal او ال dielectric و ال charges
+
+59
+00:04:13,180 --> 00:04:16,980
+بتمر في هيك او يعني هيك او هيك مش فارق انا بس
+
+60
+00:04:16,980 --> 00:04:19,600
+تخيلوا ال charges كمية ال charges اللي بتقطع ال
+
+61
+00:04:19,600 --> 00:04:24,780
+unit area اللي هي الدائرة بالزمن هي اتجاه ال
+
+62
+00:04:24,780 --> 00:04:26,800
+current او ال current density هنلاقي دايما ال
+
+63
+00:04:26,800 --> 00:04:30,400
+current density اللي ماله عمودي على اتجاه ال area
+
+64
+00:04:32,070 --> 00:04:36,050
+إذا عندي delta I ايش بتساوي J delta S لأن J هي
+
+65
+00:04:36,050 --> 00:04:38,890
+عبارة عن ال mean لل current density يعني delta I
+
+66
+00:04:38,890 --> 00:04:44,250
+على delta S إذا اتفقنا إن J هي vector عمودي على ال
+
+67
+00:04:44,250 --> 00:04:49,850
+area إذا هيكون delta I أيش بتساوي J dot DS J dot
+
+68
+00:04:49,850 --> 00:04:54,110
+DS وإحنا أصلا أخدنا إن ال S ماله ال unit vector
+
+69
+00:04:54,110 --> 00:04:57,870
+تبعها عمودي عليها برضهعشان هيك احنا قولنا dot
+
+70
+00:04:57,870 --> 00:05:01,410
+product إذا ال DS ال unit vector العمودي عليها و
+
+71
+00:05:01,410 --> 00:05:05,890
+ال J عمودي على ال area إذا ال J في delta S و عبارة
+
+72
+00:05:05,890 --> 00:05:12,810
+عن J dot DS واضح؟ as vectors طيب
+
+73
+00:05:12,810 --> 00:05:19,490
+ال total current I هذا ال delta ال total current
+
+74
+00:05:19,490 --> 00:05:24,570
+اللي هيكون التكامل على ال surface J dot DS واضح؟
+
+75
+00:05:28,740 --> 00:05:31,880
+طب احنا قولنا انه في تفريق ما بين two currents
+
+76
+00:05:31,880 --> 00:05:36,060
+احنا هنا عرفنا ال current و current density و احنا
+
+77
+00:05:36,060 --> 00:05:39,240
+بدنا نعرف اللي هو ال current انه تلت أنواع من ال
+
+78
+00:05:39,240 --> 00:05:42,500
+currents اللي هيمروا عليكم في مغساق الكهرومغناطية
+
+79
+00:05:42,500 --> 00:05:46,280
+أسوأ الواحد الأول أو الأول والتاني هم ال
+
+80
+00:05:46,280 --> 00:05:49,380
+convection ال conduction و ال displacement فهذا
+
+81
+00:05:49,380 --> 00:05:51,800
+الشبطر احنا بس هنحكي عن convection او التفريق ما
+
+82
+00:05:51,800 --> 00:05:55,490
+بين convection و conductionthis placement هتكون في
+
+83
+00:05:55,490 --> 00:06:06,930
+شباتر لاحقة في شبتر 9 اللي هتاخدوه في كهره 2 طبعا
+
+84
+00:06:06,930 --> 00:06:09,290
+إيش الفرق بين convection و conduction؟ ال
+
+85
+00:06:09,290 --> 00:06:13,950
+convection مالوش علاقة بconductor مالوش علاقة بإنه
+
+86
+00:06:13,950 --> 00:06:18,130
+تيار بمر في conductor ولا بحقق ohms law ال
+
+87
+00:06:18,130 --> 00:06:19,610
+convection لا مربوط
+
+88
+00:06:30,030 --> 00:06:36,070
+هو عبارة عن مجموعات، هو عبارة عن التيار اللي بتدفق
+
+89
+00:06:36,070 --> 00:06:40,470
+في المادة العازلة، بسخن ميا بتدفق convection
+
+90
+00:06:40,470 --> 00:06:44,350
+current يعني مش heat دي، بس يعني أنه لو مثلا بدي
+
+91
+00:06:44,350 --> 00:06:49,210
+insulators على الميا، بمر فيها تيار، هذا بسمي
+
+92
+00:06:49,210 --> 00:06:54,100
+convection currentإذن هو عبارة عن التيار اللي بمر
+
+93
+00:06:54,100 --> 00:06:57,500
+في مين في ال insulating media احنا قلنا طبيعة
+
+94
+00:06:57,500 --> 00:07:01,740
+المواد حسب ال conductivity بنقسمها لميتال وإيش
+
+95
+00:07:01,740 --> 00:07:05,920
+insulator التيار بمر في ال insulators زي ال liquid
+
+96
+00:07:05,920 --> 00:07:10,020
+ال red gases ال vacuum هدولة ماله اللي التيار
+
+97
+00:07:10,020 --> 00:07:15,900
+بمروا فيهم بنسميه convection current لكن
+
+98
+00:07:16,760 --> 00:07:21,020
+حتى مثال عليها يعني قبل ما نروح لل conduction مثال
+
+99
+00:07:21,020 --> 00:07:24,680
+عليها إذا بتذكروا ال cathode ray tube أخدتوها يمكن
+
+100
+00:07:24,680 --> 00:07:28,500
+شفتوا ال oscilloscope التلفزيونات بتاع الزمان beam
+
+101
+00:07:28,500 --> 00:07:32,760
+الإلكترونات اللي كان بسقط على الشاشة عشان يحددنا
+
+102
+00:07:32,760 --> 00:07:37,820
+موقع الصورة هذا بنسميه convection current لأنه مش
+
+103
+00:07:37,820 --> 00:07:41,020
+مرموض في ال conductor و عبارة عن beam الإلكترونات
+
+104
+00:07:41,020 --> 00:07:46,520
+بتنطلقمن اللي هو ال cathode و بتتدفق لحين ما توصل
+
+105
+00:07:46,520 --> 00:07:50,520
+للشاشة بتاعة ال cathode ray tube و بتفتح لواقع
+
+106
+00:07:50,520 --> 00:07:53,260
+الصورة هدول كل ما أمثل على convection current
+
+107
+00:07:53,260 --> 00:07:59,960
+Electro net بلعشان قلها قبل مرة فبطلقها من cathode
+
+108
+00:07:59,960 --> 00:08:03,040
+بطريقة معينة اللي بفرض voltage حواليها هذا ال
+
+109
+00:08:03,040 --> 00:08:06,780
+cathode تطلق منه Electro net ممكن تنطلق في الهواء
+
+110
+00:08:06,780 --> 00:08:11,860
+في dielectric mediaمهم انها مادة انسولاتور هذا
+
+111
+00:08:11,860 --> 00:08:15,800
+بنسميه convection conduction واضح انه له علاقة
+
+112
+00:08:15,800 --> 00:08:22,700
+ماله بالكندكتور عشان الموجودة علاقات ما بين ال
+
+113
+00:08:22,700 --> 00:08:27,120
+conduction current و current density و ohms law
+
+114
+00:08:27,120 --> 00:08:31,080
+بتنا نبدأ ان اعرف ال current الممور في filament
+
+115
+00:08:31,080 --> 00:08:37,460
+هاي filament هي قطعة من metal و بتدفق عند فيها
+
+116
+00:08:37,460 --> 00:08:44,770
+تيار بسرعة Uالتيار تجاه الحط المتقطن بمشي بسرعة U
+
+117
+00:08:44,770 --> 00:08:49,690
+U هي ال velocity بتاعة الإلكترونات اللي بتمثل
+
+118
+00:08:49,690 --> 00:08:57,570
+الكورنت احنا عرفنا ان دلتة I اش بتساوي او يعني DI
+
+119
+00:08:57,570 --> 00:09:01,810
+بس احنا بداخل دلتة I شويه اكبر من DI هي دلتة Q على
+
+120
+00:09:01,810 --> 00:09:07,380
+دلتة Tإذا عرفت إن ال charge density في هذا ال
+
+121
+00:09:07,380 --> 00:09:12,460
+filament، في هذا القطع من المتل، هي عبارة عن ρو V،
+
+122
+00:09:12,460 --> 00:09:15,280
+فهذا ال charge density رو V، إذا ال total charge
+
+123
+00:09:15,280 --> 00:09:21,600
+هي رو V في ال volume، صحيح؟ لو أخدت element من ال
+
+124
+00:09:21,600 --> 00:09:25,120
+volume، هذا ال element، هذا اللي محصول بين اللوحين
+
+125
+00:09:25,120 --> 00:09:30,170
+المقطعين، هذا ال element أخدته، هذا ال volumeهيكون
+
+126
+00:09:30,170 --> 00:09:32,970
+إيش ال volume بيساوي؟ ال area اللي هو مسميها delta
+
+127
+00:09:32,970 --> 00:09:38,030
+S اللي هو المربع ثمين في الطول طول بيساوي ال
+
+128
+00:09:38,030 --> 00:09:41,430
+velocity في الزمن اللي هو delta Y مسميها أو delta
+
+129
+00:09:41,430 --> 00:09:48,620
+L هتكأس سوى ال velocity اللي هي U في Tمعايا؟ اذا
+
+130
+00:09:48,620 --> 00:09:52,560
+احنا خدنا هذا ال delta volume اللي هو ما بين ال
+
+131
+00:09:52,560 --> 00:09:56,520
+two surfaces هذا delta volume which charges to rho
+
+132
+00:09:56,520 --> 00:09:59,920
+V اذا total charge delta V ماهي ساوية؟ rho V في
+
+133
+00:09:59,920 --> 00:10:04,200
+delta V delta V ايش هتكون؟ delta S اللي هي هذا ال
+
+134
+00:10:04,200 --> 00:10:10,120
+surface area في الطول متوازى الأطلع او يعني المكعب
+
+135
+00:10:10,120 --> 00:10:15,690
+هذاالطول هداش بيساوي ال Velocity في Delta T لو
+
+136
+00:10:15,690 --> 00:10:18,710
+عملنا هيك Delta T بتروح من الطرفين من فوق و تحت
+
+137
+00:10:18,710 --> 00:10:24,230
+هيضل عند مين رو V Delta S في U واضح؟ في S في ساعة
+
+138
+00:10:24,230 --> 00:10:28,410
+اللي حد هنا؟ اذا Delta I تتساوي رو V اللي هي ال
+
+139
+00:10:28,410 --> 00:10:31,890
+charge density في Delta S اللي هي ال cross section
+
+140
+00:10:31,890 --> 00:10:35,070
+تبع ال filament في U اللي هي Velocity تعتي
+
+141
+00:10:35,070 --> 00:10:38,090
+الإلكترونات اللي بتدفق عبر الفيلمنت
+
+142
+00:10:40,320 --> 00:10:43,100
+حنا عرفنا ال current density انها delta I على
+
+143
+00:10:43,100 --> 00:10:46,120
+delta S، إذا ال current density ايش بالساوية، لو
+
+144
+00:10:46,120 --> 00:10:49,340
+قسمنا delta I على delta S، هتساوية charge density
+
+145
+00:10:49,340 --> 00:10:55,090
+في الvolume stateهتكون ρو V في U إذا جيه بشكل عام
+
+146
+00:10:55,090 --> 00:10:57,410
+هدد جيه اللي هي في اتجاه ال Y يعني هو أنا ماخد
+
+147
+00:10:57,410 --> 00:11:00,730
+واحدة منهم مفترض ان كله في اتجاه ال Y تدفق فجيه
+
+148
+00:11:00,730 --> 00:11:04,490
+بشكل عام as a vector هي سوى رو في U اللي هي vector
+
+149
+00:11:04,490 --> 00:11:08,450
+رو ال charge density مالها scalar U ممكن تكون UX,
+
+150
+00:11:08,590 --> 00:11:14,990
+UI و Z فبشكل عام هتكون ال charge density عبارة عن
+
+151
+00:11:14,990 --> 00:11:20,640
+رو V في UI لو احنا قلنا I هي ال convection current
+
+152
+00:11:20,640 --> 00:11:24,320
+هيكون جه هي ال convection current density لو قلنا
+
+153
+00:11:24,320 --> 00:11:27,720
+I هي ال conduction current هتكون جه هي ال
+
+154
+00:11:27,720 --> 00:11:31,680
+conduction current per unit density اذا كانت I
+
+155
+00:11:31,680 --> 00:11:36,320
+بالامبير جه هتكون امبير بمتر تربيع لان هي عبارة عن
+
+156
+00:11:36,320 --> 00:11:40,860
+current على area اذا جه بقدر اخدايما اربطها بانها
+
+157
+00:11:40,860 --> 00:11:44,220
+current density بال velocity او هي عبارة من delta
+
+158
+00:11:44,220 --> 00:11:47,060
+I على delta S تمام؟
+
+159
+00:11:51,920 --> 00:11:55,080
+نكمل تعريفنا ل Ohm's law يعني إحنا قولنا ال
+
+160
+00:11:55,080 --> 00:11:58,820
+conduction له علاقة ب Ohm's law كمان مرة ال
+
+161
+00:11:58,820 --> 00:12:02,540
+conductor conduction current بده conductor مامشيش
+
+162
+00:12:02,540 --> 00:12:03,260
+إلا في conductor
+
+163
+00:12:06,450 --> 00:12:10,150
+وبعبّر عن ال current بإن هو عبارة عن كمية هائلة من
+
+164
+00:12:10,150 --> 00:12:13,290
+الإلكترونات اللي بتتدفق عبر ال cross-section
+
+165
+00:12:13,290 --> 00:12:17,910
+للكوندكتور في وحدة الزمن، فبتذكرين حتى قلنا إن ال
+
+166
+00:12:17,910 --> 00:12:21,350
+charges مالها discrete، إذا بتذكروا في الدوائر،
+
+167
+00:12:21,350 --> 00:12:25,670
+بينما ال current ماله continuous، اذا ال conductor
+
+168
+00:12:25,670 --> 00:12:28,030
+is characterized by a large amount of free
+
+169
+00:12:28,030 --> 00:12:30,350
+electrons that provide conduction current due and
+
+170
+00:12:30,350 --> 00:12:31,290
+impressed electrically
+
+171
+00:12:33,790 --> 00:12:37,690
+الإلاقة لو كان عند ال conductor في وجود electric
+
+172
+00:12:37,690 --> 00:12:41,270
+fieldهدول الإلكترونات الموجودة في القندكتور إيش
+
+173
+00:12:41,270 --> 00:12:44,670
+هيصيرلها؟ هتأثر ال electric field هيتولد عليها قوة
+
+174
+00:12:44,670 --> 00:12:48,130
+احنا عرفنا ال force إيش بتساوي minus E في E minus
+
+175
+00:12:48,130 --> 00:12:51,690
+الشحنة في ال electric field يعني لو أنا حطيت
+
+176
+00:12:51,690 --> 00:12:55,690
+القندكتور في وجود المجال ال electric field ساعتي
+
+177
+00:12:55,690 --> 00:12:59,070
+هو في ال free space بس حطيت في طريقه ال electric
+
+178
+00:12:59,070 --> 00:13:03,370
+field الإلكترونات هتتأثر في وجود ال electric field
+
+179
+00:13:03,370 --> 00:13:07,730
+لإنه هينفرض عليها قوة و القوة إيش بتساوي؟ minus E
+
+180
+00:13:07,730 --> 00:13:07,990
+في E
+
+181
+00:13:11,030 --> 00:13:13,330
+طبعا إذا هو الإلكترون، أنا بحكي عن إلكترون في قلب
+
+182
+00:13:13,330 --> 00:13:16,310
+الconductor، بيفرق عن أحكي عن إلكترون في ال free
+
+183
+00:13:16,310 --> 00:13:19,130
+space، إلكترون حاطيته في ال free space و حاطيت فيه
+
+184
+00:13:19,130 --> 00:13:22,650
+عند مجال الكهربائي electric field، حلاق الإلكترون
+
+185
+00:13:22,650 --> 00:13:25,350
+ماله، إذا الإلكترون فيه في هايك اتجاه، هو هيتجه في
+
+186
+00:13:25,350 --> 00:13:29,930
+اتجاه المعاكس صح؟ لو شحنه موجبة، هتتحرك معاه، لكن
+
+187
+00:13:29,930 --> 00:13:33,990
+إحنا بنحكي علىElectron مش لحاله، مش في ال free
+
+188
+00:13:33,990 --> 00:13:35,930
+space، هو موجود في ال conductor، إيش ما هو موجود
+
+189
+00:13:35,930 --> 00:13:37,950
+في ال conductor؟ موجود في ال atoms بتاعة ال
+
+190
+00:13:37,950 --> 00:13:41,470
+conductor، يعني مربوط في lattice من ال atoms، مش
+
+191
+00:13:41,470 --> 00:13:45,670
+حر الحركة، هو مربوط في هدول ال atoms فإيش وجود
+
+192
+00:13:45,670 --> 00:13:49,170
+electric field هيعمله؟ هيعمله اتصاد معاه، هيتحرك،
+
+193
+00:13:49,170 --> 00:13:53,070
+هو بده يتحرك، بس هو مش في ال free space يجري، هو
+
+194
+00:13:53,070 --> 00:13:56,650
+موجود في قلب atoms، في lattice من ال atoms، فهيعمل
+
+195
+00:13:56,650 --> 00:13:57,070
+collisions
+
+196
+00:14:02,080 --> 00:14:04,560
+نتيجة هذا الـ collisions اللى هيصلله نتيجة انه
+
+197
+00:14:04,560 --> 00:14:06,740
+موجود في الـ electric field هيصير فيه عند الـ
+
+198
+00:14:06,740 --> 00:14:10,420
+drift فلوستي يعني مش هيصلله انطلاق فلوستي معينة
+
+199
+00:14:10,420 --> 00:14:14,360
+هيصلله drift يعني هيتحرك collision هيصلله شوية
+
+200
+00:14:14,360 --> 00:14:21,820
+فلوستي بنسميها ال drift فلوستي اللى هى بتعبر عن
+
+201
+00:14:21,820 --> 00:14:25,780
+انتقاله من زرع لزرع تانية او استضامه من زرع لزرع
+
+202
+00:14:25,780 --> 00:14:29,680
+تانية طب اذا انا كان عندى electron ال mass بتاعته
+
+203
+00:14:29,680 --> 00:14:35,040
+سميتها Mطبعا هو بيصيله قاعد دريفت بلغة مقدار هيوم
+
+204
+00:14:35,040 --> 00:14:39,180
+القانون بيقوللي قوانين نيوتن بتقوللي تغير في كمية
+
+205
+00:14:39,180 --> 00:14:44,080
+الحركة إيش لازم تساوي القوة على الجسم صح بالنسبة
+
+206
+00:14:44,080 --> 00:14:46,560
+للإلكترونات إيش القوة اللي عالية أعملها هو قاعد في
+
+207
+00:14:46,560 --> 00:14:49,940
+electric field minus E في E صح هذا إيش لازم تساوي
+
+208
+00:14:49,940 --> 00:14:52,840
+تغير في كمية التحرك التغير في كمية التحرك اللي هو
+
+209
+00:14:52,840 --> 00:14:57,300
+عمبرا عن M في V على Ta اللي هي DMV على DT
+
+210
+00:15:01,110 --> 00:15:05,110
+أذن الـvelocity بترفت الـvelocity هتساوي minus E
+
+211
+00:15:05,110 --> 00:15:10,650
+في TAU على M في E TAU اللي هي الـaverage طاية ما
+
+212
+00:15:10,650 --> 00:15:16,290
+بين الـcollision و الـcollision التاني، باضح؟ أذن
+
+213
+00:15:16,290 --> 00:15:23,550
+velocity عبّرنا عنها minus E TAU على M في E لو
+
+214
+00:15:23,550 --> 00:15:27,070
+أحنا عبّرنا عن ناقص M في E بإنها ال charge density
+
+215
+00:15:27,070 --> 00:15:30,710
+بحيث أنه M هذه هي عبارة عن M كبتر على V
+
+216
+00:15:36,780 --> 00:15:44,820
+بترفت بالمصطفى ماهي بتساوي او
+
+217
+00:15:44,820 --> 00:15:49,980
+ارتبهم من هى كده بيديهم انا
+
+218
+00:15:49,980 --> 00:15:53,800
+كمان
+
+219
+00:15:53,800 --> 00:16:00,380
+عندى ال charge density رو V ايش بتساوي ال total
+
+220
+00:16:00,380 --> 00:16:04,600
+charge ايش يقول ال total charge بيساوي عددهم في
+
+221
+00:16:04,600 --> 00:16:11,060
+شحنة اللى بيكترههذه في V Q
+
+222
+00:16:11,060 --> 00:16:18,460
+total تساوي رو في V فإذا رو V تساوي minus N في E
+
+223
+00:16:18,460 --> 00:16:22,760
+ليه N مين؟ N capital على V number of charges per
+
+224
+00:16:22,760 --> 00:16:27,180
+unit volume ال total charge تساوي Q في V اللي هو
+
+225
+00:16:27,180 --> 00:16:32,140
+هذا ال volume بتساوي ال total N في E ال total
+
+226
+00:16:32,140 --> 00:16:37,980
+charges في ERow V هي Charge بين Volume وDensity هي
+
+227
+00:16:37,980 --> 00:16:44,440
+Charge بين Volume تساوي نقل
+
+228
+00:16:44,440 --> 00:16:48,120
+نقل نقل
+
+229
+00:16:48,120 --> 00:16:51,640
+نقل
+
+230
+00:16:51,640 --> 00:16:59,080
+نقل
+
+231
+00:16:59,080 --> 00:17:05,730
+نقل نقل نقل نقل نقل نقل نقل نقل نقلRow V منعوض
+
+232
+00:17:05,730 --> 00:17:14,330
+عنها هي minus M E متعود عن V يعني كمان minus تصير
+
+233
+00:17:14,330 --> 00:17:22,650
+plus E تربيه تو على M في E جيه
+
+234
+00:17:22,650 --> 00:17:28,070
+اللي هو current density بيساوي constant value في E
+
+235
+00:17:28,070 --> 00:17:31,190
+ايش هال constant ان E تربيه ان احنا عارفين انها ال
+
+236
+00:17:31,190 --> 00:17:35,640
+charge بتاعة الالكترون تربيهتاول average time
+
+237
+00:17:35,640 --> 00:17:41,240
+between two intervals رقم أن عددهم رقم على n رقم
+
+238
+00:17:41,240 --> 00:17:47,680
+فإذا هنكون العلاقة بين J و E هي أبارعا some value
+
+239
+00:17:47,680 --> 00:17:56,560
+بنسميها sigma sigma اللي هي conductivity sigma ال
+
+240
+00:17:56,560 --> 00:18:02,020
+conductivity اللي هي بنعبر عنها واحد على رقم تمام؟
+
+241
+00:18:11,120 --> 00:18:14,800
+في S فصرحت هنا هذا كمان بنعبر عن جيه اللي بتساوي
+
+242
+00:18:14,800 --> 00:18:21,000
+sigma E اللي هو point form of Ohm's law شكل من
+
+243
+00:18:21,000 --> 00:18:25,220
+أشكال Ohm's law هو point form of Ohm's law اللي
+
+244
+00:18:25,220 --> 00:18:29,080
+برمتلي current density جيه بال electric field
+
+245
+00:18:29,080 --> 00:18:34,420
+بواسط sigma اللي هي conductivity و بعدنا هنشوف كيف
+
+246
+00:18:34,420 --> 00:18:37,380
+هذا من انه بنطلع بOhm's law لإنه E بتساوي V على L
+
+247
+00:18:37,380 --> 00:18:43,160
+وجيه بتساوي I P على Sاللي هي current buoyant area
+
+248
+00:18:43,160 --> 00:18:50,860
+وبنستنتج منها Ohms لو برضه اذا
+
+249
+00:18:50,860 --> 00:18:55,740
+كمان مرة جيه اللي هي current density مربوطة في ال
+
+250
+00:18:55,740 --> 00:19:01,160
+electric field بواسطة signal ال
+
+251
+00:19:01,160 --> 00:19:06,890
+conductors ال conductor غالباهو عبارة عن element
+
+252
+00:19:06,890 --> 00:19:10,690
+اللي فيه إلكترونات بتحرك يعني نسبيا بالنسبالي ال
+
+253
+00:19:10,690 --> 00:19:16,390
+insulators بحرية هاي عند أنا perfect conductor هذا
+
+254
+00:19:16,390 --> 00:19:19,910
+ال perfect conductor مرقت فيه electric field بهذا
+
+255
+00:19:19,910 --> 00:19:24,350
+الشكل هاي مجال كهربائي إيش هي من مجال الكهربائي
+
+256
+00:19:24,350 --> 00:19:27,750
+الإلكترو النقلة الشحنات الموجودة هتجذب في طريقة
+
+257
+00:19:27,750 --> 00:19:31,390
+الشحنات الموجبة و تتزاحم على هذا الطرف من ال
+
+258
+00:19:31,390 --> 00:19:35,040
+conductorهذا تخيلوني على كندكتور طويل هيك المادة
+
+259
+00:19:35,040 --> 00:19:40,360
+لحالها و على الطرف التاني هيكون في عندي ال
+
+260
+00:19:40,360 --> 00:19:44,460
+negative charges اتكومت هنا ايش بيصير عندي؟ بيصير
+
+261
+00:19:44,460 --> 00:19:48,680
+الطرف من الكندكتور عليه شحنات موجبة و الطرف التاني
+
+262
+00:19:48,680 --> 00:19:52,220
+عليه شحنات سالبة ايش هيتولد؟ هيتولد عندي internal
+
+263
+00:19:52,220 --> 00:19:55,220
+electric field هذا ال internal electric field
+
+264
+00:19:55,220 --> 00:19:57,960
+بالتمام بيساوي ال electric field اللي هو ال
+
+265
+00:19:57,960 --> 00:20:03,380
+external انا اللي ابتعدتترتيب الشحنات نتج عن وجود
+
+266
+00:20:03,380 --> 00:20:06,360
+الـ External Electric Field.بالتالي الـ Internal
+
+267
+00:20:06,360 --> 00:20:10,160
+Electric Field اتجاهه معاكس للـ External وبسويه في
+
+268
+00:20:10,160 --> 00:20:15,320
+المقدار ففي داخل ال conductor لو جمعنا الـ Total
+
+269
+00:20:15,320 --> 00:20:19,040
+Electric Field هيكون ال External زاد ال Internal،
+
+270
+00:20:19,040 --> 00:20:23,600
+مش هيكون بساوة Zero إذا ال Electric Field بساوة
+
+271
+00:20:23,600 --> 00:20:27,410
+Zero في قلب ال conductorو احنا بنعرف من gauss law
+
+272
+00:20:27,410 --> 00:20:32,190
+ان ال close integral ل EWS بيساوي raw V على
+
+273
+00:20:32,190 --> 00:20:36,230
+epsilon نقطة صح؟ طب اذا E بيساوي 0 معناه ان ال
+
+274
+00:20:36,230 --> 00:20:38,830
+charge هو ما لها سفر وهذا مواضح لان كل ال charges
+
+275
+00:20:38,830 --> 00:20:43,110
+و انا ايش صار لها charges؟ اتزاحمت عند الأطراف فزا
+
+276
+00:20:43,110 --> 00:20:47,070
+ال charge تنسبش هو ما لها بيساوي سفرهذا الحكاية
+
+277
+00:20:47,070 --> 00:20:52,230
+بيعني ماله منطقي بالنسبالنا E0 معناه ال charge
+
+278
+00:20:52,230 --> 00:20:55,590
+enclosed مالها zero و طبعا أكيد ال charge enclosed
+
+279
+00:20:55,590 --> 00:20:59,830
+zero لأن كل charges مالها اتركمت عند الأطراف احنا
+
+280
+00:20:59,830 --> 00:21:04,230
+بنسمي ال conductor في وجود electric field انه
+
+281
+00:21:04,230 --> 00:21:06,730
+equipotential body طب ليش بنسميه equipotential
+
+282
+00:21:06,730 --> 00:21:10,990
+body ايش
+
+283
+00:21:10,990 --> 00:21:13,530
+معناه equipotential بتذكرين ايش احنا بقولوا معناه
+
+284
+00:21:13,530 --> 00:21:19,480
+equipotentialإيش معنى equopotential تذكرين؟
+
+285
+00:21:19,480 --> 00:21:23,360
+أخدناها لسه المحاضرة الماضية، إيش معنى
+
+286
+00:21:23,360 --> 00:21:28,360
+equopotential؟ equopotential surface، إيش معنى
+
+287
+00:21:28,360 --> 00:21:32,300
+equopotential surface؟
+
+288
+00:21:32,300 --> 00:21:34,600
+يا ده اخيل الله شوية إنجليزي، بلاش تكونوا بتعرفوا
+
+289
+00:21:34,600 --> 00:21:39,260
+كهروم، شوية إنجليزي، equi-potential equi من equal
+
+290
+00:21:39,260 --> 00:21:42,200
+و potential potential, equopotential يعني إيه ال
+
+291
+00:21:42,200 --> 00:21:46,400
+potential بقى له متساوييعني ال potential عند أي
+
+292
+00:21:46,400 --> 00:21:50,380
+نقطة ماله متساوي طب ليش هذا الحكي؟ إيش اللي نقيه
+
+293
+00:21:50,380 --> 00:21:52,640
+بساوي؟ مذاكرين إيش لفة ال electric field بال
+
+294
+00:21:52,640 --> 00:21:56,840
+potential؟ electric field بساوى minus del V ولا
+
+295
+00:21:56,840 --> 00:22:00,820
+لأ؟مش قلنا E و أثبتناها المحاضرة الماضية E بالساوة
+
+296
+00:22:00,820 --> 00:22:04,240
+و minus ال V E بالساوة 0 إذا ال differential تبع V
+
+297
+00:22:04,240 --> 00:22:06,440
+إيش بالساوة 0؟ إيش مع ال differential تبع V
+
+298
+00:22:06,440 --> 00:22:09,420
+بالساوة 0؟ يعني ال voltage عند أي نقطة و أي نقطة
+
+299
+00:22:09,420 --> 00:22:12,460
+لازم يكون متساوي إذا ال differential تبعه بالساوة
+
+300
+00:22:12,460 --> 00:22:16,140
+0 عشان هيك إحنا بنسمي ال conductor أو ال perfect
+
+301
+00:22:16,140 --> 00:22:19,480
+conductor ال occupational body يعني ال voltage عند
+
+302
+00:22:19,480 --> 00:22:22,720
+أي نقطة عند أي نقطة لازم يكون متساوي
+
+303
+00:22:26,880 --> 00:22:29,280
+طيب احنا لو رجعنا ل أومزلو و قولنا J بالثانوية و
+
+304
+00:22:29,280 --> 00:22:34,360
+ثانوية ايه؟ ايه بتروح للسفر في inside ال conductor
+
+305
+00:22:34,360 --> 00:22:39,200
+عشان J تتظل حاصلة current density يعني تكون finite
+
+306
+00:22:39,940 --> 00:22:43,760
+مش تروح لقيمة غير معينة لأن فيه اندي طيار انا
+
+307
+00:22:43,760 --> 00:22:46,400
+بأمره sigma ايش لازم تكون infinity هذا perfect
+
+308
+00:22:46,400 --> 00:22:49,480
+conductor perfect conductor ايش معناه انه مافيش
+
+309
+00:22:49,480 --> 00:22:52,740
+عنده اي resistivity احنا بنحكي ع perfect conductor
+
+310
+00:22:52,740 --> 00:22:55,400
+perfect conductors بحتويش عنده في قلبه اي
+
+311
+00:22:55,400 --> 00:22:59,930
+electrostatic electric fieldبمنع اللي خطوط المجال
+
+312
+00:22:59,930 --> 00:23:02,730
+الكهربائي اللي هتكون جوا و أثبتنا ليش ال electric
+
+313
+00:23:02,730 --> 00:23:06,130
+field إيش بيكون Zero جوا بيصير زي ال equipotential
+
+314
+00:23:06,130 --> 00:23:09,630
+surfaces إذا إذا E بيسوا Zero معناه إنه Sigma
+
+315
+00:23:09,630 --> 00:23:14,630
+بتروح ل M ثلاثين و هذا الحكي أنا حكيته E بيسوا
+
+316
+00:23:14,630 --> 00:23:18,150
+Zero معناه روف بيسوا Zero من جاسله و برضه من تعريف
+
+317
+00:23:18,150 --> 00:23:20,610
+ال electric field إنه برضه ال potential هيكون Zero
+
+318
+00:23:20,610 --> 00:23:23,210
+لأنه ال electric هي بيساوم نص لل V
+
+319
+00:23:29,720 --> 00:23:32,880
+فبنيجي ل electric fields in material space، احنا
+
+320
+00:23:32,880 --> 00:23:34,880
+لازمنا في ال material space بس في هذه الحالة أنا
+
+321
+00:23:34,880 --> 00:23:39,000
+بتعمل حاجة تانية، بديش اخلي زي ما انا طوى شوفنا ان
+
+322
+00:23:39,000 --> 00:23:41,700
+ال conductor هيكي في ال free space و حطينا في
+
+323
+00:23:41,700 --> 00:23:49,220
+الاتجاه .. فرضنا electric field فيهطريقة اما هنا
+
+324
+00:23:49,220 --> 00:23:52,320
+انا بالعكس بدأ اوصله مع اسلاك ماديش اخليه في ال
+
+325
+00:23:52,320 --> 00:23:56,340
+space بطل ال free space انا وصلها ب conductors هذا
+
+326
+00:23:56,340 --> 00:24:00,460
+ال element تبعي او المادة بتاعتى ال perfect
+
+327
+00:24:00,460 --> 00:24:04,160
+conductor او ال material space وصلته باسلاك عبر
+
+328
+00:24:04,160 --> 00:24:09,280
+بطارية الفرق بين ده الشكل و ده الشكل ان هناك
+
+329
+00:24:12,090 --> 00:24:15,310
+مافيش اي connections في ال conductor هذا، مش وصلها
+
+330
+00:24:15,310 --> 00:24:19,430
+بأي حاجة، في مجال كهربائي أنا حاططه في وجود المجال
+
+331
+00:24:19,430 --> 00:24:23,330
+الكهربائي، لكن هنا أنا وصلته بواسطة أسلاك مع
+
+332
+00:24:23,330 --> 00:24:27,760
+بطاريةهذه البطارية عملت فرق جهود بين الطرفين
+
+333
+00:24:27,760 --> 00:24:31,500
+وبالتالي هيمور electric field في قلب ال conductor
+
+334
+00:24:31,500 --> 00:24:35,880
+هذا electric field هيقدر إلى إيش؟ تدفق الشحنات
+
+335
+00:24:35,880 --> 00:24:40,140
+اللي هذا اللي هو كرسي الدوائر هيصير ان دي طيار
+
+336
+00:24:40,140 --> 00:24:43,600
+بيمور في الدائرة الكهربائية في هذه الحالة ماقدرش
+
+337
+00:24:43,600 --> 00:24:45,820
+أقول ان ال electric field inside ال conductor
+
+338
+00:24:45,820 --> 00:24:51,390
+بيساوي zeroهنا فيه قوة بتجبر الالكترونات مانا
+
+339
+00:24:51,390 --> 00:24:56,390
+تتضفق من طرف لطرف تاني في حركة مستمرة وبالتالي
+
+340
+00:24:56,390 --> 00:24:59,770
+هيكون في عندى electric field inside ال conductor
+
+341
+00:24:59,770 --> 00:25:10,170
+احنا
+
+342
+00:25:10,170 --> 00:25:15,880
+قولنا انه E ايش بساوي؟V على L او V بتساوي اذا كان
+
+343
+00:25:15,880 --> 00:25:19,100
+ال clause integral او ال integral over L E ضد DL
+
+344
+00:25:19,100 --> 00:25:27,260
+او بساطة اذا عندي اقل يعني معروف الطول فإذا كان E
+
+345
+00:25:27,260 --> 00:25:31,200
+constant هيكون E في L هذا ال general الشكل تبعه V
+
+346
+00:25:31,200 --> 00:25:36,680
+بتساوي ال integral E ضد DLE constant وقال طول معين
+
+347
+00:25:36,680 --> 00:25:40,460
+من 0 لL حلص V بيساوي E في L فهذا electric field
+
+348
+00:25:40,460 --> 00:25:44,540
+لconductor اللي له form cross section S وقال طول L
+
+349
+00:25:44,540 --> 00:25:51,550
+هيكون بيساوي E بيساوي V على Lتمام؟ فاحنا عرفنا ال
+
+350
+00:25:51,550 --> 00:25:54,850
+current density إيش بتساوي I على S J ال current
+
+351
+00:25:54,850 --> 00:25:59,590
+density إيش بتساوي I على S و J إيش بتساوي Sigma في
+
+352
+00:25:59,590 --> 00:26:04,530
+E و E إيش بتساوي V على L إذا I على S إيش بتساوي
+
+353
+00:26:04,530 --> 00:26:09,710
+Sigma V على L طب أنا بدي أعرف ال resistance علناها
+
+354
+00:26:09,710 --> 00:26:14,110
+V على I بدي أخد هذا الشكل و هذا الشكل V على I إيش
+
+355
+00:26:14,110 --> 00:26:15,610
+هتساوي L
+
+356
+00:26:27,990 --> 00:26:31,470
+القانون اللي كلنا بنعرفه من وين جيبناه من ال point
+
+357
+00:26:31,470 --> 00:26:37,730
+form تبع Ohm's law معرفتنا علاقة ال current
+
+358
+00:26:37,730 --> 00:26:40,750
+density بال current انها I على S و ال electric
+
+359
+00:26:40,750 --> 00:26:45,220
+field علاقته potential هو V على Lبالتالي بقدر اقول
+
+360
+00:26:45,220 --> 00:26:53,280
+ان R بتساوي رو L على S رو اللي هي واحد على سجنبشكل
+
+361
+00:26:53,280 --> 00:26:56,740
+عام لو كان عندي non uniform conductor هذا لو حكينا
+
+362
+00:26:56,740 --> 00:26:59,900
+انه uniform أخدنا ببساطة انه لو uniform cross
+
+363
+00:26:59,900 --> 00:27:03,120
+section هذا اللي بتاعه المواعف الدوائر عشان هي كده
+
+364
+00:27:03,120 --> 00:27:07,240
+بنعرف ان R بيساوي rho L على S لو non uniform بدي
+
+365
+00:27:07,240 --> 00:27:11,040
+استخدم ال integrals هيكون R بيساوي V على I بيساوي
+
+366
+00:27:11,040 --> 00:27:15,740
+integral E ضد L على I اللي هي ال integral ل J ضد S
+
+367
+00:27:15,740 --> 00:27:22,760
+و J اللي هي mean sigma E ضد S اذا هاي المقامةالـ
+
+368
+00:27:22,760 --> 00:27:25,580
+power لو بدها حسب الـ power اللي جاية على هذا
+
+369
+00:27:25,580 --> 00:27:30,280
+المقامة بنعرفها هي عبارة عن التغير في إيش في ال
+
+370
+00:27:30,280 --> 00:27:35,680
+energy and joules أو ال force times velocity ال
+
+371
+00:27:35,680 --> 00:27:38,860
+power بتساوي ال force times velocity هيها ال force
+
+372
+00:27:38,860 --> 00:27:43,680
+اللي رو أو يعني Q في E هي ال force و V ال velocity
+
+373
+00:27:43,680 --> 00:27:48,400
+ال Q بقدر أعبر عنها بإيش رو V دي V إذا ال total
+
+374
+00:27:48,400 --> 00:27:51,140
+power أو ال .. ال .. ال ..
+
+375
+00:28:01,720 --> 00:28:05,200
+عادة الترتيب بسيط بس يعني خلّي الرو في مقابل ال U
+
+376
+00:28:05,200 --> 00:28:09,940
+اللي هي الولوستين هستيري التكامل ل E ضد رو في U في
+
+377
+00:28:09,940 --> 00:28:14,170
+DVRow V يومين هي الـ J، مش عرفنا ال current
+
+378
+00:28:14,170 --> 00:28:19,530
+density هو عبارة عن روه V في الفلسطين، إذا الفور
+
+379
+00:28:19,530 --> 00:28:23,910
+بقدر أقول عنها إيش بالثورة التكامل ل E dot J dV،
+
+380
+00:28:23,910 --> 00:28:27,710
+هذا ما نسميه Joule's
+
+381
+00:28:27,710 --> 00:28:34,360
+law الفور ال density هي عبارة عن dP by dVالبر
+
+382
+00:28:34,360 --> 00:28:38,460
+دينستي هي البر per unit volume يعني WB البر دينستي
+
+383
+00:28:38,460 --> 00:28:43,880
+DB بي DB هروح التكمل هتكون E لجيه لو عط عن جيه ب
+
+384
+00:28:43,880 --> 00:28:49,080
+Sigma E إيش هتكون Sigma E تربية إذا البر دينستي هي
+
+385
+00:28:49,080 --> 00:28:54,080
+عبارة عن conductivity في مربع ال electric field أو
+
+386
+00:28:54,080 --> 00:28:59,500
+مجموعة تبع ال electric field تربيةتمام؟ في أي سؤال
+
+387
+00:28:59,500 --> 00:29:02,380
+لحد دينا؟ و إيش ال unit بتاعة ال power density؟
+
+388
+00:29:02,380 --> 00:29:05,440
+هتكون ال power على ال volume اللي هي watt على
+
+389
+00:29:05,440 --> 00:29:06,500
+meter cube
+
+390
+00:29:13,670 --> 00:29:16,970
+لو احنا رجعنا لل conductor اللي له uniform cross
+
+391
+00:29:16,970 --> 00:29:21,370
+-section لازم ارجع للعلاقة اللي احنا بنعرفها بتاعة
+
+392
+00:29:21,370 --> 00:29:25,430
+المقاومة بتاعة الدوائر DV ما انه uniform cross
+
+393
+00:29:25,430 --> 00:29:29,670
+-section هيكون DS في DL ال volume عد الترتيب عندي
+
+394
+00:29:29,670 --> 00:29:34,310
+جون سلوكيش بقولت P بتساوة تكمل E dot J DVأقسم
+
+395
+00:29:34,310 --> 00:29:38,490
+الـdV لـDL وDS هاخد التكامل على الـ line integral
+
+396
+00:29:38,490 --> 00:29:42,170
+E ضد DS أو E ضد DL و ال volume و ال surface
+
+397
+00:29:42,170 --> 00:29:47,150
+integral هي G ضد DS E ضد DL اللي هي ال potential و
+
+398
+00:29:47,150 --> 00:29:53,010
+G ضد DS اللي هي current فإيش هيكون V في I؟ إذا ال
+
+399
+00:29:53,010 --> 00:29:57,770
+VAR أو جوزلو اللي احنا أخدناه في الدوائر V في I لو
+
+400
+00:29:57,770 --> 00:30:01,830
+عوضنا عن V بتسوء I في R هتكون ال VAR اللي بنعرفها
+
+401
+00:30:01,830 --> 00:30:07,730
+I تربية في Rهذا اللي نطلع نكون دكتور، واضح؟ احنا
+
+402
+00:30:07,730 --> 00:30:12,250
+متذكرين قولنا التوائر هي حالة خاصة من الكهروماناط
+
+403
+00:30:12,250 --> 00:30:18,290
+الصينية، نرجعلها لما بيكون عندي lumped، linear
+
+404
+00:30:18,750 --> 00:30:23,990
+circuits صح الذاكرين لامبيراميتر linear circuits
+
+405
+00:30:23,990 --> 00:30:27,430
+وكل ال conductors اللي موجودين عندنا لهم uniform
+
+406
+00:30:27,430 --> 00:30:32,410
+فاحنا بنقدر نستخدم الدوائر otherwise لازم نستخدم
+
+407
+00:30:32,410 --> 00:30:34,550
+ال electromagnetic يعني لو فش عندى uniform
+
+408
+00:30:34,550 --> 00:30:38,730
+conductor لازم أرجع لهذه المعادلات، لهذه المعادلات
+
+409
+00:30:38,730 --> 00:30:42,990
+بشكل عاملكن يوفور بقدر اقول على طول ان البر بساوية
+
+410
+00:30:42,990 --> 00:30:47,150
+ال BFR اللى اتعلمناها فى الدوائر و اللى اصلا جاية
+
+411
+00:30:47,150 --> 00:30:53,870
+من قوانين الكهرومناطسية واضر؟
+
+412
+00:30:53,870 --> 00:30:59,190
+طب ناخد مثال مثال بقول لو كانت عارفة انا ال
+
+413
+00:30:59,190 --> 00:31:04,490
+current density J انها 1 على R3 ف2 cos θ تجاه
+
+414
+00:31:04,490 --> 00:31:09,300
+الارهاتوعندي theta هات component مقدرها 1 على R
+
+415
+00:31:09,300 --> 00:31:13,480
+cubed sin theta ال unit بتاعة current density بما
+
+416
+00:31:13,480 --> 00:31:16,340
+أن current per unit area هو أمبارع على متر تربية
+
+417
+00:31:17,980 --> 00:31:21,060
+بدنا نحسب ال current passing through أول حاجة
+
+418
+00:31:21,060 --> 00:31:25,360
+homosphere shell of radius 20 cm، homosphere shell
+
+419
+00:31:25,360 --> 00:31:30,480
+يعني نص بطيخة و shell مش مليانة، يعني مش حاجة
+
+420
+00:31:30,480 --> 00:31:34,620
+مليانة اللي هي R بتروح من zero لأ، لأ عند R ثابتة،
+
+421
+00:31:34,620 --> 00:31:38,500
+shell لأنها، ال current بيمر في ال shell بس، يعني
+
+422
+00:31:38,500 --> 00:31:41,380
+قيمة ال radius ثابتة على عشرين centimeter أو point
+
+423
+00:31:41,380 --> 00:31:44,890
+نين مترعشان اجيب الطيارة ماحنا عارفين ال I ايش
+
+424
+00:31:44,890 --> 00:31:48,610
+بتساوي ال integral ل J dot DS و DS بالنسبة
+
+425
+00:31:48,610 --> 00:31:52,450
+للهمسفير بشكل عام للاسفير هو عبارة عن مين R تربيه
+
+426
+00:31:52,450 --> 00:31:57,630
+sin θ D θ D Phi R تربيه الربالكو سبت و انتجاه ال
+
+427
+00:31:57,630 --> 00:32:01,570
+sin ده ال S دايما عمودي عمودي على ال surface اذا
+
+428
+00:32:01,570 --> 00:32:04,530
+انا عندي هاي همسفير ايش العمودي عليها بيكون اللي
+
+429
+00:32:04,530 --> 00:32:10,910
+في اتجاه ال R hat تخيلواطبا و حاجة عموديه على ال
+
+430
+00:32:10,910 --> 00:32:14,110
+surface اللى هو عموديه على ال مماس مين هو ال
+
+431
+00:32:14,110 --> 00:32:18,810
+radius فهيكون تامة في اتجاه ال R hat ف then DS
+
+432
+00:32:18,810 --> 00:32:25,150
+عبارة عن ترفيه sin θ Dθ Dφ R hat نعود طبعا ان هى
+
+433
+00:32:25,150 --> 00:32:29,410
+hemisphere θ و اين بتوقف من ال zero فهي hemisphere
+
+434
+00:32:29,410 --> 00:32:34,680
+يعني هيكى بسهدا هي هتوقف ستة من zero ل by على
+
+435
+00:32:34,680 --> 00:32:38,820
+اتنين مش هتكمل ل by لو هتكمل ل by ايش بيصير يعني
+
+436
+00:32:38,820 --> 00:32:43,080
+دي طبقة كاملة و five ده بتعمللي كل الدوارة يعني
+
+437
+00:32:43,080 --> 00:32:46,860
+هتروح five من zero ل two by شايفين كل كه يعني عند
+
+438
+00:32:46,860 --> 00:32:50,980
+أنا هاي ال hemisphere نص بطيخة ستة بتروح من zero ل
+
+439
+00:32:50,980 --> 00:32:56,130
+by على اتنين و five من zero ل two byR سابق يقدر
+
+440
+00:32:56,130 --> 00:33:01,010
+عشرين سنتمتر اذا انا هكامل ستة من زيرو ل باى ع
+
+441
+00:33:01,010 --> 00:33:06,590
+اتنين فاى من زيرو ل توباى واحدة ع ال R كيوب تون
+
+442
+00:33:06,590 --> 00:33:11,290
+اللى هى هدىطبعا الانهاجة dot ds من هيظل بال R hat
+
+443
+00:33:11,290 --> 00:33:15,270
+هذا هيروح لل سفر theta hat dot R hat zero بس ال
+
+444
+00:33:15,270 --> 00:33:18,330
+term الأول انه هيظل واحد على عرف U باتنين cosine
+
+445
+00:33:18,330 --> 00:33:22,790
+theta في ds اللي هي R تربيع sin theta d pi d theta
+
+446
+00:33:22,790 --> 00:33:26,870
+بعوض عن R طبعا R تربيع بتروح مع تنتين من هدول تصير
+
+447
+00:33:26,870 --> 00:33:32,370
+واحد على R بعوض عنها ب point تنينبطلع اتنين على R
+
+448
+00:33:32,370 --> 00:33:37,950
+الفاي تكملها two pi انا من zero ل two pi sin θ dθ
+
+449
+00:33:37,950 --> 00:33:44,330
+فيعنى cos θ sin θ dθ لعبارة عن sin θ dθ لان ال cos
+
+450
+00:33:44,330 --> 00:33:53,070
+له d cos θ هو d sin θ هو cos θ dθفبتصير sin تربية
+
+451
+00:33:53,070 --> 00:33:58,890
+على اتنين مواضحش هذا يعني دي cos θ sin θ dθ دي sin
+
+452
+00:33:58,890 --> 00:34:05,070
+θ هي ال cos θ dθ فإذا عندي sin تربية على اتنين من
+
+453
+00:34:05,070 --> 00:34:08,270
+Zero أضعها اتنين بيطلع معايا انها تشتبع التيار
+
+454
+00:34:08,270 --> 00:34:12,930
+بالأكبر هذا بالنسبة للهمسفير نجي ل ال spherical
+
+455
+00:34:12,930 --> 00:34:16,450
+shell الو ردياس عشرة برضه shell يعني بس الطبقة
+
+456
+00:34:16,450 --> 00:34:23,600
+الرئية مش مليانةبس ستة بتسير من zero ل باي five
+
+457
+00:34:23,600 --> 00:34:27,080
+بتظلها من zero ل two by و R هنا ثابت على عشرة
+
+458
+00:34:27,080 --> 00:34:32,180
+centimeter يعني بدي أكامل نفسي و طبعا R hat dot R
+
+459
+00:34:32,180 --> 00:34:36,560
+hat هي اللي هتبقى و الجزء هذا هيكون بساوة سفر لو
+
+460
+00:34:36,560 --> 00:34:41,460
+أنا عملتها كيه بتطلع معايا الجواب بساوة zeroالجواب
+
+461
+00:34:41,460 --> 00:34:45,120
+هيطلع معايا بيثاو Zero ابتيار قيمته بيثاو Zero
+
+462
+00:34:45,120 --> 00:34:49,400
+السبب لو انا طلعت على القصة هذه انا بعمل Close
+
+463
+00:34:49,400 --> 00:34:53,280
+Integral على السفر السفر كله مشهور صح؟ اذا صار
+
+464
+00:34:53,280 --> 00:34:57,920
+هدمله Close Integral لجرد ال DS صار عندي الفرنسي
+
+465
+00:34:57,920 --> 00:35:02,880
+سوى Close Integral لجرد ال DS وهذه احنا أخدنا
+
+466
+00:35:02,880 --> 00:35:06,500
+عبارة عن مين فقدر استخدم ال divergence السوري
+
+467
+00:35:06,500 --> 00:35:10,520
+ساكنين سوى التكامل ل diverge
+
+468
+00:35:14,040 --> 00:35:17,420
+لو شوفنا ال divergence ده شي حلاقيها في السوقية
+
+469
+00:35:27,870 --> 00:35:31,290
+فأنا كفالكم طبعا اعملوها في البيت جيبوا ال
+
+470
+00:35:31,290 --> 00:35:34,230
+divergence لو حسفنا ال divergence هلاقيه بال zero
+
+471
+00:35:34,230 --> 00:35:36,910
+طبعا احنا لو عملنا اول حاجة التكمل عادى هلاقيه بال
+
+472
+00:35:36,910 --> 00:35:40,770
+zero او ممكن على طول اقول انه هذا class integral
+
+473
+00:35:40,770 --> 00:35:44,270
+line integral class surface integral بستخدم ال
+
+474
+00:35:44,270 --> 00:35:47,050
+divergence theorem بربطه ب divergence J اللى
+
+475
+00:35:47,050 --> 00:35:51,450
+هيعطينى zero المثال
+
+476
+00:35:51,450 --> 00:35:52,050
+اللى بعده
+
+477
+00:35:57,700 --> 00:36:01,940
+هذا convective charge transport طبعا هذا اللي
+
+478
+00:36:01,940 --> 00:36:05,300
+ماعرفش إذا بتعرفوا Van de Graaf generator سمعتوا
+
+479
+00:36:05,300 --> 00:36:12,560
+عنه Van de Graaf في physics هو بمرق الشحنات و كلها
+
+480
+00:36:12,560 --> 00:36:21,620
+بتتجمع على السطح فإن احنا هي الشكل تبعه ل Van de
+
+481
+00:36:21,620 --> 00:36:26,860
+Graaf و عندي الشحنات بتنطلقبحد اللى هى ال charge
+
+482
+00:36:26,860 --> 00:36:32,640
+removal أو اللى ال dome بتاعك ال conducting dome
+
+483
+00:36:32,640 --> 00:36:36,640
+ال charges
+
+484
+00:36:36,640 --> 00:36:39,920
+اش بيصيرلها transported بيصيرلها عملية نقل عبر
+
+485
+00:36:39,920 --> 00:36:43,340
+moving belt هذا ال belt شايفينه ال belt اللى بالمص
+
+486
+00:36:43,340 --> 00:36:50,540
+هذا اللى بالوف هذا ونقول عماله chargesمن القاعدة
+
+487
+00:36:50,540 --> 00:36:55,160
+الدوم لدوم هذه الدوارة نسميها الدوم القبة القبة
+
+488
+00:36:55,160 --> 00:37:00,700
+بتاعة الجهاز اذا كانت ال charge density هي اللي
+
+489
+00:37:00,700 --> 00:37:04,540
+انا بنقلها مقدار ال charges الها charge density
+
+490
+00:37:04,540 --> 00:37:10,400
+عشرة قوة سبعة كيلو بر متر تراجع بتمنقلها الفولوستي
+
+491
+00:37:10,400 --> 00:37:15,920
+مقدارها اتنين متر لكل secondcalculate the charge
+
+492
+00:37:15,920 --> 00:37:19,880
+collected in five seconds اذا اعتبرنا ان ال width
+
+493
+00:37:19,880 --> 00:37:23,460
+تبع ال built عشرة centimeter ال width تبع ال built
+
+494
+00:37:23,460 --> 00:37:26,080
+يعني هذا ال built هو مرسوم كحط بس هو في الواقع
+
+495
+00:37:26,080 --> 00:37:31,420
+built فلقد حزام و لف و بلقوا ال charges يعني لو
+
+496
+00:37:31,420 --> 00:37:37,300
+انا طلعت على جزء منه و هيك الحزام هذا
+
+497
+00:37:37,300 --> 00:37:41,820
+اللي احنا شايفينه الطول تبعه و ال width تبعه كده
+
+498
+00:37:41,820 --> 00:37:48,200
+مافينه قيمة ال widthعشرة سنتين و
+
+499
+00:37:48,200 --> 00:37:53,680
+ال velocity اللى بنقل فيها عماله ال charges اتنين
+
+500
+00:37:53,680 --> 00:38:01,160
+متر هي second و هطالب منى ان احسب ال surface ال
+
+501
+00:38:01,160 --> 00:38:07,560
+total charge اتشارج ال total charge اللى في زمن
+
+502
+00:38:07,560 --> 00:38:13,500
+مقداره حمسة second ال charge اللى بيحسبهاإذا عرفنا
+
+503
+00:38:13,500 --> 00:38:17,740
+إن رو بي أو رؤس في هذه الحالة surface charge
+
+504
+00:38:17,740 --> 00:38:26,460
+density surface عشرة هو سبعة column per meter كيوه
+
+505
+00:38:26,460 --> 00:38:31,480
+إحنا إيش اللي قولنا بتساوي رؤس كمية في ال area و
+
+506
+00:38:31,480 --> 00:38:36,100
+لا لأ لأن هنا بال area لو بال volume هتكون في
+
+507
+00:38:36,100 --> 00:38:40,960
+volume ال area إيش بتساوي الطول في العرض هتكون رؤس
+
+508
+00:38:41,840 --> 00:38:47,000
+العرض، خلّيني أسميه W، في الطول، إيش الطول بيساوي؟
+
+509
+00:38:47,000 --> 00:38:53,560
+الطول بيساوي فرصة في الزمن، هيكون UFT هو بدّوياها
+
+510
+00:38:53,560 --> 00:38:57,720
+بعد خمس ثواني، فهيكون رؤس اللي هي عشرة قوة سبعة
+
+511
+00:38:57,720 --> 00:39:01,860
+كولومبر متر تربية في ال width اللي هو معطيناياه
+
+512
+00:39:01,860 --> 00:39:07,260
+أداش عشرة صنطة اللي هو point واحد متر في الفرصة
+
+513
+00:39:07,260 --> 00:39:11,670
+اللي هي اتنين متر per second فقدرش الزمن حمصةهذا
+
+514
+00:39:11,670 --> 00:39:18,030
+هتعطينا قيمة ال total charge اللى تم جمعها فى خمس
+
+515
+00:39:18,030 --> 00:39:26,850
+ثوان واضح كمان
+
+516
+00:39:26,850 --> 00:39:31,770
+مثال انا عندى led bar يعني من الرصاص قطعة من
+
+517
+00:39:31,770 --> 00:39:34,230
+الرصاص برضه هده طويل يعنى بس هدا ال cross section
+
+518
+00:39:34,230 --> 00:39:40,770
+تبعه و ممتد cross section تبعه مربع و طويل يعني زى
+
+519
+00:39:40,770 --> 00:39:41,350
+القلم هده
+
+520
+00:39:44,570 --> 00:39:52,190
+هذا ال bar أو هذا القضيب عملوا فيه خرق hall طول
+
+521
+00:39:52,190 --> 00:39:55,670
+الطول يعني مش بس من هنا على طوله زي هذا تخيلوا على
+
+522
+00:39:55,670 --> 00:40:01,170
+طول القضيب اللي هو الهادي its length القضيب طوله
+
+523
+00:40:01,170 --> 00:40:05,290
+أربع متر وال cross section تبعه زي ما هذا الشكل
+
+524
+00:40:05,290 --> 00:40:09,250
+شفناه ع طوله اللي هو أربع متر عملنا الخرق مش بس
+
+525
+00:40:09,250 --> 00:40:13,270
+مثلا نصه طوله كله أربع والخرق من أول لآخر عملناه
+
+526
+00:40:18,290 --> 00:40:22,510
+الـ sigma بتاعته اللي هي ال conductive بتاعته خمسة
+
+527
+00:40:22,510 --> 00:40:27,490
+في عشر قوة ستة Siemens per meter طوله أربع عملنا
+
+528
+00:40:27,490 --> 00:40:30,930
+فيه الخروج اللي انتوا شايفينه طوله و عرضه تلاتة في
+
+529
+00:40:30,930 --> 00:40:34,410
+تلاتة اللي هو ال cross section تبعه المربع تبعه
+
+530
+00:40:34,410 --> 00:40:39,690
+الأطول تاعته تلاتة يعني مربعة و هي ال radius او ال
+
+531
+00:40:39,690 --> 00:40:43,330
+diameter تبع الدائرة اللي عملناها في نصه واحد
+
+532
+00:40:43,330 --> 00:40:47,160
+centimeter ال radius تبعها قداش نص centimeterبدوا
+
+533
+00:40:47,160 --> 00:40:51,520
+resistance between equal square ends، يعني بدوا
+
+534
+00:40:51,520 --> 00:40:54,340
+resistance بين هدول الطرفين، إذا اتخيلنا إنه هذا
+
+535
+00:40:54,340 --> 00:40:58,540
+القضيب و هذا القاضيب، بدوا مقاوم بين هدول الطرفين،
+
+536
+00:40:58,540 --> 00:41:03,160
+إيش عرفنا المقاومة؟ أحنا شقناها مع بعض، L على
+
+537
+00:41:03,160 --> 00:41:09,300
+sigma في S، L يعطينا طوله، من هنا لهنا قلي 4 متر
+
+538
+00:41:11,400 --> 00:41:16,580
+طوله للقضيب أربعة متر، sigma ناطينية خمسة في عشر
+
+539
+00:41:16,580 --> 00:41:20,380
+أقوى ستة، إيش ضال عليها ال area؟ ال area .. ال
+
+540
+00:41:20,380 --> 00:41:23,260
+cross section area مش مربع، لو ماعملش الخرق
+
+541
+00:41:23,260 --> 00:41:26,940
+فنقولنا تلاتة في تلاتة، لكن هي عمل فيها الخرق،
+
+542
+00:41:26,940 --> 00:41:29,960
+فإيش هجيب؟ ال area بتاعة المربع ناقص ال area بتاعة
+
+543
+00:41:29,960 --> 00:41:34,210
+الدائرة، بالتلات، يعني رياضيات فاديالي دي تربيع
+
+544
+00:41:34,210 --> 00:41:39,210
+minus pi r تربيع دي تربيع ليه تلاتة تربيع minus pi
+
+545
+00:41:39,210 --> 00:41:42,410
+في نص الكل تربيع حد ال unit انها جا centimeter
+
+546
+00:41:42,410 --> 00:41:45,970
+تربيع فإذا أنا بدى أحسب كله بالأم بدى أنتبه ان
+
+547
+00:41:45,970 --> 00:41:49,470
+احول كل حاجة بالمتر يا كل حاجة لإن عند ال sigma ما
+
+548
+00:41:49,470 --> 00:41:56,010
+لها c means ع متر فبرجع بحول بحول هاي ل متربطلع
+
+549
+00:41:56,010 --> 00:41:59,850
+معايا ان المقاومة بتاعة هذا القضيب ما بين طرفين
+
+550
+00:41:59,850 --> 00:42:05,010
+هذا القضيب المقاومة بين هدول النقطتين هي 974 micro
+
+551
+00:42:05,010 --> 00:42:05,750
+ohm
+
diff --git a/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/CIPP0dKojOk.srt b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/CIPP0dKojOk.srt
new file mode 100644
index 0000000000000000000000000000000000000000..1b23f9011eb4aa14669c17aba55ebf67d1b6a7f5
--- /dev/null
+++ b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/CIPP0dKojOk.srt
@@ -0,0 +1,1988 @@
+1
+00:00:20,810 --> 00:00:22,090
+بسم الله الرحمن الرحيم
+
+2
+00:00:25,830 --> 00:00:29,670
+إحنا الفترة الماضية كانت بالنسبة لنا مراجعة للخلفية 
+
+3
+00:00:29,670 --> 00:00:32,590
+الرياضية لهذه المادة، كنا أخذنا على الـ vectors
+
+4
+00:00:32,590 --> 00:00:35,230
+أخذنا على الـ divergence، أخذنا على الـ curl، أخذنا
+
+5
+00:00:35,230 --> 00:00:38,730
+على الـ cross products والـ dot products، على 
+
+6
+00:00:38,730 --> 00:00:41,750
+الـ partial lengths والـ partial area والـ partial
+
+7
+00:00:41,750 --> 00:00:44,650
+volume، واتعلمنا divergence theorem وStokes 
+
+8
+00:00:44,650 --> 00:00:47,710
+theorems، كل هذول هي الخلفية اللي إحنا محتاجينها
+
+9
+00:00:47,710 --> 00:00:51,430
+لمادة الكهرومغناطيسية، إحنا هنبدأ بها فعليًا
+
+10
+00:00:51,430 --> 00:00:55,910
+بالكهرومغناطيسية، هنبدأ بالـ electrostatic fields، من اسم
+
+11
+00:00:55,910 --> 00:00:58,570
+الـ electrostatics يعني لا تعتمد على الزمن، معناه
+
+12
+00:00:58,570 --> 00:01:02,010
+electrostatic يعني تفاعل مُسبل زمن بساوِ zero
+
+13
+00:01:02,010 --> 00:01:04,890
+static لا تتحرك
+
+14
+00:01:10,010 --> 00:01:13,990
+إذا إحنا اليوم هناخد بعض الأساسيات لـ 
+
+15
+00:01:13,990 --> 00:01:18,150
+Electromagnetic واللي بتعتمد، أول ما هنبدأ إلا
+
+16
+00:01:18,150 --> 00:01:22,570
+بما لها static، قلنا static معناها لا تعتمد على الـ
+
+17
+00:01:22,570 --> 00:01:25,310
+time أو time invariant نقول عنها، إذا نحن نبدأ 
+
+18
+00:01:25,310 --> 00:01:28,370
+بالجزئية اللي ما لها static واللي لا تعتمد على الـ
+
+19
+00:01:28,370 --> 00:01:31,930
+time، وكمان هنعتمد على الـ electric fields في الـ free
+
+20
+00:01:31,930 --> 00:01:35,310
+space أو في الـ vacuum، يعني هندرس في الأول كيف
+
+21
+00:01:35,310 --> 00:01:38,230
+تتصرف الـ fields في الـ vacuum أو في الـ free space، و
+
+22
+00:01:38,230 --> 00:01:43,150
+بعدين هندرسها في الـ material، كمان هتعلم إنه الـ
+
+23
+00:01:43,150 --> 00:01:45,810
+electric field بينتج من الـ static charge
+
+24
+00:01:45,810 --> 00:01:47,950
+distributions، برضه الـ charge مالها static
+
+25
+00:01:47,950 --> 00:01:54,650
+distribution، ما تتحركش، مثل على الـ electrostatic
+
+26
+00:01:54,650 --> 00:01:58,710
+field اللي ناتج عن static charge هو الـ field اللي 
+
+27
+00:01:58,710 --> 00:02:01,490
+في الكاثودية tubes، كما زمان التلفزيونات كانت تعتمد
+
+28
+00:02:01,490 --> 00:02:04,870
+على الكاثودية tube، دائمًا التلسكوبات القديمة برضه
+
+29
+00:02:04,870 --> 00:02:07,490
+كانت تعتمد على الكاثودية tube، ده كله صارياتنا الـ 
+
+30
+00:02:07,490 --> 00:02:15,080
+LCD وعلى الـ polymers، على اللدات والـ polymers، أهمية
+
+31
+00:02:15,080 --> 00:02:16,800
+الـ electrostatic، أهمية إيش؟ إحنا بندرس الـ
+
+32
+00:02:16,800 --> 00:02:21,000
+electrostatic؟ الـ fields أو مجالات كتيرة بتعتمد
+
+33
+00:02:21,000 --> 00:02:25,740
+على الكهربية الساكنة، هنعمل نحكي لسه منها وهذه
+
+34
+00:02:25,740 --> 00:02:28,120
+جزء من الـ applications بتاعتها عشان نشوف ده شيء
+
+35
+00:02:28,120 --> 00:02:31,600
+مهم، ده إيش إحنا لازم نتعلمه كـ engineers، اللي
+
+36
+00:02:31,600 --> 00:02:34,860
+هي applications متعددة، من أهمها إنها بتستخدم في
+
+37
+00:02:34,860 --> 00:02:38,800
+نقل الطاقة، electric power transmission، بتستخدم في
+
+38
+00:02:38,800 --> 00:02:41,780
+الـ X-ray machine، في الـ lightning protection،
+
+39
+00:02:41,780 --> 00:02:45,840
+بتعرفوا إيش؟ اللي هي صواعق البرق، بتستخدم عشان
+
+40
+00:02:45,840 --> 00:02:48,100
+تحميل صواعق البرق، يعني فهمتوا أو فهمتي الـ
+
+41
+00:02:48,100 --> 00:02:51,440
+electrostatic بتاعتنا نفهم هذه الأمور، bipolar
+
+42
+00:02:51,440 --> 00:02:54,540
+and field effect transistor، فبنحطّها في الـ
+
+43
+00:02:54,540 --> 00:02:58,560
+electronics، almost all computer briefly are devices
+
+44
+00:02:58,560 --> 00:03:03,360
+except magnetic memory. معظم القطع الموجودة في
+
+45
+00:03:03,360 --> 00:03:05,940
+الكمبيوتر، ما عدا الـ magnetic memory، بتبقى تتبع 
+
+46
+00:03:05,940 --> 00:03:11,210
+الاستاتيك، الكهروستاتيك، touch pads، الـ pads اللي
+
+47
+00:03:11,210 --> 00:03:14,090
+أنتَ بتدعسوا عليها، بس اللي هي زي الـ ipad والأخرى هي 
+
+48
+00:03:14,090 --> 00:03:18,950
+touch، بتـ touch capacitance keyboard، يعني معظم الـ
+
+49
+00:03:18,950 --> 00:03:22,550
+elevators بتشتغل بالـ capacitance، أنت بتدعس بإصبعك،
+
+50
+00:03:22,550 --> 00:03:25,950
+بيشتغل الـ .. ما فيش شيء بتضغط ولا بتطلع، معظمهم، في 
+
+51
+00:03:25,950 --> 00:03:29,690
+منهم لازم تضغط، بس الأغلبية هي بالـ touch، بتدعس
+
+52
+00:03:29,690 --> 00:03:34,650
+عليه بيشتغل الـ .. اه، دي capacitance keyboard، Cathode ray
+
+53
+00:03:34,650 --> 00:03:38,690
+tube، Liquid crystal display، تعرفهم display زي 
+
+54
+00:03:38,690 --> 00:03:41,990
+display تبع الـ .. الكمبيوتر، بس كانوا زمان من مادة
+
+55
+00:03:41,990 --> 00:03:45,470
+اسمها Liquid crystal، لا زال في بعض منهم Liquid
+
+56
+00:03:45,470 --> 00:03:48,290
+crystal، لا زال يعني الـ hot topics Liquid crystal
+
+57
+00:03:48,290 --> 00:03:50,470
+وبعضهم لدات وبعضهم بوليمرات
+
+58
+00:03:53,570 --> 00:03:57,790
+Electrostatic Printer، طابعات كل الطابعات المطبوعة
+
+59
+00:03:57,790 --> 00:04:00,810
+عليها، مش الـ .. يعني حتى الـ laser بيرمزوا شوية على 
+
+60
+00:04:00,810 --> 00:04:04,430
+الكهربا الاستاتيكية، بس أغلبية اللي أنتجت كلها
+
+61
+00:04:04,430 --> 00:04:09,190
+Electrostatic، الفكرة تعالوا في الـ medical في حاجة
+
+62
+00:04:09,190 --> 00:04:12,330
+اللي هي اسمها electrocardiogram، هذول اللي بيبحثوا
+
+63
+00:04:12,330 --> 00:04:15,330
+فيها القلب، cardio اللي هو gram، أجهزة فياس القلب
+
+64
+00:04:16,210 --> 00:04:20,670
+Electro .. electroencephalograms
+
+65
+00:04:20,670 --> 00:04:26,030
+برضه لها علاقة بفحوصات طبية، في الصناعة بين
+
+66
+00:04:26,030 --> 00:04:30,050
+spraying اللي هو الرش تبع السيارات والأخرى
+
+67
+00:04:30,050 --> 00:04:33,210
+الدهانات بتاعتها، برضه على الكهربية الساكنة
+
+68
+00:04:33,210 --> 00:04:38,110
+Electrodopsin، يعني بيكون عندي أنا material وبتعمل
+
+69
+00:04:38,110 --> 00:04:41,030
+عليها طبقة برضه بتاعتها من على الـ electrostatics
+
+70
+00:04:42,270 --> 00:04:45,410
+Electrochemical machining، في كثير من الـ machines
+
+71
+00:04:45,410 --> 00:04:49,430
+بتعتمد على الكهروستاتيك، Separation of particles، وإحنا 
+
+72
+00:04:49,430 --> 00:04:52,290
+في الكيمياء وبنفصلها بين particles، برضه بتعتمد على
+
+73
+00:04:52,290 --> 00:04:57,690
+الكهروستاتيك، الزراعية، sorting seeds، كيف نصنفها إنه على
+
+74
+00:04:57,690 --> 00:05:00,870
+منيح، من اللي ممكن نصنفه، fertilization، إحنا برضه
+
+75
+00:05:00,870 --> 00:05:06,250
+بتعتمدوا على الكهروستاتيك، diet spray to plants، اللي هي
+
+76
+00:05:06,250 --> 00:05:09,950
+رش ضد الحشرات، measure the moistures 
+
+77
+00:05:09,950 --> 00:05:13,530
+content of its crops، قياس أد إيش الرطوبة في 
+
+78
+00:05:13,530 --> 00:05:17,830
+المحاصيل، spin cotton اللي هو نوع من أنواع القطن
+
+79
+00:05:17,830 --> 00:05:21,890
+speed، كيف بتعملوا spinning، يعني اللي هي المغزلية،
+
+80
+00:05:21,890 --> 00:05:25,550
+الغزل بتاعها، وزمان كانوا بيعملوا الغزل، وحتى الجهاز الكبير
+
+81
+00:05:25,550 --> 00:05:29,750
+بيبقى من ضمن الكهروستاتيك، speed baking of bread and 
+
+82
+00:05:29,750 --> 00:05:34,470
+smoking meat، عشان كده سرعة الطهي للـ bread والحصول 
+
+83
+00:05:34,470 --> 00:05:39,590
+على اللحمة المدخنة، هذه بعض من الـ applications بتاع
+
+84
+00:05:39,590 --> 00:05:41,890
+الـ electrostatic، key لو فتحتوا على الـ net وقلتم
+
+85
+00:05:41,890 --> 00:05:43,930
+إيش هي الـ application بتاع الـ electrostatic keys
+
+86
+00:05:43,930 --> 00:05:47,370
+هتلاقوا لعديدة بالتفصيل لكل جزء من الأجزاء اللي
+
+87
+00:05:47,370 --> 00:05:51,770
+حكينا عنها، وإذا يعني أعطانا الرابط، بسرعة بعض الوقت
+
+88
+00:05:51,770 --> 00:05:54,670
+إن شاء الله هحط لكم جزء منها من هذه الـ applications، و
+
+89
+00:05:54,670 --> 00:05:58,050
+الصور اللي لها على الـ facebook بيصير أوضح لكم إنه
+
+90
+00:05:58,050 --> 00:06:03,280
+إيش هي الـ applications، إحنا هنبدأ two laws، أهم two
+
+91
+00:06:03,280 --> 00:06:06,000
+laws اللي بتحكموا في الـ electrostatics اللي هو
+
+92
+00:06:06,000 --> 00:06:10,580
+Coulomb's law و Gauss's law، Coulomb و Gauss، اثنين experimentally 
+
+93
+00:06:10,580 --> 00:06:13,760
+approved، يعني العلماء الاثنين هذول، أسس Coulomb أو 
+
+94
+00:06:13,760 --> 00:06:19,280
+Gauss اشتغلوا بالـ .. بالمختبر، وأثبتوا قوانينهم أو 
+
+95
+00:06:19,280 --> 00:06:21,840
+يعني كان عندهم فضول يفهموا العلاقة بتاعة الـ
+
+96
+00:06:21,840 --> 00:06:25,360
+electrostatic forces، وفي المختبر درسواها ووصلوا 
+
+97
+00:06:25,360 --> 00:06:26,700
+للعلاقات اللي وصلوا لها
+
+98
+00:06:29,860 --> 00:06:33,940
+رغم إنه يعني الـ Coulomb's law بيقدر يجيب لنا الـ
+
+99
+00:06:33,940 --> 00:06:35,960
+electric field لأي نوع من أنواع الـ charge
+
+100
+00:06:35,960 --> 00:06:38,720
+distribution، لكن في بعض الـ problems اللي بيكون فيها
+
+101
+00:06:38,720 --> 00:06:42,240
+symmetry أسهل نستخدم Gauss، يعني هذيك ممكن
+
+102
+00:06:42,240 --> 00:06:45,420
+نستخدمه لأي نوع من الـ distribution بدون أي قيود أو
+
+103
+00:06:45,420 --> 00:06:48,420
+شروط اللي هو Coulomb's law، لكن لو فيه نوع من 
+
+104
+00:06:48,420 --> 00:06:51,300
+أنواع الـ symmetry، أسهل نستخدم Gauss، وهنشوف كيف الفرق
+
+105
+00:06:51,300 --> 00:06:55,180
+بينهم، Coulomb شوية أصعب تطبيقه من Gauss لكن في
+
+106
+00:06:55,180 --> 00:06:58,540
+حالات الـ symmetry بنلاقي إن استخدام Gauss سهل كثير
+
+107
+00:06:58,540 --> 00:07:02,030
+يعني إنه بستبدل Gauss to Coulomb لكن un symmetric 
+
+108
+00:07:02,030 --> 00:07:06,770
+problem بقدرش نستخدم Gauss، هنستخدم 
+
+109
+00:07:06,770 --> 00:07:09,690
+Coulomb's law عشان نوصل للـ electric field intensity 
+
+110
+00:07:09,690 --> 00:07:14,210
+فهنشوف بعض اللي هي الـ problems اللي ممكن نحلها الـ
+
+111
+00:07:14,210 --> 00:07:17,670
+Coulomb's law وكيف ممكن إحنا برضه نحلها باستخدام 
+
+112
+00:07:17,670 --> 00:07:22,240
+Gauss's law، إحنا خلال هذا الشطر، هذا التأكيد اللي 
+
+113
+00:07:22,240 --> 00:07:25,060
+حكيته وبعيده كم مرة إنه هنعتبر إن الـ electric
+
+114
+00:07:25,060 --> 00:07:28,380
+fields بيكونوا لو في الـ vacuum أو في الـ free space
+
+115
+00:07:28,380 --> 00:07:32,800
+يعني لما نحكي vacuum معناه نحكي في free space، في 
+
+116
+00:07:32,800 --> 00:07:35,240
+الـ material زي ما حكينا هيكون في الشطر اللي بعد
+
+117
+00:07:35,240 --> 00:07:40,540
+نحكي على Coulomb's law والـ field intensity، Coulomb
+
+118
+00:07:40,540 --> 00:07:45,080
+هو عبارة عن عالم عمل تجربة، وهذا التجربة وصلته
+
+119
+00:07:45,080 --> 00:07:49,080
+لقانونه في العام الف سبعمائة خمسة وثمانين، هذا
+
+120
+00:07:49,080 --> 00:07:52,900
+العالم هو عالم فرنسي اسمه Charles-Augustin de 
+
+121
+00:07:52,900 --> 00:08:00,120
+Coulomb، إيش كان قانونه بيقول؟ إن هو القوة بين
+
+122
+00:08:00,120 --> 00:08:05,800
+two charge distributions بتكون على الخط اللي بيصل
+
+123
+00:08:05,800 --> 00:08:10,760
+بين هذول، بندرس دائمًا الـ pointed charges
+
+124
+00:08:10,760 --> 00:08:14,000
+يعني .. يعني بنحطوا pointed charges، وإيش مقصود
+
+125
+00:08:14,000 --> 00:08:17,640
+pointed charge؟ إن الـ dimension بتاعتها الـ charge
+
+126
+00:08:17,640 --> 00:08:22,600
+أصغر بكثير من الجسم المحيط فيها، يعني مثلًا أنا بدأت
+
+127
+00:08:22,600 --> 00:08:27,020
+أدرس أثر طرف القلم هذا هنا هي عنده charge على طرف
+
+128
+00:08:27,020 --> 00:08:31,320
+القلم، وبدي أدرس أثر هذه الـ charge على الدفتر
+
+129
+00:08:31,320 --> 00:08:35,000
+أشمله هذا الطرف القلم هيكون صغير كثير بالنسبة
+
+130
+00:08:35,000 --> 00:08:38,160
+للدفتر، فبعتبره point of charge، إذا معناه point of
+
+131
+00:08:38,160 --> 00:08:42,780
+charge إن الـ dimension تبعها أصغر بكثير من الشيء
+
+132
+00:08:42,780 --> 00:08:48,050
+اللي بتأثر عليها أو في المحيط اللي حواليها، مش معناه 
+
+133
+00:08:48,050 --> 00:08:52,050
+point of charge؟ We mean a charge that is located
+
+134
+00:08:52,050 --> 00:08:54,890
+on a body whose dimensions are much smaller than
+
+135
+00:08:54,890 --> 00:08:57,370
+other relevant dimensions، يعني أنا قارنتها بـ
+
+136
+00:08:57,370 --> 00:09:00,270
+relevant يعني بالحاجة اللي بتأثر عليها، طرف القلم
+
+137
+00:09:00,270 --> 00:09:04,110
+أو الدبوس بعتبره point of charge
+
+138
+00:09:07,240 --> 00:09:09,840
+هذا المثال، the charges are generally measured in 
+
+139
+00:09:09,840 --> 00:09:13,900
+Coulombs، يعني لما نحكي عن الـ charge Q، الـ Q المحدد 
+
+140
+00:09:13,900 --> 00:09:17,040
+القياسي ساعتها Coulomb، نسبة لهذا العالم لدراسة الـ
+
+141
+00:09:17,040 --> 00:09:20,740
+electrostatic forces، زي ما درسنا إن Ohm إن هو
+
+142
+00:09:20,740 --> 00:09:23,880
+الذي درس التيار سمينا الـ resistance وحدتها الـ
+
+143
+00:09:23,880 --> 00:09:27,060
+Ohm، نفس الشيء بالـ charge وحدتها الـ Coulomb، one
+
+144
+00:09:27,060 --> 00:09:32,730
+Coulomb إيش بيساوي؟ 6 × 10<sup>18</sup> electrons، one Coulomb
+
+145
+00:09:32,730 --> 00:09:37,130
+يساوي 6 × 10<sup>18</sup> electrons، لأن وحدة الـ electron الـ one
+
+146
+00:09:37,130 --> 00:09:43,810
+electron charge هو 1.6019 × 10<sup>-19</sup> Coulomb، فواحد
+
+147
+00:09:43,810 --> 00:09:48,610
+Coulomb بس بيساوي واحد على هذا الرقم بطلع 6 × 10<sup>18</sup>
+
+148
+00:09:48,610 --> 00:09:52,350
+كمية كبيرة، يعني الـ one Coulomb بيحتوي على عدد هائل
+
+149
+00:09:52,750 --> 00:09:55,850
+من الإلكترونات، إنه واحد قد إيش؟ في عشرة قوّة ناقص
+
+150
+00:09:55,850 --> 00:09:58,270
+تسعة عشر، وإحنا بنحكي الـ Coulomb بيحكي عشرة قوّة 
+
+151
+00:09:58,270 --> 00:10:02,430
+ثمانية عشر، عشرة قوّة ناقص تسعة عشر، عشرة قوّة ثمانية عشر، عدد هائل
+
+152
+00:10:02,430 --> 00:10:08,810
+من الإلكترونات، طب إيش Coulomb؟ قال Coulomb إنه
+
+153
+00:10:08,810 --> 00:10:13,330
+القوة بين two charges Q واحد وQ ثاني، أول حاجة
+
+154
+00:10:13,330 --> 00:10:16,710
+بتكون على الخط الواصل بينهم، على الخط الواصل بينهم
+
+155
+00:10:16,710 --> 00:10:19,650
+يعني هالـ two charges أكيد القوة هتكون على الخط
+
+156
+00:10:19,650 --> 00:10:23,690
+الواصل بين هذول، أول حاجة، الثانية حاجة إنها بتتناسب
+
+157
+00:10:23,690 --> 00:10:28,210
+طرديًا مع قيمة Q1 وQ2، كل ما زادت قيم الـ charges
+
+158
+00:10:28,210 --> 00:10:33,830
+قيمة Q1 وQ2 كل ما زادت القوة الرابطة بينهما، قوة اللي
+
+159
+00:10:33,830 --> 00:10:38,710
+هي الـ electrostatic force، كل ما قصرت المسافة وبقت
+
+160
+00:10:38,710 --> 00:10:41,270
+المسافة راح ألاحظ برضه كلمة إيش بتأثر الـ force
+
+161
+00:10:41,270 --> 00:10:45,910
+بتقل المسافة، لو بتقل المسافة إيش بيصير؟ بتزيد الـ
+
+162
+00:10:45,910 --> 00:10:52,000
+force، بتزيد المسافة بتقل الـ force، mathematically
+
+163
+00:10:52,000 --> 00:10:55,860
+بنعبر عن الـ force، طبعًا الـ force هتكون بالنيوتن، إذا
+
+164
+00:10:55,860 --> 00:11:02,120
+كان q1 وq2 بالـ Coulomb وR بالـ meter، F بالـ Newton، هيك
+
+165
+00:11:02,120 --> 00:11:05,340
+بنعبر عن طول قيمة أو الـ unit بتاعة K، الـ unit بتاعة
+
+166
+00:11:05,340 --> 00:11:08,980
+K مش unit less، اللي هي الـ unit الشيء، K هي K، الـ
+
+167
+00:11:08,980 --> 00:11:13,300
+constant of proportionality، constant of 
+
+168
+00:11:13,300 --> 00:11:18,100
+proportionality، اللي هو أنا بقول إن F بتتناسب مع
+
+169
+00:11:18,100 --> 00:11:24,450
+q1 في q2، F بتتناسب عكسيا مع واحد على R تربيع، أو
+
+170
+00:11:24,450 --> 00:11:27,270
+بتتناسب مع واحد على R تربيع، وعكسيا مع R تربيع
+
+171
+00:11:27,270 --> 00:11:32,730
+إذا F بتساوي some constant في Q1 وQ2 على R تربيع
+
+172
+00:11:32,730 --> 00:11:34,790
+فهذا الـ constant بنسميه K
+
+173
+00:11:39,300 --> 00:11:43,300
+لذلك هذا هو الـ Coulomb's .. Coulomb's law، وقلنا K
+
+174
+00:11:43,300 --> 00:11:46,420
+هو الـ constant of proportionality، وفي الأسئلة الـ unit
+
+175
+00:11:46,420 --> 00:11:50,720
+قلنا، في واحدة كانت Q1 Coulomb، Q2 Coulomb، F Newton
+
+1
+
+201
+00:13:34,710 --> 00:13:38,430
+بدلالة سواء الفراد أو نيوتن وبقدر أوصل لهذولة
+
+202
+00:13:38,430 --> 00:13:42,230
+العلاقتين مع بعض إن K كيف أربطها اللي هي نيوتن في
+
+203
+00:13:42,230 --> 00:13:46,350
+متر تربيع على كولوم تربيع باللي هو متر على فراد
+
+204
+00:13:46,350 --> 00:13:50,330
+لأن كولوم اللي هي علاقة بالـ unit بتاعة كباستنس
+
+205
+00:13:50,330 --> 00:13:59,940
+اللي هي الفراد تمام؟ هي أي استفسار؟ احنا
+
+206
+00:13:59,940 --> 00:14:04,960
+هي two charges Q1 و Q2 الـ Q1 الموجودة في الفراغ
+
+207
+00:14:04,960 --> 00:14:10,340
+R1 هذا الـ origin XYZ البسشين قلنا بحدد فيه مكان ال
+
+208
+00:14:10,340 --> 00:14:15,310
+object في الفضاء في الـ space إذا الـ Q1 على بعد R1 و
+
+209
+00:14:15,310 --> 00:14:21,570
+Q2 على بعد R2 البعد ما بين Q1 و Q2 هو R12 هو عبارة
+
+210
+00:14:21,570 --> 00:14:27,050
+عن R2 ناقص R1 لأنه احنا قلنا قلنا هيك قلنا R1 ذات
+
+211
+00:14:27,050 --> 00:14:32,870
+R12 تساوي R2 فبالتالي R12 ده ما بتساوي R2 ناقص R1
+
+212
+00:14:32,870 --> 00:14:35,570
+بتذكرين لما حكينا عن الـ question و الـ distance
+
+213
+00:14:35,570 --> 00:14:38,920
+between two objects عشان هيك احنا كان فيه لازم أنه
+
+214
+00:14:38,920 --> 00:14:42,280
+نعرفهم الـ position هو موضوع object in space اللي
+
+215
+00:14:42,280 --> 00:14:45,140
+في هاي الحالة احنا حددنا الـ object تبعنا بطل
+
+216
+00:14:45,140 --> 00:14:51,160
+نسميها point P1 P2 صار مكان الـ charges Q1 و Q2 Q1
+
+217
+00:14:51,160 --> 00:14:55,040
+وقع على الـ distance R1 و Q2 على الـ distance R2 و
+
+218
+00:14:55,040 --> 00:14:58,300
+المسافة R12 اللي هي زي ما أنتم متذكرين المقال
+
+219
+00:14:58,300 --> 00:15:02,040
+اجمع بتكون R1 ثم R12
+
+220
+00:15:15,800 --> 00:15:18,260
+هذا هو ما ستجد على هذه الخطة
+
+221
+00:15:21,100 --> 00:15:24,180
+هتكون على طول الخط اللي واصل بينهم إذا هذول ال
+
+222
+00:15:24,180 --> 00:15:26,880
+charges اللي هم نفس الـ unit و احنا بنفرض أنهم بصفة
+
+223
+00:15:26,880 --> 00:15:31,620
+charges هلاحظ أن هذول القوة هتكون بتأثر على بعض
+
+224
+00:15:31,620 --> 00:15:37,580
+بشكل repulsive يعني الـ Q2 هتعمل قوة منافرة أو
+
+225
+00:15:37,580 --> 00:15:43,160
+نافرة repulsive على Q1 نفس الشيء Q1 هتأثر بقوة
+
+226
+00:15:43,160 --> 00:15:50,530
+repulsive على Q2 فهذا السهم يدلني على أثر Q2 على
+
+227
+00:15:50,530 --> 00:15:54,310
+Q1 فسماها
+
+228
+00:15:54,310 --> 00:16:00,950
+F12 هو القوة على واحد اللي ناتجة من اثنين وهذا
+
+229
+00:16:00,950 --> 00:16:05,030
+السهم يدل لي على القوة اللي ناتجت على Q2 أو
+
+230
+00:16:05,030 --> 00:16:11,330
+exerted على Q2 بسبب Q1 فسماها F12 اللي هي القوة
+
+231
+00:16:11,330 --> 00:16:14,970
+اللي صارت على اثنين بسبب Q1
+
+232
+00:16:17,720 --> 00:16:21,080
+نبدأ نتكلم في 1 أو 2 مثلاً اللي هي القوة على ال
+
+233
+00:16:21,080 --> 00:16:24,200
+charge الثانية بسبب الـ charge الأولى ايش بالها
+
+234
+00:16:24,200 --> 00:16:29,060
+تساوي؟ K عوضنا عنها في 1 على 4π افسى مثلاً كيو
+
+235
+00:16:29,060 --> 00:16:32,320
+واحد كيو ثانية على R ثانية واتجاه ماهي دي
+
+236
+00:16:32,320 --> 00:16:35,880
+vector force الـ force vector مش scalar بس اللي
+
+237
+00:16:35,880 --> 00:16:38,960
+لازم كلها اتجاه واتجاه اللي احنا شايفينه هو اتجاه
+
+238
+00:16:38,960 --> 00:16:43,340
+ماهو على طول الخط اللي واصل بينهم يعني هو أنا
+
+239
+00:16:43,340 --> 00:16:47,660
+عرفت الـ unit vector اللي هو في اتجاه الخط الواصل
+
+240
+00:16:47,660 --> 00:16:54,760
+بيهم A12 أو AR12 hat هذا هيكون اتجاه الـ force إذا
+
+241
+00:16:54,760 --> 00:16:59,520
+اتجاه الـ force هيكون في اتجاه الـ R قوة اللي
+
+242
+00:16:59,520 --> 00:17:03,540
+exerted على 2 ببساطة 1 اتجاهها هو اتجاهه كيف أجيب
+
+243
+00:17:03,540 --> 00:17:09,040
+الاتجاه؟ معناه إذا عرفنا R12 بقدر أجيب AR12 hat
+
+244
+00:17:09,040 --> 00:17:13,140
+اللي هو الـ unit vector بساويه الـ R12 vector على ال
+
+245
+00:17:13,140 --> 00:17:18,010
+magnitude على الـ Magnet إذا ما بقدر أحدد الـ unit
+
+246
+00:17:18,010 --> 00:17:21,610
+vector لأي vector في الـ space قلنا إنه بقسم ال
+
+247
+00:17:21,610 --> 00:17:26,210
+vector على الـ magnitude تبعه هذا بالنسبة للـ four
+
+248
+00:17:26,210 --> 00:17:31,130
+sides هذه ايش هتكون نفس المفضل أن الـ Q1 و Q2 أكثر
+
+249
+00:17:31,130 --> 00:17:34,070
+بيها بالمسافة اللي بينهم بس ايش هتغير الاتجاه
+
+250
+00:17:34,070 --> 00:17:37,390
+هتكون minus AR123
+
+251
+00:17:43,190 --> 00:17:46,170
+أنا already كتبت لكم إياها الأشياء اللي عارفينها برو
+
+252
+00:17:46,170 --> 00:17:52,850
+R1
+
+253
+00:17:52,850 --> 00:18:00,470
+تلين هي المسافة بين two charges هي R تلين ناقص R
+
+254
+00:18:00,470 --> 00:18:04,390
+واحد عرفنا R هذا أنه الـ magnitude الـ magnitude
+
+255
+00:18:04,390 --> 00:18:08,960
+بدون أي volt أو بدون أي arrow هي عموماً مجموعة R18
+
+256
+00:18:08,960 --> 00:18:12,860
+وعرفناها قبل مجلسنا بتعريفها الجذر التربيعي
+
+257
+00:18:12,860 --> 00:18:19,860
+لـ R12Vector.R12Vector هاي المجموعة هتاكدين؟ وبالـ
+
+258
+00:18:19,860 --> 00:18:24,360
+A R12Hat اللي هي unit vector هي عبارة عن الـ vector
+
+259
+00:18:24,360 --> 00:18:30,900
+R12 على المجموعة تبعها بيسميناها R إذا F12 تساوي
+
+260
+00:18:30,900 --> 00:18:38,200
+Q12 على 4π إيصال نص لو عوضت عن A hatR vector على
+
+261
+00:18:38,200 --> 00:18:42,420
+R magnitude هتسر R واحد اثنين vector على R cubed
+
+262
+00:18:42,420 --> 00:18:46,740
+يعني ممكن أكتبها بدلالة مش أكتب إنما أكتبها بدلالة من
+
+263
+00:18:46,740 --> 00:18:50,680
+الـ vector هتسر على R cubed هتسر واحد على four by
+
+264
+00:18:50,680 --> 00:18:55,120
+epsilon naught Q1 و Q2 على R cubed في R واحد اثنين
+
+265
+00:18:55,120 --> 00:18:59,120
+vector أو بكتبها بهذه الطريقة Q1 و Q2 بعوض عن R
+
+266
+00:18:59,120 --> 00:19:01,360
+واحد اثنين vector ع R تانين vector مع نصر واحد
+
+267
+00:19:01,360 --> 00:19:04,280
+vector على four by epsilon naught في الـ magnitude
+
+268
+00:19:04,280 --> 00:19:09,780
+اللي هو R2-R1 تحت الجذر للقوة 3 اللي هتكون ال
+
+269
+00:19:09,780 --> 00:19:18,540
+magnitude للقوة 3 تمام؟
+
+270
+00:19:18,540 --> 00:19:23,160
+في أي استفسار لحقتونا؟ في أي استفسار؟ احنا كمان
+
+271
+00:19:23,160 --> 00:19:27,680
+اتفقنا إن القوتين متساويتين بالمقدار أسوأ القوة
+
+272
+00:19:27,680 --> 00:19:31,980
+اللي بتأثرها Q1 على Q2 أو القوة اللي بتأثرها Q2
+
+273
+00:19:31,980 --> 00:19:37,110
+على Q1 فهذه القوة ع واحد نجم اثنين بتساوي المدنيتو
+
+274
+00:19:37,110 --> 00:19:40,490
+تبع القوة اللي على اثنين نجم واحد في الـ unit
+
+275
+00:19:40,490 --> 00:19:44,030
+vector تبع القوة المية على واحد اللي هو بالتالي
+
+276
+00:19:44,030 --> 00:19:47,750
+بيساوي minus الـ unit vector تبع القوة الأولى
+
+277
+00:19:47,750 --> 00:19:51,570
+فبالتالي F2 من واحد بتساوي minus F12 لأن الـ unit
+
+278
+00:19:51,570 --> 00:19:55,890
+vectors منهم اتجاهاتهم متعاكسة وهذا شفنا احنا من
+
+279
+00:19:55,890 --> 00:20:01,910
+الرسمة حاجة مهمة في اللي هي الـ charges أول حاجة
+
+280
+00:20:01,910 --> 00:20:10,570
+قلنا إن قوة Q1 وQ2 مالها تتعكس بالاتجاه أول ثاني
+
+281
+00:20:10,570 --> 00:20:15,550
+event إن الـ charges المتماثلة مالها تتنافر زي مثلاً
+
+282
+00:20:15,550 --> 00:20:19,190
+شفنا الـ QQ لأنهم بتنافر أسوأ positive أو negative
+
+283
+00:20:19,190 --> 00:20:23,910
+charges هلاقي أن تأثيرهم تنافر زي ما في الـ figure
+
+284
+00:20:23,910 --> 00:20:28,630
+A و الـ figure B القوة اللي بيأثروا فيها الـ charges
+
+285
+00:20:28,630 --> 00:20:34,550
+على بعض هي قوة تنافر إذا كانوا مختلفتين unlike
+
+286
+00:20:34,550 --> 00:20:37,890
+charges, unlike signs يعني إذا كانوا like charges
+
+287
+00:20:37,890 --> 00:20:41,630
+هيكونوا تنافر, unlike charges هيكون فيه تجاذب بين
+
+288
+00:20:41,630 --> 00:20:42,150
+الاثنين
+
+289
+00:20:45,950 --> 00:20:48,950
+عشان أقول عنهم pointed charges يكفيش أن أقول أن
+
+290
+00:20:48,950 --> 00:20:52,530
+هو مقارنة مع الـ dimension الـ relevant dimension
+
+291
+00:20:52,530 --> 00:20:56,150
+أنه أصغر عشان two charges سمين ولا أتر أنا بأقارن
+
+292
+00:20:56,150 --> 00:20:59,290
+الاثنين مع بعض عشان أقول الاثنين عندهم pointed charges
+
+293
+00:20:59,290 --> 00:21:02,390
+بدي أقارنهم في المسافة اللي بينهم لازم تكون مسافة
+
+294
+00:21:02,390 --> 00:21:05,630
+كبيرة كفاية أنهم يشوفوا بعض ما هو pointed charges
+
+295
+00:21:05,630 --> 00:21:09,710
+أنه أصغر من الـ dimension تبعهم هي الـ relevant
+
+296
+00:21:09,710 --> 00:21:12,170
+dimension في هالحالة الـ relevant dimension مسافة
+
+297
+00:21:12,170 --> 00:21:16,620
+اللي بينهم لو أنا اتشارج و بتأثر على الـ plane زي
+
+298
+00:21:16,620 --> 00:21:19,280
+الـ plane تبع الطاولة هقول إنها برضه point of
+
+299
+00:21:19,280 --> 00:21:21,500
+charges لأن الـ relevant dimension فيها الحالمين
+
+300
+00:21:21,500 --> 00:21:29,340
+الـ object الثاني كبير كثير بالنسبة لها كمان
+
+301
+00:21:29,340 --> 00:21:33,440
+حاجة مهمة كثير إن الـ Q1 و Q2 ممكنوا addressed احنا
+
+302
+00:21:33,440 --> 00:21:36,540
+بنحكي على الـ ecrostatic فالاثنين مش لازم يتحركوا
+
+303
+00:21:36,540 --> 00:21:39,440
+في هذه الحالة احنا فرضين نحكي على الـ ecrostatic
+
+304
+00:21:39,440 --> 00:21:44,890
+كأن ما فيش movement ما فيش اعتمادية على الزمن لما اجي
+
+305
+00:21:44,890 --> 00:21:48,950
+احسب الـ force الـ sign بتاعة q1 و q2 لازم اخذها في
+
+306
+00:21:48,950 --> 00:21:55,730
+عين الحسبان مش لازم احمل الاشارة بتاعة q1 و q2 أو
+
+307
+00:21:55,730 --> 00:21:59,580
+كان عندي أكثر من two يعني أنا اللي شفتها كان مثال
+
+308
+00:21:59,580 --> 00:22:04,080
+أولاني لك لو كان عندي عدد كبير من الـ charges Q1,
+
+309
+00:22:04,200 --> 00:22:08,860
+Q2 لحد QN اللي هيصير اللي بعمله باخذ كل الـ charge
+
+310
+00:22:08,860 --> 00:22:12,340
+و بجمع كل القوة اللي بتأثر عليها من كل الـ charges
+
+311
+00:22:12,340 --> 00:22:17,320
+يعني عندي Q1, Q2, Q3 لحد QN وعندي charge Q مثلاً
+
+312
+00:22:18,170 --> 00:22:24,010
+هشوف أثر q1 على q, q2 على q, q3 على q وهكذا, qn
+
+313
+00:22:24,010 --> 00:22:27,810
+على q وبعدين القوة هجمعها vector addition عشان
+
+314
+00:22:27,810 --> 00:22:33,610
+أطول الـ vector الـ force الكلية يعني هي, so يمشي
+
+315
+00:22:33,610 --> 00:22:36,830
+فين الـ total force هتكون احنا عاملين بندرس القوة
+
+316
+00:22:36,830 --> 00:22:41,390
+على q انها جامع q1 و q2 لحد qn فهيكون عندنا اللي
+
+317
+00:22:41,390 --> 00:22:45,450
+هو الـ principle of superposition القوة الكلية اللي
+
+318
+00:22:45,450 --> 00:22:50,970
+لو كان عندي هي q على بعد Q وهي الـ origin تبعي على
+
+319
+00:22:50,970 --> 00:22:58,990
+بعد R مثلاً وهنا بيدي الـ Q1 وعندي الـ Q2 وعندي
+
+320
+00:22:58,990 --> 00:23:03,770
+الـ Q3 وهكذا طبعاً كل بره بتأيس المسافر بينهم هذه
+
+321
+00:23:03,770 --> 00:23:10,050
+R هتكون R1 هتكون R-R1 هشوف القوة اللي الـ Q1 أثر
+
+322
+00:23:10,050 --> 00:23:16,270
+فيها على Q الـ Q2 على Q الـ Q3 على Q و لو احنا فينا
+
+323
+00:23:16,270 --> 00:23:24,410
+في الـ Q وهاي الـ QN هذا
+
+324
+00:23:24,410 --> 00:23:30,570
+هيكون RN وبرضه هشوف أثر QN على Q بعد ما أجيب كل
+
+325
+00:23:30,570 --> 00:23:36,070
+قوة نجم الـ charge مختلفة Q1 مرة مرة مرة مرة مرة
+
+326
+00:23:36,070 --> 00:23:40,340
+مرة مرة مرة على أخر بجيب أجمع كل القوة بقى زي ما حكيت
+
+327
+00:23:40,340 --> 00:23:43,500
+vector addition بتعطيني الـ total force هذا بنسميه
+
+328
+00:23:43,500 --> 00:23:48,940
+الـ superposition difference أو
+
+329
+00:23:48,940 --> 00:23:53,360
+باختصار لأن الـ Q كان راح كل المعادلة اللي قدامنا
+
+330
+00:23:53,360 --> 00:23:58,420
+بقدر أسحب الـ Q برا الـ sum و الـ 4 by epsilon نقطة و
+
+331
+00:23:58,420 --> 00:24:02,600
+هذول constants وقول الـ sum من K equal واحد لأقل
+
+332
+00:24:02,600 --> 00:24:07,680
+QK في R vector ناقص RK vector اللي هو المسافة بين
+
+333
+00:24:07,680 --> 00:24:11,040
+هذا الـ charge و الـ charge بدرس عليها الـ force على
+
+334
+00:24:11,040 --> 00:24:16,240
+المجموعة للقوة تلاتة إذا يا بكتبهم عملي واحدة واحدة
+
+335
+00:24:16,240 --> 00:24:24,200
+مخصصلين يا باستخدم اللي هو summation symbol هذا
+
+336
+00:24:24,200 --> 00:24:27,260
+بالنسبة للـ force، في أي سؤال عن الـ force؟ إذا كم مرة
+
+337
+00:24:27,260 --> 00:24:30,900
+الـ force هي تكون على طول الخط الواصل between two
+
+338
+00:24:30,900 --> 00:24:35,430
+charges بتعتمد طردياً أو بتناسب طردياً مع قيمته في
+
+339
+00:24:35,430 --> 00:24:38,910
+واحد وفي اثنين أو عكسياً مع المسافة اللي بينهم
+
+340
+00:24:38,910 --> 00:24:43,110
+تربيع الـ constant of proportionality سميناها K و K
+
+341
+00:24:43,110 --> 00:24:47,310
+هذا بعتمد على نفاذية الوسط في هذا الشطر احنا
+
+342
+00:24:47,310 --> 00:24:50,390
+ماخذه الوسط هو الـ vacuum أو الـ free space فهتكون K
+
+343
+00:24:50,390 --> 00:24:53,650
+بيساوي واحد على four by epsilon naught اللي هي ال
+
+344
+00:24:53,650 --> 00:24:57,310
+permittivity بتاعة الـ free space دلوقتي بنعرف ال
+
+345
+00:24:57,310 --> 00:25:00,630
+electric field intensity فيها لقوا عطيدة ما بين ال
+
+346
+00:25:00,630 --> 00:25:05,110
+force و الـ field خطوط الـ field في مجال الـ .. الـ ..
+
+347
+00:25:05,110 --> 00:25:09,310
+الـ .. الكهربائي و بين اللي هي القوة اللي exerted
+
+348
+00:25:09,310 --> 00:25:12,530
+على الـ charge معينة الـ electric field intensity
+
+349
+00:25:12,530 --> 00:25:16,130
+ايش بالساوي احنا جبنا القوة على Q جبنا الـ total
+
+350
+00:25:16,130 --> 00:25:21,930
+force في الـ slide السابقة على Q force اللي على Q
+
+351
+00:25:21,930 --> 00:25:27,830
+نتيجة من Q1, Q2, Q3, Q4 فالـ electric field اللي
+
+352
+00:25:27,830 --> 00:25:34,830
+بتكون فيبسابحة فيها الـ Q هو عبارة عن limit لـ F على
+
+353
+00:25:34,830 --> 00:25:40,650
+Q as Q goes to 0 يعني ببساطة E بتساوي F على Q لو
+
+354
+00:25:40,650 --> 00:25:46,710
+رجعنا لمثال السابق ايش هتصير بس هيروح الـ Q من الـ E
+
+355
+00:25:46,710 --> 00:25:50,550
+هتكون F على Q هتكون 1 على four by epsilon نوت الصماشن
+
+356
+00:25:53,910 --> 00:25:58,690
+حاجة بنستنتجها ان F vector و E vector و Q مالها
+
+357
+00:25:58,690 --> 00:26:01,570
+scalar إذا اتجاه الـ electric field ماله هو اتجاه
+
+358
+00:26:01,570 --> 00:26:06,630
+الـ force أو الحسابات بتاعته إذا الـ force بالنيوتن
+
+359
+00:26:06,630 --> 00:26:10,010
+أو الـ unit بتاعته و Q بالـ column E ايش هيكون
+
+360
+00:26:10,010 --> 00:26:15,230
+النيوتن على column أو volt على متر أو volt على 
+
+361
+00:26:15,230 --> 00:26:15,710
+meter
+
+362
+00:26:22,330 --> 00:26:27,490
+أنا إذا عندي الـ electric field اللي ناتج على نقطة
+
+363
+00:26:27,490 --> 00:26:32,230
+R في الـ space من due to a point in charge located
+
+364
+00:26:32,230 --> 00:26:37,910
+at R' يعني أنا بدي أحسب الـ electric، عندي Q، الـ Q
+
+365
+00:26:37,910 --> 00:26:42,390
+في هذه الحالة Q
+
+366
+00:26:42,390 --> 00:26:48,010
+على بعد R1 و أنا بدي أحسب الـ electric field عند
+
+367
+00:26:48,010 --> 00:26:51,710
+نقطة في الـ space على بعد R من الـ origin ماذا
+
+368
+00:26:51,710 --> 00:26:57,810
+ستساوي؟ سنقوم بتشارج Q بتأثير على هذه النقطة Q على
+
+369
+00:26:57,810 --> 00:27:02,510
+4π إبسم من نقطة R تربيع في R hat لأن القوة لو
+
+370
+00:27:02,510 --> 00:27:05,550
+كانت عندها تشارج اللي كنا سميها دائماً كيونيز
+
+371
+00:27:05,550 --> 00:27:09,070
+تشارج لو كانت عندها Q واحد ماذا ستكون Q في Q
+
+372
+00:27:09,070 --> 00:27:14,4
+
+401
+00:29:11,590 --> 00:29:17,110
+على R minus the RK لكل Q واضح يعني احنا قبل دراسنا ال
+
+402
+00:29:17,110 --> 00:29:30,370
+force اللي بتأثرها جمع من الـ charges على
+
+403
+00:29:30,370 --> 00:29:35,270
+ال point of charge جبنا مجموع ال forces قولنا
+
+404
+00:29:35,270 --> 00:29:38,330
+ال electric field اللي exerted على هذا ال point of
+
+405
+00:29:38,330 --> 00:29:45,370
+charge هيكون مجموع كل هذه القوة على ال point of
+
+406
+00:29:45,370 --> 00:29:50,020
+charge على ال Q فهيظهر بس الحصة الثانية من كل واحد
+
+407
+00:29:50,020 --> 00:29:55,240
+هيروح اللي هي قيمة Q هيظهر  بـQ1 على R ثانية في
+
+408
+00:29:55,240 --> 00:30:06,400
+K الـQ2 وهذا ده الفرق بين الـvectors بتاعنا هذا
+
+409
+00:30:06,400 --> 00:30:09,660
+الفرق بين القانون هذا وقانون ال force أنّه بصراحة
+
+410
+00:30:09,660 --> 00:30:15,020
+Q من القانون هنشوف 
+
+411
+00:30:15,020 --> 00:30:15,520
+مثلًا
+
+412
+00:30:20,340 --> 00:30:23,840
+مثال بقول عندي point charge مقدارها واحد
+
+413
+00:30:23,840 --> 00:30:27,420
+millicolum وكمان point charge مقدارها اثنين
+
+414
+00:30:27,420 --> 00:30:30,940
+ناقص اثنين millicolum الاثنين محطوطين في ال space
+
+415
+00:30:30,940 --> 00:30:35,180
+واحدة على ثلاثة اثنين ناقص واحد يعني x ثلاثة و y
+
+416
+00:30:35,180 --> 00:30:38,220
+ثلاثة اثنين ناقص واحد اللي بصي متبعها لو أنا حاولت
+
+417
+00:30:38,220 --> 00:30:45,320
+أرسم الرسمة يعني x y z النقطة الأولى اللي هي واحد
+
+418
+00:30:45,320 --> 00:30:53,050
+millicolum على ثلاثة x اثنين y مثلاً و ناقص واحد
+
+419
+00:30:53,050 --> 00:30:55,630
+يعني لو أنا أخدت هاي ال plane تبعي هو هالناقص 
+
+420
+00:30:55,630 --> 00:30:59,590
+واحد هذه النقطة دولة اللي هي علاوة ثلاثة اثنين
+
+421
+00:30:59,590 --> 00:31:07,710
+ناقص واحد هي Q واحد اللي مقدارها مقدارها واحد ملي
+
+422
+00:31:07,710 --> 00:31:12,810
+كولو والنقطة الثانية هذه ال equation تبعها هي R
+
+423
+00:31:12,810 --> 00:31:18,730
+واحد والثانية واقع على X ناقص واحد Y ناقص واحد R
+
+424
+00:31:18,730 --> 00:31:25,250
+واحد لو مديتها بهيك هيكون x-1 y-1 وطالع على فوق
+
+425
+00:31:25,250 --> 00:31:34,890
+مقدارها أربعة هدف ال space يعني مقاس واحد مقاس واحد و 4
+
+426
+00:31:34,890 --> 00:31:41,970
+هي EQ2 اللي مقدارها ناقص 2 من ال coulomb
+
+427
+00:31:44,880 --> 00:31:48,720
+بدنا من هنا أول نحسب ال electric force على ال charge
+
+428
+00:31:48,720 --> 00:31:54,420
+المقدارها عشرة nano column وهي بوقع على x بتساوي
+
+429
+00:31:54,420 --> 00:31:59,580
+صفر x بتساوي صفر يعني موقع في ال YZ plane وي Y
+
+430
+00:31:59,580 --> 00:32:07,460
+كميتها ثلاثة و Z واحد فقدر
+
+431
+00:32:07,460 --> 00:32:12,460
+مين هيحسب منها هحسب منها R واحد R اثنين وهحسب منها R
+
+432
+00:32:13,650 --> 00:32:19,410
+وهي Q المقدارها عشرة والثانية أطلب مني أن أجيب ال
+
+433
+00:32:19,410 --> 00:32:24,450
+forces ال total force على النقطة هي اللي كتبت في
+
+434
+00:32:24,450 --> 00:32:31,590
+هذا الموضوع في حابين بيجربوا هذا
+
+435
+00:32:31,590 --> 00:32:38,110
+احنا نجيب اللي بأثر عليها تمام عملنا لها مئة مئة أن
+
+436
+00:32:38,110 --> 00:32:41,890
+الفرق طبعاً الإشارات بتاعتهم هنا في الإشارة السالبة
+
+437
+00:32:42,460 --> 00:32:46,200
+عندي إشارة وموجبة أو هاي إشارة وموجبة فأولًا خلّيني 
+
+438
+00:32:46,200 --> 00:32:50,720
+أعرف كل unit كل position يعني خلّيني أحط يا R وR1
+
+439
+00:32:50,720 --> 00:32:54,500
+وR2 فهي كمضاية أي سؤال هحط ال position تبعهم
+
+440
+00:32:54,500 --> 00:32:56,900
+position vector لأنّهم اللي أحسب ال position vector
+
+441
+00:32:56,900 --> 00:33:02,360
+فحلّنا نقول R1 إيش بيساوي؟ R1 vector هحط فوق سهل
+
+442
+00:33:02,360 --> 00:33:07,500
+عشان احنا ما نقدرش نحط volt في خطّنا هيكون 3X هتحط
+
+443
+00:33:07,500 --> 00:33:09,840
+فوقها هتحط فوقها هتحط فوقها هتحط فوقها هتحط فوقها
+
+444
+00:33:09,840 --> 00:33:10,400
+هتحط فوقها هتحط فوقها هتحط فوقها هتحط فوقها هتحط
+
+445
+00:33:10,400 --> 00:33:14,990
+فوقها هتحط فوقها هتحط زائد اثنين Yها ناقص Zها
+
+446
+00:33:14,990 --> 00:33:23,030
+ناقص واحد R اثنين بتساوي سالب Xها سالب Yها زائد
+
+447
+00:33:23,030 --> 00:33:28,120
+أربعة Zها هي عند R هي موقع المقطع اللي بدأ يجيب
+
+448
+00:33:28,120 --> 00:33:32,600
+عليها ال courses عبارة عن X hat صفر عند ثلاثة Y
+
+449
+00:33:32,600 --> 00:33:37,760
+hat زائد Z hat أقع في ZY إثنين طب إحنا نبدأ
+
+450
+00:33:37,760 --> 00:33:45,440
+بالقوة اللي بتأثر فيها Q1 على Q اللي هي F1
+
+451
+00:33:45,440 --> 00:33:50,360
+خلاص أكثر بتأثر فيها وخطفوها بأكثر لإنه مش هتساوي
+
+452
+00:33:50,360 --> 00:33:52,980
+هذه النوع أولًا قول لي اللي بقرأ باصف ولا
+
+453
+00:33:58,010 --> 00:34:03,390
+احنا عشان ما سميناش R فخبرك أن R1 يعني R اليمين،
+
+454
+00:34:03,390 --> 00:34:09,590
+R1 خلّيني أسميها وR1 خلّيني أعرفها، اللي عبارة عن
+
+455
+00:34:09,590 --> 00:34:17,490
+تمام، يعني بدنا نحط ال vector إيش
+
+456
+00:34:17,490 --> 00:34:27,440
+هيساوي؟ R minus R1، تمام؟ فإذا R1 هو عبارة عن R بس
+
+457
+00:34:27,440 --> 00:34:32,100
+هو بتفترض فوق ال R R minus R واحد إذا أن أنا بدي
+
+458
+00:34:32,100 --> 00:34:37,460
+أشوف المسافة عند وقبضش تبع Q وقبضش تبع Q واحد وبدي
+
+459
+00:34:37,460 --> 00:34:41,740
+المسافة بينهم اللي هي مبالغ Q واحد و Q اللي هي R
+
+460
+00:34:41,740 --> 00:34:48,700
+ناقص R واحد تمام
+
+461
+00:34:48,700 --> 00:34:56,710
+زائد Y hat زائد Y hatوخلاص وزاق الثانية بزاقها
+
+462
+00:34:56,710 --> 00:35:03,090
+الثانية إيش نوع القوة اللي بين هدولة ال charges؟
+
+463
+00:35:03,090 --> 00:35:09,150
+هي القوة اللي لها reverse يعني هيك اتجاهها صح؟ هاي
+
+464
+00:35:09,150 --> 00:35:12,950
+بتأثر على هاي باصلة force وهذا المنطقة إذا F واحد
+
+465
+00:35:12,950 --> 00:35:21,490
+منها اللي برأسك الإشارة كاعتها موجبة حد
+
+466
+00:35:21,490 --> 00:35:26,860
+على قوة باي اكس ال نوتتور باي تور باي تور باي نعوض
+
+467
+00:35:26,860 --> 00:35:31,900
+عن R واحد فلس نحن نعوض R واحد أنت هتساوي ليه
+
+468
+00:35:31,900 --> 00:35:36,440
+تسعة فعشرة هو تسعة تسعة
+
+469
+00:35:36,440 --> 00:35:41,960
+فعشرة هو تسعة Q واحد اللي مقدارها واحد من ال
+
+470
+00:35:41,960 --> 00:35:46,920
+column فعشرة على كولوم مقاس ثلاثة على طول خليها واحد
+
+471
+00:35:46,920 --> 00:35:51,760
+فعشرة كولوم مقاس ثلاثة في Q اللي بدي أسئل عليها ليه
+
+472
+00:35:51,760 --> 00:36:00,640
+عشرة كولوم وليه عشرة فعشرة وناقص تسعة على الـR1
+
+473
+00:36:00,640 --> 00:36:07,200
+تربيعية احنا قلنا عشان أجيب ليه ال vector R1 يا بال
+
+474
+00:36:07,200 --> 00:36:10,580
+vector على RQ خلينا نعرفها بهذا الشكل احنا بحط
+
+475
+00:36:10,580 --> 00:36:13,640
+القانون اللي بتحط بيه يعني بيكتب القانون اللي
+
+476
+00:36:13,640 --> 00:36:17,400
+بتستخدميه عشان نحدد نجيب ليه ال vector ولا F
+
+477
+00:36:20,300 --> 00:36:27,500
+هقول R واحد ساوي واحد على أربع باي ابسلون نوت Q واحد
+
+478
+00:36:27,500 --> 00:36:33,420
+في Q فاسم القانون هاسميه Q في Q واحد في Q واحد
+
+479
+00:36:33,420 --> 00:36:40,700
+ثانية أما Q وQ واحد في R لبتر ممكن نأخذ هذا
+
+480
+00:36:40,700 --> 00:36:48,570
+القانون R واحد لبتر R واحد لبتر مش هيكون تحت RQعلى
+
+481
+00:36:48,570 --> 00:36:57,470
+R1 مقمتور يعني مقمتور في الـP هنحط
+
+482
+00:36:57,470 --> 00:37:03,230
+الـP تمام؟ لذا نستخدم هذا لأن هيكون ال bus مضروب
+
+483
+00:37:03,230 --> 00:37:11,870
+بـأيه؟ مش مشكلة هحط سهل R1
+
+484
+00:37:11,870 --> 00:37:16,070
+vector ليه حسبت إن هي هزيمتهم؟ R
+
+485
+00:37:17,800 --> 00:37:22,260
+YHYH YYH YYH YYH YYH YYH YYH YYH YYH YYH YYH
+
+486
+00:37:22,260 --> 00:37:24,500
+YYH YYH YYH YYH YYH YYH YYH YYH YYH YYH YYH YYH
+
+487
+00:37:24,500 --> 00:37:24,540
+YYH YYH YYH YYH YYH YYH YYH YYH YYH YYH YYH YYH
+
+488
+00:37:24,540 --> 00:37:25,960
+YYH YYH YYH YYH YYH YYH YYH YYH YYH YYH YYH YYH
+
+489
+00:37:25,960 --> 00:37:29,460
+YYH YYH YYH YYH YYH YYH YYH
+
+490
+00:37:29,460 --> 00:37:33,900
+YYH YYH YYH YYH YYH YYH YYH YYH YYH YYH YYH YYH
+
+491
+00:37:33,900 --> 00:37:45,080
+YYH YYH YYH YYH YYH YYH YYH
+
+492
+00:37:45,080 --> 00:37:50,130
+لأربعة جذر التربيعية لأربع عشرة إذا حطينا على الجذر
+
+493
+00:37:50,130 --> 00:37:53,630
+التربيعية لأربع عشرة وقوة الأدنى يعني أربع عشرة وقوة
+
+494
+00:37:53,630 --> 00:37:59,230
+الأدنى هذه F واحد جبناها دلالة ال vector يعني إلها 
+
+495
+00:37:59,230 --> 00:38:01,710
+component في ال X و component في ال Y و component
+
+496
+00:38:01,710 --> 00:38:11,570
+في ال Z طب إفتنان بحب حب يعمل إفتنان؟ وبدنا
+
+497
+00:38:11,570 --> 00:38:12,350
+نلقي جهد غير
+
+498
+00:38:17,660 --> 00:38:25,880
+R1 لينا ثلاثة Xات ثانية اثنين و اي حد ناقص و
+
+499
+00:38:25,880 --> 00:38:30,320
+أربع ثلاثة
+
+500
+00:38:30,320 --> 00:38:30,680
+Xات ثلاثة Xات ثلاثة Xات ثلاثة Xات ثلاثة
+
+501
+00:38:30,680 --> 00:38:31,180
+Xات ثلاثة Xات ثلاثة Xات ثلاثة Xات ثلاثة
+
+502
+00:38:31,180 --> 00:38:31,600
+Xات ثلاثة Xات ثلاثة Xات ثلاثة Xات ثلاثة
+
+503
+00:38:31,600 --> 00:38:40,340
+Xات ثلاثة Xات ثلاثة Xات 
+
+504
+00:38:40,340 --> 00:38:47,750
+ثلاثة Xات احنا بنأثر Q2 على Q فأثر Q2 على Q بأنه
+
+505
+00:38:47,750 --> 00:38:53,350
+Q2 إيش بتأثر على Q بهذا الشكل يعني Q2 هاتش زي ال Q
+
+506
+00:38:53,350 --> 00:38:58,350
+واحد لها فعنا R وR2 وعنا اللي هو هسميه R2 ال
+
+507
+00:38:58,350 --> 00:39:04,610
+vector اللي هو إيش بيسوي R minus R2 R minus R2
+
+508
+00:39:11,340 --> 00:39:21,720
+بش فيش هناك X هيكون عندي زائد X hat زائد
+
+509
+00:39:21,720 --> 00:39:30,480
+أربعة Y hat هي ثلاثة ناقص نقاش plus أربعة Y hat و
+
+510
+00:39:30,480 --> 00:39:33,500
+ناقص ثلاثة Zها
+
+511
+00:39:49,080 --> 00:39:54,520
+الـ force 2 خلّيني أسميها F2 لأن جبنا F1 هتكون K
+
+512
+00:39:54,520 --> 00:40:03,820
+في Q في Q2 على R2 magnitude Q في R2 vector ممتازة
+
+513
+00:40:03,820 --> 00:40:07,280
+انعوضت خلّيني أجمعها انعوضة عشان نكون معي كواسة
+
+514
+00:40:07,280 --> 00:40:13,040
+كده كما أنا قلت أهاليك الـ K هي تسعة عفوا عشرة عفوا تسعةEQ
+
+515
+00:40:13,040 --> 00:40:18,300
+اللي قداش كميتها عشرة عشرة كمان عندنا أس تسعة عشرة
+
+516
+00:40:18,300 --> 00:40:21,700
+كمان عندنا أس ثلاثة عشرة كمان عندنا أس ثمانية في اللي
+
+517
+00:40:21,700 --> 00:40:27,260
+هي ناقص اثنين في عشرة أس ثلاثة ثلاثة على ال
+
+518
+00:40:27,260 --> 00:40:32,460
+magnitude EQ اللي هتكون جذر ستة وعشرين القوة ثلاثة
+
+519
+00:40:32,460 --> 00:40:36,300
+على اثنين أو جزء من قوة ثلاثة على اثنين أو جزء من
+
+520
+00:40:36,300 --> 00:40:37,860
+قوة ثلاثة على اثنين أو جزء من قوة ثلاثة على اثنين
+
+521
+00:40:37,860 --> 00:40:40,960
+أو جزء من قوة ثلاثة على اثنين أو جزء من قوة ثلاثة
+
+522
+00:40:40,960 --> 00:40:43,880
+على اثنين أو جزء من قوة ثلاثة على اثنين أو جزء من
+
+523
+00:40:43,880 --> 00:40:46,320
+قوة ثلاثة على اثنين أو جزء من قوة ثلاثة على اثنين
+
+524
+00:40:46,320 --> 00:40:52,720
+أو جزء من قوة ثلاثة على اثنين أو جزء من قوة ثلاثة
+
+525
+00:40:52,720 --> 00:40:59,540
+على اثنين أو جزء من قوة ثلاثة على اثنين F واحد
+
+526
+00:40:59,540 --> 00:41:05,220
+زائد F تمام في أحد عنده أي استفسار بس مسموع لأ
+
+527
+00:41:05,220 --> 00:41:08,120
+خلصت السبورة زي مش أي استفسار في أحد عنده أي
+
+528
+00:41:08,120 --> 00:41:12,520
+استفسار قبل ما نمحي السبورة طب يسلموا ذاك يعني بس
+
+529
+00:41:12,520 --> 00:41:18,480
+عشان نوضح أنّه إحنا استخدمنا القانون اللي هو q في qk
+
+530
+00:41:18,480 --> 00:41:22,460
+على فور باي ابسلون نوت R minus RK على R minus RK
+
+531
+00:41:22,460 --> 00:41:26,960
+القوة ثلاثة هذا اللي استخدمناه وجمعنا K واحد و
+
+532
+00:41:26,960 --> 00:41:31,060
+اثنين وعوضنا وبيطلع معنا ال total force لأن هو
+
+533
+00:41:31,060 --> 00:41:34,140
+هذا ال vector addition بس عملية أنها يعني الخطوات
+
+534
+00:41:34,140 --> 00:41:37,400
+اللي احنا شرحناها مع بعض هي لازم تبقيها أن حساب أي 
+
+535
+00:41:37,400 --> 00:41:40,380
+قوة بدك تجيب ال position vector واحنا أخصّا أخذنا
+
+536
+00:41:40,380 --> 00:41:43,700
+chapter كام كده نجيب position vector لكل point in
+
+537
+00:41:43,700 --> 00:41:47,100
+charge بعدين نجيب ال distance بين النقاط اللي أنا
+
+538
+00:41:47,100 --> 00:41:51,580
+بدي أجيب بالهم القوة بين Q و Q1 مثلاً و QQ2 وهكذا
+
+539
+00:41:51,580 --> 00:41:54,600
+بعد ما أجيب ال distance أنا جاهزة عند قيم ال
+
+540
+00:41:54,600 --> 00:41:58,140
+charges عند المسافات اللي بينهم وعند بقدر أجيب ال
+
+541
+00:41:58,140 --> 00:42:01,220
+unit vector أو بقدر أجيب اللي هو R على R magnitude
+
+542
+00:42:01,220 --> 00:42:05,580
+of Q وبالتالي بقدر أحسب اللي هي ال force منتهى
+
+543
+00:42:05,580 --> 00:42:08,810
+البساطة طب لو بده يجيب ال electric field intensity
+
+544
+00:42:08,810 --> 00:42:13,670
+هيكون E بساومين F على Q يعني F اللي احنا حسبناها
+
+545
+00:42:13,670 --> 00:42:17,530
+مع بعض بقسمها على قيمة ال charge اللي هي عشرة قوة
+
+546
+00:42:17,530 --> 00:42:21,270
+في عشرة قوة ناقص تسعة أو عشر nano column اللي
+
+547
+00:42:21,270 --> 00:42:24,590
+بتعطيني قيمة ال electric field intensity اللي
+
+548
+00:42:24,590 --> 00:42:28,190
+exerted على ال point of charge اللي قيمتها عشرة في
+
+549
+00:42:28,190 --> 00:42:32,150
+عشرة قوة ناقص تسعة column في أي استفسار لحد هنا؟
+
+550
+00:42:32,150 --> 00:42:35,230
+في أي استفسار؟ أعطيكوا لغة 
diff --git a/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/CIPP0dKojOk_raw.json b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/CIPP0dKojOk_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..cad6ce6c739689c466413279451bc28366b2d1dc
--- /dev/null
+++ b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/CIPP0dKojOk_raw.json
@@ -0,0 +1 @@
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بيقول إن هو القوة بين two charge distribution بتكون على الخط اللي بوصل بين هدولة تنتهي", "tokens": [3224, 15730, 18863, 45340, 31439, 6225, 45340, 6156, 2288, 1863, 3794, 1829, 24525, 2304, 3224, 20666, 4117, 19528, 3660, 4602, 14501, 381, 533, 368, 1173, 298, 650, 11933, 1829, 8592, 25961, 12174, 7649, 11536, 3224, 4724, 1829, 39648, 36145, 31439, 25062, 2407, 3660, 49374, 732, 4602, 7316, 39894, 30544, 15844, 33962, 9566, 13672, 1829, 4724, 2407, 36520, 49374, 8032, 3215, 12610, 3660, 6055, 29399, 3224, 1829], "avg_logprob": -0.23134328313727878, "compression_ratio": 1.452513966480447, "no_speech_prob": 0.0, "words": [{"start": 468.72, "end": 469.08, "word": "هذا", "probability": 0.95556640625}, {"start": 469.08, "end": 469.54, "word": " العالم", "probability": 0.95947265625}, {"start": 469.54, "end": 469.8, "word": " هو", "probability": 0.92138671875}, {"start": 469.8, "end": 470.14, "word": " عالم", "probability": 0.91015625}, {"start": 470.14, "end": 470.7, "word": " فرنسي", 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"probability": 0.9033203125}, {"start": 1162.88, "end": 1163.16, "word": " كمان", "probability": 0.8468424479166666}, {"start": 1163.16, "end": 1163.62, "word": " اتفقنا", "probability": 0.9548828125}, {"start": 1163.62, "end": 1163.82, "word": " إن", "probability": 0.29248046875}, {"start": 1163.82, "end": 1164.58, "word": " القوتين", "probability": 0.8212890625}, {"start": 1164.58, "end": 1165.76, "word": " متساويتين", "probability": 0.8306477864583334}, {"start": 1165.76, "end": 1166.56, "word": " بالمقدار", "probability": 0.958740234375}, {"start": 1166.56, "end": 1167.24, "word": " أسوأ", "probability": 0.69659423828125}, {"start": 1167.24, "end": 1167.68, "word": " القوة", "probability": 0.9931640625}, {"start": 1167.68, "end": 1167.82, "word": " اللي", "probability": 0.88525390625}, {"start": 1167.82, "end": 1168.34, "word": " بتأثرها", "probability": 0.9010009765625}, {"start": 1168.34, "end": 1168.98, "word": " Q1", "probability": 0.8603515625}, {"start": 1168.98, "end": 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F2 من واحد بيساوي minus F12 لأن ال unit vectors منهم اتجاهاتهم متعاكسة وهذا شفنا احنا من الرسمة حاجة مهمة في اللي هي ال charges أول حاجة قلنا", "tokens": [5172, 3224, 24192, 25062, 2407, 3660, 6225, 36764, 24401, 8717, 7435, 2304, 1975, 2655, 1863, 9957, 39894, 3794, 995, 45865, 9673, 3215, 22653, 2655, 2407, 6055, 3555, 3615, 25062, 2407, 3660, 13672, 1829, 15844, 1975, 2655, 1863, 9957, 8717, 7435, 2304, 36764, 24401, 8978, 2423, 4985, 8062, 6055, 3555, 3615, 25062, 2407, 3660, 9673, 10632, 15844, 36764, 24401, 13672, 1829, 31439, 20666, 2655, 6027, 1829, 4724, 1829, 3794, 995, 45865, 3175, 2423, 4985, 8062, 6055, 3555, 3615, 25062, 2407, 3660, 42963, 12610, 7578, 6156, 3555, 6027, 2655, 6027, 1829, 479, 17, 9154, 36764, 24401, 4724, 1829, 3794, 995, 45865, 3175, 479, 4762, 5296, 33456, 2423, 4985, 18875, 9154, 16095, 1975, 2655, 7435, 40294, 9307, 16095, 44650, 3615, 995, 4117, 3794, 3660, 37037, 15730, 13412, 5172, 8315, 1975, 5016, 8315, 9154, 34892, 38251, 3660, 11331, 26108, 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unit", "probability": 0.939453125}, {"start": 1191.57, "end": 1192.01, "word": " vectors", "probability": 0.9384765625}, {"start": 1192.01, "end": 1192.51, "word": " منهم", "probability": 0.88134765625}, {"start": 1192.51, "end": 1193.63, "word": " اتجاهاتهم", "probability": 0.8895670572916666}, {"start": 1193.63, "end": 1194.43, "word": " متعاكسة", "probability": 0.8592936197916666}, {"start": 1194.43, "end": 1194.85, "word": " وهذا", "probability": 0.20849609375}, {"start": 1194.85, "end": 1195.17, "word": " شفنا", "probability": 0.8277994791666666}, {"start": 1195.17, "end": 1195.55, "word": " احنا", "probability": 0.9384765625}, {"start": 1195.55, "end": 1195.89, "word": " من", "probability": 0.9912109375}, {"start": 1195.89, "end": 1197.05, "word": " الرسمة", "probability": 0.8380533854166666}, {"start": 1197.05, "end": 1199.63, "word": " حاجة", "probability": 0.9788411458333334}, {"start": 1199.63, "end": 1200.11, "word": " مهمة", "probability": 0.9684244791666666}, {"start": 1200.11, "end": 1200.31, "word": " في", "probability": 0.88134765625}, {"start": 1200.31, "end": 1200.65, "word": " اللي", "probability": 0.7115478515625}, {"start": 1200.65, "end": 1200.89, "word": " هي", "probability": 0.8671875}, {"start": 1200.89, "end": 1201.03, "word": " ال", "probability": 0.732421875}, {"start": 1201.03, "end": 1201.39, "word": " charges", "probability": 0.8671875}, {"start": 1201.39, "end": 1201.65, "word": " أول", "probability": 0.7021484375}, {"start": 1201.65, "end": 1201.91, "word": " حاجة", "probability": 0.9923502604166666}, {"start": 1201.91, "end": 1202.25, "word": " قلنا", "probability": 0.8473307291666666}], "temperature": 1.0}, {"id": 52, "seek": 123045, "start": 1203.03, "end": 1230.45, "text": "إن قوة Q1 وQ2 مالها تتعكس بالاتجاه أول تاني event إن ال charges المتماثلة مالها تتنافر زي مثلا شفنا ال QQ لأنهم بتنافر أسوأ positive أو negative charges هلاقى أن تأثيرهم تنافر زي ما في ال figure A و ال figure B القوة اللي بيأثروا فيها ال charges على بعض هي قوة تنافر", "tokens": [28814, 1863, 12174, 2407, 3660, 1249, 16, 4032, 48, 17, 3714, 6027, 11296, 6055, 2655, 3615, 4117, 3794, 20666, 9307, 7435, 40294, 5551, 12610, 6055, 7649, 1829, 2280, 36145, 2423, 12235, 9673, 39237, 5718, 104, 37977, 3714, 6027, 11296, 6055, 2655, 8315, 5172, 2288, 30767, 1829, 50113, 15040, 13412, 5172, 8315, 2423, 1249, 48, 5296, 33456, 16095, 39894, 8315, 5172, 2288, 5551, 3794, 2407, 10721, 3353, 34051, 3671, 12235, 8032, 15040, 4587, 7578, 14739, 6055, 10721, 12984, 13546, 16095, 6055, 8315, 5172, 2288, 30767, 1829, 19446, 8978, 2423, 2573, 316, 4032, 2423, 2573, 363, 25062, 2407, 3660, 13672, 1829, 4724, 1829, 10721, 49115, 14407, 8978, 11296, 2423, 12235, 15844, 45030, 11242, 39896, 12174, 2407, 3660, 6055, 8315, 5172, 2288], "avg_logprob": -0.2786458204189936, "compression_ratio": 1.778723404255319, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 1203.03, "end": 1203.35, "word": "إن", "probability": 0.60284423828125}, {"start": 1203.35, 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عن ar hat بقى شهرنا ال vector r minus r prime على ال magnitude بتصير r cubed يعني r minus r prime على r cubed اللي هي ال magnitude ل r minus r prime هو تلاتة", "tokens": [2304, 43020, 1975, 3615, 2407, 11242, 18871, 594, 2385, 4724, 4587, 7578, 13412, 3224, 2288, 8315, 2423, 8062, 367, 3175, 367, 5835, 15844, 2423, 15668, 39894, 9381, 13546, 367, 36510, 37495, 22653, 367, 3175, 367, 5835, 15844, 367, 36510, 13672, 1829, 39896, 2423, 15668, 5296, 367, 3175, 367, 5835, 31439, 6055, 1211, 9307, 3660], "avg_logprob": -0.35511362769386984, "compression_ratio": 1.5277777777777777, "no_speech_prob": 0.0, "words": [{"start": 1690.13, "end": 1690.55, "word": "ممكن", "probability": 0.7166748046875}, {"start": 1690.55, "end": 1690.87, "word": " اعوض", "probability": 0.8660888671875}, {"start": 1690.87, "end": 1690.97, "word": " عن", "probability": 0.67431640625}, {"start": 1690.97, "end": 1691.21, "word": " ar", "probability": 0.2626953125}, {"start": 1691.21, "end": 1691.51, "word": " hat", 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انعوضت خلّيني أجمعها انعوضة عشان نكون معايا كواسعة كده كما انا قلت أهاليك الـ K هي 9 عفوا 10 عفوا 9", "tokens": [6027, 39184, 3464, 568, 16490, 1211, 11703, 9957, 1829, 5551, 38251, 1829, 11296, 479, 17, 5296, 28814, 1863, 10874, 1829, 3555, 8315, 479, 16, 8032, 2655, 30544, 591, 8978, 1249, 8978, 1249, 17, 15844, 497, 17, 15668, 1249, 8978, 497, 17, 8062, 3714, 2304, 2655, 31377, 3660, 16472, 3615, 2407, 11242, 2655, 16490, 1211, 11703, 9957, 1829, 5551, 7435, 2304, 3615, 11296, 16472, 3615, 2407, 11242, 3660, 6225, 8592, 7649, 8717, 30544, 20449, 995, 25528, 9122, 14407, 3794, 27884, 9122, 3215, 3224, 9122, 15042, 1975, 8315, 12174, 1211, 2655, 5551, 3224, 6027, 1829, 4117, 2423, 39184, 591, 39896, 1722, 6225, 5172, 14407, 1266, 6225, 5172, 14407, 1722], "avg_logprob": -0.48495370149612427, "compression_ratio": 1.5119617224880382, "no_speech_prob": 2.086162567138672e-06, "words": [{"start": 2389.08, "end": 2389.88, "word": "الـ", "probability": 0.1093597412109375}, {"start": 2389.88, 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"word": " او", "probability": 0.75244140625}, {"start": 2539.77, "end": 2540.05, "word": " عشر", "probability": 0.938232421875}, {"start": 2540.05, "end": 2540.31, "word": " nano", "probability": 0.6435546875}, {"start": 2540.31, "end": 2540.81, "word": " column", "probability": 0.39013671875}, {"start": 2540.81, "end": 2541.27, "word": " اللي", "probability": 0.68115234375}, {"start": 2541.27, "end": 2541.91, "word": " بتعطيني", "probability": 0.84501953125}, {"start": 2541.91, "end": 2542.51, "word": " قيمة", "probability": 0.9930013020833334}, {"start": 2542.51, "end": 2542.67, "word": " ال", "probability": 0.96875}, {"start": 2542.67, "end": 2542.97, "word": " electric", "probability": 0.87646484375}, {"start": 2542.97, "end": 2543.29, "word": " field", "probability": 0.85009765625}, {"start": 2543.29, "end": 2543.93, "word": " intensity", "probability": 0.94873046875}, {"start": 2543.93, "end": 2544.59, "word": " اللي", "probability": 0.98583984375}, {"start": 2544.59, "end": 2545.23, "word": " exerted", "probability": 0.968017578125}, {"start": 2545.23, "end": 2545.55, "word": " على", "probability": 0.833984375}, {"start": 2545.55, "end": 2545.79, "word": " ال", "probability": 0.89453125}, {"start": 2545.79, "end": 2546.01, "word": " point", "probability": 0.58935546875}, {"start": 2546.01, "end": 2546.15, "word": " of", "probability": 0.94580078125}, {"start": 2546.15, "end": 2546.45, "word": " charge", "probability": 0.98876953125}, {"start": 2546.45, "end": 2546.61, "word": " اللي", "probability": 0.983642578125}, {"start": 2546.61, "end": 2547.15, "word": " قمتها", "probability": 0.956787109375}, {"start": 2547.15, "end": 2547.93, "word": " عشرة", "probability": 0.9798177083333334}, {"start": 2547.93, "end": 2548.19, "word": " في", "probability": 0.7763671875}, {"start": 2548.19, "end": 2548.59, "word": " عشرة", "probability": 0.97998046875}, {"start": 2548.59, "end": 2549.05, "word": " قوة", "probability": 0.98095703125}, {"start": 2549.05, "end": 2549.39, "word": " ناقص", "probability": 0.988037109375}, {"start": 2549.39, "end": 2549.79, "word": " تسعة", "probability": 0.9876302083333334}, {"start": 2549.79, "end": 2550.19, "word": " column", "probability": 0.291748046875}, {"start": 2550.19, "end": 2550.75, "word": " في", "probability": 0.73828125}, {"start": 2550.75, "end": 2550.87, "word": " اي", "probability": 0.57275390625}, {"start": 2550.87, "end": 2551.15, "word": " استفسار", "probability": 0.9475911458333334}, {"start": 2551.15, "end": 2551.35, "word": " لحد", "probability": 0.947998046875}, {"start": 2551.35, "end": 2552.15, "word": " هنا؟", "probability": 0.91845703125}, {"start": 2552.15, "end": 2553.03, "word": " في", "probability": 0.88623046875}, {"start": 2553.03, "end": 2553.13, "word": " اي", "probability": 0.8251953125}, {"start": 2553.13, "end": 2554.01, "word": " استفسار؟", "probability": 0.9776611328125}, {"start": 2554.01, "end": 2555.07, "word": " اعطيكوا", "probability": 0.7474772135416666}, {"start": 2555.07, "end": 2555.23, "word": " لغة", "probability": 0.4789225260416667}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2556.37775, "duration_after_vad": 2431.239999999994}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/CIPP0dKojOk_raw.srt b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/CIPP0dKojOk_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..ffc5d1b275da7f0e0ca33820240d01de6deb345c
--- /dev/null
+++ b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/CIPP0dKojOk_raw.srt
@@ -0,0 +1,2208 @@
+1
+00:00:20,810 --> 00:00:22,090
+بسم الله الرحمن الرحيم
+
+2
+00:00:25,830 --> 00:00:29,670
+أحنا الفترة الماضية كانت بالنسبالنا مراجعة للخلفية
+
+3
+00:00:29,670 --> 00:00:32,590
+الرياضية لهذه المادة كان أخدنا على ال vectors
+
+4
+00:00:32,590 --> 00:00:35,230
+أخدنا على ال divergence أخدنا على ال curl أخدنا
+
+5
+00:00:35,230 --> 00:00:38,730
+على ال course of products و ال dot of products على
+
+6
+00:00:38,730 --> 00:00:41,750
+ال partial lengths و ال partial area و ال partial
+
+7
+00:00:41,750 --> 00:00:44,650
+volume و اتعلمنا divergence theorem و stock
+
+8
+00:00:44,650 --> 00:00:47,710
+theorems كل هدولة هي الخلفية اللي احنا محتاجينها
+
+9
+00:00:47,710 --> 00:00:51,430
+لمادة الكهرمانصية احنا هنبدأ بيها فعليا
+
+10
+00:00:51,430 --> 00:00:55,910
+بالكهرمانصيةهنبدأ بال electrostatic fields من اسم
+
+11
+00:00:55,910 --> 00:00:58,570
+ال electrostatics يعني لأ تمت عالة زمان معناه
+
+12
+00:00:58,570 --> 00:01:02,010
+electrostatic يعني تفاوض مسبل زمن بساوة zero
+
+13
+00:01:02,010 --> 00:01:04,890
+static لأ تتحرك
+
+14
+00:01:10,010 --> 00:01:13,990
+إذا إحنا اليوم هناخد بعض الأساسيات لـ
+
+15
+00:01:13,990 --> 00:01:18,150
+Electromagnetic و اللي بتاعتمد أول ما هنبدأ إلا
+
+16
+00:01:18,150 --> 00:01:22,570
+بما لها static قولنا static معناها لا تعتمد على ال
+
+17
+00:01:22,570 --> 00:01:25,310
+time أو time invariant نقول عنها، إذا نحن نبدأ
+
+18
+00:01:25,310 --> 00:01:28,370
+بالجزئية اللي ما لها static و اللي لا تعتمد على ال
+
+19
+00:01:28,370 --> 00:01:31,930
+timeوكمان هنعتمد على ال electric fields في ال tree
+
+20
+00:01:31,930 --> 00:01:35,310
+space أو في ال vacuum يعني هندرس في الأول كيف
+
+21
+00:01:35,310 --> 00:01:38,230
+تتصرف ال fields في ال vacuum أو في ال tree space و
+
+22
+00:01:38,230 --> 00:01:43,150
+بعدين هندرسها في ال material كمان هتعلم انه ال
+
+23
+00:01:43,150 --> 00:01:45,810
+electric field بنتج من ال static charge
+
+24
+00:01:45,810 --> 00:01:47,950
+distributions برضه ال charge مالها static
+
+25
+00:01:47,950 --> 00:01:54,650
+distribution ماتتحركشمثال على ال electrostatic
+
+26
+00:01:54,650 --> 00:01:58,710
+field اللى ناتج عن static charge هو ال field اللى
+
+27
+00:01:58,710 --> 00:02:01,490
+فى الكاثدرية tubes كما زمان التلفزيونات بعتمدوا
+
+28
+00:02:01,490 --> 00:02:04,870
+على الكاثدرية tube دايما الاسلسكوبات القديمة برضه
+
+29
+00:02:04,870 --> 00:02:07,490
+بعتمدوا على الكاثدرية tube ده كله الصارياتنا ال
+
+30
+00:02:07,490 --> 00:02:15,080
+LCD وعلى ال polymers على اللدات و ال polymersأهمية
+
+31
+00:02:15,080 --> 00:02:16,800
+ال electrostatic، أهمية إيش إحنا بندرس ال
+
+32
+00:02:16,800 --> 00:02:21,000
+electrostatic؟ ال fields أو مجالات كتيرة بتعتمد
+
+33
+00:02:21,000 --> 00:02:25,740
+على الكهره الستاتيكية هنعمل نحكي لسه منها و هدي
+
+34
+00:02:25,740 --> 00:02:28,120
+جزء من ال applications بتاعتها عشان نشوف ده شي
+
+35
+00:02:28,120 --> 00:02:31,600
+مهمة، ده إيش إحنا لازم نتعلمها ك engineers، اللي
+
+36
+00:02:31,600 --> 00:02:34,860
+هي applications متعددة، من أهمها إنها بتستخدم في
+
+37
+00:02:34,860 --> 00:02:38,800
+نقل الطاقة electric power transmissionبتستخدم في
+
+38
+00:02:38,800 --> 00:02:41,780
+ال X-ray machine، في ال lightning protection،
+
+39
+00:02:41,780 --> 00:02:45,840
+بتعرفوا إيش؟ اللي هي السواق البرق، بتستخدم عشان
+
+40
+00:02:45,840 --> 00:02:48,100
+تحميل السواق البرق، يعني فهمت أو فهمت ال
+
+41
+00:02:48,100 --> 00:02:51,440
+electrostatic، بتاعتنا نفهم هاي الأمور، bipolar
+
+42
+00:02:51,440 --> 00:02:54,540
+and field effect transistor، فحطوك في ال
+
+43
+00:02:54,540 --> 00:02:58,560
+electronicsalmost all computer briefly are devices
+
+44
+00:02:58,560 --> 00:03:03,360
+except magnetic memory. معظم القطع الموجودة في
+
+45
+00:03:03,360 --> 00:03:05,940
+الكمبيوتر ما عدا ال magnetic memory بتبقى تتبع
+
+46
+00:03:05,940 --> 00:03:11,210
+الاستاتيك الاكتروستاتيكtouch pads، ال pads اللي
+
+47
+00:03:11,210 --> 00:03:14,090
+أنت بتدعسوا عليها بس اللي هي زي ال ipad و الأخر هي
+
+48
+00:03:14,090 --> 00:03:18,950
+touch، بت touch capacitance keyboard، يعني معظم ال
+
+49
+00:03:18,950 --> 00:03:22,550
+elevators دولة بال capacitance، أنت بتدعس بأصبعي،
+
+50
+00:03:22,550 --> 00:03:25,950
+بشتغل ال .. مافيش اشي بتضغط و لا بتطلع، معظمهم، في
+
+51
+00:03:25,950 --> 00:03:29,690
+منهم لازم تضغط، بس الأغلبية هي بال touch، بتدعس
+
+52
+00:03:29,690 --> 00:03:34,650
+عليه بشغل .. اه دي capacitance keyboardCathode ray
+
+53
+00:03:34,650 --> 00:03:38,690
+tube، ليكود كريستال ديسبلاي، تعرفهم ديسبلاي زي
+
+54
+00:03:38,690 --> 00:03:41,990
+ديسبلاي تبع ال .. الكمبيوتر بس كانوا زمان من مادة
+
+55
+00:03:41,990 --> 00:03:45,470
+اسمها ليكود كريستال، لازال في بعض منهم ليكود
+
+56
+00:03:45,470 --> 00:03:48,290
+كريستال، لازال يعني ال hot topics ليكود كريستال
+
+57
+00:03:48,290 --> 00:03:50,470
+وبعضهم لدات وبعضهم بوليمارس
+
+58
+00:03:53,570 --> 00:03:57,790
+Electrostatic Printer طابعات كل الطابعات المطبعة
+
+59
+00:03:57,790 --> 00:04:00,810
+عليهم مش ال .. يعني حتى ال laser بيرمضوا شويه على
+
+60
+00:04:00,810 --> 00:04:04,430
+الكهربا الاستاتيكية بس أغلبية اللي انجت كلها
+
+61
+00:04:04,430 --> 00:04:09,190
+Electrostatic الفكرة تعالية في ال medical في حاجة
+
+62
+00:04:09,190 --> 00:04:12,330
+اللي هي اسمها electrocardiogram هدول اللي بيبحثوا
+
+63
+00:04:12,330 --> 00:04:15,330
+فيها القلب cardio اللي هو gram أجزة فياس القلب
+
+64
+00:04:16,210 --> 00:04:20,670
+Electro .. electroencephalograms
+
+65
+00:04:20,670 --> 00:04:26,030
+برضه لها علاقة بيفحّر فحوصات طبية فى الصناعة بين
+
+66
+00:04:26,030 --> 00:04:30,050
+spraying اللى هو الرش تبع السيارات و الأخرى
+
+67
+00:04:30,050 --> 00:04:33,210
+الادهانات بتاعت من برضه على الجهربية الأستاتيكية
+
+68
+00:04:33,210 --> 00:04:38,110
+Electrodopsin يعني بكون عندى أنا material و بتعمل
+
+69
+00:04:38,110 --> 00:04:41,030
+عليها طبقة برضه بتاعت من على ال electroesthetics
+
+70
+00:04:42,270 --> 00:04:45,410
+Electrochemical machining في كتير من ال machines
+
+71
+00:04:45,410 --> 00:04:49,430
+بتتمد على الكروستيك Separation of particles و احنا
+
+72
+00:04:49,430 --> 00:04:52,290
+في الكيميا و بنفسها بين particles برضه بتتمد على
+
+73
+00:04:52,290 --> 00:04:57,690
+الكروستيك الزراع sorting seeds كيف نصله انه على
+
+74
+00:04:57,690 --> 00:05:00,870
+منيح من اللي ممكن نصله fertilization احنا برضه
+
+75
+00:05:00,870 --> 00:05:06,250
+بتدلوا على الكهرستيكيةdiet spray to plants اللي هي
+
+76
+00:05:06,250 --> 00:05:09,950
+رشط ضد الموبادات الحشرية measure the moistures
+
+77
+00:05:09,950 --> 00:05:13,530
+content of its crops قياس أديش الرطوبة في
+
+78
+00:05:13,530 --> 00:05:17,830
+المحصولات spin cotton اللي هو نوع من أنواع القطن
+
+79
+00:05:17,830 --> 00:05:21,890
+speed كيف بتعملهم spinning يعني اللي هي المغزلية،
+
+80
+00:05:21,890 --> 00:05:25,550
+الغزل بتاع و زمان بيعملوا الغزل وحتى الجهاز الكبير
+
+81
+00:05:25,550 --> 00:05:29,750
+بيبقى من ضلع الكتسوركية speed baking of bread and
+
+82
+00:05:29,750 --> 00:05:34,470
+smoking meatعشان كفت سرعة الطهي لل bread و الحصول
+
+83
+00:05:34,470 --> 00:05:39,590
+على اللحمة المدخنة هذه بعض من ال applications بتاع
+
+84
+00:05:39,590 --> 00:05:41,890
+ال electrostatic key لو فتحتوا على ال net و قولتوا
+
+85
+00:05:41,890 --> 00:05:43,930
+إيش هي ال application بتاع ال electrostatic keys
+
+86
+00:05:43,930 --> 00:05:47,370
+هتلاقوا لعديده بالتفصيل لكل جزء من الأجزاء اللي
+
+87
+00:05:47,370 --> 00:05:51,770
+حكينا عنها و إذا يعني أعطانا الرابط سرعة بعض الوقت
+
+88
+00:05:51,770 --> 00:05:54,670
+ان شاء الله هحطكم جزء منها من هال applications و
+
+89
+00:05:54,670 --> 00:05:58,050
+الصور اللي لها على ال facebook بيصير أوضح لكم انه
+
+90
+00:05:58,050 --> 00:06:03,280
+إيش هي ال applicationsاحنا هنبدأ two laws أهم two
+
+91
+00:06:03,280 --> 00:06:06,000
+laws اللي بتحكموه في ال electrostatics اللي هو
+
+92
+00:06:06,000 --> 00:06:10,580
+column و gauss column و gauss اتنين experimentally
+
+93
+00:06:10,580 --> 00:06:13,760
+approved يعني العلماء اتنين هدول أسوأ column او
+
+94
+00:06:13,760 --> 00:06:19,280
+gauss اشتغلوا بال .. بالمخبر و أثبتوا قوانينهم أو
+
+95
+00:06:19,280 --> 00:06:21,840
+يعني كان عندهم فضول يفهموا العلاقة بتاعة ال
+
+96
+00:06:21,840 --> 00:06:25,360
+electrostatic forces و في المختبر درسوها و وصلوا
+
+97
+00:06:25,360 --> 00:06:26,700
+للعلاقات اللي وصلوها
+
+98
+00:06:29,860 --> 00:06:33,940
+رغم إنه يعنيالـ column blow بيقدر يجيبلنا الـ
+
+99
+00:06:33,940 --> 00:06:35,960
+electric heat لأي نوع من أنواع ال charge
+
+100
+00:06:35,960 --> 00:06:38,720
+distribution لكن في بعض ال problem اللي بيكون فيها
+
+101
+00:06:38,720 --> 00:06:42,240
+symmetry أسهل نستخدم gauss يعني أهداكي ممكن
+
+102
+00:06:42,240 --> 00:06:45,420
+أستخدمه لأي نوع من ال distribution بدون أي قيود أو
+
+103
+00:06:45,420 --> 00:06:48,420
+شرمط اللي هو column blow لكن لو فيه ندي نوع من
+
+104
+00:06:48,420 --> 00:06:51,300
+أنواع السيمتري أسهل نستخدم gauss وحنشوف كيف الفرق
+
+105
+00:06:51,300 --> 00:06:55,180
+بينهم column شويه أصعب تطبيقه من gauss لكن في
+
+106
+00:06:55,180 --> 00:06:58,540
+حالات السيمتري بنلاقي أن استخدام gauss سهل كتير
+
+107
+00:06:58,540 --> 00:07:02,030
+يعني أنه بستبدل gauss to columnلكن un symmetric
+
+108
+00:07:02,030 --> 00:07:06,770
+problem بقدرش استخدام gauss هنستخدم
+
+109
+00:07:06,770 --> 00:07:09,690
+column law عشان نوصل لل electric field intensity
+
+110
+00:07:09,690 --> 00:07:14,210
+فهنشوف بعض اللي هي ال problems اللي ممكن نحلها ال
+
+111
+00:07:14,210 --> 00:07:17,670
+columns law وكيف ممكن احنا برضه نحلها باستخدام
+
+112
+00:07:17,670 --> 00:07:22,240
+gauss lawاحنا خلال هاد الشفطر هاد التأكيد اللي
+
+113
+00:07:22,240 --> 00:07:25,060
+حكيتها و بعيدها كام مرة انه هنعتبر ان ال electric
+
+114
+00:07:25,060 --> 00:07:28,380
+fields بقى لو في ال vacuum او في ال free space
+
+115
+00:07:28,380 --> 00:07:32,800
+يعني لما نحكي vacuum معناه نحكي في free space في
+
+116
+00:07:32,800 --> 00:07:35,240
+ال material زي ما حكينا هيكون في الشفطر اللي بعد
+
+117
+00:07:35,240 --> 00:07:40,540
+نحكي على columb's law و ال field intensity columb
+
+118
+00:07:40,540 --> 00:07:45,080
+هو عبارة عن عالم عمل تجربة و هاد التجربة وصلته
+
+119
+00:07:45,080 --> 00:07:49,080
+لقانونه في العام الف سبعمائه خمسة و تمانينهذا
+
+120
+00:07:49,080 --> 00:07:52,900
+العالم هو عالم فرنسي اسمه بالكلمة charge augustine
+
+121
+00:07:52,900 --> 00:08:00,120
+de colombe إيش كان قانونه بيقول إن هو القوة بين
+
+122
+00:08:00,120 --> 00:08:05,800
+two charge distribution بتكون على الخط اللي بوصل
+
+123
+00:08:05,800 --> 00:08:10,760
+بين هدولة تنتهيهو بدرس دائما ال pointed charges
+
+124
+00:08:10,760 --> 00:08:14,000
+يعني .. يعني بحطوا pointed charges و إيش مقصود
+
+125
+00:08:14,000 --> 00:08:17,640
+pointed charge؟ إن ال dimension بتاعتها ال charge
+
+126
+00:08:17,640 --> 00:08:22,600
+أصغر بكتير من الجسم المحيط فيها، يعني مثلا أنا بدأ
+
+127
+00:08:22,600 --> 00:08:27,020
+أدرس أثر طرفالقلم هذا هنا هي عنده charge على طرف
+
+128
+00:08:27,020 --> 00:08:31,320
+القلم و بدي أدرس أثر هذه ال charge على الدفتر
+
+129
+00:08:31,320 --> 00:08:35,000
+اشمله هذا الطرف القلم هيكون صغير كتير بالنسبة
+
+130
+00:08:35,000 --> 00:08:38,160
+للدفتر فبعتبره point of charge اذا معناه point of
+
+131
+00:08:38,160 --> 00:08:42,780
+charge ان ال dimension تبعها أصغر بكتير من الشهق
+
+132
+00:08:42,780 --> 00:08:48,050
+اللي بتأثر عليها أو في المحيط اللي حوالهامش معناه
+
+133
+00:08:48,050 --> 00:08:52,050
+point of charge؟ we mean a charge that is located
+
+134
+00:08:52,050 --> 00:08:54,890
+on a body whose dimensions are much smaller than
+
+135
+00:08:54,890 --> 00:08:57,370
+other relevant dimensions يعني أنا قارنتها ب
+
+136
+00:08:57,370 --> 00:09:00,270
+relevant يعني بالحاجة اللي بتأثر عليها، طرف القلم
+
+137
+00:09:00,270 --> 00:09:04,110
+أو الدبوس بعتبره point of charge
+
+138
+00:09:07,240 --> 00:09:09,840
+هذا المثال ال charges are generally measured in
+
+139
+00:09:09,840 --> 00:09:13,900
+columns يعني لما نحكي عن ال charge Q ال Q المحدد
+
+140
+00:09:13,900 --> 00:09:17,040
+القياسي ساعتها column نسبة لهذا العالم لدراس ال
+
+141
+00:09:17,040 --> 00:09:20,740
+electrostatic forces زي ما درسنا ان Ohm ان هو
+
+142
+00:09:20,740 --> 00:09:23,880
+الدراسي الاستيمتي سمينا ال resistance واحدتها ال
+
+143
+00:09:23,880 --> 00:09:27,060
+Ohm نفس الشيء بالcharge واحدتها ال column one
+
+144
+00:09:27,060 --> 00:09:32,730
+column ايش بيساوي 6 في 10 و 18 electronone column
+
+145
+00:09:32,730 --> 00:09:37,130
+سوى 6×10×18 electron لأن وحدة ال electron ال one
+
+146
+00:09:37,130 --> 00:09:43,810
+electron charge هو 1.6019×10×18-19 column فواحد
+
+147
+00:09:43,810 --> 00:09:48,610
+column بس بأسس واحد على هذا الرقم بطنيه 6×10 هو 18
+
+148
+00:09:48,610 --> 00:09:52,350
+كمية كبيرة يعني ال one column بيحتوي على لدد هائل
+
+149
+00:09:52,750 --> 00:09:55,850
+من الإلكترونات أنه واحدة قدش في عشرة قو نقص
+
+150
+00:09:55,850 --> 00:09:58,270
+تمانتاش و احنا بنحكي ال column بيحكي عشرة قو
+
+151
+00:09:58,270 --> 00:10:02,430
+تمانتاش عشرة قو نقص سنتاش عشرة قو تمانتاش أدت هائب
+
+152
+00:10:02,430 --> 00:10:08,810
+C من الإلكترونات طب إيش column قال ال column أنه
+
+153
+00:10:08,810 --> 00:10:13,330
+القوة بين two charges Q واحد و Q تانيان أول حاجة
+
+154
+00:10:13,330 --> 00:10:16,710
+بتكون على الخط الواصل بينهم على الخط الواصل بينهم
+
+155
+00:10:16,710 --> 00:10:19,650
+يعني هال two charges أكيد القوة هتكون على الخط
+
+156
+00:10:19,650 --> 00:10:23,690
+الواصل بين هدولأول حاجة، التانية حاجة انها بتتناسب
+
+157
+00:10:23,690 --> 00:10:28,210
+ترضية مع قيمة Q1 و Q2 كل ما زادت قيم ال charges
+
+158
+00:10:28,210 --> 00:10:33,830
+قيمة Q1 و Q2 كل ما زادت القوة الرابطة بين قوة اللي
+
+159
+00:10:33,830 --> 00:10:38,710
+هي ال electrostatic force كل ما قصرت المسافة و بقت
+
+160
+00:10:38,710 --> 00:10:41,270
+المسافة راح ألاحظ برضه كلمة إيش بتأثر ال force
+
+161
+00:10:41,270 --> 00:10:45,910
+بتقل المسافة، لو بتقل المسافة إيش بيصير؟ بتزيد ال
+
+162
+00:10:45,910 --> 00:10:52,000
+force، بتزيد المسافة، بتقل ال forcemathematically
+
+163
+00:10:52,000 --> 00:10:55,860
+بنعبر عن ال force طبعا ال force هتكون بالنيوتن إذا
+
+164
+00:10:55,860 --> 00:11:02,120
+كان q1 و q2 بالcolumn و R بالmeter F بالنيوتن هيك
+
+165
+00:11:02,120 --> 00:11:05,340
+بنقدر عن طول قيمة أو ال unit بتاعة K ال unit بتاعة
+
+166
+00:11:05,340 --> 00:11:08,980
+K مش unit less اللي هي unit الشي K هي K ال
+
+167
+00:11:08,980 --> 00:11:13,300
+constant of proportionality constant of
+
+168
+00:11:13,300 --> 00:11:18,100
+proportionality اللي هو أنا بقول أن F بتتناسب مع
+
+169
+00:11:18,100 --> 00:11:24,450
+q1 في q2F بتتناسب عكسيا مع واحد على أرض تربية او
+
+170
+00:11:24,450 --> 00:11:27,270
+بتتناسب مع واحد على أرض تربية وعكسيا مع أرض تربية
+
+171
+00:11:27,270 --> 00:11:32,730
+اذا F بتساوي some constant في Q1 وQ2 على أرض تربية
+
+172
+00:11:32,730 --> 00:11:34,790
+فهذا ال constant بنسميه K
+
+173
+00:11:39,300 --> 00:11:43,300
+لذن هذا هو ال column .. ال column plot و قولنا K
+
+174
+00:11:43,300 --> 00:11:46,420
+هو ال constant of proportionality و في الأسعى unit
+
+175
+00:11:46,420 --> 00:11:50,720
+قولنا في واحد كترينين columns are meter F نيوتن
+
+176
+00:11:50,720 --> 00:11:57,340
+فإيش هتكون K النيوتن في متر تربيع على column تربيع
+
+177
+00:11:57,340 --> 00:12:03,220
+هذا ال unit بتاعة Kطبعا ال Newton إيش هي عبارة؟
+
+178
+00:12:03,220 --> 00:12:06,400
+ممكن أعبر عنها برضه في تلاتة لإنه عندي M تربية ال
+
+179
+00:12:06,400 --> 00:12:12,140
+Newton هي عبارة عن mass في متر على second تربية
+
+180
+00:12:12,140 --> 00:12:15,000
+برضه و أقدر أعبر عنها عشان أخلص من المتر مع التر
+
+181
+00:12:16,310 --> 00:12:21,510
+هذه هي ال units بتاعة ال K كمان ال K إيش بقدر
+
+182
+00:12:21,510 --> 00:12:25,490
+أكتبها بدلالة طبعا ال K مش عشوائية ال K اللي هي
+
+183
+00:12:25,490 --> 00:12:29,010
+علاقة بالوصف اللي إحنا بندرس فيه القوة الستاتيكية
+
+184
+00:12:29,010 --> 00:12:32,130
+و إحنا في هذا ال chapter بندرس القوة الستاتيكية في
+
+185
+00:12:32,130 --> 00:12:36,770
+الفرع لأ قوله إن K high ساوة واحد على four by
+
+186
+00:12:36,770 --> 00:12:41,270
+epsilon not و مين هو epsilon not هو معامل النفازية
+
+187
+00:12:41,270 --> 00:12:44,010
+بتاعة ال free space أو ال vacuum اللي هو ال
+
+188
+00:12:44,010 --> 00:12:48,520
+permittivity of a free spaceإذاً K تتناسب أو تهمد
+
+189
+00:12:48,520 --> 00:12:52,500
+على معامل النفاذية تبع ال space اللي إحنا بندرس
+
+190
+00:12:52,500 --> 00:12:55,540
+فيه عامة ال static force وفي هالحالة إحنا بندرس ال
+
+191
+00:12:55,540 --> 00:12:59,180
+free space فإذاً K هي واحد على four by epsilon not
+
+192
+00:12:59,180 --> 00:13:02,600
+اللي هي epsilon not قلنا ال permittivity of free
+
+193
+00:13:02,600 --> 00:13:05,920
+space ال unit بتاعة ال permittivity هي فرعة برميتر
+
+194
+00:13:06,660 --> 00:13:11,360
+أخدنا احنا C إيش بتساوي؟ Epsilon not و تعريف ال ..
+
+195
+00:13:11,360 --> 00:13:15,560
+ال .. ال .. C ال charges فحلاقي إن Epsilon not
+
+196
+00:13:15,560 --> 00:13:19,600
+بتساوي فرعاد على متر Epsilon not في دي زي ما
+
+197
+00:13:19,600 --> 00:13:24,170
+تذكرينها بتاع ال two platesفإذا epsilon note ال
+
+198
+00:13:24,170 --> 00:13:27,570
+unit بتاعتها فراد على متر okay بالتالي اللي هي
+
+199
+00:13:27,570 --> 00:13:30,250
+واحد على epsilon note كمان بقدر أقول إنها unitاش
+
+200
+00:13:30,250 --> 00:13:34,710
+متر على فراد و بقدر أحصل عليها برضه من تعريفي لقوة
+
+201
+00:13:34,710 --> 00:13:38,430
+بدلالة سواء الفراد أو نيوتون و بقدر أوصل لهدولة
+
+202
+00:13:38,430 --> 00:13:42,230
+العلاقتين مع بعض إن K كيف أربطها اللي هي نيوتون في
+
+203
+00:13:42,230 --> 00:13:46,350
+متر تربيع على كولوم تربيع باللي هو متر على فراد
+
+204
+00:13:46,350 --> 00:13:50,330
+لإن كولوم اللي هي علاقة بال unit بتاعة كباستنس
+
+205
+00:13:50,330 --> 00:13:59,940
+اللي هي الفراد تمام؟هي اي استفسار؟ احنا
+
+206
+00:13:59,940 --> 00:14:04,960
+هي two charges Q1 و Q2 الـ Q1 الموجودة في الفراغ
+
+207
+00:14:04,960 --> 00:14:10,340
+R1 هذا ال origin XYZ البسشين قلنا بحدد فيه مكان ال
+
+208
+00:14:10,340 --> 00:14:15,310
+object في الفضاء في ال space اذا ال Q1 على بعد R1و
+
+209
+00:14:15,310 --> 00:14:21,570
+Q2 على بعض R2 البعد ما بين Q1 و Q2 هو R12 هو عبارة
+
+210
+00:14:21,570 --> 00:14:27,050
+عن R2 minus R1 لأنه احنا قلش قلنا هيكي قلنا R1 زات
+
+211
+00:14:27,050 --> 00:14:32,870
+R12 تسوى R2 فبالتالي R12 ده ما بتسوى R2 ناقص R1
+
+212
+00:14:32,870 --> 00:14:35,570
+بتذكرين لما حكينا عن ال question و ال distance
+
+213
+00:14:35,570 --> 00:14:38,920
+between two objectsعشان هيك احنا كان فيه لازم انه
+
+214
+00:14:38,920 --> 00:14:42,280
+نعرفهم ال position هو موضوع object in space اللي
+
+215
+00:14:42,280 --> 00:14:45,140
+في هاي الحالة احنا حددنا ال object تبعنا بطل
+
+216
+00:14:45,140 --> 00:14:51,160
+نسميها point P1 P2 صار مكان ال charges Q1 و Q2 Q1
+
+217
+00:14:51,160 --> 00:14:55,040
+وقع على ال distance R1 و Q2 على ال distance R2 و
+
+218
+00:14:55,040 --> 00:14:58,300
+المسافة R12 اللي هي زي ما انتوا متذكروا المقال
+
+219
+00:14:58,300 --> 00:15:02,040
+اجمع تكون R1 ثم R12
+
+220
+00:15:15,800 --> 00:15:18,260
+هذا هو ما ستجد على هذه الخطة
+
+221
+00:15:21,100 --> 00:15:24,180
+هتكون على طول خط اللي واصل بينهم إذا هدول ال
+
+222
+00:15:24,180 --> 00:15:26,880
+charges اللي هم نفس ال unit و احنا بترضه انهم بصفة
+
+223
+00:15:26,880 --> 00:15:31,620
+charges هلاحظ انه هدول القوة هتكون بتأثر على بعض
+
+224
+00:15:31,620 --> 00:15:37,580
+بشكل repulsive يعني ال Q2 هتعمل قوة منافرة أو
+
+225
+00:15:37,580 --> 00:15:43,160
+نافرة repulsive على Q1 نفس الشيء Q1 هتأثر بقوة
+
+226
+00:15:43,160 --> 00:15:50,530
+repulsive على Q2 فهذا السهم يدللني على أثرQ2 على
+
+227
+00:15:50,530 --> 00:15:54,310
+Q1 فساميه
+
+228
+00:15:54,310 --> 00:16:00,950
+F12 هو القوة على واحد اللي ناتجة من اتنين وهذا
+
+229
+00:16:00,950 --> 00:16:05,030
+السهم يدللي لي على القوة اللي ناتجت على Q2 او
+
+230
+00:16:05,030 --> 00:16:11,330
+exerted على Q2 بسبب Q1 فساميها F12 اللي هي القوة
+
+231
+00:16:11,330 --> 00:16:14,970
+اللي صارت على اتنين بسبب Q1
+
+232
+00:16:17,720 --> 00:16:21,080
+نبدأ اتقف فى 1 او 2 مثلا اللى هى القوة على ال
+
+233
+00:16:21,080 --> 00:16:24,200
+charge التانية سب ال charge الاولى ايش بالها
+
+234
+00:16:24,200 --> 00:16:29,060
+تساوي؟ K عوضنا عنها فى 1 على 4pi افسى مثلا كيو
+
+235
+00:16:29,060 --> 00:16:32,320
+واحد كيو تانية على الأرض تانية واتجاه ماهى دى
+
+236
+00:16:32,320 --> 00:16:35,880
+vector force ال force vector مش scalar بس اللى
+
+237
+00:16:35,880 --> 00:16:38,960
+لازم كلها اتجاه واتجاه اللى احنا شايفينه هى اتجاه
+
+238
+00:16:38,960 --> 00:16:43,340
+ماهو على طول الخط اللى واصل بيننا يعني هو انا
+
+239
+00:16:43,340 --> 00:16:47,660
+اعرفت ال unit vector اللى هو في اتجاهالخط الواصل
+
+240
+00:16:47,660 --> 00:16:54,760
+بيهم A12 أو AR12 hat هذا هيكون اتجاه ال force إذا
+
+241
+00:16:54,760 --> 00:16:59,520
+اتجاه ال force هيكون في اتجاه ال R قوة اللي
+
+242
+00:16:59,520 --> 00:17:03,540
+exerted على 2 بساطه 1 اتجاهها هو اتجاهه كيف أجيب
+
+243
+00:17:03,540 --> 00:17:09,040
+الاتجاه؟ معناه إذا عرفنا R12 بقدر أجيب AR12 hat
+
+244
+00:17:09,040 --> 00:17:13,140
+اللي هو ال unit vector بساوة ال R12 vector على ال
+
+245
+00:17:13,140 --> 00:17:18,010
+magnitudeعلى الـ Magnet إذا ما بقدر أحدد ال unit
+
+246
+00:17:18,010 --> 00:17:21,610
+vector لأي vector في ال space قلنا إنه بقسم ال
+
+247
+00:17:21,610 --> 00:17:26,210
+vector على ال magnitude تبعه هذا بالنسبة لل four
+
+248
+00:17:26,210 --> 00:17:31,130
+sides هذه إيش هتكون نفس المفضل إنه ال Q1 و Q2 أكتر
+
+249
+00:17:31,130 --> 00:17:34,070
+بيها بالمسافة اللي بينهم بس إيش هتغير الإتجاه
+
+250
+00:17:34,070 --> 00:17:37,390
+هتكون minus AR123
+
+251
+00:17:43,190 --> 00:17:46,170
+أنا already كتبتلكم إياها الأشياء اللي عارفون برو
+
+252
+00:17:46,170 --> 00:17:52,850
+R1
+
+253
+00:17:52,850 --> 00:18:00,470
+تلين هي المسافة بين two charges هي R تلين minus R
+
+254
+00:18:00,470 --> 00:18:04,390
+واحد عارفنا R هذا انه ال magnitude ال magnitude
+
+255
+00:18:04,390 --> 00:18:08,960
+بدون اي volt او بدون اي arrowهي عمورة مجموعة R18
+
+256
+00:18:08,960 --> 00:18:12,860
+وعرفناها قبل مجلسنا بتعريفها الجذر التربيهي
+
+257
+00:18:12,860 --> 00:18:19,860
+لـR12Vector.R12Vector هاي المجموعة هتاكدين؟ و بالـ
+
+258
+00:18:19,860 --> 00:18:24,360
+A R12Hat اللي هي unit vector هي عبارة عن ال vector
+
+259
+00:18:24,360 --> 00:18:30,900
+R12 على المجموعة تبعها بيسميناها R إذا F12 لساوة
+
+260
+00:18:30,900 --> 00:18:38,200
+Q12 على 4 π إيصال نص لو عوضت عن A hatR vector على
+
+261
+00:18:38,200 --> 00:18:42,420
+R magnitude هسير ر واحد اثنين vector على R cubed
+
+262
+00:18:42,420 --> 00:18:46,740
+يعني ممكن اكتبها دلات مش اكتب انما اكتبها دلات من
+
+263
+00:18:46,740 --> 00:18:50,680
+ال vector هسير على R cubed هسير واحد على four by
+
+264
+00:18:50,680 --> 00:18:55,120
+epsilon naught Q1 و Q2 على R cubed في R واحد اثنين
+
+265
+00:18:55,120 --> 00:18:59,120
+vector او بكتبها بهذه الطريقة Q1 و Q2 بعوض عن R
+
+266
+00:18:59,120 --> 00:19:01,360
+واحد اثنين vector ع ر تانين vector مع نصر واحد
+
+267
+00:19:01,360 --> 00:19:04,280
+vector على four by epsilon naught في المagnitude
+
+268
+00:19:04,280 --> 00:19:09,780
+اللي هوR2-R1 تحت الجزر للقوة 3 اللي هتكون ال
+
+269
+00:19:09,780 --> 00:19:18,540
+magnitude للقوة 3 تمام؟
+
+270
+00:19:18,540 --> 00:19:23,160
+في أي استفسار لحقتنا؟ في أي استفسار؟ احنا كمان
+
+271
+00:19:23,160 --> 00:19:27,680
+اتفقنا إن القوتين متساويتين بالمقدار أسوأ القوة
+
+272
+00:19:27,680 --> 00:19:31,980
+اللي بتأثرها Q1 على Q2 أو القوة اللي بتأثرها Q2
+
+273
+00:19:31,980 --> 00:19:37,110
+على Q1فهذه القوة ع واحد نجم اتنين بتساوي المدنيتو
+
+274
+00:19:37,110 --> 00:19:40,490
+تبع القوة اللي على اتنين نجم واحد في ال unit
+
+275
+00:19:40,490 --> 00:19:44,030
+vector تبع القوة المية على واحد اللي هو بالتالي
+
+276
+00:19:44,030 --> 00:19:47,750
+بيساوي minus ال unit vector تبع القوة الاولى
+
+277
+00:19:47,750 --> 00:19:51,570
+فبالتالي F2 من واحد بيساوي minus F12 لأن ال unit
+
+278
+00:19:51,570 --> 00:19:55,890
+vectors منهم اتجاهاتهم متعاكسة وهذا شفنا احنا من
+
+279
+00:19:55,890 --> 00:20:01,910
+الرسمة حاجة مهمة في اللي هي ال charges أول حاجة
+
+280
+00:20:01,910 --> 00:20:10,570
+قلناإن قوة Q1 وQ2 مالها تتعكس بالاتجاه أول تاني
+
+281
+00:20:10,570 --> 00:20:15,550
+event إن ال charges المتماثلة مالها تتنافر زي مثلا
+
+282
+00:20:15,550 --> 00:20:19,190
+شفنا ال QQ لأنهم بتنافر أسوأ positive أو negative
+
+283
+00:20:19,190 --> 00:20:23,910
+charges هلاقى أن تأثيرهم تنافر زي ما في ال figure
+
+284
+00:20:23,910 --> 00:20:28,630
+A و ال figure B القوة اللي بيأثروا فيها ال charges
+
+285
+00:20:28,630 --> 00:20:34,550
+على بعض هي قوة تنافرإذا كانوا مختلفتين unlike
+
+286
+00:20:34,550 --> 00:20:37,890
+charges, unlike signs يعني إذا كانوا like charges
+
+287
+00:20:37,890 --> 00:20:41,630
+هيكونوا تنافر, unlike charges هيكون فيه تجاذب بين
+
+288
+00:20:41,630 --> 00:20:42,150
+التنتين
+
+289
+00:20:45,950 --> 00:20:48,950
+عشان اقول عنهم pointed charges بكافيش ان اقول ان
+
+290
+00:20:48,950 --> 00:20:52,530
+هو مقارنة مع ال dimension ال relevant dimension
+
+291
+00:20:52,530 --> 00:20:56,150
+انه اصغير عشان two charges سمين و لا اتر انا بقارن
+
+292
+00:20:56,150 --> 00:20:59,290
+تنتين مع بعض عشان اقول تنتين عندهم pointed charges
+
+293
+00:20:59,290 --> 00:21:02,390
+بدي اقارنهم في المسافة اللي بينهم لازم تكون مسافة
+
+294
+00:21:02,390 --> 00:21:05,630
+كبيرة كفاية انهم يشوفوا بعض ما هو pointed charges
+
+295
+00:21:05,630 --> 00:21:09,710
+انه احمل ال dimension تبعهم هي ال relevant
+
+296
+00:21:09,710 --> 00:21:12,170
+dimension في هالحالة ال relevant dimension مسافة
+
+297
+00:21:12,170 --> 00:21:16,620
+اللي بينهم لو انا اتشارج و بتأثر علىالـ plane زي
+
+298
+00:21:16,620 --> 00:21:19,280
+الـ plane تبع الطاولة هقول إنها برضه point of
+
+299
+00:21:19,280 --> 00:21:21,500
+charges لأنه ال relevant dimension فيها الحالمين
+
+300
+00:21:21,500 --> 00:21:29,340
+ال object التاني كبير كثير بالنسبالها كمان
+
+301
+00:21:29,340 --> 00:21:33,440
+حاجة مهمة كتير إن ال Q1 و Q2 ممكنوا addressed إحنا
+
+302
+00:21:33,440 --> 00:21:36,540
+بنحكي على ال ecrostatic فالتنتين مش لازم يتحركوا
+
+303
+00:21:36,540 --> 00:21:39,440
+في هذه الحالة إحنا فرضين نحكي على ال ecrostatic
+
+304
+00:21:39,440 --> 00:21:44,890
+كأن مافيش movement مافيش اعتمادية على الزمنلما أجى
+
+305
+00:21:44,890 --> 00:21:48,950
+أحسب ال force ال sign بتاعة q1 و q2 لازم أخدها في
+
+306
+00:21:48,950 --> 00:21:55,730
+عين الحسبان مش لازم أحمل الإشارة بتاعة q1 و q2 أو
+
+307
+00:21:55,730 --> 00:21:59,580
+كان عندي أكتر من twoيعني انا اللى شفتها كان مثال
+
+308
+00:21:59,580 --> 00:22:04,080
+اولانى لك لو كان عندى عدد كبير من ال charges Q1,
+
+309
+00:22:04,200 --> 00:22:08,860
+Q2 لحد QN اللى هيصير اللى بعمله باخد كل ال charge
+
+310
+00:22:08,860 --> 00:22:12,340
+و بجمع كل القوة اللى بتأثر عليها من كل ال charges
+
+311
+00:22:12,340 --> 00:22:17,320
+يعني عندى Q1, Q2, Q3 لحد QN و عندى charge Q مثلا
+
+312
+00:22:18,170 --> 00:22:24,010
+هشوف أثر q1 على q, q2 على q, q3 على q و هكذا, qn
+
+313
+00:22:24,010 --> 00:22:27,810
+على q و بعدين القوة هجمعها vector addition عشان
+
+314
+00:22:27,810 --> 00:22:33,610
+أطول ال vector ال force الكلية يعني هى, so يمشي
+
+315
+00:22:33,610 --> 00:22:36,830
+فين ال total force هتكون احنا عاملا بندرس القوة
+
+316
+00:22:36,830 --> 00:22:41,390
+على q انها جامع q1 و q2 لحد qn فهيكون عندنا اللى
+
+317
+00:22:41,390 --> 00:22:45,450
+هو ال principle of superposition القوة الكلية اللى
+
+318
+00:22:45,450 --> 00:22:50,970
+لو كان عندى هي qعلى بُعد Q وهي الـ origin تبعي على
+
+319
+00:22:50,970 --> 00:22:58,990
+بُعد R مثلا و هنا بيدي الـ Q1 وعندي الـ Q2 وعندي
+
+320
+00:22:58,990 --> 00:23:03,770
+الـ Q3 و هكذا طبعا كل بره بتأيس المسافر بينهم هذه
+
+321
+00:23:03,770 --> 00:23:10,050
+R هتكون R1 هتكون R-R1 هشف القوة اللي الـ Q1 أثر
+
+322
+00:23:10,050 --> 00:23:16,270
+فيها على Q الـ Q2 على Q الـ Q3 على Qو لو احنا فينا
+
+323
+00:23:16,270 --> 00:23:24,410
+في ال Q و هاي ال QN هذا
+
+324
+00:23:24,410 --> 00:23:30,570
+هيكون RN و برضه هشوف أثر QN على Q بعد ما أجيب كل
+
+325
+00:23:30,570 --> 00:23:36,070
+قوة نجم ال charge مختلفة Q1 مره مره مره مره مره
+
+326
+00:23:36,070 --> 00:23:40,340
+مره مره على أخر بجيب أجمع كل القوةبقى زى ما حكيت
+
+327
+00:23:40,340 --> 00:23:43,500
+vector addition بتعطينى ال total force هذا بنسميه
+
+328
+00:23:43,500 --> 00:23:48,940
+ال superposition difference أو
+
+329
+00:23:48,940 --> 00:23:53,360
+باختصار لإن ال Q كان راح كل المعادلة اللى قدامنا
+
+330
+00:23:53,360 --> 00:23:58,420
+بقدر أسحب ال Q برا ال sum و ال 4 by epsilon نقطة و
+
+331
+00:23:58,420 --> 00:24:02,600
+هدولة constants وقول ال sum من K equal واحد لأقل
+
+332
+00:24:02,600 --> 00:24:07,680
+QK في R vector minus RK vector اللى هو المسافة بين
+
+333
+00:24:07,680 --> 00:24:11,040
+هذا ال chargeوالـ charge بدرس عليها الforce على
+
+334
+00:24:11,040 --> 00:24:16,240
+المجموعة للقوة تلتة اذا يا بكتبهم عملي واحدة واحدة
+
+335
+00:24:16,240 --> 00:24:24,200
+مخصّلين يا باستخدم اللي هو summation symbol هذا
+
+336
+00:24:24,200 --> 00:24:27,260
+بالنسبة لل force، في اي سؤال عن ال force؟ اذا كمرة
+
+337
+00:24:27,260 --> 00:24:30,900
+ال force هي تكون على طول الخط الواصل between two
+
+338
+00:24:30,900 --> 00:24:35,430
+chargesبعتمد ترضيا أو بتناسب ترضيا مع قيمته في
+
+339
+00:24:35,430 --> 00:24:38,910
+واحد وفي اتنين أو عكسيا مع المسافة اللي بينهم
+
+340
+00:24:38,910 --> 00:24:43,110
+تربية ال constant of proportionality سميناها K وK
+
+341
+00:24:43,110 --> 00:24:47,310
+هذا بعتمد على نفاذية الوسط في هذا الشطر احنا
+
+342
+00:24:47,310 --> 00:24:50,390
+ماخدينه وسط هو ال vacuum او ال free space فهتكون K
+
+343
+00:24:50,390 --> 00:24:53,650
+بيساوة واحد على four by epsilon naught اللي هي ال
+
+344
+00:24:53,650 --> 00:24:57,310
+permittivity بتاعة ال free space دلوقتي بنعرف ال
+
+345
+00:24:57,310 --> 00:25:00,630
+electric field intensity فيها لقوا عطيدة ما بين ال
+
+346
+00:25:00,630 --> 00:25:05,110
+force و ال fieldخطوط ال field في مجال ال .. ال ..
+
+347
+00:25:05,110 --> 00:25:09,310
+ال .. الكهربائي و بين اللي هي القوة اللي exerted
+
+348
+00:25:09,310 --> 00:25:12,530
+على ال charge معينة ال electric field intensity
+
+349
+00:25:12,530 --> 00:25:16,130
+ايش بالساوي احنا جبنا القوة على Q جبنا ال total
+
+350
+00:25:16,130 --> 00:25:21,930
+force في ال slide السادقة على Q force اللي على Q
+
+351
+00:25:21,930 --> 00:25:27,830
+نتجة من Q1, Q2, Q3, Q4 فال electric field اللي
+
+352
+00:25:27,830 --> 00:25:34,830
+بتكون فيبسابحة فيها ال Q هو عبارة عن limit ل F على
+
+353
+00:25:34,830 --> 00:25:40,650
+Q as Q goes to 0 يعني ببساطة E بتساوي F على Q لو
+
+354
+00:25:40,650 --> 00:25:46,710
+رجعنا لمثال السابق إيش هتصير بس هيروح ال Q من ال E
+
+355
+00:25:46,710 --> 00:25:50,550
+هتكون F على Q هتكون 1 الفوربا إيبسون نوت الصماشن
+
+356
+00:25:53,910 --> 00:25:58,690
+حاجة بنستنتجها ان F vector و E vector و Q مالها
+
+357
+00:25:58,690 --> 00:26:01,570
+scalar اذا انتجاه ال electric field ماله فانتجاه
+
+358
+00:26:01,570 --> 00:26:06,630
+ال force او الحسابات بتاعته اذا ال force بالنيوتن
+
+359
+00:26:06,630 --> 00:26:10,010
+او ال unit بتاعته و Q بال column E ايش هيكون
+
+360
+00:26:10,010 --> 00:26:15,230
+النيوتن على column او volt على متر او volt على
+
+361
+00:26:15,230 --> 00:26:15,710
+meter
+
+362
+00:26:22,330 --> 00:26:27,490
+أنا إذا عندي ال electric field اللي ناتج على نقطة
+
+363
+00:26:27,490 --> 00:26:32,230
+R في ال space من due to a point in charge located
+
+364
+00:26:32,230 --> 00:26:37,910
+at R' يعني أنا بدي أحسب ال electric، عندي Q، ال Q
+
+365
+00:26:37,910 --> 00:26:42,390
+في هذه الحالة Q
+
+366
+00:26:42,390 --> 00:26:48,010
+على بُعد R1 و أنا بدي أحسب ال electric field عند
+
+367
+00:26:48,010 --> 00:26:51,710
+نقطة في ال space على بُعد R من ال originماذا
+
+368
+00:26:51,710 --> 00:26:57,810
+ستساوي؟ سنقوم بتشارج Q بتأثير على هذه النقطة Q على
+
+369
+00:26:57,810 --> 00:27:02,510
+4 π إبسم من نقطة R ترقية في R hat لأن القوة لو
+
+370
+00:27:02,510 --> 00:27:05,550
+كانت عندها تشارج، اللي كنا سميها دايما كيونيز
+
+371
+00:27:05,550 --> 00:27:09,070
+تشارج، لو كانت عندها Q واحد، ماذا ستكون Q في Q
+
+372
+00:27:09,070 --> 00:27:14,470
+واحد على المسافة اللي بينهم، اللي R واحد minus R
+
+373
+00:27:14,470 --> 00:27:19,590
+أو كما سميها R وR prime، فهيكون المسافة اللي بينهم
+
+374
+00:27:20,270 --> 00:27:25,210
+Q حصد ضربهم ال force على المسافة اللي بينهم تربية
+
+375
+00:27:25,210 --> 00:27:31,790
+في K احنا قلنا E ايش بتساوي E بتساوي ال force على
+
+376
+00:27:31,790 --> 00:27:36,990
+Q واحد ال force على Q واحد وبالتالي هتكون ان تنقل
+
+377
+00:27:36,990 --> 00:27:41,370
+ال Q على 4 πا يسموه R تربية في R hat وR hat هو
+
+378
+00:27:41,370 --> 00:27:47,120
+اتجاه الحط اللي واصلبين النقطة بقيسها ال electric
+
+379
+00:27:47,120 --> 00:27:51,520
+field و ال charge المسددة ل ال electric field اللي
+
+380
+00:27:51,520 --> 00:27:55,200
+هو نفس اتجاه ال force اذا لو انا اعتبرت ان عندي
+
+381
+00:27:55,200 --> 00:27:58,720
+pointed charge located at R' و انا عمال بقيس ال
+
+382
+00:27:58,720 --> 00:28:01,940
+field عند R و ال pointed charge قيمتها Q و عمال
+
+383
+00:28:01,940 --> 00:28:06,240
+بقيس ال field عند النقطة R فهيكون E ايش بتساوي Q
+
+384
+00:28:06,240 --> 00:28:10,870
+على four by epsilon mod R تربيه A R hatممكن اعوض
+
+385
+00:28:10,870 --> 00:28:14,650
+عن ar hat بقى شهرنا ال vector r minus r prime على
+
+386
+00:28:14,650 --> 00:28:18,770
+ال magnitude بتصير r cubed يعني r minus r prime
+
+387
+00:28:18,770 --> 00:28:22,310
+على r cubed اللي هي ال magnitude ل r minus r prime
+
+388
+00:28:22,310 --> 00:28:28,650
+هو تلاتةلو كان عندي N Pointed Charges عندي Q1 في
+
+389
+00:28:28,650 --> 00:28:32,470
+ال space و Q2 و Q3 و لحد QN مليان ال space عندي
+
+390
+00:28:32,470 --> 00:28:35,610
+charges و أنا بده أحسب ال field من نقطة معينة في
+
+391
+00:28:35,610 --> 00:28:40,570
+ال space بحسب مجموع أثار هدولة النقاط أو ال field
+
+392
+00:28:40,570 --> 00:28:44,350
+اللي exerted أو الناتج من كل pointed charge على
+
+393
+00:28:44,350 --> 00:28:46,310
+النقطة في ال space اللي بتروس عندها ال electric
+
+394
+00:28:46,310 --> 00:28:48,970
+field اذا عشان أعرف ال electric field في ال space
+
+395
+00:28:48,970 --> 00:28:52,050
+بجيب ال electric field الناتج من كلpointed charge
+
+396
+00:28:52,050 --> 00:28:55,470
+و بالاخر بجمعهم قلنا ع شكل و هو vector addition
+
+397
+00:28:55,470 --> 00:29:00,230
+فعندي E ايش هتكون ال field الناتج من ال Q1 زاد ال
+
+398
+00:29:00,230 --> 00:29:03,370
+field الناتج من ال Q2 و هكذا لحد ال field الناتج
+
+399
+00:29:03,370 --> 00:29:06,490
+من ال QN يعني E ايش بتسوى هذا ال four by epsilon
+
+400
+00:29:06,490 --> 00:29:11,590
+note ال summation من K واحد ل N QK في R minus RK
+
+401
+00:29:11,590 --> 00:29:17,110
+على R minus RK لكل Q واضح يعني احنا قبل دراسنا ال
+
+402
+00:29:17,110 --> 00:29:30,370
+force اللي بتأثرها جمع منالـ charges على
+
+403
+00:29:30,370 --> 00:29:35,270
+ال point of charge جبنا مجموع ال processor قولنا
+
+404
+00:29:35,270 --> 00:29:38,330
+ال electric field اللي exerted على هذا ال point of
+
+405
+00:29:38,330 --> 00:29:45,370
+charge هيكون مجموع كل هذه القوة على ال point of
+
+406
+00:29:45,370 --> 00:29:50,020
+charge على ال Q فهيظهر بس الحصة ثانيةمن كل وام
+
+407
+00:29:50,020 --> 00:29:55,240
+هيروح اللي هي قيمة Q هيظبراً بـQ1 على R ثانوية في
+
+408
+00:29:55,240 --> 00:30:06,400
+K الـQ2 وهذا ده الرعاية بين الـvectors بتاعنا هذا
+
+409
+00:30:06,400 --> 00:30:09,660
+الفرق بين القانون هذا وقانون ال force انها بصراحة
+
+410
+00:30:09,660 --> 00:30:15,020
+Q من القانون هنشوف
+
+411
+00:30:15,020 --> 00:30:15,520
+مثلًا
+
+412
+00:30:20,340 --> 00:30:23,840
+مثال بقول عندي point at charge مقدارها واحد
+
+413
+00:30:23,840 --> 00:30:27,420
+millicolum وكمان point at charge مقدارها اتنين
+
+414
+00:30:27,420 --> 00:30:30,940
+minus اتنين millicolum التنتين محطوطين في ال space
+
+415
+00:30:30,940 --> 00:30:35,180
+واحدة على تلاتة اتنين ناقص واحد يعني x تلاتة و y
+
+416
+00:30:35,180 --> 00:30:38,220
+تلاتة اتنين ناقص واحد اللي بصي متبعها لو انا حاولت
+
+417
+00:30:38,220 --> 00:30:45,320
+أسهم الرسمة يعني x y z النقطة الأولى اللي هي واحد
+
+418
+00:30:45,320 --> 00:30:53,050
+millicolum على تلاتة x اتنين yمثلا و minus واحد
+
+419
+00:30:53,050 --> 00:30:55,630
+يعني لو انا اخدت هاي ال plane تبعي هو هال minus
+
+420
+00:30:55,630 --> 00:30:59,590
+واحد هذه النقطة دولة اللي هي علاوة تلاتة اثنين
+
+421
+00:30:59,590 --> 00:31:07,710
+ماقص واحد هي Q واحد اللي مقدارها مقدارها واحد ملي
+
+422
+00:31:07,710 --> 00:31:12,810
+كولو والنقطة التانية هذه ال equation تبعها هي R
+
+423
+00:31:12,810 --> 00:31:18,730
+واحد والتانية واقع على X ماقص واحد Y ماقص واحد R
+
+424
+00:31:18,730 --> 00:31:25,250
+واحدلو مديتها بهيك هيكون a-1 y-1 وطالع على فوق
+
+425
+00:31:25,250 --> 00:31:34,890
+مقدار 4 هدف ال space يعني مقاس واحد مقاس واحد و 4
+
+426
+00:31:34,890 --> 00:31:41,970
+هي EQ2 اللي مقدارها minus 2 من ال code
+
+427
+00:31:44,880 --> 00:31:48,720
+بدوا مننا أول نحسب ال electric force على ال charge
+
+428
+00:31:48,720 --> 00:31:54,420
+المقدارها عشرة nano column وهي بوقع على x بتساوة
+
+429
+00:31:54,420 --> 00:31:59,580
+zero x بتساوة zero يعني موقع في ال YZ plane وي Y
+
+430
+00:31:59,580 --> 00:32:07,460
+كميتها ثلاثة و Z واحد فقدر
+
+431
+00:32:07,460 --> 00:32:12,460
+مين هيحسب منها هسب منها R واحد R تمين و هسب منها R
+
+432
+00:32:13,650 --> 00:32:19,410
+وهي Q المقدارها عشرة وتانية أطلب مني أن أجيب ال
+
+433
+00:32:19,410 --> 00:32:24,450
+forces ال total force على النقطة هي اللي كتت في
+
+434
+00:32:24,450 --> 00:32:31,590
+هذا الموضوع في حابكوا بيجرب ده
+
+435
+00:32:31,590 --> 00:32:38,110
+احنا نجيب اللي بأثر عنها تمام عملنا لها مية مية ان
+
+436
+00:32:38,110 --> 00:32:41,890
+الرعي طبعا الإشارات بتاعتهم هنا في الإشارة السالدة
+
+437
+00:32:42,460 --> 00:32:46,200
+عندي إشارة وموجبة أو هاي إشارة وموجبة فأولا خلّيني
+
+438
+00:32:46,200 --> 00:32:50,720
+أعرف كل unit كل position يعني خلّيني أحط يام R وR1
+
+439
+00:32:50,720 --> 00:32:54,500
+وR2 فهي كمضاية أي سؤال هحط ال position تبعهم
+
+440
+00:32:54,500 --> 00:32:56,900
+position vector لإنهم اللي أحس ال position vector
+
+441
+00:32:56,900 --> 00:33:02,360
+فحلنا نقول R1 ايش بيساوي؟ R1 vector هحط فوق سهل
+
+442
+00:33:02,360 --> 00:33:07,500
+عشان احنا مقدرش نحط volt في خطنا هيكون 3X هتحط
+
+443
+00:33:07,500 --> 00:33:09,840
+فوقها هتحط فوقها هتحط فوقها هتحط فوقها هتحط فوقها
+
+444
+00:33:09,840 --> 00:33:10,400
+هتحط فوقها هتحط فوقها هتحط فوقها هتحط فوقها هتحط
+
+445
+00:33:10,400 --> 00:33:14,990
+فوقها هتحط فوقها هتحطزائد تنين يها ماينوس زدها
+
+446
+00:33:14,990 --> 00:33:23,030
+هدئة واحد R تنين بتساوي سالب Xها سالب Yها زائد
+
+447
+00:33:23,030 --> 00:33:28,120
+أربعة زدهاهي عند R هي موقع المقطع اللي بدأ يجيب
+
+448
+00:33:28,120 --> 00:33:32,600
+عليها ال courses عبارة عن X hat Zero عند تلاتة Y
+
+449
+00:33:32,600 --> 00:33:37,760
+hat زائد Z hat أقع في ZY إتلاني طب إحنا نبدأ
+
+450
+00:33:37,760 --> 00:33:45,440
+بالقوة اللي بتأثر فيها Q1 على Q1 اللي هي F1
+
+451
+00:33:45,440 --> 00:33:50,360
+خلاص أكتر بتأثر فيها وخطفوها بكتر لإنه مش هتساوي
+
+452
+00:33:50,360 --> 00:33:52,980
+هدى النوع أولا أقولي اللي بقر باصف ولا
+
+453
+00:33:58,010 --> 00:34:03,390
+أحنا عشان ماسميناش R فتخبركي أن R1 تني R اليمين،
+
+454
+00:34:03,390 --> 00:34:09,590
+R1 خلّيني أسميها وR1 خلّيني أعرفها، اللي عبارة عن
+
+455
+00:34:09,590 --> 00:34:17,490
+تمام، يعني بدنا نحط ال vector إيش
+
+456
+00:34:17,490 --> 00:34:27,440
+هيساوي؟ R minus R1، تمام؟ فإذا R1 هو عبارة عن Rبس
+
+457
+00:34:27,440 --> 00:34:32,100
+هو بتفتر فوق ال R R minus R واحد اذا ان انا بده
+
+458
+00:34:32,100 --> 00:34:37,460
+اشوف المسافة عند وقبضش تبع Q وقبضش تبع Q واحد وبده
+
+459
+00:34:37,460 --> 00:34:41,740
+المسافة بينهم اللي هي مبالغ Q واحد و Q اللي هي R
+
+460
+00:34:41,740 --> 00:34:48,700
+minus R واحد تمام
+
+461
+00:34:48,700 --> 00:34:56,710
+زائد Y hat زائد Y hatوخلاص وزاق التانية بزاقها
+
+462
+00:34:56,710 --> 00:35:03,090
+التانية إيش نوع القوة اللي بين هدولة ال charges؟
+
+463
+00:35:03,090 --> 00:35:09,150
+هي القوة اللي لها reverse يعني هيك اتجاهها صح؟ هاي
+
+464
+00:35:09,150 --> 00:35:12,950
+بتأثر على هاي باصلة force وهذا المنطقة إذا أف واحد
+
+465
+00:35:12,950 --> 00:35:21,490
+منها اللي برأسك الإشارة كاعتها موجة حد
+
+466
+00:35:21,490 --> 00:35:26,860
+على قوة باي أكسر النوتتور باى تور باى تور باى نعوض
+
+467
+00:35:26,860 --> 00:35:31,900
+عن اكتر واحد فلس نحن نعوض اكتر واحد انت هتساوى ليه
+
+468
+00:35:31,900 --> 00:35:36,440
+تسعة فعشرة هو تسعة تسعة
+
+469
+00:35:36,440 --> 00:35:41,960
+فعشرة هو تسعة كيو واحد اللي نقطارها واحد من ال
+
+470
+00:35:41,960 --> 00:35:46,920
+column فعشرة على كوه ماقس ثلاثة على طول خليها واحد
+
+471
+00:35:46,920 --> 00:35:51,760
+فعشرة كوه ماقس ثلاثةفى Q اللى بدى أسئل عليها ليه
+
+472
+00:35:51,760 --> 00:36:00,640
+عشرة قنان وليه عشرة فعشرة ونائس تسعة على الـR1
+
+473
+00:36:00,640 --> 00:36:07,200
+تردية احنا قلنا عشان أجيب ليه ال vector R1 يا بال
+
+474
+00:36:07,200 --> 00:36:10,580
+vector على RQ خلينا نعرفها بهذا الشكل احنا بحط
+
+475
+00:36:10,580 --> 00:36:13,640
+القانون اللى بتحط بيه يعني بيكتبي القانون اللى
+
+476
+00:36:13,640 --> 00:36:17,400
+بتستخدميه عشان نحدد نجيب ليه ال vector ولا F
+
+477
+00:36:20,300 --> 00:36:27,500
+هقول أك واحد ساوي واحد على قوة الرئيس للنوت Q واحد
+
+478
+00:36:27,500 --> 00:36:33,420
+في Q فاسم القانون هاسمه Q في Q واحد في Q واحد
+
+479
+00:36:33,420 --> 00:36:40,700
+ثانوي اما Q وQ واحد في R لبتر ممكن ناخد هذا
+
+480
+00:36:40,700 --> 00:36:48,570
+القانون ر واحد لبتر ر واحد لبتر مش هيكون تحت RQعلى
+
+481
+00:36:48,570 --> 00:36:57,470
+R1 مقمتور يعني مقمتور في الـP هنحط
+
+482
+00:36:57,470 --> 00:37:03,230
+الـP تمام؟ لذا نستخدم هذا لإن هيكون ال bus مضروب
+
+483
+00:37:03,230 --> 00:37:11,870
+ايه؟ مش مشكلة هحط سهل R1
+
+484
+00:37:11,870 --> 00:37:16,070
+vector ليه حسبت إن هي هزيمتكم؟ R
+
+485
+00:37:17,800 --> 00:37:22,260
+YHYH YYH YYH YYH YYH YYH YYH YYH YYH YYH YYH YYH
+
+486
+00:37:22,260 --> 00:37:24,500
+YYH YYH YYH YYH YYH YYH YYH YYH YYH YYH YYH YYH
+
+487
+00:37:24,500 --> 00:37:24,540
+YYH YYH YYH YYH YYH YYH YYH YYH YYH YYH YYH YYH
+
+488
+00:37:24,540 --> 00:37:25,960
+YYH YYH YYH YYH YYH YYH YYH YYH YYH YYH YYH YYH
+
+489
+00:37:25,960 --> 00:37:29,460
+YYH YYH YYH YYH YYH YYH YYH
+
+490
+00:37:29,460 --> 00:37:33,900
+YYH YYH YYH YYH YYH YYH YYH YYH YYH YYH YYH YYH
+
+491
+00:37:33,900 --> 00:37:45,080
+YYH YYH YYH YYH YYH YYH YYH
+
+492
+00:37:45,080 --> 00:37:50,130
+Yلأربعة الجزر التربيه لاربعتاش اذا نحطنا على الجزر
+
+493
+00:37:50,130 --> 00:37:53,630
+التربيه لاربعتاش وقوة الأدنى يعني اربعتاش وقوة
+
+494
+00:37:53,630 --> 00:37:59,230
+الأدنى هدى F واحد جفناها دلالة ال vector يعني إلها
+
+495
+00:37:59,230 --> 00:38:01,710
+component في ال X و component في ال Y و component
+
+496
+00:38:01,710 --> 00:38:11,570
+في ال Z طب افتنان بحب حب يعمل افتنان؟ و بدنا
+
+497
+00:38:11,570 --> 00:38:12,350
+نلقي جهد غير
+
+498
+00:38:17,660 --> 00:38:25,880
+R1 لينيا تلاتة اكسات ثانو اتنين و اي حد مينوس و
+
+499
+00:38:25,880 --> 00:38:30,320
+اربع تلاتة
+
+500
+00:38:30,320 --> 00:38:30,680
+اكسات تلاتة اكسات تلاتة اكسات تلاتة اكسات تلاتة
+
+501
+00:38:30,680 --> 00:38:31,180
+اكسات تلاتة اكسات تلاتة اكسات تلاتة اكسات تلاتة
+
+502
+00:38:31,180 --> 00:38:31,180
+اكسات تلاتة اكسات تلاتة اكسات تلاتة اكسات تلاتة
+
+503
+00:38:31,180 --> 00:38:31,600
+اكسات تلاتة اكسات تلاتة اكسات تلاتة اكسات تلاتة
+
+504
+00:38:31,600 --> 00:38:31,600
+اكسات تلاتة اكسات تلاتة اكسات تلاتة اكسات تلاتة
+
+505
+00:38:31,600 --> 00:38:40,340
+اكسات تلاتة اكسات تلاتة اكسات
+
+506
+00:38:40,340 --> 00:38:47,750
+تلاتة اكساتأحنا بنأثر Q2 على Q فأثر Q2 على Q بإنه
+
+507
+00:38:47,750 --> 00:38:53,350
+Q2 إيش بتأثر على Q بهذا الشكل يعني Q2 هاتش زي ال Q
+
+508
+00:38:53,350 --> 00:38:58,350
+واحد لها فعنا R وR2 وعنا اللي هو هسميه R2 ال
+
+509
+00:38:58,350 --> 00:39:04,610
+vector اللي هو إيش بيسوي R minus R2 R minus R2
+
+510
+00:39:11,340 --> 00:39:21,720
+بش فيش هناك X هيكون عندى زائد X hat زائد
+
+511
+00:39:21,720 --> 00:39:30,480
+اربع Y hat هي تلاتة ناقص نقاش plus اربع Y hat و
+
+512
+00:39:30,480 --> 00:39:33,500
+minus تلاتة زدها
+
+513
+00:39:49,080 --> 00:39:54,520
+الـ force 2 خلّيني أسميها F2 لإن جيبنا F1 هتكون K
+
+514
+00:39:54,520 --> 00:40:03,820
+في Q في Q2 على R2 magnitude Q في R2 vector ممتازة
+
+515
+00:40:03,820 --> 00:40:07,280
+انعوضت خلّيني أجمعها انعوضة عشان نكون معايا كواسعة
+
+516
+00:40:07,280 --> 00:40:13,040
+كده كما انا قلت أهاليك الـ K هي 9 عفوا 10 عفوا 9EQ
+
+517
+00:40:13,040 --> 00:40:18,300
+اللي قداش كمتها عشرة عشرة كمان عنا اس تسعة عشرة
+
+518
+00:40:18,300 --> 00:40:21,700
+كمان عنا اس ثلاث عشرة كمان عنا اس ثمانية في اللي
+
+519
+00:40:21,700 --> 00:40:27,260
+هي minus تنين في عشرة أس ثالث تلاتة على ال
+
+520
+00:40:27,260 --> 00:40:32,460
+magnitude EQ اللي هتكون جزر ستة وعشرينالقوة ثلاثة
+
+521
+00:40:32,460 --> 00:40:36,300
+على اثنين او جزء من قوة ثلاثة على اثنين او جزء من
+
+522
+00:40:36,300 --> 00:40:37,860
+قوة ثلاثة على اثنين او جزء من قوة ثلاثة على اثنين
+
+523
+00:40:37,860 --> 00:40:40,960
+او جزء من قوة ثلاثة على اثنين او جزء من قوة ثلاثة
+
+524
+00:40:40,960 --> 00:40:43,880
+على اثنين او جزء من قوة ثلاثة على اثنين او جزء من
+
+525
+00:40:43,880 --> 00:40:46,320
+قوة ثلاثة على اثنين او جزء من قوة ثلاثة على اثنين
+
+526
+00:40:46,320 --> 00:40:52,720
+او جزء من قوة ثلاثة على اثنين او جزء من قوة ثلاثة
+
+527
+00:40:52,720 --> 00:40:59,540
+على اثنين او جزء من قوة ثلاثة على اثنين اأف واحد
+
+528
+00:40:59,540 --> 00:41:05,220
+زائد أف تمام فى أحد عنده أي استفسار بس مسموه لأ
+
+529
+00:41:05,220 --> 00:41:08,120
+خلص الصبورة زى مش اي استفسار فى أحد عنده أي
+
+530
+00:41:08,120 --> 00:41:12,520
+استفسار قبل ما نمحي الصبورة طب يسلموا داكى يعنى بس
+
+531
+00:41:12,520 --> 00:41:18,480
+عشان نوضح أنه إحنا استخدمنا القوان اللى هو q في qk
+
+532
+00:41:18,480 --> 00:41:22,460
+على four by epsilon ر minus رك على ر minus رك
+
+533
+00:41:22,460 --> 00:41:26,960
+القوة تلاتة هذا اللى استخدمناهو جمعنا K واحد و
+
+534
+00:41:26,960 --> 00:41:31,060
+اتنين و عوضنا و بطلع معنا ال total force لأن هو
+
+535
+00:41:31,060 --> 00:41:34,140
+هاد ال vector addition بس عملية انها يعني الخطوات
+
+536
+00:41:34,140 --> 00:41:37,400
+اللي احنا شرحناها مع بعض هي لازم تبقيها ان حساب اي
+
+537
+00:41:37,400 --> 00:41:40,380
+قوة بدك تجيب ال position vector و احنا اخصا اخدنا
+
+538
+00:41:40,380 --> 00:41:43,700
+chapter كام كده نجيب position vector لكل point in
+
+539
+00:41:43,700 --> 00:41:47,100
+charge بعدين نجيب ال distance بين النقاط اللي انا
+
+540
+00:41:47,100 --> 00:41:51,580
+بده اجيب بالهم القوةبين Q و Q1 مثلا و QQ2 و هكذا
+
+541
+00:41:51,580 --> 00:41:54,600
+بعد ما أجيب ال distance أنا جاهزة عند قيم ال
+
+542
+00:41:54,600 --> 00:41:58,140
+charges عند المسافات اللي بينهم و عند بقدر أجيب ال
+
+543
+00:41:58,140 --> 00:42:01,220
+unit vector أو بقدر أجيب اللي هو R على R magnitude
+
+544
+00:42:01,220 --> 00:42:05,580
+of Q و بالتالي بقدر أحسب اللي هي ال force المنتهى
+
+545
+00:42:05,580 --> 00:42:08,810
+البساطةطب لو بده يجيب ال electric field intensity
+
+546
+00:42:08,810 --> 00:42:13,670
+هيكون E بساومين F على Q يعني F اللي احنا حسبناها
+
+547
+00:42:13,670 --> 00:42:17,530
+مع بعض بقسمها على قيمة ال charge اللي هي عشرة قوة
+
+548
+00:42:17,530 --> 00:42:21,270
+في عشرة قوة ناقص تسعة او عشر nano column اللي
+
+549
+00:42:21,270 --> 00:42:24,590
+بتعطيني قيمة ال electric field intensity اللي
+
+550
+00:42:24,590 --> 00:42:28,190
+exerted على ال point of charge اللي قمتها عشرة في
+
+551
+00:42:28,190 --> 00:42:32,150
+عشرة قوة ناقص تسعة column في اي استفسار لحد هنا؟
+
+552
+00:42:32,150 --> 00:42:35,230
+في اي استفسار؟ اعطيكوا لغة
+
diff --git a/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/Fb7Ppx0QZeo.srt b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/Fb7Ppx0QZeo.srt
new file mode 100644
index 0000000000000000000000000000000000000000..07d4e03905f7d97c08ad3f45a062392184a24c6a
--- /dev/null
+++ b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/Fb7Ppx0QZeo.srt
@@ -0,0 +1,1977 @@
+1
+00:00:20,910 --> 00:00:23,410
+بسم الله الرحمن الرحيم السلام عليكم ورحمة الله
+
+2
+00:00:23,410 --> 00:00:27,270
+وبركاته إحنا اليوم إن شاء الله هنتابع جزئية ال
+
+3
+00:00:27,270 --> 00:00:31,450
+magnetostatic fields إحنا في الأمثلة وقفنا لحد ما
+
+4
+00:00:31,450 --> 00:00:34,930
+شوفنا كيف الـ magnetic field ناتج عن ring قلنا
+
+5
+00:00:34,930 --> 00:00:38,170
+هنشوف كيف إن حساب الـ magnetic field ناتج عن solenoid
+
+6
+00:00:38,170 --> 00:00:42,470
+الـ solenoid هو عبارة عن مجموعة ringات  مر فيهم الـ
+
+7
+00:00:42,470 --> 00:00:47,280
+current إذا طلعنا المثال تبعنا هي الـ solenoid وهي 
+
+8
+00:00:47,280 --> 00:00:51,180
+current مر في قدر الـ loops لإن كنتوا مهما أقطال
+
+9
+00:00:51,180 --> 00:00:54,940
+يمكننا نقولهم إنه كأنهم خط continuous التيار بيجي
+
+10
+00:00:54,940 --> 00:00:57,400
+من طرفه وروح من طرف التاني تجاه الـ current زي ما
+
+11
+00:00:57,400 --> 00:01:00,620
+إنتوا شايفينه في المثال يعني الـ axis تبع الـ
+
+12
+00:01:00,620 --> 00:01:06,260
+solenoid بنطبق على الـ z axis و الـ x axis عند أحد
+
+13
+00:01:06,260 --> 00:01:10,760
+أطرافه يعني الـ zero هنا نصف القطر للـ solenoid هو
+
+14
+00:01:10,760 --> 00:01:13,910
+إيه solenoid يعني استغلاله زي هذه هذه المرفوعة
+
+15
+00:01:13,910 --> 00:01:15,590
+الموجودة حول السلك المرفوعة في الطيارة وهي
+
+16
+00:01:15,590 --> 00:01:18,290
+المرفوعة الموجودة حول السيناير وإن الماكنة تكفيت
+
+17
+00:01:18,290 --> 00:01:23,310
+في نقطة على الـ axis اللي هي النقطة اللي معلمنيا
+
+18
+00:01:23,310 --> 00:01:28,030
+بيه بيه على الواقع الـ axis on وماله بنطبق على الـ z
+
+19
+00:01:28,030 --> 00:01:33,850
+axis طبعًا النقطة B ممكن أنا أجيب الزاوية اللي بتحد
+
+20
+00:01:33,850 --> 00:01:38,770
+مابين النقطة B و أطراف الـ solenoid اللي هو الخط
+
+21
+00:01:38,770 --> 00:01:42,590
+مابين النقطة B ولو اللي ناتج عنها المجلة field من
+
+22
+00:01:42,590 --> 00:01:46,610
+النقطة اللي عند طرف الاقصى اليمين الزاوية هلاقيها
+
+23
+00:01:46,610 --> 00:01:51,430
+بأسميها θ2 والزاوية ما بين النقطة اللي بتحسب
+
+24
+00:01:51,430 --> 00:01:54,250
+عندها المجلة field وطرف الـ solenoid اللي هو أقصى
+
+25
+00:01:54,250 --> 00:01:58,230
+الشمال هأسميها θ1 ما بين الـ axis اللي هو الـ z axis و
+
+26
+00:01:58,230 --> 00:02:04,920
+النقطة والزاوية بين أي element هاخده أسميه dz هذا
+
+27
+00:02:04,920 --> 00:02:08,680
+الـ element والنقطة بتحسب عندها المجلة الـ field مع
+
+28
+00:02:08,680 --> 00:02:13,140
+الـ z axis هأسميها theta تمام أول حاجة أهم شيء في
+
+29
+00:02:13,140 --> 00:02:16,480
+الصينات إن أنا أعرف إن كيف ده أتعامل مع الـ problem
+
+30
+00:02:16,480 --> 00:02:22,330
+هاي أول مطالب منها إنه الـ magnet field عند أي نقطة
+
+31
+00:02:22,330 --> 00:02:27,170
+بي يساوي ni على اثنين بكساين ثتا اثنين ناقص كساين ثتا
+
+32
+00:02:27,170 --> 00:02:31,330
+واحد واتجاهه الـ z axis طبعًا الـ z axis هذه إحنا
+
+33
+00:02:31,330 --> 00:02:35,230
+فاهمينها قلنا إحنا بنلف إيدنا حسب اللي هي right
+
+34
+00:02:35,230 --> 00:02:38,730
+hand rule اتجاه الـ current لو كان على axis بنحط
+
+35
+00:02:38,730 --> 00:02:41,950
+اللي هو الـ thumb تبعنا الـ current وإيدنا بتمثل الـ
+
+36
+00:02:41,950 --> 00:02:44,770
+magnet field فدقة عشان أعرف اتجاه الـ magnet field
+
+37
+00:02:44,770 --> 00:02:49,820
+بلف إيدي مع التيار التيار طالع من هنا وداخل هنا،
+
+38
+00:02:49,820 --> 00:02:52,660
+إيش هتكون لفة إيدي؟ طالع من هنا وداخل ..  و أين
+
+39
+00:02:52,660 --> 00:02:55,540
+تجهة الـ magnetic field؟ في تجاه الـ z-axis، هاي
+
+40
+00:02:55,540 --> 00:02:58,040
+تجهة الـ magnetic field، إحنا عارفينه already، لإنه
+
+41
+00:02:58,040 --> 00:03:02,620
+من الـ right hand rule، الإبهام طالع من هنا وداخل في
+
+42
+00:03:02,620 --> 00:03:07,150
+تجهة التطبيق، إذا هاتجهة من هنا حيث أن من هي أن هي
+
+43
+00:03:07,150 --> 00:03:11,170
+عدد اللفات per unit length يعني لو أخذت لي طول معين
+
+44
+00:03:11,170 --> 00:03:15,490
+الـ هيكون عدد اللفات per unit length اللي هي أن أن
+
+45
+00:03:15,490 --> 00:03:19,050
+من كل عدد اللفات أعدي أن من اللفات أن per unit
+
+46
+00:03:19,050 --> 00:03:23,220
+length هيعطيني small  n  أوستا واحد وستة اثنين عرفناهم
+
+47
+00:03:23,220 --> 00:03:27,680
+وستة اثنين هي الزاوية اللي بتحد الـ solenoid من
+
+48
+00:03:27,680 --> 00:03:30,800
+أقصى اليمين اللي هو يعني الخط الزاوية بين الخط
+
+49
+00:03:30,800 --> 00:03:34,040
+الواصل بين الـ magrav field الموجود في أقصى اليمين الـ
+
+50
+00:03:34,040 --> 00:03:37,040
+current عند أقصى يمين الـ solenoid والنقطة ب
+
+51
+00:03:37,040 --> 00:03:40,460
+عند الـ magrav field مع الـ z axis هي ثتا اثنين وثتا
+
+52
+00:03:40,460 --> 00:03:44,720
+واحد بالمثل اللي مع طرف الأقصى اليسار تبع الـ
+
+53
+00:03:44,720 --> 00:03:49,220
+solenoid تمام إيش كمان؟ بقولنا كمان illustrate
+
+54
+00:03:50,960 --> 00:03:54,580
+الأشياء ذات إذا كان L أكبر بكثير من L هو طول
+
+55
+00:03:54,580 --> 00:03:57,200
+السيلونويد زي ما أنتو شايفينه إذا كان أكبر بكثير
+
+56
+00:03:57,200 --> 00:04:00,420
+من L هو نصف طول السيلونويد هتتبسط هاي المعادلة
+
+57
+00:04:00,420 --> 00:04:04,280
+لـ actually 1000 في I على طول واتجاهها بتتغير عشان هو Z
+
+58
+00:04:04,280 --> 00:04:10,360
+هذا أول حاجة بنتعامل معها إن السيلونويد هو مجموعة
+
+59
+00:04:10,360 --> 00:04:14,300
+من circular loops ملاصقين في بعض مكترتهم كأنهم
+
+60
+00:04:14,300 --> 00:04:18,940
+continuous loops يعني بعضها راحت DZ زي ما أنتو
+
+61
+00:04:18,940 --> 00:04:23,980
+شايفين هي DZ واللي بيحد ما بين هذا الـ element اللي
+
+62
+00:04:23,980 --> 00:04:28,240
+أخذته والنقطة بيحسب عندها الـ magnet field مع
+
+63
+00:04:28,240 --> 00:04:32,080
+الـ z  أكسر زاوية بنسميها z تمام؟ إذا مين الـ
+
+64
+00:04:32,080 --> 00:04:35,860
+element تبعي؟ الـ element تبعي هاخده اللي هو dH هو
+
+65
+00:04:35,860 --> 00:04:38,660
+الـ magnet field الناتج من مين؟ من الـ loop إن
+
+66
+00:04:38,660 --> 00:04:42,020
+النقطة بيه الموجود فيها لو أنا تخيلت عند dz
+
+67
+00:04:42,020 --> 00:04:46,440
+هاي النقطة عندي dz هاي دي dz بتاعتي وهي نقطة عند
+
+68
+00:04:46,440 --> 00:04:49,640
+الـ loop وهذا الـ loop هو الـ element تبعي إذا الـ dH
+
+69
+00:04:49,640 --> 00:04:52,780
+هيكون هو الـ magnetic field اللي ناتجة على هذه
+
+70
+00:04:52,780 --> 00:04:56,700
+النقطة من وين؟ من الـ loop اللي هو حسب في المثال
+
+71
+00:04:56,700 --> 00:04:59,100
+السابق واللي حسبته في الـ .. في الـ .. في الـ .. في
+
+72
+00:04:59,100 --> 00:05:06,780
+البيت طبعًا فإذا DH هيكون هو الـ magnetic field اللي
+
+73
+00:05:06,780 --> 00:05:11,780
+ناتج من ring اللي الـ thickness تبعه DZ أو DL هيكون
+
+74
+00:05:11,780 --> 00:05:16,060
+I فهو كذ بع I ρ وتربية كنا ماخدين الـ radius تبع الـ
+
+75
+00:05:16,060 --> 00:05:21,940
+loop I A تربيع على اثنين A تربيع زي زي تربيع أقوى
+
+76
+00:05:21,940 --> 00:05:29,140
+ثلاثة على اثنين و DL لإن أنا أنادي D HZ تمام أعوض عن
+
+77
+00:05:29,140 --> 00:05:35,720
+إيش عن DL DL هي عبارة عن NDZ DL هي عبارة عن NDZ
+
+78
+00:05:35,720 --> 00:05:40,880
+اللي هو جزئية DL اللي هي النقطة اللي على الـ hoop
+
+79
+00:05:40,880 --> 00:05:47,880
+تبعي عبارة عن NDZ تمام حلت عشان أجيب الـ HZ بتبدأ
+
+80
+00:05:47,880 --> 00:05:52,420
+كامل يعني البداية كذلك البداية إن أول حاجة بتخيل
+
+81
+00:05:52,420 --> 00:05:56,180
+إيش هي إنها ضارع الـ ringات وكل ring بتأثر على
+
+82
+00:05:56,180 --> 00:05:58,360
+magnet field أحد هذه النقطة بـ magnet field أكيد
+
+83
+00:05:58,360 --> 00:06:01,540
+magnet field اللي من الـ ring إذا الـ element هو من
+
+84
+00:06:01,540 --> 00:06:02,260
+الـ ring
+
+85
+00:06:06,970 --> 00:06:09,870
+التغير أو الـ element بتاعي هو dH ب كارنوت بتعطينا
+
+86
+00:06:09,870 --> 00:06:13,890
+كل المعلن فيه للنتج عند النقطة بتاعتي DL هي N DZ
+
+87
+00:06:13,890 --> 00:06:18,230
+إذا بأعوض عن N اللي هي Capital N على L زي ما هو
+
+88
+00:06:18,230 --> 00:06:20,970
+عرفنا إياها اللي هي number of rings per unit
+
+89
+00:06:20,970 --> 00:06:27,170
+length بـ DZ عشان إن أكامل هذا الـ integration مجرد إن
+
+90
+00:06:27,170 --> 00:06:31,190
+هذا خلص الـ مثال بس هذا اللي ما بعده هو قضية كيف
+
+91
+00:06:31,190 --> 00:06:34,590
+نحلها الـ integral كما لو قلنا إن تان ثتا من هي تان
+
+92
+00:06:34,590 --> 00:06:37,950
+ثتا هي ثتا تبعها المقابلة على المجاور قبل
+
+93
+00:06:37,950 --> 00:06:42,570
+مين وأكبر عن أين وإيه المجاور هو z إذا تان ثتا
+
+94
+00:06:42,570 --> 00:06:46,050
+هو a على z واشتق اتفاضلها عشان دي بدي z
+
+95
+00:06:47,770 --> 00:06:51,030
+سيكن تربيع بس إحنا بدنا الـ z فبنشقلب بنحط الـ z
+
+96
+00:06:51,030 --> 00:06:55,850
+بتساوي a على tan θ فـ d z أشبه ساوي a كوسيكن تربيع
+
+97
+00:06:55,850 --> 00:06:59,970
+لأن a على tan اللي هي مين كتان وتفاضل كتان minus
+
+98
+00:06:59,970 --> 00:07:04,430
+كوسيكن تربيع ثتا دي ثتا فده هي كوسيكن تربيع إذا d z هي
+
+99
+00:07:04,430 --> 00:07:08,990
+minus a كوسيكن تربيع الـ tan تفاضلها سيكن تربيع كتان
+
+100
+00:07:08,990 --> 00:07:11,950
+minus كوسيكن تربيع إذا إحنا زي ما حكيت لكم
+
+101
+00:07:15,610 --> 00:07:20,470
+كيف إنّي بدي أحل الـ integration بأحط عن هذه الأرقام
+
+102
+00:07:20,470 --> 00:07:25,690
+اللي حصلت عنها بأحصل على حجم مبسط جدًا لـ dz minus ni
+
+103
+00:07:25,690 --> 00:07:30,450
+على 2 sin θ dθ مجرد إن أعوض عن اللي هي إن tan θ a
+
+104
+00:07:30,450 --> 00:07:34,830
+على z أو z بساوي a كتان θ والتفاضل أعوض عنها
+
+105
+00:07:34,830 --> 00:07:38,490
+لأن زي ما تشوفين هذا بيروح مع هذا والـ a تربيع
+
+106
+00:07:38,490 --> 00:07:43,770
+بتروح مع الـ a تربيع لو عوضت عن dz إيش بيظل عندي ni
+
+107
+00:07:43,770 --> 00:07:48,450
+على 2 sin θ dθ واضح؟
+
+108
+00:07:50,790 --> 00:07:54,190
+لما آجي أكمل ثتا منهم بدي أكملها من ثتا واحد لـ ثتا
+
+109
+00:07:54,190 --> 00:07:59,450
+اثنين ناقص n I على اثنين الـ sin إيش تكامل الـ sin
+
+110
+00:07:59,450 --> 00:08:02,970
+اللي هو الـ cosine أو minus cosine minus cosine
+
+111
+00:08:02,970 --> 00:08:08,110
+تفضلها بتاعتنا الـ sign فبتروح الـ minus مع الـ sign
+
+112
+00:08:08,110 --> 00:08:11,610
+بـ cosine أعوض على الـ cosine ثتا اثنين minus يعني
+
+113
+00:08:11,610 --> 00:08:13,650
+الـ cosine ثتا اثنين ناقص الـ cosine ثتا واحد
+
+114
+00:08:13,650 --> 00:08:18,030
+المشكلة إذا الـ H اللي هي تجاهها بالـ z axis هي Ni على
+
+115
+00:08:18,030 --> 00:08:22,750
+2 Cos ثتا اثنين ناقص Cos ثتا واحد Z hat زي ما هو طالب هو هيك
+
+116
+00:08:22,750 --> 00:08:27,370
+طالب بالنسبة إذا كل الفكرة إن أتخيل إن Solenoid
+
+117
+00:08:27,370 --> 00:08:31,510
+عبارة عن رنجات وآخذ دي actual magnetic field ناتج
+
+118
+00:08:31,510 --> 00:08:33,390
+من واحد من هاد دولار رنجات
+
+119
+00:08:38,160 --> 00:08:40,840
+طيب الخطوة الثانية طالب مننا اللي هي إنه لما تصير
+
+120
+00:08:40,840 --> 00:08:43,720
+قال L أكبر كتير من A فعشان هيك أنا بدي أجيب علاقة
+
+121
+00:08:43,720 --> 00:08:46,500
+بين مين؟ قال L A ما فيش هنا في هذه العلاقة اللي
+
+122
+00:08:46,500 --> 00:08:49,480
+قدامي علاقة بين L A من هم بدي أجيبها من قيم
+
+123
+00:08:49,480 --> 00:08:52,640
+الـ cosine إذا تطلع على Cos ثتا واحد و Cos
+
+124
+00:08:52,640 --> 00:08:55,720
+ثتا اثنين طبعًا هو إيش حاجة أول حاجة بدي أجيبها عند الـ
+
+125
+00:08:55,720 --> 00:08:57,440
+center لأنه عند الـ center
+
+126
+00:09:02,360 --> 00:09:06,400
+اللي هي at the center of the solenoid هو بده إذا
+
+127
+00:09:06,400 --> 00:09:09,440
+كانت L أكبر من A at the center of the solenoid
+
+128
+00:09:09,440 --> 00:09:12,500
+فإذا بده أروح للـ center يعني أتخيل B صار تمام عند
+
+129
+00:09:12,500 --> 00:09:15,200
+الـ center of the solenoid يعني صار على شمالها
+
+130
+00:09:15,200 --> 00:09:19,260
+ويمينها L على 2 فهذه اللحظة إيش بيصير في ثتا واحد
+
+131
+00:09:19,260 --> 00:09:22,380
+وثتا اثنين هاي الرسمة هنا لما تصير B في الـ
+
+132
+00:09:22,380 --> 00:09:25,520
+center تبع الـ solenoid Cos ثتا واحد و Cos
+
+133
+00:09:25,520 --> 00:09:28,900
+ثتا اثنين بيساوي بعض وبيشارع سالبة لإن كل واحدة
+
+134
+00:09:28,900 --> 00:09:35,610
+إيش بتمامه بيكون L على 2 وعلى مين اللي هو الوتر اللي
+
+135
+00:09:35,610 --> 00:09:39,610
+هو عبارة عن A تربيع زائد L على 2 تربيع تحت
+
+136
+00:09:39,610 --> 00:09:47,150
+الجذر صح؟ لو إحنا زحفت هذه النقطة سترونويد وصارت
+
+137
+00:09:47,150 --> 00:09:52,090
+D المتصرف يعني ما صار ليه D L على 2 ما صارت
+
+138
+00:09:52,090 --> 00:09:55,730
+كلها دي مجرد رياضيات يعني قبل هيك هو الحاجة
+
+139
+00:09:55,730 --> 00:10:01,400
+المفيدة هي θ واحد وهي θ ثمانية كل واحدة جيب
+
+140
+00:10:01,400 --> 00:10:05,960
+تلوها إيش هو المجاور على وتر هو جذر التنبيه لـ a
+
+141
+00:10:05,960 --> 00:10:10,440
+تنبيه زي L على 2 ويكون تنبيه بس الفرق منهم واحدة
+
+142
+00:10:10,440 --> 00:10:14,320
+سلبية لأنها جيب ليه أكثر من تسعين فهي جيب تلوها
+
+143
+00:10:14,320 --> 00:10:17,060
+سالب وهي جيب تلوها مجاور أما التان جيب تلوهم
+
+144
+00:10:17,060 --> 00:10:20,980
+اللي هو a على L على 2 ويقل وطنهم لذا هم بيساووا واحد
+
+145
+00:10:20,980 --> 00:10:23,520
+لكن الـ cosine ثتا اثنين بيساوي سالب cosine ثتا
+
+146
+00:10:23,520 --> 00:10:26,920
+واحد اللي هو إيش بيساوي المجاور اللي هو L على 
+
+147
+00:10:26,920 --> 00:10:31,850
+2 على مين؟ المجاور بس الكتر كساين الكساين الوقال
+
+148
+00:10:31,850 --> 00:10:37,690
+على اثنين على الوتر لو عوضنا عن كساين ثتا اثنين
+
+149
+00:10:37,690 --> 00:10:40,530
+كساين ثتا واحد إيش بيصير؟ واحدة منهم سلب التانية
+
+150
+00:10:40,530 --> 00:10:43,690
+كساين ثتا واحد اثنين بتساوي سالب كساين ثتا واحد
+
+151
+00:10:43,690 --> 00:10:47,490
+فبيصير عندي مجموع اثنين تان كساين ثتا اثنين بتساوي
+
+152
+00:10:47,490 --> 00:10:52,050
+سالب كساين ثتا واحد فبيصير عندي minus ni على اثنين
+
+153
+00:10:52,050 --> 00:10:56,700
+الـ كساين ثتا مين؟ اللي هي 2 أو كوسين ثتا واحد لأن
+
+154
+00:10:56,700 --> 00:10:59,900
+كوسين ثتا واحد اللي إحنا متأكدين هي L على 2 فناخدها
+
+155
+00:10:59,900 --> 00:11:04,180
+هي فبأعوض عن كوسين ثتا اثنين على هيك حاجات minus
+
+156
+00:11:04,180 --> 00:11:07,980
+ثتا واحد اللي هي مين؟ بتعمل ثتا واحد L على 2 على
+
+157
+00:11:07,980 --> 00:11:11,700
+اللي هو جذر التربيع لـ A تربيع زائد L تربيع على أربعة
+
+158
+00:11:11,700 --> 00:11:16,300
+تحت الجذر فهي كوسين ثتا اثنين كوسين ثتا اثنين
+
+159
+00:11:16,300 --> 00:11:19,790
+الموجبة و ثتا واحد اللي هي السالبة عشان هيك إحنا
+
+160
+00:11:19,790 --> 00:11:26,310
+عوضنا لـ cosθ2 cosθ1 تبدأ لـ cosθ2 cosθ2 ليه هذه
+
+161
+00:11:26,310 --> 00:11:35,110
+الـ حادة هي L على 2 L على 2 على جذر التربيع لـ A
+
+162
+00:11:35,110 --> 00:11:38,330
+تربيع L على 2 L على 2 لـ A تربيع لـ A تربيع
+
+163
+00:11:38,330 --> 00:11:38,970
+لـ A تربيع لـ A تربيع لـ A تربيع لـ A تربيع
+
+164
+00:11:38,970 --> 00:11:39,290
+لـ A تربيع لـ A تربيع لـ A تربيع لـ A تربيع
+
+165
+00:11:39,290 --> 00:11:43,470
+لـ A تربيع لـ A تربيع لـ A تربيع لـ A تربيع الـ
+
+166
+00:11:44,870 --> 00:11:48,890
+بيصير اثنين كوساين ثتا اثنين A بأعوض عن كوساين ثتا
+
+167
+00:11:48,890 --> 00:11:51,550
+واحد بسالب كوساين ثتا اثنين فبيصير plus كوساين ثتا
+
+168
+00:11:51,550 --> 00:11:54,830
+اثنين لو يصير اثنين n I على اثنين الـ بتروح
+
+169
+00:11:54,830 --> 00:11:58,310
+الاثنين مع اثنين لو يصير n I على L كوساين ثتا
+
+170
+00:11:58,310 --> 00:12:00,890
+اثنين اللي هي مين؟ ك
+
+201
+00:14:22,130 --> 00:14:27,920
+enclosed بتساوي الـ closed path الـ h.dl لو استخدمت
+
+202
+00:14:27,920 --> 00:14:32,280
+stock theorem بتقول
+
+203
+00:14:32,280 --> 00:14:35,280
+الـ closed path للـ field.dl بيساوي الـ surface
+
+204
+00:14:35,280 --> 00:14:40,400
+integral لكل الـ field.ds
+
+205
+00:14:47,000 --> 00:14:49,560
+الـ Current هو عبارة عن Surface Integral لـ
+
+206
+00:14:49,560 --> 00:14:52,860
+Current Density  ضرب الـ Ds لو قررنا الـ two
+
+207
+00:14:52,860 --> 00:14:56,180
+equations بلاقى إن الـ Surface Integral لكرل الـ H
+
+208
+00:14:56,180 --> 00:14:59,860
+بالـ Ds بيساوي Surface Integral لجهده الـ Ds لإنهم 
+
+209
+00:14:59,860 --> 00:15:04,220
+بيساوي الـ enclosed current من Ampere's law اللي هو 
+
+210
+00:15:04,220 --> 00:15:07,620
+هيتعريفه Ampere's law اللي هو الـ closed line لتنجش الـ
+
+211
+00:15:07,620 --> 00:15:10,140
+component ما يفيض around a closed بس هو enclosed
+
+212
+00:15:10,140 --> 00:15:14,860
+استنتجت إن كرل الـ H بيساوي جهد هذه بنسميها third
+
+213
+00:15:14,860 --> 00:15:18,570
+Maxwell's equation, third Maxwell's equation صار لنا
+
+214
+00:15:18,570 --> 00:15:22,050
+تلاتة Maxwell's equations اذا كل اتش بيساوي جيه؟
+
+215
+00:15:22,050 --> 00:15:26,130
+ايش مستنتج إن كل اتش بيساوي جيه؟ إن اول هي مالها 
+
+216
+00:15:26,130 --> 00:15:30,370
+rotational كلها لا يساوي صفر فهي rotational و حاجة
+
+217
+00:15:30,370 --> 00:15:33,650
+تانية إن هي non conservative أنا بقول لأ الـ 
+
+218
+00:15:33,650 --> 00:15:37,250
+electric field كل الـ E بيساوي zero هو قولنا ماله
+
+219
+00:15:37,250 --> 00:15:41,910
+irrotational بيلفشوكمان conservative لكن الـ
+
+220
+00:15:41,910 --> 00:15:45,690
+magnetic field curl H بساوة J فهو ماله أولا إله 
+
+221
+00:15:45,690 --> 00:15:49,610
+curl، curlه rotational يعني و تاني حاجة is not
+
+222
+00:15:49,610 --> 00:15:50,310
+conservative
+
+223
+00:15:56,930 --> 00:15:59,710
+لو احنا اعتبرنا النوبة دي إن هي ب infinitely long
+
+224
+00:15:59,710 --> 00:16:03,530
+filament أو wire يعني بنسميها filament أو wire 
+
+225
+00:16:03,530 --> 00:16:06,790
+اللي مور فيها تيار اه إذا ما انتوا شايفينها رسمها
+
+226
+00:16:06,790 --> 00:16:10,390
+وناخد الـ filament واقع على الـ z axis إذا الـ 
+
+227
+00:16:10,390 --> 00:16:12,930
+filament بتاعتي أو الـ wire اللي مور فيه تيار واقع
+
+228
+00:16:12,930 --> 00:16:16,110
+على الـ z axis نفس القضية بقدر احدد اتجاه magnetic
+
+229
+00:16:16,110 --> 00:16:19,590
+field على طول من الـ right hand rule الـ current على
+
+230
+00:16:19,590 --> 00:16:22,070
+الـ z axis و الاتجاه الـ magnetic field اتجاه أيدي
+
+231
+00:16:22,070 --> 00:16:25,670
+اللي هو ايش هيكون اتجاهها إن هي φ hat
+
+232
+00:16:29,910 --> 00:16:33,390
+فالاتجاه counter clockwise هتكون الـ Φ hat لو
+
+233
+00:16:33,390 --> 00:16:37,310
+كان لتحت هتكون minus Φ hat تمام؟ إذا احنا 
+
+234
+00:16:37,310 --> 00:16:40,650
+المجنون الكبير طبعنا هيكون بلف حوالين الـ wire
+
+235
+00:16:40,650 --> 00:16:44,810
+اتجاه الـ Φ hat لو انا بتاخد اللي هو الـ current
+
+236
+00:16:44,810 --> 00:16:47,710
+احنا ايش قايل إن الـ current بيساوي؟ الـ current
+
+237
+00:16:47,710 --> 00:16:51,650
+بيساوي الـ closed integral لـ H2TL اللي هو ايش
+
+238
+00:16:51,650 --> 00:16:56,710
+هيساوي؟ الـ DL بتذكرين الـ DL ايش بتساوي؟ ρ dΦ
+
+239
+00:17:02,790 --> 00:17:09,590
+DL قوس ρ dΦ واتجاه Φ hat Φ hat وعندي
+
+240
+00:17:09,590 --> 00:17:13,110
+الماقن فيلد إن هو في اتجاه Φ hat لازم هيكون H5Φ 
+
+241
+00:17:13,110 --> 00:17:18,110
+hat الـ product تبعهم هو H5 ρ dΦ ρ constant
+
+242
+00:17:18,110 --> 00:17:22,650
+لإنها ring هذهالـ ρ تبقى حسب مين بتغير الـ Φ من 
+
+243
+00:17:22,650 --> 00:17:26,990
+zero لـ two π فهذا هتكون HΦ 2π ρ وبالتالي
+
+244
+00:17:26,990 --> 00:17:31,910
+H vector بتسوي I على 2π ρ فى اتجاه الـ πهاد،
+
+245
+00:17:31,910 --> 00:17:36,970
+فهذا الـ magnetic field اللى ناتج من filament موقع
+
+246
+00:17:36,970 --> 00:17:38,130
+على z اكسس
+
+247
+00:17:42,090 --> 00:17:45,070
+لو انا بدي احسب الـ magnetic field اللى ناتج من مين
+
+248
+00:17:45,070 --> 00:17:48,190
+من sheet انا عندي sheet هال اتا و هذا الـ sheet
+
+249
+00:17:48,190 --> 00:17:51,630
+ماله infinitely بتمدد infinitely اتجاه الـ X و الـ Y
+
+250
+00:17:51,630 --> 00:17:57,690
+واقع إن Z equal 0 واقع إن Z equal 0 و بدي احسب الـ
+
+251
+00:17:57,690 --> 00:18:01,630
+magnetic field اللى ناتج من هذه الـ sheet اللى
+
+252
+00:18:01,630 --> 00:18:04,610
+بيهور فيها الـ current زى ما انتوا شايفينه surface
+
+253
+00:18:04,610 --> 00:18:09,280
+current كي بتساوي Ky ay يعني اتجاهه يعني هذا الـ
+
+254
+00:18:09,280 --> 00:18:12,120
+surface كانت أول الحاجة يعني لانفهمها إن انا بقدر
+
+255
+00:18:12,120 --> 00:18:16,740
+اعتبره إنه حطوط من filaments يعني هو عبارة عن
+
+256
+00:18:16,740 --> 00:18:24,980
+تيار بتطفوق على الـ surface بتاع الـ sheet عايزة
+
+257
+00:18:24,980 --> 00:18:29,320
+نفسي اكتر حقيبتي يعني فانا ايش ممكن اتخيله إنه كل
+
+258
+00:18:29,320 --> 00:18:33,120
+واحد هو مثل اياش filament نفس السؤال اللي السابق
+
+259
+00:18:33,950 --> 00:18:39,130
+أتخيلوا خطوط كل حط ماله حامل current density Ky
+
+260
+00:18:39,130 --> 00:18:44,630
+y و y hat هي اتجاه الـ current بتضغط في اتجاه الـ y
+
+261
+00:18:44,630 --> 00:18:48,530
+direction إذا هفترضوا الـ surface هذا عبارة عن
+
+262
+00:18:48,530 --> 00:18:53,010
+filaments يعني خطوط نقل زي اللي هو في المثال اللي 
+
+263
+00:18:53,010 --> 00:18:58,190
+قبله filaments اللي ملزقين في بعض فهم بيعملولي الـ
+
+264
+00:18:58,190 --> 00:19:04,520
+plane و الـ current هو current density Ky y hat الهى 
+
+265
+00:19:04,520 --> 00:19:08,420
+current per length and inverse per meter الهى الـ 
+
+266
+00:19:08,420 --> 00:19:12,860
+current density اللي هناخدله فى هالحالة الـ
+
+267
+00:19:12,860 --> 00:19:16,100
+symmetry تبع الـ problem هاخد rectangle مش هاخد
+
+268
+00:19:16,100 --> 00:19:19,520
+اسطوانة هاخد rectangular لإن هي عندي الـ surface
+
+269
+00:19:19,520 --> 00:19:25,480
+مربعة مش دائرة مش هو ولا دائرة مليانة الـ surface
+
+270
+00:19:25,480 --> 00:19:28,740
+تبعي مربع فده الـ symmetry هاخد اللي هو زى ما كنتوا
+
+271
+00:19:28,740 --> 00:19:33,820
+شايفين المستطيل اللي قدامي اللي بتحسب عليه لإنه
+
+272
+00:19:33,820 --> 00:19:38,140
+احنا عارفين إنه هيكون magnet field حوالاه طالما إيه
+
+273
+00:19:38,140 --> 00:19:40,220
+طال يعني مش هيكون في البلاد
+
+274
+00:19:50,060 --> 00:19:52,880
+عشان انا افهم ايش اللي بيصير احنا قلنا ايش هنسوي 
+
+275
+00:19:52,880 --> 00:19:59,000
+هم file elements فهي أنا بتقعد الـ x axis الـ dress
+
+276
+00:19:59,000 --> 00:20:02,340
+ده تبسيط هي الـ x axis عندي أنا two file elements
+
+277
+00:20:02,340 --> 00:20:04,360
+واحدة بتقطع من هنا و واحدة بتقطع من هنا
+
+278
+00:20:11,670 --> 00:20:14,870
+فهي الـ filament اللي عندها هذه النقطة و الـ 
+
+279
+00:20:14,870 --> 00:20:18,530
+filament اللي عندها هذه النقطة بالتمام أو أي نقطة
+
+280
+00:20:18,530 --> 00:20:21,050
+تانية مش فارقة يعني بس ناخد دولة النقطة تانية
+
+281
+00:20:21,050 --> 00:20:25,590
+قسمها بساعة ولو أخد المربع أكبر أو أصغر أخد أي
+
+282
+00:20:25,590 --> 00:20:31,210
+نقطة تانية على الـ axis أي نقطة تانية واضح؟ على الـ 
+
+283
+00:20:31,210 --> 00:20:34,330
+X axis ايش شكلهم التانية؟ كيف بيقطعوا الـ X axis؟
+
+284
+00:20:34,330 --> 00:20:38,330
+هاي الـ X axis بيقطعوا التانية طالعين منها التانية
+
+285
+00:20:38,330 --> 00:20:43,300
+طالعين منها فهذه الـ X axis هذا X-axis وهذه الـ 
+
+286
+00:20:43,300 --> 00:20:46,680
+filaments اللي تنتهي من هنا طالعين من هنا وهذه
+
+287
+00:20:46,680 --> 00:20:50,500
+الواحدة وهذه التانية two filaments على الـ X-axis
+
+288
+00:20:50,500 --> 00:20:58,900
+وتنتين طالعين من هنا ومن هنا كل
+
+289
+00:20:58,900 --> 00:21:01,780
+filament لحالها من المثال السابق شرحنا الـ
+
+290
+00:21:01,780 --> 00:21:06,760
+magnetic field ناتج منها هي دائرة
+
+291
+00:21:09,450 --> 00:21:11,950
+بنعمل نفس الحاجة لكل واحدة من هادولة الـ fire mint
+
+292
+00:21:11,950 --> 00:21:15,130
+هاد الـ fire mint المغناطك هي بالنتج منها
+
+293
+00:21:15,130 --> 00:21:19,350
+tangential لدائرة يعني إذا ما رسمتش الدائرة بتبقى
+
+294
+00:21:19,350 --> 00:21:25,950
+بسمها الدكتور يصعد
+
+295
+00:21:25,950 --> 00:21:29,190
+زي الـ .. زي الـ .. بيطلس مش مشكلة قريبة من الدائرة
+
+296
+00:21:29,190 --> 00:21:32,410
+صح؟ شوية قريبة من الدائرة ولا بيبقى قريبة من
+
+297
+00:21:32,410 --> 00:21:41,170
+الدائرة؟ قريبة؟ تشبهها؟ أسام فيه إيديعال الـ z axis
+
+298
+00:21:41,170 --> 00:21:44,350
+أو يعني قريب لو انا اتطلع اعيش الـ magnet field
+
+299
+00:21:44,350 --> 00:21:47,510
+هلاقي إن عند أي نقطة مثلا لو أخدها الـ z axis
+
+300
+00:21:47,510 --> 00:21:51,110
+واحدة هتكون هنا و واحدة هتكون هنا tangential
+
+301
+00:21:51,110 --> 00:21:55,470
+tangential لمين؟ اللي اللي عندها نفس الشيء لو فكرت
+
+302
+00:21:55,470 --> 00:22:00,150
+في الـ filament اللي هنا هيكون عندي برضه في دائرة
+
+303
+00:22:00,150 --> 00:22:06,990
+مافيش
+
+304
+00:22:06,990 --> 00:22:10,630
+فعلا بس هنكملها بس هذه الدائرة برضه المجنة الكفيل
+
+305
+00:22:10,630 --> 00:22:15,250
+تنتج عن هذه الـ file من الـ tangent لها طبعا هذا 
+
+306
+00:22:15,250 --> 00:22:19,050
+الحكي بنطبق على كل الـ filements اللي هو عيين على 
+
+307
+00:22:19,050 --> 00:22:23,010
+الـ x-axis صحيح؟ طبعا و طلعنا نعدلها to fields إذا
+
+308
+00:22:23,010 --> 00:22:26,070
+مثلا ما عارفين إنه عند أي نقطة هيكون فيه two
+
+309
+00:22:26,070 --> 00:22:30,050
+fields عند أي نقطة هيكون فيه two fields واحد ناتج
+
+310
+00:22:30,050 --> 00:22:35,210
+من مين؟ من الـ filement فانا راح أدلها المجنة
+
+311
+00:22:35,210 --> 00:22:39,950
+الكفيل الناتج من هذا الـ filement وحدة نجم من هذا
+
+312
+00:22:39,950 --> 00:22:47,050
+الوضع و وحدة نجم من هذا الوضع هاي الـ 6 اكس اش
+
+313
+00:22:47,050 --> 00:22:53,430
+هلاحظ إنه لو انا حللت الـ h1 و الـ h2 هيتكون في يدي
+
+314
+00:22:53,430 --> 00:22:59,710
+تلتي h1 component الـ x و 1 في zواتشنين هيكون واحدة
+
+315
+00:22:59,710 --> 00:23:02,510
+في الـ X واحدة في الـ Z طب هم بيساوي بعض مافيش فرق
+
+316
+00:23:02,510 --> 00:23:05,090
+بين الفقرين في الأولى والتالى نفس التغيير بيقوموا
+
+317
+00:23:05,090 --> 00:23:08,790
+فيهم في اللي ع ز أكس اسمه هم هيروحوا هضلوا عندهم
+
+318
+00:23:08,790 --> 00:23:12,730
+ويعملوا في الـ X axis نفس الشيء عند هذه النقطة هل
+
+319
+00:23:12,730 --> 00:23:16,690
+ألاحظ إنه هيكون في واحدة في الـ X واحدة في السالب X
+
+320
+00:23:16,690 --> 00:23:20,590
+أي واحدة في البسط Z واحدة في السالب Z و التنتين
+
+321
+00:23:20,590 --> 00:23:24,070
+هيكون هم component في البسط X إذا اللي على الـ Z
+
+322
+00:23:24,070 --> 00:23:30,330
+axis جروبه إذا أنت تلاحظ إنه هيكون عندهم دائما
+
+323
+00:23:30,330 --> 00:23:36,310
+magnetic field في اتجاه الـ X negative negative X
+
+324
+00:23:36,310 --> 00:23:40,310
+اللي هو لو أنا نظرت على Z ماعنها أكبر من صفر لو Z
+
+325
+00:23:40,310 --> 00:23:48,710
+موجبة و سالب لو Z أكبر من صفر اللي هي بُسط في X 
+
+326
+00:23:48,710 --> 00:23:53,450
+سهل بُسط في X هتكون في بُسط في X و لو كانت Z أقل 
+
+327
+00:23:53,450 --> 00:23:56,390
+من صفر هتكون في سالب X فانا احنا أخدنا هاي الـ X
+
+328
+00:23:56,390 --> 00:23:57,770
+أحسس تمام؟
+
+329
+00:24:02,930 --> 00:24:06,490
+إذا لو أنا طلعت على above و below الـ sheet هلاحظ
+
+330
+00:24:06,490 --> 00:24:10,690
+دائما هيكون عندي ارحمكم الله above الـ sheet و
+
+331
+00:24:10,690 --> 00:24:12,930
+below الـ sheet هيكون في عندي الـ magnetic field
+
+332
+00:24:12,930 --> 00:24:18,310
+واحد هيكون positive و الثاني negative اللي هو above
+
+333
+00:24:18,310 --> 00:24:21,450
+الـ sheet هيكون موجب و اللي below الـ sheet هيكون
+
+334
+00:24:21,450 --> 00:24:23,990
+سالب، واضح؟
+
+335
+00:24:39,760 --> 00:24:42,580
+الحاجة التانية إنه احنا عارفين إن الـ closed
+
+336
+00:24:42,580 --> 00:24:47,940
+integral لـ H2DL ايش بيسموه I enclosed I enclosed و
+
+337
+00:24:47,940 --> 00:24:51,020
+I enclosed إذا أطلع عنوان I enclosed مش هيكون فيه
+
+338
+00:24:51,020 --> 00:24:54,500
+يمدي أي حاجة في اتجاه الـ Z-axis الـ I enclosed فعلا 
+
+339
+00:24:54,500 --> 00:24:57,540
+من جنب بعيد وقدش period length هي احنا قدش الطول
+
+340
+00:24:57,540 --> 00:25:00,220
+تبعنا لو أخدت هذا المربع تبعي هذا الـ closed loop
+
+341
+00:25:00,220 --> 00:25:06,250
+هو الـ B يعني هيكون I enclosed keep K وY في مين؟ في 
+
+342
+00:25:06,250 --> 00:25:10,270
+بيك عدد الـ file elements كلهم مع بعض و الـ unit
+
+343
+00:25:10,270 --> 00:25:14,430
+lengths كده الـ links هيكون الـ file elements واحدة
+
+344
+00:25:14,430 --> 00:25:17,610
+جانب التانية و جانب التانية و جانب التانية فكده هو
+
+345
+00:25:17,610 --> 00:25:22,590
+طول بيك K اللي هي amps per meter و الـ meter تبعي
+
+346
+00:25:22,590 --> 00:25:26,270
+أو الـ links تبعي هيكون الـ بيك أنا عملت اللي
+
+347
+00:25:26,270 --> 00:25:30,110
+element الـ loop طوله بيك هيكون كل الـ current
+
+348
+00:25:30,110 --> 00:25:34,730
+enclosed هو مين؟ هذا الـ current اللي هو K وY فمين 
+
+349
+00:25:34,730 --> 00:25:38,830
+فمين تمام؟ واضحة هذه النقطة؟ إذا ماقدش الـ current
+
+350
+00:25:38,830 --> 00:25:43,550
+enclosed اللي هو KY اللي هو M سبيرميتا في أي طول
+
+351
+00:25:43,550 --> 00:25:44,010
+اللي هو P
+
+352
+00:26:04,090 --> 00:26:07,490
+الآن نعمل الـ integration طبعا اش ما احنا استنتجناه
+
+353
+00:26:07,490 --> 00:26:10,790
+لحد الاية أول حاجة استنتجنا إن الـ closed integral
+
+354
+00:26:10,790 --> 00:26:14,870
+H2TL بساوي Ky بB وكمان حاجة استنتجناها من الـ
+
+355
+00:26:14,870 --> 00:26:18,570
+symmetry لو أخدنا two filaments و حاولنا نحسب الـ
+
+356
+00:26:18,570 --> 00:26:21,210
+magnetic field إن الـ magnetic field واحد بيكون
+
+357
+00:26:21,210 --> 00:26:23,850
+above و واحد below عند أي نقطة لو عملت زبدة اكسس
+
+358
+00:26:23,850 --> 00:26:26,810
+هيك ولا هيك سحبته دلن ما هيكون عندي magnetic
+
+359
+00:26:26,810 --> 00:26:31,090
+field above موجبة اتجاه القسط في X و بالـ low سالب 
+
+360
+00:26:31,090 --> 00:26:34,550
+كمان مجرد constant فيمة اتش نوت أو مش constant
+
+361
+00:26:34,550 --> 00:26:38,510
+يعني رقم انا ما اعرفهش بس متساوي فوق و تحت متساوي 
+
+362
+00:26:38,510 --> 00:26:42,510
+أسواق فوق اللي هو ناتج من كل الـ filaments اللي على
+
+363
+00:26:42,510 --> 00:26:46,450
+الدنيا من هنا لهنا هيكون الـ total magnetic field
+
+364
+00:26:46,450 --> 00:26:49,630
+هده دي اتش لإن انا بس خدته filaments لو حطيت كل الـ
+
+365
+00:26:49,630 --> 00:26:52,950
+filaments اللي محبوسين في الـ links بيه هيكون عند
+
+366
+00:26:52,950 --> 00:26:58,090
+الـ total H هسميه H نوت واضح؟ أسوأ فوق ولا تحت،
+
+367
+00:26:58,090 --> 00:27:00,190
+أسوأ اللي في الاتجاه الـ positive X ولا الـ
+
+368
+00:27:00,190 --> 00:27:02,630
+negative X، بضعنا نعرف مين الـ H نود، من هون 
+
+369
+00:27:02,630 --> 00:27:04,650
+بتعرف الـ H نود، ده من الـ symmetry اللي حكينا
+
+370
+00:27:04,650 --> 00:27:07,370
+عنه، احنا بنرجع للقانون اللي قولنا الـ closed
+
+371
+00:27:07,370 --> 00:27:13,950
+integral لـ H dot DL، ايش بتساوي؟ KY كبيرة بنكمل على
+
+372
+00:27:13,950 --> 00:27:18,610
+الـ buses الـ bus الأول من 1 إلى 2 ثم التكامل من 2 
+
+373
+00:27:18,610 --> 00:27:22,670
+إلى 3 لإن close loop ثم التكامل من 3 إلى 4 ثم 
+
+374
+
+401
+00:29:25,610 --> 00:29:33,190
+الـ Closed Integral X و T L بتساوي KYPB اللي هي
+
+402
+00:29:33,190 --> 00:29:36,590
+عدد ال filaments اللي بتخترقوا ال links بيه فإذا 
+
+403
+00:29:36,590 --> 00:29:39,290
+أنا أكتشف نوتش بها تساوي المشكلة اللي بعانيها عرفنا
+
+404
+00:29:39,290 --> 00:29:45,130
+فيه بتروح معادي هيكون KY على 2 فبجرب أجيب الفيل H
+
+405
+00:29:45,130 --> 00:29:50,310
+هيكون above ال plane هو فرصة أكثر من Zero نص KY
+
+406
+00:29:50,310 --> 00:29:51,370
+Xها
+
+407
+00:30:12,790 --> 00:30:17,530
+بشكل عام هذه العلاقة بقدر أكتبها بشكل التالي نص كيه
+
+408
+00:30:17,530 --> 00:30:21,790
+اللي هو ال vector تبعنا اللي هو ال current في
+
+409
+00:30:21,790 --> 00:30:26,170
+حالتنا كان ky تجاهه cross انهات من هي انهات هو 
+
+410
+00:30:26,170 --> 00:30:28,930
+unit vector directed from the current shape to the
+
+411
+00:30:28,930 --> 00:30:33,070
+point of interest هيتغير ايه انهات نيجي نطبقه على
+
+412
+00:30:33,070 --> 00:30:36,430
+المثال تبعنا كي علنا ايش تجاهها ky
+
+413
+00:30:47,470 --> 00:30:51,290
+من ال surface بالنقطة اللي أنا بدي أدرس عندها ال
+
+414
+00:30:51,290 --> 00:30:57,070
+magnitude لتطلع فوق ال plane هذا طبعا نص T Y Y
+
+415
+00:30:57,070 --> 00:31:04,210
+cross فوق البندش هيكون ايه انها هيكون بوستر Z hat
+
+416
+00:31:04,210 --> 00:31:09,490
+Y hat يكون Z hat هيكون X hat
+
+417
+00:31:29,920 --> 00:31:35,160
+النور من الـplane لنقطة بدائيسة ماينص اكروس 
+
+418
+00:31:35,160 --> 00:31:41,180
+ماينص زي دي 
+
+419
+00:31:41,180 --> 00:31:46,320
+هذه هي العلاقة العامة إذا بشكل عام لما أنا بحسب
+
+420
+00:31:46,320 --> 00:31:50,200
+الماجنيتود دي ال field الناتج من ال surface current
+
+421
+00:31:50,200 --> 00:31:53,880
+بقى بطلع فوق ال plane و تحت ال plane وبحسب اللي 
+
+422
+00:31:53,880 --> 00:32:02,390
+هو العلاقة العامة لو كان عندي الـ coaxial line لو 
+
+423
+00:32:02,390 --> 00:32:06,750
+أنا كان عندي مثال هيندي two lines او يعني two
+
+424
+00:32:06,750 --> 00:32:11,490
+conductors واحد هعمل طيار الطيار اللي في الداخلي
+
+425
+00:32:11,490 --> 00:32:16,530
+في ال coaxial cable ماله الطيار طالع هتجاه I طالع
+
+426
+00:32:16,530 --> 00:32:20,870
+بينما التاني اللي هم اللي هم بالازرق الطيار ماله
+
+427
+00:32:20,870 --> 00:32:25,030
+داخل وهذا قيلك انه طالع Z axis
+
+428
+00:32:26,990 --> 00:32:30,610
+الـ core في الـ core التيار مو يتعلق من الصفحة و
+
+429
+00:32:30,610 --> 00:32:34,930
+في اللي حولها داخل الصفحة و تعلق منها الـ magnetic
+
+430
+00:32:34,930 --> 00:32:39,450
+field ما بين الـ 0 و الـ B ليها الـ 0 و الـ B و
+
+431
+00:32:39,450 --> 00:32:45,590
+بعدين ما بين ال raw من A ل B هي أول حاجة من الـ 0
+
+432
+00:32:45,590 --> 00:32:50,240
+ل A بس فهي الـ A اللي محددنا إياها ليها وبعدين 
+
+433
+00:32:50,240 --> 00:32:53,960
+مابين ال A و ال B اللي هي هي ال region وبعدين
+
+434
+00:32:53,960 --> 00:32:59,720
+مابين ال B و B plus T اللي هو ال conductor الخارجي
+
+435
+00:32:59,720 --> 00:33:03,780
+ال thickness بتاعه T لازم هتكون مابين ال B ل B
+
+436
+00:33:03,780 --> 00:33:04,220
+plus
+
+437
+00:33:15,280 --> 00:33:19,300
+عشان أعرف قداش I enclosed فى قلب ال line اللي
+
+438
+00:33:19,300 --> 00:33:22,020
+بتاخده لانه بدي row أقل من V
+
+439
+00:33:26,900 --> 00:33:32,220
+عشان نعرف I enclosed هو I constant لازم بقدر أجيب
+
+440
+00:33:32,220 --> 00:33:36,200
+أداش I عند أي per unit area لانه بدي في الآخر اللي
+
+441
+00:33:36,200 --> 00:33:40,710
+enclosed في هذا ال line أو per unit length إننا
+
+442
+00:33:40,710 --> 00:33:43,750
+بلوز انتجرال اتشد دي اك تساوي اي بلوز و اي بلوز شو
+
+443
+00:33:43,750 --> 00:33:47,350
+بتساوي الانتجرال اتشد ال DS ال current density في
+
+444
+00:33:47,350 --> 00:33:51,370
+دي ال DS ايش ال current density يعني ال I constant
+
+445
+00:33:51,370 --> 00:33:55,170
+فهتكون جيه شو بتساوي I على ال area بتاعتها ال
+
+446
+00:33:55,170 --> 00:34:01,550
+cross section تبع ال line الداخلي ال core تبع ال
+
+447
+00:34:01,550 --> 00:34:04,990
+coaxial line اللي هي بره I على Y ايه الترفيه و
+
+448
+00:34:04,990 --> 00:34:09,790
+تجاهه بص تفزدها تبع الطالع Jدوت دي اس اللي هي رو
+
+449
+00:34:09,790 --> 00:34:14,070
+دي فاي دي رو زدها تبرده اتجاهها فان عمودي عليها ال
+
+450
+00:34:14,070 --> 00:34:19,910
+DS لو أنا خدنا I enclosed مش هتساوي J دوت DS J
+
+451
+00:34:19,910 --> 00:34:22,370
+اللي هي I على Pi اتر بيها constant تطلع بره ال
+
+452
+00:34:22,370 --> 00:34:27,810
+Integral و ال DS رو دي فاي دي رو دي رو رو دي رو من
+
+453
+00:34:27,810 --> 00:34:33,740
+وين الرو بتروح من Zero لآخر أو حتى النقطة التي أريد
+
+454
+00:34:33,740 --> 00:34:36,740
+قياسها عندها أقصرهم لإيه بس أنا بدي عند أي نقطة
+
+455
+00:34:36,740 --> 00:34:40,000
+بقياسها زي هذا ال surface ال line اللي أنا حاطيته ال
+
+456
+00:34:40,000 --> 00:34:44,120
+imaginary line و بدي ال tangential له و أخد أفرض
+
+457
+00:34:44,120 --> 00:34:48,980
+ان ال radius تبعه ρو لذا سيكون ال S بديها حوالي
+
+458
+00:34:48,980 --> 00:34:52,860
+هذا ال line سيكون جزء من ال total current density
+
+459
+00:34:52,860 --> 00:34:57,720
+موجودة هنا اللي هي فقط محبوسة من zero ل رو عند أي
+
+460
+00:34:57,720 --> 00:34:59,500
+نقطة في هذا ال surface
+
+461
+00:35:12,230 --> 00:35:18,770
+عن طريق الاريه
+
+462
+00:35:18,770 --> 00:35:25,280
+الاريه هي الدائرة الجوانية الـ Y بتروح مع الـ Y
+
+463
+00:35:25,280 --> 00:35:28,700
+هيكون I رو تربيع على I تربيع هي الـ I enclosed هاي
+
+464
+00:35:28,700 --> 00:35:32,040
+الـ I enclosed طب اتش dot dl إيش هتكون اتش؟ احنا
+
+465
+00:35:32,040 --> 00:35:34,840
+قلنا ال current طالع تجاه Z-axis إيش ال magnetic
+
+466
+00:35:34,840 --> 00:35:39,000
+field تجاه هو؟ الفي داريكشن الفي داريكشن
+
+467
+00:35:39,000 --> 00:35:42,220
+tangential لمن؟ لل line اللي محيط فيه ال area اللي
+
+468
+00:35:42,220 --> 00:35:44,940
+موجود فيها ال current ال current موجود في قلب هذه
+
+469
+00:35:44,940 --> 00:35:48,440
+ال area و ال magnetic field tangential له في تجاه
+
+470
+00:35:48,440 --> 00:35:53,470
+الفيو DL هتكون 2π رو يعني إذا أنا اكملتها أو أنا
+
+471
+00:35:53,470 --> 00:35:57,790
+ارفعها 2π رو إذا H5 في 2π رو هتكون I رو تربيع على
+
+472
+00:35:57,790 --> 00:36:02,450
+A تربيع إذا H5 هتكون I رو على 2π A تربيع لو أخذنا
+
+473
+00:36:02,450 --> 00:36:05,810
+هنا هيكون ال total current enclosed mean اللي هو
+
+474
+00:36:05,810 --> 00:36:09,250
+هذا اللي موجود هنا I كل ال current هيكون enclosed
+
+475
+00:36:09,250 --> 00:36:13,090
+يعني إذا هيكون H dot DL بتساوي I اللي هو ال
+
+476
+00:36:13,090 --> 00:36:15,370
+current اللي موجود في قلب ال conductor الأول يعني
+
+477
+00:36:15,370 --> 00:36:17,050
+كله هنا هتكون
+
+478
+00:36:17,050 --> 00:36:43,270
+I²I²I²I²I²I²I²I²I²I²I²I²I²I²I²I²I²I²I²I²I²I²I²I²I²I²I²I²I
+
+479
+00:36:46,000 --> 00:36:49,560
+كمان مرة بدي أجيب مين هو ال جيب و ال current
+
+480
+00:36:49,560 --> 00:36:51,780
+enclosed في هذه ال region
+
+481
+00:37:04,920 --> 00:37:09,740
+الـ I enclosed بيساوي مجموعة طيارات هذا الطيار I
+
+482
+00:37:09,740 --> 00:37:13,080
+إشارته موجبة والطيار اللي هنا إشارته سالبة
+
+483
+00:37:13,080 --> 00:37:23,320
+هيكون I Gts و G هذه ما لها سالبة سالبة I على ال
+
+484
+00:37:23,320 --> 00:37:29,800
+area اللي هو current per unit الاريه الصغيرة الى
+
+485
+00:37:29,800 --> 00:37:35,940
+هنا زائد الاريه الكبيرة كلها الاريه الاريه الكبيرة
+
+486
+00:37:35,940 --> 00:37:35,960
+كلها الاريه الكبيرة كلها الاريه الاريه الكبيرة
+
+487
+00:37:35,960 --> 00:37:36,260
+كلها الاريه الاريه الكبيرة كلها الاريه الاريه
+
+488
+00:37:36,260 --> 00:37:37,180
+الكبيرة كلها الاريه الاريه الكبيرة كلها الاريه
+
+489
+00:37:37,180 --> 00:37:38,920
+الاريه الكبيرة كلها الاريه الاريه الكبيرة كلها
+
+490
+00:37:38,920 --> 00:37:43,960
+الاريه الاريه الكبيرة كلها الاريه الاريه الكبيرة
+
+491
+00:37:43,960 --> 00:37:47,100
+كلها الاريه الاريه الكبيرة كلها الاريه الاريه
+
+492
+00:37:47,100 --> 00:37:47,660
+الاريه الكبيرة كلها الاريه الاريه الكبيرة كلها
+
+493
+00:37:47,660 --> 00:37:49,160
+الاريه الاريه الكبيرة 
+
+494
+00:37:59,180 --> 00:38:04,340
+j بتساوي I على ال area فاهمين أنتو الفكرة اه إذا
+
+495
+00:38:04,340 --> 00:38:06,120
+احنا بنجيب اللي هي ال current على ال area اللي
+
+496
+00:38:06,120 --> 00:38:09,200
+بتكون ال area الكلية مقص ال area اللي داخلية
+
+497
+00:38:09,200 --> 00:38:12,960
+بتعطينا اللي هو بس هاي ال area واضح؟ هاي ال area
+
+498
+00:38:12,960 --> 00:38:16,240
+فاحنا جبنا هكذا ال current density نفس التطبيق
+
+499
+00:38:16,240 --> 00:38:19,960
+اللي عمله بس هنا أسفلت التيار اللي كل مين I minus
+
+500
+00:38:19,960 --> 00:38:22,720
+اللي هي ال current اللي موجود هنا هذا ال current
+
+501
+00:38:22,720 --> 00:38:29,910
+اللي موجود في ال current density كلها لهذا
+
+502
+00:38:29,910 --> 00:38:32,050
+الدائرة احنا جبناها لكن انا بديها ال a اللي موجود
+
+503
+00:38:32,050 --> 00:38:34,230
+في قلب اللي هي ال ring اللي أنا حطيتها ال imaginary
+
+504
+00:38:34,230 --> 00:38:38,550
+ring نفس الحاجة هكامل ρو D5D رو ال current density
+
+505
+00:38:38,550 --> 00:38:41,710
+constant بتطلع على برا فبكون عند ال total current
+
+506
+00:38:41,710 --> 00:38:45,290
+بعد ما اخد ال I عن المشترك بتساوي 1-R و تربيع مع
+
+507
+00:38:45,290 --> 00:38:50,470
+نسبة تربيع أ ت ت تربيع زي 2B ت ت تربيع ال 5 إذا هتساوى
+
+508
+00:38:50,470 --> 00:38:56,190
+I enclosed على 2 by rho لأكبر هذه الدقلة الأخيرة
+
+509
+00:38:56,190 --> 00:38:59,910
+اللي هو أكبر من B زي ال T هيكون عندي two currents
+
+510
+00:38:59,910 --> 00:39:03,510
+متساوين وإشارتهم سالبا in class I و minus I هتكون
+
+511
+00:39:03,510 --> 00:39:08,290
+zero واضحة الفكرة؟ طب احنا بس على السريع هي النتائج
+
+512
+00:39:08,290 --> 00:39:11,070
+بتاعتنا كانت اللي هي ما بين ال raw من zero ل a
+
+513
+00:39:11,070 --> 00:39:14,130
+قيمتها القدر ما بين ال a و b هي قيمتها القدر لقيظه
+
+514
+00:39:14,130 --> 00:39:18,650
+انها مالها خطية constant في raw h متساوئان في رو خط
+
+515
+00:39:18,650 --> 00:39:24,070
+مستقيم علاقة من h في raw ما بين a و b صحيح واحد
+
+516
+00:39:24,070 --> 00:39:27,770
+على raw فهي مضروبة some constant مضروف mean في
+
+517
+00:39:27,770 --> 00:39:32,340
+واحد على raw بعدينها شوي يعني بس مش كتير اصعب يعني
+
+518
+00:39:32,340 --> 00:39:36,320
+تقريبا جزء منها واحد على row التاني في جزء منه
+
+519
+00:39:36,320 --> 00:39:40,400
+rotor B فهيكون هذا الشكل فعاملا بنحدد ال limits
+
+520
+00:39:40,400 --> 00:39:45,320
+عند ال boundaries هنا هتكون عند ال A هتساوى I على
+
+521
+00:39:45,320 --> 00:39:49,480
+two by A اوضع ال row A فعند ال A هتكون قيمتها I
+
+522
+00:39:49,480 --> 00:39:53,920
+على two by A هأجينا هنا ال واحد على row فاش نهيتها
+
+523
+00:39:53,920 --> 00:39:59,830
+تكون عند ال B فاوضع هتكون I على two by B هذه اخر
+
+524
+00:39:59,830 --> 00:40:03,870
+واحدة هتبدأ من ال B لو قعدنا عن ال B هذا ال term
+
+525
+00:40:03,870 --> 00:40:08,210
+بيروح لل سفر هتكانها I على 2 by B صح؟ و اخر نقطة
+
+526
+00:40:08,210 --> 00:40:12,050
+اللي هي ال B زي T لو قعدت عن رو تربيع ال B زي T
+
+527
+00:40:12,050 --> 00:40:15,190
+هتكون B تربيع بتروح مع ناقص ب T إيش بيضلع لنا T
+
+528
+00:40:15,190 --> 00:40:19,390
+تربيع زي 2BT بروحوا مع بعض بيعطيني واحد واحد ناقص
+
+529
+00:40:19,390 --> 00:40:26,130
+واحد سفر هذه هي العلاقة بين H5 روك على طول
+
+530
+00:40:26,130 --> 00:40:31,790
+الكيوكسيا الكابر من أقل من A أكبر من A مابين ال B
+
+531
+00:40:31,790 --> 00:40:40,410
+و B زائد T و بعدين أكبر من B زائد T سهلة تطبيقها بعد 
+
+532
+00:40:40,410 --> 00:40:43,650
+ذلك اللقاء القادم هتشوف لو كان عندي two planes
+
+533
+00:40:43,650 --> 00:40:47,430
+هدول two planes واحد في current طالع من الصفحة
+
+534
+00:40:47,430 --> 00:40:51,110
+اتجاه ال X-axis واحد داخل الصفحة اتجاه ال Z-axis
+
+535
+00:40:51,110 --> 00:40:53,690
+او حتى يعني هذا لأنه تطبيق على المثال اللي احنا 
+
+536
+00:40:53,690 --> 00:40:57,450
+حليناه المرة الماضية بدي اكتحله في البيت يعني طبعا
+
+537
+00:40:57,450 --> 00:41:00,210
+اللي كنت تبقى اللي أنا كنت احكيه تحت ال plane of
+
+538
+00:41:00,210 --> 00:41:02,570
+all بين المطالب يعني نقطة هنا بين ال two planes
+
+539
+00:41:02,570 --> 00:41:05,650
+بتطلع هيكون ال magnetic field بالنسبة لهذا ال
+
+540
+00:41:05,650 --> 00:41:09,760
+plane فوقه لكن مجنتين بالنسبة لهذا البلاين ماله
+
+541
+00:41:09,760 --> 00:41:13,340
+تحته، لما النقطة صارت هنا عن العشرة، التنين كان
+
+542
+00:41:13,340 --> 00:41:19,200
+المجنت كيلو التنين ماله فوقهم، أول نقطة هنا هتكون،
+
+543
+00:41:19,200 --> 00:41:22,280
+هتكون بالنسبة لهذا البلاين مالها فوقها، هتكون
+
+544
+00:41:22,280 --> 00:41:25,980
+الإشارة موجبة، بالنسبة لهذا البلاين تحته، الإشارة
+
+545
+00:41:25,980 --> 00:41:29,220
+سالبة، لو النقطة هنا، هيكون بالنسبة لهذا البلاين
+
+546
+00:41:29,220 --> 00:41:32,720
+ماله فوقهم، بحلوه في البيت و بنقش اللقاء القادم إن
+
+547
+00:41:32,720 --> 00:41:33,020
+شاء الله
+
+548
+00:41:37,120 --> 00:41:39,440
+مافيش ضاعي إلا مثال واحد يعني، ان شاء الله أدى
+
+549
+00:41:39,440 --> 00:41:42,780
+الخمسة لقاء القادم و بنحلم اللي هي ال .. بقى أنا
+
+550
+00:41:42,780 --> 00:41:46,980
+كنت حاول نبدأ اللي هو الشفرة الأخيرة، يعطيكوا 
+
+551
+00:41:46,980 --> 00:41:47,720
+العافية إن شاء الله 
diff --git a/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/Fb7Ppx0QZeo_postprocess.srt b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/Fb7Ppx0QZeo_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..3d129e65c356a635a4c15a631d6a56a06244759e
--- /dev/null
+++ b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/Fb7Ppx0QZeo_postprocess.srt
@@ -0,0 +1,2204 @@
+1
+00:00:20,910 --> 00:00:23,410
+بسم الله الرحمن الرحيم السلام عليكم ورحمة الله
+
+2
+00:00:23,410 --> 00:00:27,270
+وبركاته احنا اليوم ان شاء الله هنتابع جزئية ال
+
+3
+00:00:27,270 --> 00:00:31,450
+magnetostatic fields احنا في الأمثلة وقفنا لحد ما
+
+4
+00:00:31,450 --> 00:00:34,930
+شوفنا كيف ال magnetic field ناتج عن ring قولنا
+
+5
+00:00:34,930 --> 00:00:38,170
+هنشوف كيف ان حساب magnetic field ناتج عن solenoid
+
+6
+00:00:38,170 --> 00:00:42,470
+ال solenoid هو عبارة عن مجموعة ringات مور فيهم ال
+
+7
+00:00:42,470 --> 00:00:47,280
+current اذا طلعناالمثال تبعنا هي ال solenoid وهي
+
+8
+00:00:47,280 --> 00:00:51,180
+current مر في قدر ال loops لإن كنتوا مهما اقطال
+
+9
+00:00:51,180 --> 00:00:54,940
+يمكننا يقولهم انه كأنهم خط continuous التيار بيجي
+
+10
+00:00:54,940 --> 00:00:57,400
+من طرفه وروح من طرف التاني تجاه ال current زى ما
+
+11
+00:00:57,400 --> 00:01:00,620
+انتوا شايفينه في المثال يعنى ال axis تبع ال
+
+12
+00:01:00,620 --> 00:01:06,260
+solenoid بنطبق على ال z axis و ال x axis عند أحد
+
+13
+00:01:06,260 --> 00:01:10,760
+أطرافه يعني ال zero هنا نصف القطر لل solenoid هو
+
+14
+00:01:10,760 --> 00:01:13,910
+ايه solenoid يعني استغالة زى هذههذه المرفوظة
+
+15
+00:01:13,910 --> 00:01:15,590
+الموجودة حول السلك المرفوظة في الطيارة وهي
+
+16
+00:01:15,590 --> 00:01:18,290
+المرفوظة الموجودة حول السيناير وان الماكنة تكفيت
+
+17
+00:01:18,290 --> 00:01:23,310
+في نقطة على ال axis اللى هي النقطة اللى معلمنيا
+
+18
+00:01:23,310 --> 00:01:28,030
+بيه بيه على الواقع ال axis on وماله بنطبق على ال z
+
+19
+00:01:28,030 --> 00:01:33,850
+axisطبعا النقطة B ممكن انا اجيب الزاوية اللى بتحد
+
+20
+00:01:33,850 --> 00:01:38,770
+مابين النقطة B و اطراف ال solenoid اللى هو الحط
+
+21
+00:01:38,770 --> 00:01:42,590
+مابين النقطة B و لو اللى ناتج عنها المجلة field من
+
+22
+00:01:42,590 --> 00:01:46,610
+النقطة اللى عند طرف الاقصى اليمين الزاوية هلاقيها
+
+23
+00:01:46,610 --> 00:01:51,430
+بسميها θ2 و الزاوية المابين النقطة اللى بتحسب
+
+24
+00:01:51,430 --> 00:01:54,250
+عندها المجلة field و طرف ال solenoid اللى هو اقصى
+
+25
+00:01:54,250 --> 00:01:58,230
+الشمال هسميها θ1 مابين ال axis اللى هو ال z axis و
+
+26
+00:01:58,230 --> 00:02:04,920
+النقطةوالزاوية بين اي element هاخده اسميه dz هذا
+
+27
+00:02:04,920 --> 00:02:08,680
+ال element و النقطة بتحسب عندها المجلة ال field مع
+
+28
+00:02:08,680 --> 00:02:13,140
+ال z axis هسميها theta تمام اول حاجة اهم اشي في
+
+29
+00:02:13,140 --> 00:02:16,480
+الصينات ان انا اعرف ان كيف ده اتعامل مع ال problem
+
+30
+00:02:16,480 --> 00:02:22,330
+هاي اول مطالب منهاانه ال magnet field عند اي نقطة
+
+31
+00:02:22,330 --> 00:02:27,170
+بي سوى ni على اتنين بكساين ست تنين نقص كساين ستة
+
+32
+00:02:27,170 --> 00:02:31,330
+واحد واتجاهه ال z axis طبعا ال z axis هذه احنا
+
+33
+00:02:31,330 --> 00:02:35,230
+فاهمينها قولنا احنا بنلف ايدنا حسب اللي هي right
+
+34
+00:02:35,230 --> 00:02:38,730
+hand rule اتجاه ال current لو كان على axis بنحط
+
+35
+00:02:38,730 --> 00:02:41,950
+اللي هو ال thumb تبعنا ال current و ايدنا بتمثل ال
+
+36
+00:02:41,950 --> 00:02:44,770
+magnet field فدقت عشان اعرف اتجاه ال magnet field
+
+37
+00:02:44,770 --> 00:02:49,820
+بلف ايدي مع التيار التيارطالع من هنا و داخل هنا،
+
+38
+00:02:49,820 --> 00:02:52,660
+إيش هتكون لفة إيدي؟ طالع من هنا و داخل .. و اين
+
+39
+00:02:52,660 --> 00:02:55,540
+تجهة ال magnetic field؟ في تجاه ال z-axis، هاي
+
+40
+00:02:55,540 --> 00:02:58,040
+تجهة ال magnetic field، احنا عارفينه already، لإنه
+
+41
+00:02:58,040 --> 00:03:02,620
+من ال right hand rule، القرن طالع من هنا و داخل في
+
+42
+00:03:02,620 --> 00:03:07,150
+تجهة التطبيق، إذا هاتجهة من هناحيث أن من هي أن هي
+
+43
+00:03:07,150 --> 00:03:11,170
+عدد اللفات per unit length يعني لو أخدتلي طول معين
+
+44
+00:03:11,170 --> 00:03:15,490
+ال هيكون عدد اللفات per unit length اللي هي أن أن
+
+45
+00:03:15,490 --> 00:03:19,050
+من كل عدد اللفات اعدي أن من اللفات أن per unit
+
+46
+00:03:19,050 --> 00:03:23,220
+length هعطيني small أنوستة واحد وستة اتنين عرفناهم
+
+47
+00:03:23,220 --> 00:03:27,680
+وستة اتنين هي الزاوية اللى بتحد ال solenoid من
+
+48
+00:03:27,680 --> 00:03:30,800
+أقصى اليمين اللى هو يعني الخط الزاوية بين الخط
+
+49
+00:03:30,800 --> 00:03:34,040
+الواصل بين ال magrav field المور في أقصى اليمين ال
+
+50
+00:03:34,040 --> 00:03:37,040
+current عند أقصى يمين ال solenoid و النقطة البقية
+
+51
+00:03:37,040 --> 00:03:40,460
+عند ال magrav field مع ال z axis هى ستة اتنين وستة
+
+52
+00:03:40,460 --> 00:03:44,720
+واحد بالمتل اللى مع طرف الأقصى اليسار تبع ال
+
+53
+00:03:44,720 --> 00:03:49,220
+solenoid تمام اش كمان بقولنا كمان illustrate
+
+54
+00:03:50,960 --> 00:03:54,580
+الأشياء ذات إذا كان L أكبر بكتير من L هو طول
+
+55
+00:03:54,580 --> 00:03:57,200
+السيلونويد زي ما انتوا شايفينه إذا كان أكبر بكتير
+
+56
+00:03:57,200 --> 00:04:00,420
+من L هو نصف طول السيلونويد هتتبسط هاي المعادلة
+
+57
+00:04:00,420 --> 00:04:04,280
+لأكتشر 1000 في I على طول و اتجاهها بتغير عشان هو Z
+
+58
+00:04:04,280 --> 00:04:10,360
+هذا أول حاجة بنتعامل معها ان السيلونويد هو مجموعة
+
+59
+00:04:10,360 --> 00:04:14,300
+من circular loops ملاسقين في بعض مكترتهم كأنهم
+
+60
+00:04:14,300 --> 00:04:18,940
+continuous loops يعني بعضها راحت DZ زي ما انتوا
+
+61
+00:04:18,940 --> 00:04:23,980
+شايفين هي DZواللي بيحد ما بين هذا ال element اللي
+
+62
+00:04:23,980 --> 00:04:28,240
+أخدته و النقطة بيحسب عندها ال magnet field مع
+
+63
+00:04:28,240 --> 00:04:32,080
+الذبذ أكسر زاوية بنسميها z تمام؟ اذا مين ال
+
+64
+00:04:32,080 --> 00:04:35,860
+element تبعي؟ ال element تبعي هاخده اللي هو dH هو
+
+65
+00:04:35,860 --> 00:04:38,660
+ال magnet field الناتج من مين؟ من ال loop ان
+
+66
+00:04:38,660 --> 00:04:42,020
+النقطة بيه المagnet فيها لو انا اتخيلت عند الذبذ
+
+67
+00:04:42,020 --> 00:04:46,440
+هاي النقطة عندي ذبز هاي دي ذبز بتاعتي وهي نقطة عند
+
+68
+00:04:46,440 --> 00:04:49,640
+ال loop وهذا ال loop هو ال element تبعي اذا ال dH
+
+69
+00:04:49,640 --> 00:04:52,780
+هيكون هوالـ magnetic field اللى ناتجة على هذه
+
+70
+00:04:52,780 --> 00:04:56,700
+النقطة من وين؟ من ال loop اللى هو الحسب في المثال
+
+71
+00:04:56,700 --> 00:04:59,100
+السابق و اللى حسبته في ال .. في ال .. في ال .. في
+
+72
+00:04:59,100 --> 00:05:06,780
+البيت طبعا فإذا DH هيكون هو ال magnetic field اللى
+
+73
+00:05:06,780 --> 00:05:11,780
+ناتج من رنك اللى ال thickness تبعه DZ أو DL هيكون
+
+74
+00:05:11,780 --> 00:05:16,060
+I فهو كذبع I ρو تربية كنا ماخدين ال radius تبع ال
+
+75
+00:05:16,060 --> 00:05:21,940
+loopI A تربيه على اتنين A تربيه زي زي تربيه اقوى
+
+76
+00:05:21,940 --> 00:05:29,140
+تلاتة ع اتنين و DL لان انا انادي D HZ تمام اعوض عن
+
+77
+00:05:29,140 --> 00:05:35,720
+ايش عن DL DL هي عبارة عن NDZ DL هي عبارة عن NDZ
+
+78
+00:05:35,720 --> 00:05:40,880
+اللى هو جزئية DL اللى هي النقطة اللى على ال hoop
+
+79
+00:05:40,880 --> 00:05:47,880
+تبعى عبارة عن NDZتمام حلت عشان اجيب ال HZ بتبدأ
+
+80
+00:05:47,880 --> 00:05:52,420
+كامل يعني البداية كذلك البداية ان اول حاجة بتخيل
+
+81
+00:05:52,420 --> 00:05:56,180
+ايش هي انها ضارع ال ringات و كل ring بتأثر على
+
+82
+00:05:56,180 --> 00:05:58,360
+magnet field احد هذه النقطة ب magnet field اكيد
+
+83
+00:05:58,360 --> 00:06:01,540
+magnet field اللي من ال ring اذا ال element هو من
+
+84
+00:06:01,540 --> 00:06:02,260
+ال ring
+
+85
+00:06:06,970 --> 00:06:09,870
+التغير او ال element بتاعي هو dH بكارنوت بتعطينا
+
+86
+00:06:09,870 --> 00:06:13,890
+كل المعلن فيه للنتج عند النقطة بتاعتي DL هي N DZ
+
+87
+00:06:13,890 --> 00:06:18,230
+اذا بعوض عن N اللي هي capital N على L زي ما هو
+
+88
+00:06:18,230 --> 00:06:20,970
+عرفنا إياها اللي هي number of rings per unit
+
+89
+00:06:20,970 --> 00:06:27,170
+length بDZعشان ان كامل هذا ال integration مجرد ان
+
+90
+00:06:27,170 --> 00:06:31,190
+هدا خلص ال مثال بس هذا اللي ما بعده هو قضية كيف
+
+91
+00:06:31,190 --> 00:06:34,590
+نأحل ال integral كما لو قولنا ان تان ثتا من هى تان
+
+92
+00:06:34,590 --> 00:06:37,950
+ثتا هى ثتا التار دبعها المقابلة على المجاور قبل
+
+93
+00:06:37,950 --> 00:06:42,570
+مين و أكبر عن اين و ايه المجاور هو z اذا تان ثتا
+
+94
+00:06:42,570 --> 00:06:46,050
+هو ايه على z و اشتكب اتفاضلها عشان دي بدي z
+
+95
+00:06:47,770 --> 00:06:51,030
+سيكنتربير بس احنا بدنا ال z فبنشقلب بنحط ال z
+
+96
+00:06:51,030 --> 00:06:55,850
+بتسوء a على ten theta فd z أشبه سوء a كسيكنتربير
+
+97
+00:06:55,850 --> 00:06:59,970
+لأن a على ten اللي هي مين كتان و تفاضل كتان minus
+
+98
+00:06:59,970 --> 00:07:04,430
+كسيكنتربير تتا دي ستة فده هي كسيكنتربير اذا d z هي
+
+99
+00:07:04,430 --> 00:07:08,990
+minus a كسيكنتربير التان تفاضلها سيكنتربير كتان
+
+100
+00:07:08,990 --> 00:07:11,950
+minus كسيكنتربير اذا احنا زي ما حكيتلكم
+
+101
+00:07:15,610 --> 00:07:20,470
+كيف أني بدي أحل ال integrationبحقوط عن هذه الأرقاب
+
+102
+00:07:20,470 --> 00:07:25,690
+اللي حصلت عنها بحصل على حجم مبسط جدا ل dz minus ni
+
+103
+00:07:25,690 --> 00:07:30,450
+على 2 sin θ d6 مجرد ان اعوض عن اللي هي أن tan θ a
+
+104
+00:07:30,450 --> 00:07:34,830
+على z او z بساوي a كتان ثتا و التفاضل اعوض عنها
+
+105
+00:07:34,830 --> 00:07:38,490
+لان زى ما تشوفين هدا بروح مع هدا و ال a تربية
+
+106
+00:07:38,490 --> 00:07:43,770
+بتروح مع ال a تربية لو عوضت عن dz ايش بيظل عندي in
+
+107
+00:07:43,770 --> 00:07:48,450
+على 2 sin θ d6 واضح؟
+
+108
+00:07:50,790 --> 00:07:54,190
+لما اجي اكمل ستة منهم بدي اكملها من ستة واحد لستة
+
+109
+00:07:54,190 --> 00:07:59,450
+اتنين ناقص ن I على اتنين ال sign ايش تكمل ال sign
+
+110
+00:07:59,450 --> 00:08:02,970
+اللي هو ال cosine او minus cosine minus cosine
+
+111
+00:08:02,970 --> 00:08:08,110
+تفضلها بتاعتنا ال sign فبتروح ال minus مع ال sign
+
+112
+00:08:08,110 --> 00:08:11,610
+ب cosine اعوض على ال cosine ستة اتنين minus يعني
+
+113
+00:08:11,610 --> 00:08:13,650
+ال cosine ستة اتنين minus ال cosine ستة واحدة
+
+114
+00:08:13,650 --> 00:08:18,030
+المشكلة اذا ال H اللي هي تجاهة بالزد اكسسهي Ni على
+
+115
+00:08:18,030 --> 00:08:22,750
+2 Cos 6 N minus Cos 6 1 Z hat زي ما هو طالب هو هيك
+
+116
+00:08:22,750 --> 00:08:27,370
+طالب بالنسبة اذا كل الفكرة ان اتخيل ان Solenoid
+
+117
+00:08:27,370 --> 00:08:31,510
+عبارة عن رنجات و اخد دي actual magnetic field ناتج
+
+118
+00:08:31,510 --> 00:08:33,390
+من واحد من هاد دولار رنجات
+
+119
+00:08:38,160 --> 00:08:40,840
+طب الخطوة التانية طالب مننا اللى هى انه لما تصير
+
+120
+00:08:40,840 --> 00:08:43,720
+قال اكبر كتير من اى فعشان هيك انا بدي اجيب علاقة
+
+121
+00:08:43,720 --> 00:08:46,500
+بين مين قاله ايه مافيش هنا في هذه العلاقة اللى
+
+122
+00:08:46,500 --> 00:08:49,480
+قدامى علاقة بين قاله ايه من هم بدي اجيبها من قيم
+
+123
+00:08:49,480 --> 00:08:52,640
+ال cosine اذا تطلع على cosine ستة واحد و cosine
+
+124
+00:08:52,640 --> 00:08:55,720
+ستين طبعا هو ايش حاجة اول حاجة بدي اجيبها عند ال
+
+125
+00:08:55,720 --> 00:08:57,440
+center لأنه عند ال center
+
+126
+00:09:02,360 --> 00:09:06,400
+اللي هي at the center of the solenoid هو بده إذا
+
+127
+00:09:06,400 --> 00:09:09,440
+كانت L أكبر من A at the center of the solenoid
+
+128
+00:09:09,440 --> 00:09:12,500
+فإذا بده أروح للcenter يعني أتخيل بيه صار تمام عند
+
+129
+00:09:12,500 --> 00:09:15,200
+ال center of the solenoid يعني صار على شمالها
+
+130
+00:09:15,200 --> 00:09:19,260
+ويمينها L على 2 فهذه اللحظة إيش بيصير في ستة واحد
+
+131
+00:09:19,260 --> 00:09:22,380
+وستة اتنين هاي الرسمة هنا لما تصير بيه في ال
+
+132
+00:09:22,380 --> 00:09:25,520
+center تبع ال solenoid cosine ستة واحد و cosine
+
+133
+00:09:25,520 --> 00:09:28,900
+ستة اتنين بيساوي بعض و بيشارع سالبة لإن كل واحدة
+
+134
+00:09:28,900 --> 00:09:35,610
+إش بتمامه بيكون L على 2وعلى مين اللي هو الوطر اللي
+
+135
+00:09:35,610 --> 00:09:39,610
+هو عبارة عن آن تربية زائد أقل على اتنين تربية تحت
+
+136
+00:09:39,610 --> 00:09:47,150
+الجزر صح؟ لو احنا زحفت هذه النقطة هسترونويد وصارت
+
+137
+00:09:47,150 --> 00:09:52,090
+D المتصرف يعني ما صار ليه D أقل على اتنين ما صارت
+
+138
+00:09:52,090 --> 00:09:55,730
+كلها دي مجرد رياضيات يعني قبل هيك هو الحاجة
+
+139
+00:09:55,730 --> 00:10:01,400
+المفيدة هي θتة واحد وهي ثتة ثمانيةكل واحدة جيب
+
+140
+00:10:01,400 --> 00:10:05,960
+تلوها إيش هو المجاور على وطن هو جزر التنبيه لإيه
+
+141
+00:10:05,960 --> 00:10:10,440
+تنبيه زي أقل على 2 ويكون تنبيه بس الفرق منهم واحدة
+
+142
+00:10:10,440 --> 00:10:14,320
+سالبة لأنها جيب ليه أكتر من تسعين فهي جيب تلوها
+
+143
+00:10:14,320 --> 00:10:17,060
+سالب وهي جيب تلوها مجاور أما التنتين جيب تلوهم
+
+144
+00:10:17,060 --> 00:10:20,980
+اللي هو ألعلى على 2 ويقل وطنهم لذا هم بيساووا واحد
+
+145
+00:10:20,980 --> 00:10:23,520
+لكن ال cosine ستة تنين بيساووا سالق cosine ستة
+
+146
+00:10:23,520 --> 00:10:26,920
+واحد اللي هو إيش بيساوي المجاور اللي هو ألعلى على
+
+147
+00:10:26,920 --> 00:10:31,850
+2 على مين المجاوربس الكتر كيساين الكساين الوقال
+
+148
+00:10:31,850 --> 00:10:37,690
+على اتنين على الوتر لو عوضنا عن كساين ستة اتنين
+
+149
+00:10:37,690 --> 00:10:40,530
+كساين ستة واحد ايش بيصير واحدة منهم سلب التانية
+
+150
+00:10:40,530 --> 00:10:43,690
+كساين ستة واحد اتنين بتساوي سلب كساين ستة واحد
+
+151
+00:10:43,690 --> 00:10:47,490
+فبيصير عندي مجموع اتن تان كساين ستة اتنين بتساوي
+
+152
+00:10:47,490 --> 00:10:52,050
+سلب كساين ستة واحد فبيصير عندي minus ni على اتنين
+
+153
+00:10:52,050 --> 00:10:56,700
+الف كساين ستة مينالتي هي 2 او كسين سيتا واحد لان
+
+154
+00:10:56,700 --> 00:10:59,900
+كسين سيتا واحد اللي احنا متأكدة هي L على 2 فناخدها
+
+155
+00:10:59,900 --> 00:11:04,180
+هي فبعوض عن كسين سيتا تينين على هيك حاجات minus
+
+156
+00:11:04,180 --> 00:11:07,980
+سيتا واحد اللي هي مينج بتعمل سيتا واحد L على 2 على
+
+157
+00:11:07,980 --> 00:11:11,700
+اللي هو جزر التربيه لأي تربيه زي L تينين على أربع
+
+158
+00:11:11,700 --> 00:11:16,300
+تحت الجزر فهي كسين سيتا تينين كسين سيتا تينين
+
+159
+00:11:16,300 --> 00:11:19,790
+الموجبة و سيتا واحد اللي هي السالبةعشان هيك احنا
+
+160
+00:11:19,790 --> 00:11:26,310
+عوضنا لـcosθ2 cosθ1 تبدأ لـcosθ2 cosθ2 ليه هذه
+
+161
+00:11:26,310 --> 00:11:35,110
+الحادة هي L على 2 L على 2 على جزر التربيه لإيه
+
+162
+00:11:35,110 --> 00:11:38,330
+التربيه L على 2 L على 2 لإيه التربيه لإيه التربيه
+
+163
+00:11:38,330 --> 00:11:38,970
+لإيه التربيه لإيه التربيه لإيه التربيه لإيه
+
+164
+00:11:38,970 --> 00:11:39,290
+التربيه لإيه التربيه لإيه التربيه لإيه التربيه
+
+165
+00:11:39,290 --> 00:11:43,470
+لإيه التربيه لإيه التربيه لإيه التربيه لإيه التر
+
+166
+00:11:44,870 --> 00:11:48,890
+بصير اتنين كوصين ستة اتنين اي بعوض عن كوصين ستة
+
+167
+00:11:48,890 --> 00:11:51,550
+واحد بسب كوصين ستة اتنين فبصير plus كوصين ستة
+
+168
+00:11:51,550 --> 00:11:54,830
+اتنين لو تصير اتنين ن اي على اتنين ال بتروح
+
+169
+00:11:54,830 --> 00:11:58,310
+الاتنين مع اتنين لو تصير ن اي على ال كوصين ستة
+
+170
+00:11:58,310 --> 00:12:00,890
+اتنين اللى هى مين كوصين ستة اتنين ال على اتنين على
+
+171
+00:12:00,890 --> 00:12:06,990
+الجزر نعود فى H زى ما انا عوضت بتاعكم هتكون I n أل
+
+172
+00:12:06,990 --> 00:12:10,950
+على اتنين ا تربيه زى ده تربيه على أربع تحت الجزر
+
+173
+00:12:10,950 --> 00:12:16,560
+طريقة الاتجاه Z hat تمامالتاني بتيجي من أقل على
+
+174
+00:12:16,560 --> 00:12:20,140
+اتنين لان اتنين كوساين بتضيع التاني اللي هنا وفيه
+
+175
+00:12:20,140 --> 00:12:25,360
+الاقل على اتنينهل إنت لو كانت L أكبر بكتير من A L
+
+176
+00:12:25,360 --> 00:12:28,720
+كبير كتير لأن دول صعار infinity صعار طوله infinity
+
+177
+00:12:28,720 --> 00:12:33,460
+لكن قطره ضاله A نص قطره إيش بيصير؟ L كبيرة كتير
+
+178
+00:12:33,460 --> 00:12:37,200
+بالنسبة ل A بحمل ال A بتصير تقريبا سفر ال A
+
+179
+00:12:37,200 --> 00:12:41,220
+بالنسبة لل links فإيش بيصير هذا؟ L على 2 هى بتروح
+
+180
+00:12:41,220 --> 00:12:46,320
+السفر بيصير IML على 2 وهى بتطلع من دحت جزر L على 2
+
+181
+00:12:46,320 --> 00:12:49,000
+التنين بتروح مع التنين و L بتروح مع ال L بيظهر مين
+
+182
+00:12:49,000 --> 00:12:50,940
+M في I واضح؟
+
+183
+00:13:01,480 --> 00:13:10,220
+هو I NL على 2L تربيه على 4 تحت الجسر سبقها هذي
+
+184
+00:13:10,220 --> 00:13:14,600
+تصير I NL على 2L على 2
+
+185
+00:13:24,290 --> 00:13:27,810
+لو عوضنا عن N انها capital N per unit length
+
+186
+00:13:27,810 --> 00:13:30,890
+فهتكون ال magnetic field عند ال center تبع ال
+
+187
+00:13:30,890 --> 00:13:34,330
+solenoid infinite solenoid مش اللي هو ال finite
+
+188
+00:13:34,330 --> 00:13:38,390
+infinite solenoid بيكون ال magnetic field عند ال
+
+189
+00:13:38,390 --> 00:13:43,810
+center بيساوي عدد اللفات في ال current على طول ال
+
+190
+00:13:43,810 --> 00:13:45,690
+solenoid في اتجاه ال z hat
+
+191
+00:13:48,920 --> 00:13:52,740
+ميجي لانبيرز سيركت لاو او Maxwell's equation
+
+192
+00:13:52,740 --> 00:13:56,080
+انبيرز لاو ايش بقولنا انه ال integration او ال
+
+193
+00:13:56,080 --> 00:13:59,740
+clause integral لل tangential magnetic field على
+
+194
+00:13:59,740 --> 00:14:01,740
+closed path ال tangential magnetic field على
+
+195
+00:14:01,740 --> 00:14:04,420
+closed path ايش معناه؟ تت ال product H تت ال
+
+196
+00:14:04,420 --> 00:14:07,290
+closed pathطبت اللي هو ال element في ال closed
+
+197
+00:14:07,290 --> 00:14:10,190
+path اذا ال integration لل tangential component
+
+198
+00:14:10,190 --> 00:14:12,730
+around a closed path بتساوي مين ال enclosed
+
+199
+00:14:12,730 --> 00:14:17,990
+current بتساوي التيار اللي في قلب ال loop او ال
+
+200
+00:14:17,990 --> 00:14:22,130
+closed path عشان يكون نوع ال closed path اذا I
+
+201
+00:14:22,130 --> 00:14:27,920
+enclosed بتساوي ال closed pathالـ h.dl لو استخدمت
+
+202
+00:14:27,920 --> 00:14:32,280
+stock theorem بتقول
+
+203
+00:14:32,280 --> 00:14:35,280
+الـ closed path لل field.dl بيساوي ال surface
+
+204
+00:14:35,280 --> 00:14:40,400
+integral لكل ال field.ds
+
+205
+00:14:47,000 --> 00:14:49,560
+الـ Current هو عبارة عن Surface Integral لـ
+
+206
+00:14:49,560 --> 00:14:52,860
+Current Density دو الـ Ds لو قررنا ال two
+
+207
+00:14:52,860 --> 00:14:56,180
+equations بلاقى ان ال Surface Integral لكرل الـ H
+
+208
+00:14:56,180 --> 00:14:59,860
+بالـ Ds بيساوي Surface Integral لجهده الـ Ds لإنهم
+
+209
+00:14:59,860 --> 00:15:04,220
+بيساوي ال enclosed current من Amberslaw اللي هو
+
+210
+00:15:04,220 --> 00:15:07,620
+هيتعريفه Amberslaw اللي هو ال clause line لتنجش ال
+
+211
+00:15:07,620 --> 00:15:10,140
+component ما يفيض around a clause بس هو enclosed
+
+212
+00:15:10,140 --> 00:15:14,860
+استنتجت انكرل الـ H بيساوي جهد هذه بنسميها third
+
+213
+00:15:14,860 --> 00:15:18,570
+Maxwell's equationthird Maxwell's equation صار لنا
+
+214
+00:15:18,570 --> 00:15:22,050
+تلاتة Maxwell's equation اذا كل اتش بيساوي جيه؟
+
+215
+00:15:22,050 --> 00:15:26,130
+ايش مستنتج انه كل اتش بيساوي جيه؟ انه اول هي مالها
+
+216
+00:15:26,130 --> 00:15:30,370
+rotational كلها لا يساوي صفر فهي rotational و حاجة
+
+217
+00:15:30,370 --> 00:15:33,650
+تانية انها non conservative انا بقول لأ ال
+
+218
+00:15:33,650 --> 00:15:37,250
+electric field كل ال E بيساوي zero هو قولنا ماله
+
+219
+00:15:37,250 --> 00:15:41,910
+irrotational بيلفشوكمان conservative لكن ال
+
+220
+00:15:41,910 --> 00:15:45,690
+magnetic field curl H بساوة J فهو ماله أولا إله
+
+221
+00:15:45,690 --> 00:15:49,610
+curl curlه rotational يعني و تاني حاجة is not
+
+222
+00:15:49,610 --> 00:15:50,310
+conservative
+
+223
+00:15:56,930 --> 00:15:59,710
+لو احنا اعتبر النوبة دي انها ب infinitely long
+
+224
+00:15:59,710 --> 00:16:03,530
+filament او wire يعني بنسميها filament او wire
+
+225
+00:16:03,530 --> 00:16:06,790
+اللي مور فيها تيار اه اذا ما انتوا شايفينها رسمها
+
+226
+00:16:06,790 --> 00:16:10,390
+وناخد ال filament واقع على ال z axis اذا ال
+
+227
+00:16:10,390 --> 00:16:12,930
+filament بتاعتي او ال wire اللي مور فيه تيار واقع
+
+228
+00:16:12,930 --> 00:16:16,110
+على ال z axis نفس القضية بقدر احدد اتجاه magnetic
+
+229
+00:16:16,110 --> 00:16:19,590
+field على طول من ال right hand rule ال current على
+
+230
+00:16:19,590 --> 00:16:22,070
+ال z axis و الاتجاه ال magnetic field اتجاه أيدي
+
+231
+00:16:22,070 --> 00:16:25,670
+اللي هو ايش هيكون اتجاه فيهات انه هي raw hat
+
+232
+00:16:29,910 --> 00:16:33,390
+فالاتجاه counter clockwise هتكون الـ Phi hat لو
+
+233
+00:16:33,390 --> 00:16:37,310
+كان لتحت هتكون minus Phi hat تمام؟ اذا احنا
+
+234
+00:16:37,310 --> 00:16:40,650
+المجنون الكبير طبعنا هيكون بلف حوالين ال wire
+
+235
+00:16:40,650 --> 00:16:44,810
+اتجاه ال Phi hat لو انا بتاخد اللي هو ال current
+
+236
+00:16:44,810 --> 00:16:47,710
+احنا ايش قايل ان ال current بيساوي؟ ال current
+
+237
+00:16:47,710 --> 00:16:51,650
+بيساوي ال clause integral ل H2TL اللي هو ايش
+
+238
+00:16:51,650 --> 00:16:56,710
+هيساوي؟ ال DL بتذكرين ال DL ايش بتساوي؟ rho D Phi
+
+239
+00:17:02,790 --> 00:17:09,590
+DL قوس رو دي فاي واتجاه فاي هات فاي هات وعندي
+
+240
+00:17:09,590 --> 00:17:13,110
+الماقن فيلد انه في اتجاه فاي هات لازم هيكون H5 فاي
+
+241
+00:17:13,110 --> 00:17:18,110
+هات ال product تبعهم هو H5 رو دي فاي رو constant
+
+242
+00:17:18,110 --> 00:17:22,650
+لانها ring هذهالـ rho تبقى حسب مين بتغير ال phi من
+
+243
+00:17:22,650 --> 00:17:26,990
+zero ل two pi فهذا هتكون H phi two pi rho وبالتالي
+
+244
+00:17:26,990 --> 00:17:31,910
+H vector بتسوي I على two pi rho فى اتجاه ال πهاد،
+
+245
+00:17:31,910 --> 00:17:36,970
+فهذا ال magnetic field اللى ناتج من filament موقع
+
+246
+00:17:36,970 --> 00:17:38,130
+على z اكسس
+
+247
+00:17:42,090 --> 00:17:45,070
+لو انا بدى احسب ال magnetic field اللى ناتج من مين
+
+248
+00:17:45,070 --> 00:17:48,190
+من sheet انا عندى sheet هال اتا و هذا ال sheet
+
+249
+00:17:48,190 --> 00:17:51,630
+ماله infinitely بتمدد infinitely اتجاه ال X و ال Y
+
+250
+00:17:51,630 --> 00:17:57,690
+واقع ان Z equal 0 واقع ان Z equal 0 و بدى احسب ال
+
+251
+00:17:57,690 --> 00:18:01,630
+magnetic field اللى ناتج من هذه ال sheet اللى
+
+252
+00:18:01,630 --> 00:18:04,610
+بيهور فيها ال current زى ما انتوا شايفينه surface
+
+253
+00:18:04,610 --> 00:18:09,280
+currentكي بتساوي ky ay يعني اتجاهه يعني هذا ال
+
+254
+00:18:09,280 --> 00:18:12,120
+surface كانت أول الحاجة يعني لانفهمها ان انا بقدر
+
+255
+00:18:12,120 --> 00:18:16,740
+اعتبره انه حطوط من filaments يعني هو اعباره عن
+
+256
+00:18:16,740 --> 00:18:24,980
+تيار بتطفوق على ال surface بتاع ال sheet عايزة
+
+257
+00:18:24,980 --> 00:18:29,320
+نفسي اكتر حقيبتي يعني فانا ايش ممكن اتخيله انه كل
+
+258
+00:18:29,320 --> 00:18:33,120
+واحد هو مثل اياش filament نفس السؤال اللي السابق
+
+259
+00:18:33,950 --> 00:18:39,130
+أتخيلوا خطوط كل حط ماله حامل current density درها
+
+260
+00:18:39,130 --> 00:18:44,630
+ky و y hat هي اتجاه ال current بتضغط في اتجاه ال y
+
+261
+00:18:44,630 --> 00:18:48,530
+direction اذا هفترضوا ال surface هذا عبارة عن
+
+262
+00:18:48,530 --> 00:18:53,010
+filaments يعني خطوط نقل زي اللي هو في المثال اللي
+
+263
+00:18:53,010 --> 00:18:58,190
+قبله filaments اللي ملزقين في بعض فهم بيعملولي ال
+
+264
+00:18:58,190 --> 00:19:04,520
+plan و ال current هو current densityكي ويهات الهى
+
+265
+00:19:04,520 --> 00:19:08,420
+current per length and inverse per meter الهى ال
+
+266
+00:19:08,420 --> 00:19:12,860
+current density اللى هناخدله فى هالحالة ال
+
+267
+00:19:12,860 --> 00:19:16,100
+symmetry تبع ال problem هاخد rectangle مش هاخد
+
+268
+00:19:16,100 --> 00:19:19,520
+استوانه هاخد rectangular لإن هى عندى ال surface
+
+269
+00:19:19,520 --> 00:19:25,480
+مربعة مش دائرة مش هو ولا دائرة مليانة ال surface
+
+270
+00:19:25,480 --> 00:19:28,740
+تبعى مربع فده ال symmetry هاخد اللى هو زى ما كنتوا
+
+271
+00:19:28,740 --> 00:19:33,820
+شايفين المستطيل اللى قدامىاللي بتحسب عليه لإنه
+
+272
+00:19:33,820 --> 00:19:38,140
+احنا عارفين انه هيكون magnet field حوالاه طال إيه
+
+273
+00:19:38,140 --> 00:19:40,220
+طال يعني مش هيكون في البلاد
+
+274
+00:19:50,060 --> 00:19:52,880
+عشان انا افهم ايش اللي بيصير احنا قلنا ايش هسويه
+
+275
+00:19:52,880 --> 00:19:59,000
+هم file elements فهي انا بتقعد ال x axis ال dress
+
+276
+00:19:59,000 --> 00:20:02,340
+ده تبسيط هي ال x axis عندى انا two file elements
+
+277
+00:20:02,340 --> 00:20:04,360
+واحدة بتقطع من هنا و واحدة بتقطع من هنا
+
+278
+00:20:11,670 --> 00:20:14,870
+فهي الـ filament اللى عندها هذه النقطة والـ
+
+279
+00:20:14,870 --> 00:20:18,530
+filament اللى عندها هذه النقطة بالتمام او اي نقطة
+
+280
+00:20:18,530 --> 00:20:21,050
+تانية مش فارقة يعني بس ناخد دولة النقطة تانية
+
+281
+00:20:21,050 --> 00:20:25,590
+قسمها بساعة ولو اخد المربع اكبر او اصغر اخد اي
+
+282
+00:20:25,590 --> 00:20:31,210
+نقطة تانية على ال axis اي نقطة تانية واضح؟ على ال
+
+283
+00:20:31,210 --> 00:20:34,330
+X axis ايش شكلهم التانية؟ كيف بيقطعوا ال X axis؟
+
+284
+00:20:34,330 --> 00:20:38,330
+هاي ال X axis بيقطعوا التانية طالعين منها التانية
+
+285
+00:20:38,330 --> 00:20:43,300
+طالعين منها فهذه ال X axisهذا X-axis وهذه ال
+
+286
+00:20:43,300 --> 00:20:46,680
+filaments اللي تنتهي من هنا طالعين من هنا وهذه
+
+287
+00:20:46,680 --> 00:20:50,500
+الواحدة وهذه التانية two filaments على ال X-axis
+
+288
+00:20:50,500 --> 00:20:58,900
+وتنتين طالعين من هنا ومن هنا كل
+
+289
+00:20:58,900 --> 00:21:01,780
+filament لحالها من المثال السابق أشهرنا ال
+
+290
+00:21:01,780 --> 00:21:06,760
+magnetic field ناتج منها هي دائرة
+
+291
+00:21:09,450 --> 00:21:11,950
+بنعمل نفس الحاجة لكل واحدة من هادولة ال fire mint
+
+292
+00:21:11,950 --> 00:21:15,130
+هاد ال fire mint المغناطك هي بالنتج منها
+
+293
+00:21:15,130 --> 00:21:19,350
+tangential لدائرة يعني إذا ما رسمتش الدائرة بتبقى
+
+294
+00:21:19,350 --> 00:21:25,950
+بسمها الدكتور يصعد
+
+295
+00:21:25,950 --> 00:21:29,190
+زي ال .. زي ال .. بيطلس مش مشكلة قريبة من الدائرة
+
+296
+00:21:29,190 --> 00:21:32,410
+صح؟ شوية قريبة من الدائرة ولا بيبقى قريبة من
+
+297
+00:21:32,410 --> 00:21:41,170
+الدائرة؟ قريبة؟ تشبهها؟ أسام فيه إيديعال ال z axis
+
+298
+00:21:41,170 --> 00:21:44,350
+او يعني قريب لو انا اتطلع اعيش ال magnet field
+
+299
+00:21:44,350 --> 00:21:47,510
+هلاقي انه عند اي نقطة مثلا لو أخدها ال z axis
+
+300
+00:21:47,510 --> 00:21:51,110
+واحده هتكون هنا و واحده هتكون هنا tangential
+
+301
+00:21:51,110 --> 00:21:55,470
+tangential لمين اللي اللي عندها نفس الشيء لو فكرت
+
+302
+00:21:55,470 --> 00:22:00,150
+في ال filament اللي هنا هيكون عندي برضه في دائرة
+
+303
+00:22:00,150 --> 00:22:06,990
+مافيش
+
+304
+00:22:06,990 --> 00:22:10,630
+فعلا بس هنكملهابس هذه الدائرة برضه المجنة الكفيل
+
+305
+00:22:10,630 --> 00:22:15,250
+تنتج عن هذه ال file من ال tangent لها طبعا هذا
+
+306
+00:22:15,250 --> 00:22:19,050
+الحكي بنطبق على كل ال filements اللي هو عيين على
+
+307
+00:22:19,050 --> 00:22:23,010
+ال x-axis صحيح؟ طبعا و طلعنا نعدلها to fields إذا
+
+308
+00:22:23,010 --> 00:22:26,070
+مثلا ما عارفين أنه عند أي نقطة هيكون فيه two
+
+309
+00:22:26,070 --> 00:22:30,050
+fields عند أي نقطة هيكون فيه two fields واحد ناتج
+
+310
+00:22:30,050 --> 00:22:35,210
+من مين؟ من ال filement فانا راح أدلها المجنة
+
+311
+00:22:35,210 --> 00:22:39,950
+الكفيل الناتج من هذا ال filementوحدة نجم من هذا
+
+312
+00:22:39,950 --> 00:22:47,050
+الوضع و وحدة نجم من هذا الوضع هاي ال 6 اكس اش
+
+313
+00:22:47,050 --> 00:22:53,430
+هلاحظ انه لو انا حللت ال h1 و ال h2 هيتكون في يدي
+
+314
+00:22:53,430 --> 00:22:59,710
+تلتي h1 component ال x و 1 في zواتشنين هيكون واحدة
+
+315
+00:22:59,710 --> 00:23:02,510
+في ال X واحدة في ال Z طب هم بيساوي بعض مافيش فرق
+
+316
+00:23:02,510 --> 00:23:05,090
+بين الفقرين في الأولى والتالى نفس التغيير بيقوموا
+
+317
+00:23:05,090 --> 00:23:08,790
+فيهم في اللي ع ز أكس اسمه هم هيروحوا هضلوا عندهم
+
+318
+00:23:08,790 --> 00:23:12,730
+ويعملوا في ال X axis نفس الشيء عند هذه النقطة هل
+
+319
+00:23:12,730 --> 00:23:16,690
+ألاحظ انه هيكون في واحدة في ال X واحدة في السالب X
+
+320
+00:23:16,690 --> 00:23:20,590
+اي واحدة في البسط Z واحدة في السالب Z والتنتين
+
+321
+00:23:20,590 --> 00:23:24,070
+هيكون هم component في البسط X اذا اللي على ال Z
+
+322
+00:23:24,070 --> 00:23:30,330
+axis جروبه اذا انت تلاحظ انه هيكون عندهمدائما
+
+323
+00:23:30,330 --> 00:23:36,310
+magnetic field في اتجاه ال X negative negative X
+
+324
+00:23:36,310 --> 00:23:40,310
+اللي هو لو أنا نظرت على Z ماعنها أكبر من صفر لو Z
+
+325
+00:23:40,310 --> 00:23:48,710
+موجبة و سالب لو Z أكبر من صفر اللي هي بُسط في X
+
+326
+00:23:48,710 --> 00:23:53,450
+سهل بُسط في X هتكون في بُسط في X و لو كانت Z أقل
+
+327
+00:23:53,450 --> 00:23:56,390
+من صفر هتكون في سالب X فانا احنا أخدنا هاي ال X
+
+328
+00:23:56,390 --> 00:23:57,770
+أحسس تمام؟
+
+329
+00:24:02,930 --> 00:24:06,490
+إذا لو أنا طلعت على above و below ال sheet هلاحظ
+
+330
+00:24:06,490 --> 00:24:10,690
+دائما هيكون عندى ارحمكم الله above ال sheet و
+
+331
+00:24:10,690 --> 00:24:12,930
+below ال sheet هيكون في عندي ال magnetic field
+
+332
+00:24:12,930 --> 00:24:18,310
+واحد هيكون positive والثاني negative اللى هو above
+
+333
+00:24:18,310 --> 00:24:21,450
+ال sheet هيكون موجة و اللى below ال sheet هيكون
+
+334
+00:24:21,450 --> 00:24:23,990
+سالم، واضح؟
+
+335
+00:24:39,760 --> 00:24:42,580
+الحاجة التانية انه احنا عارفين ان ال clause
+
+336
+00:24:42,580 --> 00:24:47,940
+integral ل H2DL ايش بيسموه I enclosed I enclosed و
+
+337
+00:24:47,940 --> 00:24:51,020
+I enclosed اذا أطلع عنوان I enclosed مش هيكون فيه
+
+338
+00:24:51,020 --> 00:24:54,500
+يمدى اي حاجة في اتجاه ال Z-axis ال I enclosed فعلا
+
+339
+00:24:54,500 --> 00:24:57,540
+من جنب بعيد و قدش period length هي احنا قدش الطول
+
+340
+00:24:57,540 --> 00:25:00,220
+تبعنا لو أخدت هذا المربع تبعي هذا ال clause boss
+
+341
+00:25:00,220 --> 00:25:06,250
+هو ال B يعني هيكون I enclosedkeep K وY في مين في
+
+342
+00:25:06,250 --> 00:25:10,270
+بيك عدد ال file elements كلهم مع بعض و ال unit
+
+343
+00:25:10,270 --> 00:25:14,430
+lengths كده ال links هيكون ال file elements واحدة
+
+344
+00:25:14,430 --> 00:25:17,610
+جانب التانية و جانب التانية و جانب التانية فكده هو
+
+345
+00:25:17,610 --> 00:25:22,590
+طول نبيك K اللي هي amps per meter و ال meter تبعي
+
+346
+00:25:22,590 --> 00:25:26,270
+او ال links تبعي هيكون ال بيك انا عملت اللي
+
+347
+00:25:26,270 --> 00:25:30,110
+element ال boss طوله بيك هيكون كل ال current
+
+348
+00:25:30,110 --> 00:25:34,730
+enclosed هو مين هذا ال current اللي هو KوY فمين
+
+349
+00:25:34,730 --> 00:25:38,830
+فمين تمام؟ واضحة هذه النقطة؟ اذا ماقدش ال current
+
+350
+00:25:38,830 --> 00:25:43,550
+enclosed اللي هو KY اللي هو M سبيرميتا في اي طول
+
+351
+00:25:43,550 --> 00:25:44,010
+اللي هو P
+
+352
+00:26:04,090 --> 00:26:07,490
+الان نعمل ال integration طبعا اش ما احنا استنتجناه
+
+353
+00:26:07,490 --> 00:26:10,790
+لحد الاية اول حاجة استنتجنا ان ال clause integral
+
+354
+00:26:10,790 --> 00:26:14,870
+h2tL بساوي ky بb وكمان حاجة استنتجناها من ال
+
+355
+00:26:14,870 --> 00:26:18,570
+symmetry لو أخدنا two filaments و حاولنا نحسب ال
+
+356
+00:26:18,570 --> 00:26:21,210
+magnetic field انه ال magnetic field واحد بيكون
+
+357
+00:26:21,210 --> 00:26:23,850
+above و واحد below عند اي نقطة لو عملت زبدة اكسس
+
+358
+00:26:23,850 --> 00:26:26,810
+هيك و لا هيك سحبته دلن ما هيكون عندى magnetic
+
+359
+00:26:26,810 --> 00:26:31,090
+field above موجة اتجاه القسط في Xو بالـ low سألكوش
+
+360
+00:26:31,090 --> 00:26:34,550
+كمان مجرد constant فيمة اتش نوت او مش constant
+
+361
+00:26:34,550 --> 00:26:38,510
+يعني رقم انا ماعرفهش بس متساوي فوق و تحت متساوي
+
+362
+00:26:38,510 --> 00:26:42,510
+أسواق فوق اللي هو ناتج من كل ال filaments اللي على
+
+363
+00:26:42,510 --> 00:26:46,450
+الدنيا من هنا لهنا هيكون ال total magnetic field
+
+364
+00:26:46,450 --> 00:26:49,630
+هده دي اتش لإن أنا بس خدته filaments لو حطت كل ال
+
+365
+00:26:49,630 --> 00:26:52,950
+filaments اللي محبوسين في ال links بيه هيكون عند
+
+366
+00:26:52,950 --> 00:26:58,090
+ال total etch هسمي اتش نوتواضح؟ أسوأ فوق ولا تحت،
+
+367
+00:26:58,090 --> 00:27:00,190
+أسوأ اللي في الاتجاه الـ positive X ولا الـ
+
+368
+00:27:00,190 --> 00:27:02,630
+negative X، بضعنا نعرف مين الـ H node، من هون
+
+369
+00:27:02,630 --> 00:27:04,650
+بتعرف الـ H node، ده من الـ symmetry اللي حكينا
+
+370
+00:27:04,650 --> 00:27:07,370
+عنه، احنا بنرجع القانون اللي قولنا ال clause
+
+371
+00:27:07,370 --> 00:27:13,950
+integral لH dot DL، إيش بتساوي؟ KY كبيرةبنكمل على
+
+372
+00:27:13,950 --> 00:27:18,610
+الـ buses الـ bus الأول من 1 إلى 2 ثم التكامل من 2
+
+373
+00:27:18,610 --> 00:27:22,670
+إلى 3 لأنه close bus ثم التكامل من 3 إلى 4 ثم
+
+374
+00:27:22,670 --> 00:27:26,030
+التكامل من 4 إلى 1 نحن نعرف أن magnetic field هذا
+
+375
+00:27:26,030 --> 00:27:29,990
+تجاههم يعني أننا نعمل tangential لأنه H to DL ال
+
+376
+00:27:29,990 --> 00:27:32,870
+magnetic field اللي نكتبه في ال X-axis إذن من 1
+
+377
+00:27:32,870 --> 00:27:35,650
+إلى 2 و من 3 إلى 4 اللي هم في تجاه Z-axis يكون
+
+378
+00:27:35,650 --> 00:27:39,980
+التكامل Zeroانه من السيمتري استنتجنا المجلة فيه
+
+379
+00:27:39,980 --> 00:27:45,280
+دوان ال X Axis اتجاهه اذا في الباصين 1 و 2 و 3 و 4
+
+380
+00:27:45,280 --> 00:27:48,720
+اللي هم على ال Z Axis ال dot product ل H اللي في
+
+381
+00:27:48,720 --> 00:27:53,240
+الاتجاه X dot Z ايش بده يكون سفر اذا هدولة و باصس
+
+382
+00:27:53,240 --> 00:28:00,170
+1 ل 2 و 3 ل 4 ال dot product H dot DL بيساو سفرمين
+
+383
+00:28:00,170 --> 00:28:03,750
+بقى علينا التكامل من اتنين تلاتة و اربعة واحد
+
+384
+00:28:03,750 --> 00:28:09,070
+التكامل من اتنين تلاتة H dot DL اتنين وتلاتة وهو
+
+385
+00:28:09,070 --> 00:28:13,530
+هذا اللي قاله سالب H في اتجاه سالب H ايش كانت ال
+
+386
+00:28:13,530 --> 00:28:19,050
+magnetic field اول حاجة الطول تبعنا اللي هو B
+
+387
+00:28:19,050 --> 00:28:24,150
+واتجاهه في سالب X minus B و ال magnetic field تحت
+
+388
+00:28:24,150 --> 00:28:27,350
+ال Z axis انا هذا اللي بدى اركز عليه تحت و فوق ال
+
+389
+00:28:27,350 --> 00:28:30,710
+Z axisتحت الـ z-axis قولنا إيش بيساوي minus h0
+
+390
+00:28:30,710 --> 00:28:36,930
+minus h0 تحت ال z-axis فهدي ال bus اتنين تلاتة
+
+391
+00:28:36,930 --> 00:28:41,790
+ماله تحت ال z-axis إذا قيمته minus h0 و طول طبعا
+
+392
+00:28:41,790 --> 00:28:44,710
+من اتنين لتلاتة إيش قيمته بيه باتجاهه ماله سالب x
+
+393
+00:28:44,710 --> 00:28:49,170
+إذا minus b فإذا عندي من اتنين لتلاتة minus h0
+
+394
+00:28:49,170 --> 00:28:53,190
+minus b ناقص h0 لإنه تحت ال z-axis و b لإنه تجاهها
+
+395
+00:28:53,190 --> 00:29:01,060
+بسالب xمضمين عندى من 4 على 1 فوق الـ positive
+
+396
+00:29:01,060 --> 00:29:05,800
+z axis فوق ال plan فوقه قولنا تحت ال plan و فوق ال
+
+397
+00:29:05,800 --> 00:29:10,100
+plan تحت ال plan سالبة فوق ال plan موجبة فوق ال
+
+398
+00:29:10,100 --> 00:29:13,860
+plan موجبة هي h0 و b مالها في ال positive x axis
+
+399
+00:29:13,860 --> 00:29:18,760
+فهيكون عندى minus h0 minus b0 اللى هي plus h0b و
+
+400
+00:29:18,760 --> 00:29:25,610
+h0b هيصير 2h0b إيش بتسوى هذه كلها kybهذه القيمة
+
+401
+00:29:25,610 --> 00:29:33,190
+الـ Closed Integral X و T L بتساوي KYPB اللي هي
+
+402
+00:29:33,190 --> 00:29:36,590
+عدد ال filaments اللي بتختربوا ال links بيه فإذا
+
+403
+00:29:36,590 --> 00:29:39,290
+أنا أكتش نوتش بها تساوي المشكلة اللي بعناها اعرفنا
+
+404
+00:29:39,290 --> 00:29:45,130
+فيه بتروح معادي هيكون KY على 2 فبجرب أجيب الفيل H
+
+405
+00:29:45,130 --> 00:29:50,310
+هيكون above ال plane هو فرصة أكتر من Zero نص KY
+
+406
+00:29:50,310 --> 00:29:51,370
+Xها
+
+407
+00:30:12,790 --> 00:30:17,530
+بشكل عام هذه العلاقة بقدر تبعها بشكل التالي نص كيه
+
+408
+00:30:17,530 --> 00:30:21,790
+اللي هو ال vector تبعنا اللي هو ال currentفي
+
+409
+00:30:21,790 --> 00:30:26,170
+حالتنا كان ky تجاهه cross انهات من هي انهات هو
+
+410
+00:30:26,170 --> 00:30:28,930
+unit vector directed from the current shape to the
+
+411
+00:30:28,930 --> 00:30:33,070
+point of interest هيتغير ايه انهات نيجي نطبقه على
+
+412
+00:30:33,070 --> 00:30:36,430
+المثال تبعنا كي علنا ايش تجاهها ky
+
+413
+00:30:47,470 --> 00:30:51,290
+من ال surface بالنقطة اللى انا بدى ادرس عندها ال
+
+414
+00:30:51,290 --> 00:30:57,070
+magnitude لتطلع فوق ال plane هذا طبعا نص T Y Y
+
+415
+00:30:57,070 --> 00:31:04,210
+cross فوق البندش هيكون ايه انها هيكون بوستر Z hat
+
+416
+00:31:04,210 --> 00:31:09,490
+Y hat يكون Z hat هيكون X hat
+
+417
+00:31:29,920 --> 00:31:35,160
+النور من الـplane لنقطة بدائيسة ماينوس اكروس
+
+418
+00:31:35,160 --> 00:31:41,180
+ماينوس زي دي
+
+419
+00:31:41,180 --> 00:31:46,320
+هذه هي العلاقة العامة اذا بشكل عام لما انا بتحسب
+
+420
+00:31:46,320 --> 00:31:50,200
+الماجنة دي ال field الناتج من ال surface current
+
+421
+00:31:50,200 --> 00:31:53,880
+بقى بطلع فوق ال plane و دولير ال plane وبحسب اللي
+
+422
+00:31:53,880 --> 00:32:02,390
+هو العلاقة العامةلو كان عندي الـ coaxial line لو
+
+423
+00:32:02,390 --> 00:32:06,750
+انا كان عندي مثال هيندي two lines او يعني two
+
+424
+00:32:06,750 --> 00:32:11,490
+conductors واحد هعمل طيار الطيار اللي في الداخلي
+
+425
+00:32:11,490 --> 00:32:16,530
+في ال coaxial cable ماله الطيار طالع هتجاه I طالع
+
+426
+00:32:16,530 --> 00:32:20,870
+بينما التاني اللي هم اللي هم بالازرق الطيار ماله
+
+427
+00:32:20,870 --> 00:32:25,030
+داخل وهذا قيلك انه طالع Z axis
+
+428
+00:32:26,990 --> 00:32:30,610
+الـ core في الـ core التيار مو يتعلق من الصفحة و
+
+429
+00:32:30,610 --> 00:32:34,930
+في اللي حولها داخل الصفحة و تعلق منها الـ magnetic
+
+430
+00:32:34,930 --> 00:32:39,450
+field ما بين الـ 0 و الـ B ليها الـ 0 و الـ B و
+
+431
+00:32:39,450 --> 00:32:45,590
+بعدين ما بين ال raw من A ل B هي أول حاجة من الـ 0
+
+432
+00:32:45,590 --> 00:32:50,240
+ل A بس فهي الـ A اللي محددنا إياها ليها ديبعدين
+
+433
+00:32:50,240 --> 00:32:53,960
+مابين ال A و ال B اللى هى هى ال region وبعدين
+
+434
+00:32:53,960 --> 00:32:59,720
+مابين ال B و B plus T اللى هو ال conductor الخارجى
+
+435
+00:32:59,720 --> 00:33:03,780
+ال thickness بتاعه T لازم هتكون مابين ال B ل B
+
+436
+00:33:03,780 --> 00:33:04,220
+plus
+
+437
+00:33:15,280 --> 00:33:19,300
+عشان اعرف قداش I enclosed فى قلب ال line اللى
+
+438
+00:33:19,300 --> 00:33:22,020
+بتاخده لانه بدى row أقل من V
+
+439
+00:33:26,900 --> 00:33:32,220
+عشان نعرف I enclosed هو I constant لازم بقدر أجيب
+
+440
+00:33:32,220 --> 00:33:36,200
+أداش I عند أي per unit area لأنه بدي في الآخر اللي
+
+441
+00:33:36,200 --> 00:33:40,710
+enclosed في هذا ال line أو per unit lengthإننا
+
+442
+00:33:40,710 --> 00:33:43,750
+بلوز انتجرال اتشد دي اك تساوي اي بلوز و اي بلوز شو
+
+443
+00:33:43,750 --> 00:33:47,350
+بتساوي الانتجرال اتشده ال DS ال current density في
+
+444
+00:33:47,350 --> 00:33:51,370
+دي ال DS ايش ال current density يعني ال I constant
+
+445
+00:33:51,370 --> 00:33:55,170
+فهتكون جيه شو بتساوي I على ال area بتاعةها ال
+
+446
+00:33:55,170 --> 00:34:01,550
+cross section تبع ال line الداخلي ال core تبع ال
+
+447
+00:34:01,550 --> 00:34:04,990
+coaxial line اللي هي بره I على Y ايه الترفيه و
+
+448
+00:34:04,990 --> 00:34:09,790
+تجاهه بص تفزدها تبع الطالع Jدوت دي اس اللي هي رو
+
+449
+00:34:09,790 --> 00:34:14,070
+دي فاي دي رو زدها تبرده اتجاهها فان عمودي عليها ال
+
+450
+00:34:14,070 --> 00:34:19,910
+DS لو انا خدنا I enclosed مش هتساوي J دوت DS J
+
+451
+00:34:19,910 --> 00:34:22,370
+اللي هي I على Pi اتر بيها constant تطلع برا ال
+
+452
+00:34:22,370 --> 00:34:27,810
+Integral و ال DS رو دي فاي دي رو دي رو رو دي رو من
+
+453
+00:34:27,810 --> 00:34:33,740
+وين الرو بتروح من Zero لآخرأو حتى النقطة التي أريد
+
+454
+00:34:33,740 --> 00:34:36,740
+إيسة عندها أقصرهم لإيه بس انا بدي عند أي نقطة
+
+455
+00:34:36,740 --> 00:34:40,000
+بقيسة زي هذا ال surface ال line اللي انا حاطيته ال
+
+456
+00:34:40,000 --> 00:34:44,120
+imaginary line و بدي ال tangential له و أخد أفرض
+
+457
+00:34:44,120 --> 00:34:48,980
+ان ال radius تبعه ρو لذا سيكون ال S بديها حوالي
+
+458
+00:34:48,980 --> 00:34:52,860
+هذا ال line سيكون جزء من ال total current density
+
+459
+00:34:52,860 --> 00:34:57,720
+موجودة هنا اللي هي فقط محبوسة من zero ل رو عند أي
+
+460
+00:34:57,720 --> 00:34:59,500
+نقطة في هذا ال surface
+
+461
+00:35:12,230 --> 00:35:18,770
+عن طريق الاريه
+
+462
+00:35:18,770 --> 00:35:25,280
+الاريه هي الدائرة الجوانيةالـ Y بتروح مع الـ Y
+
+463
+00:35:25,280 --> 00:35:28,700
+هيكون I رو تربيه على I تربيه هي الـ I enclosed هاي
+
+464
+00:35:28,700 --> 00:35:32,040
+الـ I enclosed طب اتش dot dl إيش هتكون اتش؟ احنا
+
+465
+00:35:32,040 --> 00:35:34,840
+قولنا ال current طالع تجاه Z-axis إيش ال magnetic
+
+466
+00:35:34,840 --> 00:35:39,000
+field تجاه هو؟ الفي داريكشن الفي داريكشن
+
+467
+00:35:39,000 --> 00:35:42,220
+tangential لمن؟ لل line اللي محيط فيه ال area اللي
+
+468
+00:35:42,220 --> 00:35:44,940
+موجود فيها ال current ال current موجود في قلب هذه
+
+469
+00:35:44,940 --> 00:35:48,440
+ال area و ال magnetic field tangential له في تجاه
+
+470
+00:35:48,440 --> 00:35:53,470
+الفيو DL هتكون 2π رو يعني اذا انا اكملتها او انا
+
+471
+00:35:53,470 --> 00:35:57,790
+ارفعها 2π رو اذا H5 في 2π رو هتكون I رو تربيه على
+
+472
+00:35:57,790 --> 00:36:02,450
+A تربيه اذا H5 هتكون I رو على 2π A تربيه لو اخدنا
+
+473
+00:36:02,450 --> 00:36:05,810
+هنا هيكون ال total current enclosed mean اللي هو
+
+474
+00:36:05,810 --> 00:36:09,250
+هذا اللي موجود هنا I كل ال current هيكون enclosed
+
+475
+00:36:09,250 --> 00:36:13,090
+يعني اذا هيكون H dot DL بتساوي I اللي هو ال
+
+476
+00:36:13,090 --> 00:36:15,370
+current اللي موجود في قلب ال conductor الأول يعني
+
+477
+00:36:15,370 --> 00:36:17,050
+كلههنا هتكون
+
+478
+00:36:17,050 --> 00:36:43,270
+I²I²I²I²I²I²I²I²I²I²I²I²I²I²I²I²I²I²I²I²I²I²I²I²I²I²I²I²I
+
+479
+00:36:46,000 --> 00:36:49,560
+كمان مرة بدي أجيب مين هو ال جيب و ال current
+
+480
+00:36:49,560 --> 00:36:51,780
+enclosed في هذه ال region
+
+481
+00:37:04,920 --> 00:37:09,740
+الـ I enclosed بيساوم مجموعة طيارات هذا الطيار I
+
+482
+00:37:09,740 --> 00:37:13,080
+الإشارته موجبة والطيار اللي هنا الإشارته سالبة
+
+483
+00:37:13,080 --> 00:37:23,320
+هيكون I Gts و G هذه ما لها سالبة سالبة I على ال
+
+484
+00:37:23,320 --> 00:37:29,800
+area اللي هو current per unitالاريه الصغيرة الى
+
+485
+00:37:29,800 --> 00:37:35,940
+هنا زائد الاريه الكبيرة كلها الاريه الاريه الكبيرة
+
+486
+00:37:35,940 --> 00:37:35,960
+كلها الاريه الكبيرة كلها الاريه الاريه الكبيرة
+
+487
+00:37:35,960 --> 00:37:36,260
+كلها الاريه الاريه الكبيرة كلها الاريه الاريه
+
+488
+00:37:36,260 --> 00:37:37,180
+الكبيرة كلها الاريه الاريه الكبيرة كلها الاريه
+
+489
+00:37:37,180 --> 00:37:38,920
+الاريه الكبيرة كلها الاريه الاريه الكبيرة كلها
+
+490
+00:37:38,920 --> 00:37:43,960
+الاريه الاريه الكبيرة كلها الاريه الاريه الكبيرة
+
+491
+00:37:43,960 --> 00:37:47,100
+كلها الاريه الاريه الكبيرة كلها الاريه الاريه
+
+492
+00:37:47,100 --> 00:37:47,660
+الاريه الكبيرة كلها الاريه الاريه الكبيرة كلها
+
+493
+00:37:47,660 --> 00:37:49,160
+الاريه الاريه الكبيرة
+
+494
+00:37:59,180 --> 00:38:04,340
+j بتساوي I على ال area فاهمين انتوا الفكرة اه إذا
+
+495
+00:38:04,340 --> 00:38:06,120
+إحنا بنجيب اللي هي ال current على ال area اللي
+
+496
+00:38:06,120 --> 00:38:09,200
+بتكون ال area الكلية مقص ال area اللي دوانية
+
+497
+00:38:09,200 --> 00:38:12,960
+بتعطينا اللي هو بس هاي ال area واضح؟ هاي ال area
+
+498
+00:38:12,960 --> 00:38:16,240
+فإحنا جيبنا هكذا ال current density نفس التطبيق
+
+499
+00:38:16,240 --> 00:38:19,960
+اللي عمله بس هنا أسفلت التيار اللي كل مين I minus
+
+500
+00:38:19,960 --> 00:38:22,720
+اللي هي ال current اللي موجود هنا هذا ال current
+
+501
+00:38:22,720 --> 00:38:29,910
+اللي موجود في الالـ current density كلها لهذا
+
+502
+00:38:29,910 --> 00:38:32,050
+الدائرة احنا جبناها لكن انا بديها ال a اللى موجود
+
+503
+00:38:32,050 --> 00:38:34,230
+فى قلب اللى هى ال ring اللى انا حطها ال imaginary
+
+504
+00:38:34,230 --> 00:38:38,550
+ring نفس الحاجة هكامل ρو D5D رو ال current density
+
+505
+00:38:38,550 --> 00:38:41,710
+constant بتطلع على برا فبكون عند ال total current
+
+506
+00:38:41,710 --> 00:38:45,290
+بعد ما اخد ال I عن المشترك بتسوى 1-Rو تربية مع
+
+507
+00:38:45,290 --> 00:38:50,470
+نسبة تربية ا ت تربية زى 2B ت تربية ال 5 اذا هتسوى
+
+508
+00:38:50,470 --> 00:38:56,190
+I enclosed على 2 by rho لأكبرلهذه الدقلة الأخيرة
+
+509
+00:38:56,190 --> 00:38:59,910
+اللي هو أكبر من B زي ال T هيكون عندي two currents
+
+510
+00:38:59,910 --> 00:39:03,510
+متساوين واشهرتهم سلبا in class I و minus I هتكون
+
+511
+00:39:03,510 --> 00:39:08,290
+zero واضحة الفكرة؟طب احنا بس على السريع هي النتائج
+
+512
+00:39:08,290 --> 00:39:11,070
+بتاعتنا كانت اللي هي ما بين ال raw من zero ل a
+
+513
+00:39:11,070 --> 00:39:14,130
+قيمتها القدر ما بين ال a و b هي قيمتها القدر لقظه
+
+514
+00:39:14,130 --> 00:39:18,650
+انه مالها خطية constant في raw h متساوئان في رو خط
+
+515
+00:39:18,650 --> 00:39:24,070
+مستقيم علاقة من h في raw ما بين a و b صحيح واحد
+
+516
+00:39:24,070 --> 00:39:27,770
+على raw فهي مضروبة some constant مضروف mean في
+
+517
+00:39:27,770 --> 00:39:32,340
+واحد على rawبعدينها شوي يعني بس مش كتير أصعب يعني
+
+518
+00:39:32,340 --> 00:39:36,320
+تقريبا جزء منها واحد على row التانى في جزء منه
+
+519
+00:39:36,320 --> 00:39:40,400
+rotor B فهيكون هذا الشكل فعاملا بنحدد ال limits
+
+520
+00:39:40,400 --> 00:39:45,320
+عند ال boundaries هنا هتكون عند ال A هتسوى I على
+
+521
+00:39:45,320 --> 00:39:49,480
+two by A اوضع ال row A فعند ال A هتكون قيمتها I
+
+522
+00:39:49,480 --> 00:39:53,920
+على two by A هأجينا هنا ال واحد على row فاش نهيتها
+
+523
+00:39:53,920 --> 00:39:59,830
+تكون عند ال B فاوضع هتكون I على two by Bهذه اخر
+
+524
+00:39:59,830 --> 00:40:03,870
+واحدة هتبدأ من ال B لو قعدنا عن ال B هذا ال term
+
+525
+00:40:03,870 --> 00:40:08,210
+بروح لل سفر هتكانها I على 2 by B صح؟ و آخر نقطة
+
+526
+00:40:08,210 --> 00:40:12,050
+اللي هي ال B زي T لو قعدت عن رو تربيع ال B زي T
+
+527
+00:40:12,050 --> 00:40:15,190
+هتكون B تربيع بتروح مع ناقص ب T إيش بيضلع لنا T
+
+528
+00:40:15,190 --> 00:40:19,390
+تربيع زي 2BT بروحوا مع بعض بيعطيني واحد واحد ناقص
+
+529
+00:40:19,390 --> 00:40:26,130
+واحد سفرهذه هي العلاقة بين H5 روك على طول
+
+530
+00:40:26,130 --> 00:40:31,790
+الكيوكسيا الكابر من أقل من A أكبر من A مابين ال B
+
+531
+00:40:31,790 --> 00:40:40,410
+و B زائد T و بعدين أكبر من B زائد T سهل تطبيقهابعد
+
+532
+00:40:40,410 --> 00:40:43,650
+ذلك اللقاء القادم هتشوف لو كان عندي two planes
+
+533
+00:40:43,650 --> 00:40:47,430
+هدولة two planes واحد في current طالع من الصفحة
+
+534
+00:40:47,430 --> 00:40:51,110
+اتجاه ال X-axis واحد داخل الصفحة اتجاه ال Z-axis
+
+535
+00:40:51,110 --> 00:40:53,690
+او حتى يعني هذا لإنه تطبيق على المثال اللي احنا
+
+536
+00:40:53,690 --> 00:40:57,450
+حلناه المرة الماضية بدي اكتحله في البيت يعني طبعا
+
+537
+00:40:57,450 --> 00:41:00,210
+اللي كنت تبقى اللي انا كنت احكيه تحت ال plane of
+
+538
+00:41:00,210 --> 00:41:02,570
+all بين المطالب يعني نقطة هنا بين ال two planes
+
+539
+00:41:02,570 --> 00:41:05,650
+بتطلع هيكون ال magnetic field بالنسبة لهذا ال
+
+540
+00:41:05,650 --> 00:41:09,760
+plane فوقهلكن مجنتين بالنسبة لهذا البلاين ماله
+
+541
+00:41:09,760 --> 00:41:13,340
+تحته، لما النقطة صارت هنا عن العشرة، التنين كان
+
+542
+00:41:13,340 --> 00:41:19,200
+المجنت كيلو التنين ماله فوقهم، أول نقطة هنا هتكون،
+
+543
+00:41:19,200 --> 00:41:22,280
+هتكون بالنسبة لهذا البلاين مالها فوقها، هتكون
+
+544
+00:41:22,280 --> 00:41:25,980
+الإشارة موجبة، بالنسبة لهذا البلاين تحته، الإشارة
+
+545
+00:41:25,980 --> 00:41:29,220
+سالبة، لو النقطة هنا، هيكون بالنسبة لهذا البلاين
+
+546
+00:41:29,220 --> 00:41:32,720
+ماله فوقهم، بحلوه في البيت و بنقش اللقاء القادم إن
+
+547
+00:41:32,720 --> 00:41:33,020
+شاء الله
+
+548
+00:41:37,120 --> 00:41:39,440
+مافيش ضاعي إلا مثال واحد يعني، ان شاء الله أدى
+
+549
+00:41:39,440 --> 00:41:42,780
+الخمسة لقاء القادم و بنحلم اللي هي ال .. بقى انا
+
+550
+00:41:42,780 --> 00:41:46,980
+كنت حاول نبدأ اللي هو الشفرة الأخيرة، يعطيكوا
+
+551
+00:41:46,980 --> 00:41:47,720
+العافية ان شاء الله
+
diff --git a/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/I8ZXjFEyO9A_postprocess.srt b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/I8ZXjFEyO9A_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..f9e518aa96cdc47f21230833f3345f1510b9f928
--- /dev/null
+++ b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/I8ZXjFEyO9A_postprocess.srt
@@ -0,0 +1,2232 @@
+1
+00:00:20,690 --> 00:00:24,310
+بسم الله الرحمن الرحيم السلام عليكم ورحمة الله
+
+2
+00:00:24,310 --> 00:00:28,290
+وبركاته احنا اليوم ان شاء الله هنتبع واطينا في
+
+3
+00:00:28,290 --> 00:00:33,510
+الكهر استاتيكية و هنتقل ل magnetostatic fields
+
+4
+00:00:33,510 --> 00:00:39,510
+الشكتر 7 اللي بتحدث عن magnetostatic field فارجينا
+
+5
+00:00:39,510 --> 00:00:42,230
+ال new field احنا كلنا مركزين على ال electric
+
+6
+00:00:42,230 --> 00:00:47,280
+field و اليوم هنشوف ال magnetic fieldتذكروا في
+
+7
+00:00:47,280 --> 00:00:50,880
+شبطر 4 و 6 كان الحديث دائما عن static electric
+
+8
+00:00:50,880 --> 00:00:56,980
+field اللي بنعبر عنه ب E و D و D بتساوي E E و E هي
+
+9
+00:00:56,980 --> 00:01:00,880
+ال dialectic constant للميديا زي ما قولنا في هذا
+
+10
+00:01:00,880 --> 00:01:05,120
+الشبطر هنتعمل من static magnetic fields اللي بنعبر
+
+11
+00:01:05,120 --> 00:01:10,580
+عنه بH و B و B بتساوي Mu في B .. ب .. ب .. B
+
+12
+00:01:10,580 --> 00:01:11,760
+بتساوي Mu في H
+
+13
+00:01:15,140 --> 00:01:24,820
+B بيساو ميو في H التمييز
+
+14
+00:01:24,820 --> 00:01:27,540
+بين ال electric و ال magnetic field واضح عنه
+
+15
+00:01:27,540 --> 00:01:32,880
+Orsted اللي هو واحدة قياس ال magnetic field أصلا
+
+16
+00:01:32,880 --> 00:01:36,640
+متعبرة بال Orsted اللي قال إن ال electrostatic
+
+17
+00:01:36,640 --> 00:01:41,970
+field تنتج اللي هو ال E field و ال D fieldبنتج لما
+
+18
+00:01:41,970 --> 00:01:45,130
+يكون عندنا ال charges صافين احنا طول الشبات الماضي
+
+19
+00:01:45,130 --> 00:01:49,170
+عمرنا حكينا عن ال charges بتجري كله بنحكي عن ال
+
+20
+00:01:49,170 --> 00:01:52,610
+charges في حالة static field يعني في حالة وضع
+
+21
+00:01:52,610 --> 00:01:58,710
+مابتجريش ولا بتتصارى ولا بتكون عليها velocity لكن
+
+22
+00:01:58,710 --> 00:02:03,050
+ال static magnetic field هي عبارة عن field بنتج
+
+23
+00:02:03,050 --> 00:02:07,430
+لما بيكون عنده charging، charge بتتحرك ال constant
+
+24
+00:02:07,430 --> 00:02:12,040
+velocity بسميها ال static magnetic fieldعشان هي
+
+25
+00:02:12,040 --> 00:02:14,580
+الفرق من ال aesthetic electric field و aesthetic
+
+26
+00:02:14,580 --> 00:02:18,400
+magnetic field احنا بناخد في هذا الشبط .. في هذا
+
+27
+00:02:18,400 --> 00:02:21,840
+الفصل اللي هو ال electrostatic في فصول قادمة
+
+28
+00:02:21,840 --> 00:02:25,040
+بتاخده اللي هو electrodynamics ال dynamics اللي هو
+
+29
+00:02:25,040 --> 00:02:31,090
+بيكون في علنا ال fields function of Tهذا ال table
+
+30
+00:02:31,090 --> 00:02:34,110
+مش هأقعدكوا ياه بس يعني انه مجرد table هفرجيكي ال
+
+31
+00:02:34,110 --> 00:02:36,890
+analogy بين electric و magnetic field و احنا في
+
+32
+00:02:36,890 --> 00:02:41,210
+هذا الشبكة رح نشوف هل القوانين شوية شوية بس بعد ما
+
+33
+00:02:41,210 --> 00:02:46,290
+نخلصهم هتسيروا اتقارنوا بين اللي هي القوانين عشان
+
+34
+00:02:46,290 --> 00:02:49,270
+يساعدكم على انكم تتذكروا القوانين اذا الواحد حفظ
+
+35
+00:02:49,270 --> 00:02:52,810
+قوانين معينة لما يمشي يحفظ قوانين تانية بيكون كويس
+
+36
+00:02:52,810 --> 00:02:55,610
+انه يعمل بينهم analogy يقولها ده اه بشبه داك
+
+37
+00:02:55,610 --> 00:03:02,920
+القانون و هكذانبدأ في biosafety law biosafety law
+
+38
+00:03:02,920 --> 00:03:07,400
+هو القانون اللى بحدد لقيمة ال magnetic field عن
+
+39
+00:03:07,400 --> 00:03:14,960
+نقطة بالقرب من تيار متحرك احنا قلنا ال magnetic
+
+40
+00:03:14,960 --> 00:03:20,780
+field بتولد في وجود ال charges متحركة ال constant
+
+41
+00:03:20,780 --> 00:03:30,080
+velocityمثلا حركة مستمرة في الوسط تيار بيو سفارتلو
+
+42
+00:03:30,080 --> 00:03:37,000
+بيجيبلي ال magnetic field في نقطة بالقرب من تيار
+
+43
+00:03:37,000 --> 00:03:43,060
+اذا احنا شفنا هذا ال element في تيار اتجاه التيار
+
+44
+00:03:43,060 --> 00:03:46,640
+زي ما انتوا شايفينه بالساعة و احنا بدي ال magnetic
+
+45
+00:03:46,640 --> 00:03:50,060
+field عند ال point اللي زي ما انتوا شايفينها في
+
+46
+00:03:50,060 --> 00:03:58,420
+هذه النقطة عند النقطة Bبنحدد element من اللي هو خط
+
+47
+00:03:58,420 --> 00:04:02,200
+مصار او يعني ال silica المورفي الكرام باخد element
+
+48
+00:04:02,200 --> 00:04:08,540
+منه و بسميه di و di هي عبارة عن IDL يعني هذا ال
+
+49
+00:04:08,540 --> 00:04:11,880
+element بحتوي على المعلومتين اللي هي طول ال
+
+50
+00:04:11,880 --> 00:04:16,700
+element و الطيار المورفي اخد
+
+51
+00:04:16,700 --> 00:04:21,090
+المسافة بين ال element والنقطة اللى بدى اجيب عندها
+
+52
+00:04:21,090 --> 00:04:25,230
+المجال و بسميها R اللى هى ما بين ال source و
+
+53
+00:04:25,230 --> 00:04:27,830
+النقطة اللى بدأ اقاس فيها زى دائما بحدد ال
+
+54
+00:04:27,830 --> 00:04:30,850
+position تبع النقطة اللى بدأ اقاس فيها عندها
+
+55
+00:04:30,850 --> 00:04:34,790
+المجال و بحدد ال position تبع ال element و R اللى
+
+56
+00:04:34,790 --> 00:04:39,570
+هى الفرق بينهم زى دائما الفرق ما بين R capital
+
+57
+00:04:39,570 --> 00:04:42,430
+بيساوي R minus R prime R اللى هى المكان اللى بتحدد
+
+58
+00:04:42,430 --> 00:04:46,350
+عنده المثيل و R prime اللى هو عند اللى هو وين ال
+
+59
+00:04:46,350 --> 00:04:51,490
+sourceبيو سوفارتلوش بقول ان دي اتش لان دي اتش بدي
+
+60
+00:04:51,490 --> 00:04:54,930
+اسميها انا جاي من دي ال حبيبنا المجرد فيه من كل ال
+
+61
+00:04:54,930 --> 00:04:57,930
+او من كل طول اللي هو ال element اللي فيه التيار
+
+62
+00:04:57,930 --> 00:05:02,050
+فبقول دي اتش اللي هو ال magnetic field الناتج من
+
+63
+00:05:02,050 --> 00:05:07,890
+هذا ال element دي ال اللي عبارة عن IDL sin α على
+
+64
+00:05:07,890 --> 00:05:12,950
+أرثر بيومين هي Alpha Alpha هي الزاوية اللي بين ال
+
+65
+00:05:12,950 --> 00:05:17,680
+elementو مين هو الخط الواصل ما بين ال element و
+
+66
+00:05:17,680 --> 00:05:22,020
+نقطة قياس ال field هاي alpha إذا تذكروا من ال
+
+67
+00:05:22,020 --> 00:05:26,220
+calculus دي ال alpha دي sine alpha احنا مثلا بيه
+
+68
+00:05:26,220 --> 00:05:29,740
+cosine alpha قولنا إيش هذا dot product مذاكرين؟ و
+
+69
+00:05:29,740 --> 00:05:33,440
+بيه sine أي field يعني أي field في cosine الزاوية
+
+70
+00:05:33,440 --> 00:05:37,040
+قولنا هذا ال dot product ال component في ال dot
+
+71
+00:05:37,040 --> 00:05:42,360
+product ال projectionأي field sin α هو ما يسمى
+
+72
+00:05:42,360 --> 00:05:45,920
+cross product متذكرين؟ انا مجنوطة في الأول في
+
+73
+00:05:45,920 --> 00:05:48,760
+التاني في ال sign الزاوية بينهم فهذه عبارة عن
+
+74
+00:05:48,760 --> 00:05:51,320
+مجنوطة الأول في ال sign الزاوية اذا بتكون cross
+
+75
+00:05:51,320 --> 00:05:56,180
+product ما بين DL و إيش و unit vector فالمجنوطة
+
+76
+00:05:56,180 --> 00:06:01,320
+بقى هيكون واحد هتكون DL في ال unit vector اللي في
+
+77
+00:06:01,320 --> 00:06:08,060
+اتجاه R أنا زاوية بينهم مين Alpha ف DL across مين
+
+78
+00:06:08,060 --> 00:06:15,710
+A R hatهذه الـ magnitude لمن؟ لDL vector across AR
+
+79
+00:06:15,710 --> 00:06:20,010
+hat vector اذا كنت تعرف برنامج DH vector هتكون I
+
+80
+00:06:20,010 --> 00:06:26,570
+DL vector across AR hat ليش AR hat؟ لأن مجنوط
+
+81
+00:06:26,570 --> 00:06:29,030
+الأول في مجنوط التاني في sign زي و لا بينهم مجنوط
+
+82
+00:06:29,030 --> 00:06:33,270
+الارهات هيكون واحد معين؟ أخدناه قبل هيك لما كنا
+
+83
+00:06:33,270 --> 00:06:38,430
+نراجع الكلب ببساطةDL هتساوي طبعا احنا قولنا هذا
+
+84
+00:06:38,430 --> 00:06:42,910
+يتناسب اول حاجة انه لأ بيو سفرتلو انه بتناسب مع
+
+85
+00:06:42,910 --> 00:06:46,470
+قيمة التيار مع طول ال element مع الزاوية اللي بين
+
+86
+00:06:46,470 --> 00:06:49,390
+ال element و مكان قياس .. و الخط الواصل ما بين ال
+
+87
+00:06:49,390 --> 00:06:54,210
+element و مكان قياس المجنت كتيروعكسيا مع R تربيع
+
+88
+00:06:54,210 --> 00:06:58,450
+اللي هي المسافة بين ال element و المكان اللي بده
+
+89
+00:06:58,450 --> 00:07:01,750
+اقياس عنه بالمجال تفير إذا بتتناسب معناه بقدر أحط
+
+90
+00:07:01,750 --> 00:07:06,890
+معامل تناسب هنسميه K ومعادم التناسب سواء واحد على
+
+91
+00:07:06,890 --> 00:07:10,870
+four by اذا بقدر أقول DH ايش بتساوي I D L Sin
+
+92
+00:07:10,870 --> 00:07:14,650
+Alpha على four by R تربيع وانا حكيت انه D L Sin
+
+93
+00:07:14,650 --> 00:07:19,210
+Alphaهي عبارة عن cross product ما بين DL cross AR
+
+94
+00:07:19,210 --> 00:07:22,690
+hat magnitude لو بديها vector بقول DH vector
+
+95
+00:07:22,690 --> 00:07:26,090
+خليتها bold احنا قلنا في الكتاب بنحطه bold على
+
+96
+00:07:26,090 --> 00:07:30,150
+الصبورة او في البرقة بيدنا بنكتب اللي هو السهم ف
+
+97
+00:07:30,150 --> 00:07:34,630
+DH vector هيكون I DL vector cross AR hat على 4 by
+
+98
+00:07:34,630 --> 00:07:40,110
+R تربية او بقدر اعبر عن AR hat عبارة عن R vector
+
+99
+00:07:40,110 --> 00:07:44,890
+على R magnitude هتكون I DL cross R على 4 by R cube
+
+100
+00:07:46,260 --> 00:07:49,840
+تمام؟ في أي سؤال حتى هنا هي bios of earth law اللي
+
+101
+00:07:49,840 --> 00:07:55,800
+هو يعني ال field اللي ناتج من جزء من الخط أو من
+
+102
+00:07:55,800 --> 00:07:59,420
+السلك الماري في التيارة في حاجة مهمة انتوا شفتوا
+
+103
+00:07:59,420 --> 00:08:03,960
+في الرسمة انه حاطط ال cross هال cross بتقول اتجاه
+
+104
+00:08:03,960 --> 00:08:07,220
+ال magnetic field عند هاي النقطة كيف بتحدد اتجاه
+
+105
+00:08:07,220 --> 00:08:11,610
+ال magnetic field عند هاي النقطة؟إحنا قولنا إن دي
+
+106
+00:08:11,610 --> 00:08:16,190
+H وصلنا إنها بالساوية K I دي ال vector across AR
+
+107
+00:08:16,190 --> 00:08:20,310
+hat إذا معناه إحنا بنتعلم اللي هي ال cross product
+
+108
+00:08:20,310 --> 00:08:23,990
+و إحنا اتعلمناه و قولنا إنه بقدر أستخدم اللي هي ال
+
+109
+00:08:23,990 --> 00:08:28,030
+right hand rule A cross B بيعطييني C نفس الاشي هنا
+
+110
+00:08:28,030 --> 00:08:34,830
+عندى I I across R المفروض إنها تعطييني مين؟ هاي I
+
+111
+00:08:34,830 --> 00:08:41,710
+هاي اتجاه ال Iيعني I cross R بديكون داخل فاحنا
+
+112
+00:08:41,710 --> 00:08:46,770
+قولنا دي للسهم معناه أنه داخل، نقطة أنه طالع،
+
+113
+00:08:46,770 --> 00:08:51,650
+طبعا؟ فبالنسبة لل current أو يعني اتجاه حساب مجند
+
+114
+00:08:51,650 --> 00:08:55,890
+كثير غير أنه انا بقول I cross I أو يعني A cross B
+
+115
+00:08:55,890 --> 00:08:58,310
+بتعطيني C اللي هو ال cross product فقلنا cross
+
+116
+00:08:58,310 --> 00:09:02,740
+product نبال اللي هو اتجاه ال currentمع اللي هو
+
+117
+00:09:02,740 --> 00:09:07,240
+اتجاه المسافة ما بين ال element و ايه فانا دي L
+
+118
+00:09:07,240 --> 00:09:11,560
+اكروس R فاحنا متأكدين انه جوا بالنسبة لحساب ال
+
+119
+00:09:11,560 --> 00:09:14,480
+magnetic field لو عندي انا خاطب و امر فيه طيار في
+
+120
+00:09:14,480 --> 00:09:18,780
+قانون تاني كمان برضه بسهل عليا ان احدد where اتجاه
+
+121
+00:09:18,780 --> 00:09:23,660
+ال magnetic field وهو التاني اني بحط ال thumb تبعي
+
+122
+00:09:23,660 --> 00:09:27,910
+في اتجاه ال magnetic fieldالصمت في اتجاه المجمة
+
+123
+00:09:27,910 --> 00:09:32,350
+الفيض واتجاه يدي بلف اتجاه المجمة الفيض اذا انا
+
+124
+00:09:32,350 --> 00:09:37,310
+اجي على الرسمة هاي ال right hand بتاعتي هاي اتجاه
+
+125
+00:09:37,310 --> 00:09:42,710
+القناة و لوف ايدي هيكون طالع من هنا للمجمة الفيض و
+
+126
+00:09:42,710 --> 00:09:45,870
+النقطة اللي بقس عندها فعليا إيش داخل أنا مختارة
+
+127
+00:09:45,870 --> 00:09:50,090
+هاي النقطة لو مختارتها هنا هيكون طالع فهي كممرة
+
+128
+00:09:50,090 --> 00:09:55,560
+بحط الصمت على الأصبع الكبير في اتجاه التيارةوالإيد
+
+129
+00:09:55,560 --> 00:09:59,540
+بتلف بتوضحلي اتجاه ال magnetic field فال magnetic
+
+130
+00:09:59,540 --> 00:10:03,360
+field خلاجها ما لو داخله في السكورة وقعد لو كانت
+
+131
+00:10:03,360 --> 00:10:07,200
+النقطة هنا إيش هيكون طالع من السكورة واضحة هاي
+
+132
+00:10:07,200 --> 00:10:11,920
+النقطة طبعا هادي جاية من اللي هي ال hand ال right
+
+133
+00:10:11,920 --> 00:10:16,180
+hand rule اللي شفناها هذا زي ما أنتوا شايفين نحط
+
+134
+00:10:16,180 --> 00:10:20,580
+الصندوق اتجاه التيار وإيدي لفتها بتقولي وين اتجاه
+
+135
+00:10:20,580 --> 00:10:25,100
+ال magnetic field واضح؟فهي زي ما تشوفين هنا اتجاه
+
+136
+00:10:25,100 --> 00:10:27,880
+ال magnet field هيكون مع لفة الإيد، هي اتجاه ال
+
+137
+00:10:27,880 --> 00:10:30,300
+magnet field و هذا اتجاه ال current اللي هو اتجاه
+
+138
+00:10:30,300 --> 00:10:34,120
+ال sun، ال sun بيقول اتجاه ال current و لفة الإيد
+
+139
+00:10:34,120 --> 00:10:37,140
+بتقول اتجاه ال magnet field، هنا هيكون طالع و هنا
+
+140
+00:10:37,140 --> 00:10:42,920
+داخل، في ناس بتفضلش بتعمل هيك و هيكفي ناس يقولوا
+
+141
+00:10:42,920 --> 00:10:47,600
+ان هاي بتعملهم مشاكل يعني، كانوا زمان يعني يقعدوا
+
+142
+00:10:47,600 --> 00:10:51,920
+يروحوا على البراندات و يهوبوا و يعملوا هيك و تصير
+
+143
+00:10:51,920 --> 00:10:54,700
+مشاكل أبقى بيفكروا الولد بينادي للبنت و البنت
+
+144
+00:10:54,700 --> 00:10:57,480
+بينادي للولد، ينزلوا الأهالي و يقولوا المشاكل، هدر
+
+145
+00:10:57,480 --> 00:11:01,900
+على ذمة القراء يعني أو الرواد، هيك الرواد، فصاروا
+
+146
+00:11:01,900 --> 00:11:05,880
+الدكاترة يعطوا حاجة تانية، بيه برضه مش أسهل يعني،
+
+147
+00:11:05,880 --> 00:11:09,220
+بتخيلي أنه في عندك screwdriver، يعني ال screw هو
+
+148
+00:11:09,220 --> 00:11:13,440
+البرغيبرغي و انت بدك تلف البرغي، بدك تلف اتجاه
+
+149
+00:11:13,440 --> 00:11:17,120
+البرغي في اتجاه من الطيار يعني اذا الطيار لفوق بده
+
+150
+00:11:17,120 --> 00:11:20,520
+ألف انه يخش يعني كأنه بدخل في خرق و بده يروح اخر
+
+151
+00:11:20,520 --> 00:11:24,420
+فانا بلف البرغي و انا بلف البرغي و البرغي بطلع في
+
+152
+00:11:24,420 --> 00:11:26,980
+اتجاه ال current و اتجاه اللف بقول اتجاه ال
+
+153
+00:11:26,980 --> 00:11:31,280
+magnetic field لو ال current لتحت فإيش بسوي بلف
+
+154
+00:11:31,280 --> 00:11:34,620
+البرغي في هذا الاتجاه و هذا بقول اتجاه المالك يعني
+
+155
+00:11:34,620 --> 00:11:35,580
+هدا هي طريقتها
+
+156
+00:11:41,260 --> 00:11:44,600
+انت فاهمه ان النقطة هي بوز السهم و بتقوللي انه
+
+157
+00:11:44,600 --> 00:11:47,540
+طالع ال magnetic field طالع من سطح الورقة زي ما
+
+158
+00:11:47,540 --> 00:11:53,000
+انتوا شايفين ال X انه داخل هذا الطرف النهائي للسهم
+
+159
+00:11:53,000 --> 00:11:59,800
+ديش
+
+160
+00:11:59,800 --> 00:12:02,520
+نشوف ايش هي ال elements بتاعة ال current يعني احنا
+
+161
+00:12:02,520 --> 00:12:07,740
+في ال in the charges شوفنا eq, rho s هم ذاكرين و
+
+162
+00:12:07,740 --> 00:12:08,100
+rho v
+
+163
+00:12:17,390 --> 00:12:20,770
+لما كنا نحسب الـelectric field بالنسبة للتيار
+
+164
+00:12:20,770 --> 00:12:25,610
+هيكون عندنا دائما DL I DL هذا لو بحكي عن line
+
+165
+00:12:25,610 --> 00:12:32,590
+current I فال element هيكون I DLDL طبعا فكتور او
+
+166
+00:12:32,590 --> 00:12:38,290
+هيكون عندي surface KDS و DS احنا بعبر عن اللي هو
+
+167
+00:12:38,290 --> 00:12:43,950
+current density ب KS اللي هي ال Vector تبعي و عندي
+
+168
+00:12:43,950 --> 00:12:47,110
+اللي هو ال volume اللي هو J DV و DV زي ما انتوا
+
+169
+00:12:47,110 --> 00:12:51,810
+بتذكرين احنا قولنا دايما ال scalar فJ هي اللي
+
+170
+00:12:51,810 --> 00:12:56,190
+هتكون فكتور طبعا ال units عامهم بتتناسب مع اللي هو
+
+171
+00:12:56,190 --> 00:13:01,110
+القيمة بتاعتهمالـ DL أو I اللى هى ال line current
+
+172
+00:13:01,110 --> 00:13:06,750
+اللى هو ال M M برمتر ال surface current K هتكون A
+
+173
+00:13:06,750 --> 00:13:10,710
+برمتر تربية و ال volume current G هتكون A برمتر
+
+174
+00:13:10,710 --> 00:13:16,910
+cube ال magnetic field هيكون ال integral احنا جبنا
+
+175
+00:13:16,910 --> 00:13:20,310
+ال D أدشل ولا element فالأدشل كلش هيكون ال
+
+176
+00:13:20,310 --> 00:13:25,220
+integralإذا line هيكون integral over line إذا كان
+
+177
+00:13:25,220 --> 00:13:29,420
+surface يعني بال IDL قلنا KDS هيكون integral over
+
+178
+00:13:29,420 --> 00:13:33,700
+surface لو كان volume هيكون integral over volume
+
+179
+00:13:33,700 --> 00:13:40,300
+وهذه ال three equations
+
+180
+00:13:40,300 --> 00:13:46,000
+لل line و ال surface و ال volume نجي
+
+181
+00:13:46,000 --> 00:13:50,680
+نشوف مثال لو كان عندي أنا line محدد الطول إلوزي ما
+
+182
+00:13:50,680 --> 00:13:54,040
+انتوا شايفين ما بين النقطة A والنقطة B هذا هو ال
+
+183
+00:13:54,040 --> 00:13:58,840
+line وفيه طيار الطيار بيجي من النقطة A ويروح لنقطة
+
+184
+00:13:58,840 --> 00:14:05,000
+B وانا بدي أجيب ال magnet field لنقطة زي B زي
+
+185
+00:14:05,000 --> 00:14:10,480
+تقريبا بتحدد axis انا لو انا حددت ال axis انه الحط
+
+186
+00:14:10,480 --> 00:14:13,080
+اللي في مورفي الكرانت اللي هو ال conductor المورفي
+
+187
+00:14:13,080 --> 00:14:18,690
+الكرانت هو اعلى ال Z axisع ال z axis وهي ال origin
+
+188
+00:14:18,690 --> 00:14:22,550
+تبعي وهي النقطة a والنقطة b هو ال line تبعي أو ال
+
+189
+00:14:22,550 --> 00:14:25,790
+current تبعي اللي على ال z axis بيه هتكون زى ما
+
+190
+00:14:25,790 --> 00:14:28,810
+انتوا شايفين على ال raw axis على واحد انا ال
+
+191
+00:14:28,810 --> 00:14:34,150
+cylindrical coordinate هتكون ال raw طبعا اذا نقلش
+
+192
+00:14:34,150 --> 00:14:37,710
+البعد تبع النقطة اللى بدأيسي عندها ال magnet field
+
+193
+00:14:37,710 --> 00:14:42,010
+هو ال raw raw hat و ال element تبعي هي udl ايش
+
+194
+00:14:42,010 --> 00:14:48,400
+هيكون z z hatصح؟ هذه المسافة سماها Z مابين هي
+
+195
+00:14:48,400 --> 00:14:51,880
+حددنا ال element DL عشان أحل في بايت و سافرت له
+
+196
+00:14:51,880 --> 00:14:57,700
+بده أحدد ال element DL هنا line يعني DL I في DL DL
+
+197
+00:14:57,700 --> 00:15:01,760
+بعضها عن ال zero نسميها مثلا Z وبتجاه مين هيكون Z
+
+198
+00:15:01,760 --> 00:15:05,320
+hatالنقطة اللي بدي ايس عندها المجد كفيد في هالحالة
+
+199
+00:15:05,320 --> 00:15:10,300
+هاخد cylindrical coordinate رو رو هات اذا R اللي
+
+200
+00:15:10,300 --> 00:15:13,820
+مابين ال element و النقطة اللي بدي ايس عندها المجد
+
+201
+00:15:13,820 --> 00:15:20,380
+كفيد هايكون رو رو هات minus Z Z hat تمام؟ اذا هدا
+
+202
+00:15:20,380 --> 00:15:23,880
+هي القانون تبعنا DH اللي هو vector بالسوء ال DL
+
+203
+00:15:23,880 --> 00:15:27,700
+cross R على 4 by R cubed بحدد اللي هو ال element
+
+204
+00:15:27,700 --> 00:15:36,080
+تبعي DL اللي هو عبارة عن مين DZDL DZ واضح هنا DZ I
+
+205
+00:15:36,080 --> 00:15:43,760
+DZ ال element DZ Z hat وR رورو hat نقل Z Z hat ليش
+
+206
+00:15:43,760 --> 00:15:47,880
+لأن Z هي موقع ال DZ بتاعتي و أنا حددت ال element
+
+207
+00:15:47,880 --> 00:15:52,200
+تبعنا DL cross R إيش هتساوي إن أنا أخد ال cross
+
+208
+00:15:52,200 --> 00:15:55,980
+product بين اتنين ال Z hat مع ال رو hat تعطينا فيه
+
+209
+00:15:55,980 --> 00:15:58,040
+hat لكن Z hat مع Z hat zero
+
+210
+00:16:03,900 --> 00:16:09,660
+واضح؟ نعود في ال Hهتكون الـ integral I عوض ع ال
+
+211
+00:16:09,660 --> 00:16:15,040
+cross product DL cross R rho DZ by hat على 4 by R
+
+212
+00:16:15,040 --> 00:16:19,200
+cube، mean R هي R، المجنيتو التبعها إيش هيكون؟ رو
+
+213
+00:16:19,200 --> 00:16:23,000
+تربيع زي زي التربيع تحت الجزر، كل cube هتصبح رو
+
+214
+00:16:23,000 --> 00:16:26,680
+تربيع زي زي التربيع القوة تلاتة على اتنين طبعاً
+
+215
+00:16:26,680 --> 00:16:30,790
+ممكن أكمل هذا ال integral عشان أكملهبدي أشوف إيش
+
+216
+00:16:30,790 --> 00:16:33,690
+الطريقة اللي بدها تناسبني للتكامل عندي row و dz
+
+217
+00:16:33,690 --> 00:16:38,170
+الحل هي أني هستخدم ال trick اللي هي العلاقة بين z
+
+218
+00:16:38,170 --> 00:16:42,910
+و row إذا أحنا طلعنا ع z و row العلاقة بينهم دلالة
+
+219
+00:16:42,910 --> 00:16:47,050
+alpha اللي هي الزاوية بين ال element و الخط الواصم
+
+220
+00:16:47,050 --> 00:16:50,750
+بين z و نقطة القياس لأيه زي ما تشوفين alpha
+
+221
+00:16:50,750 --> 00:16:57,010
+هتعطينا z اللي بتسوي row كتان alpha row كتان alpha
+
+222
+00:16:59,550 --> 00:17:04,370
+لو انا أخدت لأنه z زد على raw الكتان ال raw على ال
+
+223
+00:17:04,370 --> 00:17:07,970
+z هي التان ف ال z بتسوى raw كتان alpha ف دي z ايش
+
+224
+00:17:07,970 --> 00:17:13,250
+بتسوى minus raw cosecant تربيه alpha d alpha لو
+
+225
+00:17:13,250 --> 00:17:19,010
+عوضنا بال variables هكون ان انا اخلصت من الواحد
+
+226
+00:17:19,010 --> 00:17:19,870
+بالدلالة التانية
+
+227
+00:17:22,620 --> 00:17:26,520
+هتكون Alpha عندي تتغير من Alpha 1 ل Alpha 2، واضحش
+
+228
+00:17:26,520 --> 00:17:29,820
+اللي صار؟ احنا عندنا اللي هي ال Raw وعندي ال Z
+
+229
+00:17:29,820 --> 00:17:34,090
+فأول بجيب العلاقة بين ال Raw و ال Zو بحر ال
+
+230
+00:17:34,090 --> 00:17:37,550
+integration تبعي بطلع معايا ان ال magnetic field
+
+231
+00:17:37,550 --> 00:17:41,070
+بساوي I على 4 by rho cosine alpha 2 minus cosine
+
+232
+00:17:41,070 --> 00:17:45,250
+alpha 1 في Phi hat اتجاه ال magnetic field في
+
+233
+00:17:45,250 --> 00:17:47,690
+اتجاه ال Phi hat طبعا احنا ممكن نستخدم الرواية
+
+234
+00:17:47,690 --> 00:17:51,130
+hand rule احنا نستخدمها cross product لو انا حاطيت
+
+235
+00:17:51,130 --> 00:17:55,630
+ال thumb تبعي في اتجاه ال line هلاقي ان ايدي ماله
+
+236
+00:17:55,630 --> 00:17:56,830
+هطلو في هاي ال rho احنا
+
+237
+00:18:16,780 --> 00:18:21,920
+بشكل عام بدي أجيب ال magnet field من ال lineبدنا
+
+238
+00:18:21,920 --> 00:18:25,880
+نحط يعني حاجة بتسهل علينا الحل كتير أنه Phi hat
+
+239
+00:18:25,880 --> 00:18:30,880
+هتساوي DL بحدد اتجاه ال line اللي هو هيمثل زي ال
+
+240
+00:18:30,880 --> 00:18:37,680
+axis تبع الاستوانة DL باتجاه وين AL hat cross mean
+
+241
+00:18:37,680 --> 00:18:40,920
+rho رو اللي هو العمودي ما بين نقطة قياس ال
+
+242
+00:18:40,920 --> 00:18:44,520
+magnetic field على مين على الخط ال morphic الكانت
+
+243
+00:18:44,520 --> 00:18:48,620
+يعني هدبكوا تحفظوها بتسهل عليكوا تحديد اتجاه ال
+
+244
+00:18:48,620 --> 00:18:53,090
+magnetic fieldطبعا إذا إحنا بنحفظ كيف نجيب الـ Phi
+
+245
+00:18:53,090 --> 00:18:56,730
+hat لإن إذا .. يعني هنلاحظ على .. تشوف كمان أمثلة
+
+246
+00:18:56,730 --> 00:18:59,830
+قد قلتها كيف إنه سهل عليه أستخدم هذه العلاقة بيضل
+
+247
+00:18:59,830 --> 00:19:03,310
+إني دايما أجيب اتجاه ال Phi hat ف Phi hat هي هتكون
+
+248
+00:19:03,310 --> 00:19:06,970
+DL hat اللي هو وين اتجاه ال current ال cross اللي
+
+249
+00:19:06,970 --> 00:19:10,850
+هو الخط الواصل العمودي مش الواصل بين ال element و
+
+250
+00:19:10,850 --> 00:19:15,470
+نقطة قياس المجد فيه العمودي ما بين نقطة قياس وين
+
+251
+00:19:15,470 --> 00:19:20,490
+بدأيش المجد فيه و من الخط اللي بيور فيه التيارهذا
+
+252
+00:19:20,490 --> 00:19:24,930
+هو ال raw هيتعريفه، واضح؟ إذا ال hat cross raw hat
+
+253
+00:19:24,930 --> 00:19:29,370
+يبقى تقنين ال file hat نشوف أمثلة زي حالات خاصة
+
+254
+00:19:29,370 --> 00:19:33,010
+نعتبرها للمثال السابق أول حاجة لو كان عندي semi
+
+255
+00:19:33,010 --> 00:19:35,790
+-infinite، إيش semi-infinite؟ يعني النقطة A صارت
+
+256
+00:19:35,790 --> 00:19:41,210
+عند 0 0 0 و النقطة B صارت عند 0 0 infinity، صارت
+
+257
+00:19:41,210 --> 00:19:43,570
+semi-infinite يعني بروحش من ما يناسب infinity لما
+
+258
+00:19:43,570 --> 00:19:47,150
+يناسب infinity، بروح من 0 ل infinity الخط اللي بمر
+
+259
+00:19:47,150 --> 00:19:52,180
+فيه ال currentمايعني ألف واحد صارت تسعين ألف واحد
+
+260
+00:19:52,180 --> 00:19:55,740
+ما بين الخط المورفي التيار و أقرب صرت هنا ألف واحد
+
+261
+00:19:55,740 --> 00:20:04,360
+اذا قلنا a صارت zero zero zero هي
+
+262
+00:20:04,360 --> 00:20:11,120
+صارت هنا ال a فالألف هو صارت ألف واحد ما بين الخط
+
+263
+00:20:11,120 --> 00:20:15,900
+المورفي التيار و النقطة اللي واصلة لي ال a الحدود
+
+264
+00:20:15,900 --> 00:20:19,560
+بتاعة ال lineالـ α1 و الـ α2 اللي عملنا
+
+265
+00:20:19,560 --> 00:20:23,300
+integration فإذا النقطة A صارت عند الـ 00، الـ α1
+
+266
+00:20:23,300 --> 00:20:28,680
+تصير 90 و الـ α2 تصير عند الـ infinity فكأنه في
+
+267
+00:20:28,680 --> 00:20:31,320
+end ال infinity إيش بيصيروا خطين متوازية، فبصير 0
+
+268
+00:20:31,320 --> 00:20:39,500
+فإذا الـ α1 90 و الـ α2 تصير 0 أنا هو السمية
+
+269
+00:20:39,500 --> 00:20:43,290
+infinite، فأنا لو عقدتفالقيام في المعادلة اللى
+
+270
+00:20:43,290 --> 00:20:46,870
+اشتغلها مع بعض لها ال element اللى من نقطة A لنقطة
+
+271
+00:20:46,870 --> 00:20:52,290
+D بعود عن Alpha 91 و Alpha 2 ب Zero جبتنا Zero
+
+272
+00:20:52,290 --> 00:20:57,050
+واحد جبتنا سنين سفر فهى كل ناتج H بتساوي I على
+
+273
+00:20:57,050 --> 00:21:02,660
+four by rho Phi hatلو كان infinite مش infinite
+
+274
+00:21:02,660 --> 00:21:06,700
+infinite يعني النقطة A بتروح من 0 عند ال 0 0 minus
+
+275
+00:21:06,700 --> 00:21:11,800
+infinity و النقطة B 00 infinity بدي أحدد من Alpha
+
+276
+00:21:11,800 --> 00:21:15,960
+1 و Alpha 2 Alpha 1 هي عند ال 180 و Alpha 2 عند ال
+
+277
+00:21:15,960 --> 00:21:22,340
+0 اعود جبت من ال 01 جبت من ال 180 ناقص 1 ناقص ناقص
+
+278
+00:21:22,340 --> 00:21:26,860
+فسيصبح plus فسيصبح 2 I على 4 by rho اذا هتكون I
+
+279
+00:21:26,860 --> 00:21:29,500
+على 2 by rho Phi hat تمام؟
+
+280
+00:21:34,850 --> 00:21:38,470
+كمان مثال عندي زى ما انتوا شايفين هذا ال loop اللى
+
+281
+00:21:38,470 --> 00:21:41,650
+هو عبارة عن شكل ال triangle ال current مر في
+
+282
+00:21:41,650 --> 00:21:45,210
+الاتجاهات اللى انتوا شايفينها اللى هو بروح من zero
+
+283
+00:21:45,210 --> 00:21:50,790
+لتنين وعلى ال x axis و بكمل و برجع ل ال zero فعندي
+
+284
+00:21:50,790 --> 00:21:54,950
+three buses واحد اتنين تلاتة و التيار قيمته عشرة
+
+285
+00:21:54,950 --> 00:21:59,990
+امبير وعندي طول ال element على ال x axis اتنين و
+
+286
+00:21:59,990 --> 00:22:04,690
+هكذا هى اللى معطيتو طبعا ال top point او يعني ال y
+
+287
+00:22:04,690 --> 00:22:09,410
+axis اللي هو العمود ال vertical من الرأس للقاعدة
+
+288
+00:22:09,410 --> 00:22:14,110
+قيمته واحدبتاع المعطيات اللي هي بدنا ال magnetic
+
+289
+00:22:14,110 --> 00:22:19,810
+field النقطة 005 وين وقع ال z axis عمودي على هذا
+
+290
+00:22:19,810 --> 00:22:26,190
+ال plan هذا ال plan xy وانا بدي النقطة عند 005
+
+291
+00:22:26,190 --> 00:22:31,250
+يعني عمودي على هذا ال axis x0 y0 ويه في القسط في x
+
+292
+00:22:31,250 --> 00:22:37,870
+axis على النقطة 5 وبدوا مين؟بدو هذا ناتج من مين
+
+293
+00:22:37,870 --> 00:22:42,450
+فقط من ال side 1 يعني بدو يحسب ان ال magnetic
+
+294
+00:22:42,450 --> 00:22:48,470
+field عنده نقطة 005 الناتجة من مرور التيار في ال
+
+295
+00:22:48,470 --> 00:22:54,160
+side رقم 1 هو معلمهم 123ديها فقط منها، للتسهيل بدي
+
+296
+00:22:54,160 --> 00:22:57,380
+أعيد رسم ال .. الرسم اللي قدامي بدي أوضح وين
+
+297
+00:22:57,380 --> 00:23:00,960
+النقطة بحسب عندها الماجنة تكفيها عشان بدي أجيب انا
+
+298
+00:23:00,960 --> 00:23:04,620
+ال .. ال .. ال .. البعد تبع النقطة هاي من ..
+
+299
+00:23:04,620 --> 00:23:08,000
+بالنسبة لل coordinate زي البعد ال .. ال .. ال
+
+300
+00:23:08,000 --> 00:23:11,820
+element فالرسمة كانت تانية بسيطة بدي أوضح فيها ال
+
+301
+00:23:11,820 --> 00:23:14,480
+z axis و ال element ال element أواقع مين على ال x
+
+302
+00:23:14,480 --> 00:23:19,610
+axisو الـ z axis النقطة بدقيس عندها ال field هي
+
+303
+00:23:19,610 --> 00:23:25,610
+النقطة الخامسة هاي ال element تبعا بادي نرجع كمرة
+
+304
+00:23:25,610 --> 00:23:29,090
+من zero ل اتنين هاي طوله من zero ل اتنين هذا ماله
+
+305
+00:23:29,090 --> 00:23:36,130
+محدد طوله مش واحد لل infinity من a ل b واضح و ال z
+
+306
+00:23:36,130 --> 00:23:41,950
+axis عمودي علين و نتجاهه xyz يعني على قوة i فعشان
+
+307
+00:23:41,950 --> 00:23:47,070
+هيك قعدنا الرسمهذه الـ x وهذه الـ element الموجود
+
+308
+00:23:47,070 --> 00:23:51,350
+في تيارة من النقطة 0 إلى 2 عشرة أنفر هذه الـ mean
+
+309
+00:23:51,350 --> 00:23:56,030
+اللي هي a ال hat اتجاه mean ال current a ال hat
+
+310
+00:23:56,030 --> 00:23:59,510
+والنقطة اللي بدأ اسمها ال magnet field على بعض
+
+311
+00:23:59,510 --> 00:24:03,410
+خمسة وهنا بالتمام عمودية على ال zero فهذه ال mean
+
+312
+00:24:03,410 --> 00:24:09,170
+ال raw hat تمام a hat raw hat نحط القانون طبعاأيش
+
+313
+00:24:09,170 --> 00:24:12,850
+القانون قال ان H vector بتساوي I على 4 by rho
+
+314
+00:24:39,550 --> 00:24:42,870
+الطولة ده اتنين وعارفة الطولة ده خمسة صفر و بقدر
+
+315
+00:24:42,870 --> 00:24:47,330
+اجيب هى بجيبها من التان المقابل على المجاور خمسة
+
+316
+00:24:47,330 --> 00:24:51,470
+على اتنين و هكذا و بعدين بجيب قيمة ال cosine دبعها
+
+317
+00:24:51,470 --> 00:24:54,830
+او على طول بجيب انه هذا جزر التربيع لها اتنين
+
+318
+00:24:54,830 --> 00:24:57,890
+تربيع زي خمس تربيع يعني اربعة زي خمسة و عشرين عشان
+
+319
+00:24:57,890 --> 00:25:03,990
+تربيع تسعة و عشرينفإذا ان هي عبارة ال cos α جب
+
+320
+00:25:03,990 --> 00:25:07,150
+تمام التسعين اللي هو سفر جب تمام ال alpha اتنين
+
+321
+00:25:07,150 --> 00:25:12,290
+اللي هي اتنين على جزر التسعة وعشرين رو عارفينها رو
+
+322
+00:25:12,290 --> 00:25:15,110
+واضحة اللي هي ما بين النقطة باسعة و ده المجلة فيه
+
+323
+00:25:15,110 --> 00:25:21,690
+و عمودي هو العمودي على المسار تبع التيارة فهنا رو
+
+324
+00:25:21,690 --> 00:25:27,770
+جاهزة خمسة واضح؟ بنعود عندي I عشرة أمبير معطيني
+
+325
+00:25:27,770 --> 00:25:32,470
+إياها رو عارفناها خمسةبظلمين اللي هي ال a fi hat
+
+326
+00:25:32,470 --> 00:25:37,070
+احنا قولنا كيف بنحدد ال a fi hat a l hat cross a
+
+327
+00:25:37,070 --> 00:25:42,430
+rho hat a l hat اللي هي x hat cross rho hat اللي
+
+328
+00:25:42,430 --> 00:25:48,850
+هي z hat x cross z عكس الدائرة هيك x y z x cross z
+
+329
+00:25:48,850 --> 00:25:52,670
+minus y hat فعرفنا ان انا اتجاه ال fi hat نفس
+
+330
+00:25:52,670 --> 00:25:58,400
+الشيء لو عملنا اللي هي ال x ولفنااتجاه المجلد فيه
+
+331
+00:25:58,400 --> 00:26:02,980
+طالع من النقطة طالع هذا اتجاه مين احنا عشان نعرفه
+
+332
+00:26:02,980 --> 00:26:08,360
+انتجاه ال Y X Y لازم تكون لجوا XYZ صح ال right
+
+333
+00:26:08,360 --> 00:26:11,760
+hand rule فإذا هي طالع على برا و إش هذا minus Y
+
+334
+00:26:11,760 --> 00:26:18,680
+طبعا إذا نعرفين كل ناسر إش عشرة كل حاجة صارت
+
+335
+00:26:18,680 --> 00:26:22,360
+معروفة عشرة أمبير Alpha by خمسة cosine ال Alpha
+
+336
+00:26:22,360 --> 00:26:25,700
+اتنين اللي هي اتنين ع جزر الخمسة وعشرين cosine
+
+337
+00:26:25,700 --> 00:26:26,800
+Alpha واحد سفر
+
+338
+00:26:33,640 --> 00:26:37,480
+المثال التاني يقول ان انا بدي ال magnet field نقطة
+
+339
+00:26:37,480 --> 00:26:40,920
+ماينوس تلاتة اكس ماينوس تلاتة ماينوس تلاتة ماينوس
+
+340
+00:26:40,920 --> 00:26:47,340
+تلاتة ماينوس تلاتة ماينوس تلاتة ماينوس
+
+341
+00:26:47,340 --> 00:26:49,800
+تلاتة ماينوس تلاتة
+
+342
+00:26:53,870 --> 00:26:57,430
+طالب منها انه نجيب ال magnetic field عند النقطة X
+
+343
+00:26:57,430 --> 00:27:05,110
+-3 Y4 و Z0 يعني وين وقع النقطة على ال XY plane Z
+
+344
+00:27:05,110 --> 00:27:09,270
+قيمتها 0 النقطة بدأت تطور منها ال magnetic field
+
+345
+00:27:09,270 --> 00:27:12,970
+وقع على ال XY plane زي اسم طلعته انتوا هتلاقوا ان
+
+346
+00:27:12,970 --> 00:27:15,630
+فينا two contributors ل magnetic field عندها
+
+347
+00:27:15,630 --> 00:27:21,460
+النقطة واحد جاي من ال line اللي على ال Z axisاللي
+
+348
+00:27:21,460 --> 00:27:26,620
+على الـ z axis اللي بيمتد من infinity لصفر تجاه ال
+
+349
+00:27:26,620 --> 00:27:30,160
+current التجاهه جاي من ال infinity لصفر semi
+
+350
+00:27:30,160 --> 00:27:35,500
+infinite line و التاني اللي ببدأ من ال zero و بروح
+
+351
+00:27:35,500 --> 00:27:39,680
+ل ال infinity ع ال x axis فعشان نسهل ع بعض هنقول
+
+352
+00:27:39,680 --> 00:27:42,300
+ان انا بعرف اجيب المجنة الفيلة اللي جاي من me من
+
+353
+00:27:42,300 --> 00:27:45,260
+semi infinite line و عنده two semi infinite line
+
+354
+00:27:45,260 --> 00:27:48,840
+فهسمي ان المجنة الفيلة ال total هو اللي جاي من
+
+355
+00:27:49,780 --> 00:27:52,160
+المجد فيه اللي جاي من ال semi infinite line اللي
+
+356
+00:27:52,160 --> 00:27:56,140
+على X axis هسميه HX زائد المجد فيه اللي جاي من ال
+
+357
+00:27:56,140 --> 00:28:00,340
+semi infinite line اللي على ال Z axis زائد HZ فإذا
+
+358
+00:28:00,340 --> 00:28:03,400
+بدي أجيب إن كل واحد بتدور أجمعه في النهاية مع بعض
+
+359
+00:28:03,400 --> 00:28:07,300
+بس دائما بدي أسهل الصورة اللي عشان أقدر أحدد اللي
+
+360
+00:28:07,300 --> 00:28:15,600
+هي Y hat هنبدأ بالـ line اللى وين على ال z axis لو
+
+361
+00:28:15,600 --> 00:28:20,980
+انا حطيت ال x و ال y ال current ايش اتجاهه داخل
+
+362
+00:28:20,980 --> 00:28:26,740
+ايه احطتلك يا داخل اذا انا حطتها ال x و ال y ال
+
+363
+00:28:26,740 --> 00:28:30,800
+current اتجاهه داخل لكن ال z اتجاهه وين لفوق لبره
+
+364
+00:28:30,800 --> 00:28:35,900
+لكن ال current اتجاهه داخل x y z و ال current داخل
+
+365
+00:28:38,720 --> 00:28:42,800
+هي ال current احنا مش بنحدد في المعادلة بتاعتنا ان
+
+366
+00:28:42,800 --> 00:28:46,960
+دي L بنحددها و دي L واضح اللي هي mean minus z hat
+
+367
+00:28:56,300 --> 00:29:01,680
+I على 4 by rho cos α2 وcos α1 وφيها تدول بنجيبهم
+
+368
+00:29:01,680 --> 00:29:04,920
+عشان أستخدم العلاقة اللي اشتقناها بناشنا إيه
+
+369
+00:29:04,920 --> 00:29:07,140
+بنشتقها من أول و جديد هي تاعت اسم Infinite line زى
+
+370
+00:29:07,140 --> 00:29:10,800
+ما شوفنا في الأمس لسه علاقة فبدي أحدد ال rho هات
+
+371
+00:29:10,800 --> 00:29:15,220
+cos α2 وcos α1 هى بسم كام مرة راح أحطيتها هى كام
+
+372
+00:29:15,220 --> 00:29:19,600
+مرة أذكركم XYZ طالع اتجاه ال current ماله في ال
+
+373
+00:29:19,600 --> 00:29:24,680
+negative Z فهو داخلأول حاجة نحدد ميه ال current ال
+
+374
+00:29:24,680 --> 00:29:28,360
+current هو ماعطينا قيمته في ال file amount قداش
+
+375
+00:29:28,360 --> 00:29:33,760
+قيمة ال current تلاتة أمبير I تلاتة أمبير current
+
+376
+00:29:33,760 --> 00:29:37,480
+تلاتة أمبير بدنا نجيب ال raw ايش يومنا ال raw هي
+
+377
+00:29:37,480 --> 00:29:41,940
+المسافة العمودية ما بين النقطة اللي بدأيس عليها ال
+
+378
+00:29:41,940 --> 00:29:44,880
+magnet field و الخط الممر فيه الطيارة العمودية
+
+379
+00:29:45,610 --> 00:29:49,530
+النقطة اللى بدأيش عندها التيار هي x-3 ال magnetic
+
+380
+00:29:49,530 --> 00:29:51,870
+field اصلا النقطة اللى بدأيش عندها magnetic field
+
+381
+00:29:51,870 --> 00:29:57,970
+هي النقطة اللى واقع عند x-3 و y4 هي هالنقطة ايه
+
+382
+00:29:57,970 --> 00:30:00,910
+النقطة؟ x عندها minus 3 و y minus 4 اذا ال raw
+
+383
+00:30:00,910 --> 00:30:03,990
+بتاعة تكون العمودية منها على الخط اللى مر في
+
+384
+00:30:03,990 --> 00:30:08,910
+التيار هي اللى هسميها rawلأن ما هي X ولا Y فهي
+
+385
+00:30:08,910 --> 00:30:13,570
+رقم، مش مثل سوى جزر التربيع لأ اللي اتنقص ثلاثة
+
+386
+00:30:13,570 --> 00:30:17,570
+تربيع زاد أربعة تربيع، صح؟ يعني جزر التربيع لتسعة
+
+387
+00:30:17,570 --> 00:30:22,630
+زاد ستاشر دحت الجزر، خمسة، لذا هي رقم عرفناها،
+
+388
+00:30:22,630 --> 00:30:26,790
+اللي هي المسافة قولنا كمان مرة الخط العمودي على
+
+389
+00:30:26,790 --> 00:30:29,870
+مرور التيار اللي بيوصل ما بين اللي .. اللي هو
+
+390
+00:30:29,870 --> 00:30:33,270
+العمود هذا اللي بيوصل ما بين الخط المرور فيه
+
+391
+00:30:33,270 --> 00:30:36,420
+التيار ونقطة الرئيس عندها ال magnetic fieldعن مين
+
+392
+00:30:36,420 --> 00:30:39,600
+الخط المورفي الطيارة الـ z-axis والنقطة هي واقع
+
+393
+00:30:39,600 --> 00:30:46,820
+هنا عند (-3,4). هذه الروح. واقع؟ إذن هي جيبنا
+
+394
+00:30:46,820 --> 00:30:51,720
+الروح من مين؟ Alpha 2 و Alpha 1 Alpha 1 و Alpha 2
+
+395
+00:30:51,720 --> 00:30:57,460
+بدرجة على الرسم اللي قدامنا هاي ال z-axis وهي
+
+396
+00:30:57,460 --> 00:31:02,380
+Alpha 1 هي Alpha 1 العمودية بين النقطة
+
+397
+00:31:10,590 --> 00:31:13,950
+عمودي لأن هذا الـ z axis وهذا هو أعوان في ال XY
+
+398
+00:31:13,950 --> 00:31:17,530
+plane فأكيد عمودي عليه أي خط في ال plane العمودي
+
+399
+00:31:17,530 --> 00:31:21,830
+على ال line هيكون عمودي عليه هذه النقطة البدئيسة
+
+400
+00:31:21,830 --> 00:31:27,050
+في ال z axis وهذه النقطة الوقعز اللي بديها اللي هي
+
+401
+00:31:27,050 --> 00:31:30,670
+الطرف ما بينعشان أجيب الزاوية، هتكون تسعين درجة،
+
+402
+00:31:30,670 --> 00:31:34,850
+واضح؟ وAlpha 2 اللي هي البعيدة، التنين بيصيروا
+
+403
+00:31:34,850 --> 00:31:38,530
+كأهم جواز و بعيد، فهتكون Zero فإذا هنا هتكون Alpha
+
+404
+00:31:38,530 --> 00:31:42,370
+1 تسعين، لكن Alpha 2 هتكون سفر، أنا رايحة ال
+
+405
+00:31:42,370 --> 00:31:46,610
+Infinity فالحطيم ينتقل طويلا إلى أن يكون السفر،
+
+406
+00:31:46,610 --> 00:31:48,430
+فعرفنا Alpha 1 و Alpha 2
+
+407
+00:31:54,280 --> 00:31:57,140
+مثلنا عارفين Alpha 1 و Alpha 3، مين ضال علينا؟ ال
+
+408
+00:31:57,140 --> 00:31:59,820
+Phi hat إيش اتجاهها؟ إيش قلنا ال Phi hat؟ هي عالي
+
+409
+00:31:59,820 --> 00:32:06,900
+ورا عني، ال rho hat، ال L hatالهات اكروس الهات
+
+410
+00:32:06,900 --> 00:32:12,980
+الهات الهات
+
+411
+00:32:12,980 --> 00:32:18,060
+الهات الهات الهات الهات الهات الهات الهات الهات
+
+412
+00:32:18,060 --> 00:32:21,000
+الهات الهات الهات الهات الهات الهات الهات الهات
+
+413
+00:32:21,000 --> 00:32:21,680
+الهات الهات الهات الهات الهات الهات الهات الهات
+
+414
+00:32:21,680 --> 00:32:24,540
+الهات الهات الهات الهات الهات الهات الهات الهات
+
+415
+00:32:24,540 --> 00:32:25,120
+الهات الهات الهات الهات الهات الهات الهات الهات
+
+416
+00:32:25,120 --> 00:32:25,200
+الهات الهات الهات الهات الهات الهات الهات الهات
+
+417
+00:32:25,200 --> 00:32:25,520
+الهات الهات الهات الهات الهات الهات الهات الهات
+
+418
+00:32:26,410 --> 00:32:32,450
+فإذن row hat هتكون minus 3x hat زي 4y hat على
+
+419
+00:32:32,450 --> 00:32:36,970
+المقدار اللي هو 5 فباخد ال cross product لal hat
+
+420
+00:32:36,970 --> 00:32:41,670
+اللي هي minus z hat cross row hat طبعا هذه ممكن
+
+421
+00:32:41,670 --> 00:32:47,790
+شوية تفكير كيف ممكن أبسط ال a pi hat ل 4 5 على 5 x
+
+422
+00:32:47,790 --> 00:32:52,330
+hat زي 3 على 5 a y hat ده هي ال a pi hat ممكن
+
+423
+00:32:52,330 --> 00:32:58,770
+أحطها إبساطة 3 على 4 by 5في جيب تمام اللي هي 01
+
+424
+00:32:58,770 --> 00:33:04,770
+جيب تم 90 0 فهيكون عندي 1 before x hat زي 3 y hat
+
+425
+00:33:04,770 --> 00:33:09,150
+على 5 بحصل على اللي هي ال magnetic field بجانب مين
+
+426
+00:33:09,150 --> 00:33:13,010
+من ال current اللي ع ال z axis عند النقطة اللي
+
+427
+00:33:13,010 --> 00:33:18,090
+بديها اللي هي x ناقص 3 y أربع HZ قلنا مين اللي هو
+
+428
+00:33:18,090 --> 00:33:21,090
+ال magnetic field الناتج من ال current اللي بمر في
+
+429
+00:33:21,090 --> 00:33:24,660
+ال filament اللي قاعد ع ال z axis هاي معناهامش ال
+
+430
+00:33:24,660 --> 00:33:27,340
+magnetic field في ال z direction لأ هي عبارة عن
+
+431
+00:33:27,340 --> 00:33:32,660
+magnetic field الناتج عند النقطة minus 340 من ال
+
+432
+00:33:32,660 --> 00:33:35,580
+filament اللي قاعدة على ال z axis طب بدنا نجيب
+
+433
+00:33:35,580 --> 00:33:39,140
+اللي هي مين ال magnetic اللي ناتج من ال filament
+
+434
+00:33:39,140 --> 00:33:43,300
+اللي على ال x axis كمان نفس الحاجة بدي أبسطها بشكل
+
+435
+00:33:43,300 --> 00:33:46,750
+اللي أقدر أتعامل معاهاهذا بدنا ناخد الـ plan يلي
+
+436
+00:33:46,750 --> 00:33:50,130
+هو minus 3 لإن النقطة وين قاعدة عند الـ minus 3
+
+437
+00:33:50,130 --> 00:33:53,190
+النقطة اللي بدأ إيسها عند ال filement تبدأ من zero
+
+438
+00:33:53,190 --> 00:33:57,210
+ال filement بتبدأ من zero ل infinity على ال X axis
+
+439
+00:33:57,210 --> 00:34:00,170
+بس النقطة اللي بدأ إيسها عندها وين وقع عند minus 3
+
+440
+00:34:00,170 --> 00:34:03,570
+فلو أخدت ال plan يلي عند minus 3 على ال X axis
+
+441
+00:34:03,570 --> 00:34:10,810
+هتكون ال Y كمتها 4 فإذا أنا بده النقطة اللي عند Y
+
+442
+00:34:10,810 --> 00:34:17,060
+4 و X minus 3 فهذا ال plan يليبدأ أو اللى عنده
+
+443
+00:34:17,060 --> 00:34:18,880
+النقطة اللى اسمها ال magnetic field لكن ال
+
+444
+00:34:18,880 --> 00:34:22,120
+filement بتاعتى كمان مره بذكركوا بتنموين من zero ل
+
+445
+00:34:22,120 --> 00:34:25,780
+infinity اذا هنا انا بدأ ايس ال magnetic field
+
+446
+00:34:25,780 --> 00:34:30,080
+اللى عندها النقطة اللى عندها X minus 3 و Y بتساوي
+
+447
+00:34:30,080 --> 00:34:35,920
+4 نبدأ نحدد اللى هي القلاعب بتاعتنا ال current
+
+448
+00:34:35,920 --> 00:34:40,740
+اللى بيمر فيها ال filement قيمته 3 أمبير نفس
+
+449
+00:34:40,740 --> 00:34:43,540
+القيمة بتمر في ال two filements 3 أمبير
+
+450
+00:34:50,420 --> 00:34:52,040
+نحدد قيمة ال raw
+
+451
+00:35:07,420 --> 00:35:10,760
+حدد قيمة ال raw ال raw واضح انها اربعة اللى هى
+
+452
+00:35:10,760 --> 00:35:14,280
+المسافة ما بين النقطة اللى بدى ايس عندها ال
+
+453
+00:35:14,280 --> 00:35:19,460
+magnetic field اللى هي هدى x-3 أو 4 او y4 ومين
+
+454
+00:35:19,460 --> 00:35:23,640
+وعموديه على ال line اللى بمر فيه ال current طبعا
+
+455
+00:35:23,640 --> 00:35:27,100
+احنا ال current ماله في الوسط في x axis عشان هيك
+
+456
+00:35:27,100 --> 00:35:32,070
+انا ماخده انه طالع من ال planeإذا أخدنا من ال X ال
+
+457
+00:35:32,070 --> 00:35:37,410
+right hand rule X X Y Z الاتجاه صحيح X X Y Z اتجاه
+
+458
+00:35:37,410 --> 00:35:41,910
+ال Z صحيح ف ال X في اتجاه طالع ال point بتدللي ان
+
+459
+00:35:41,910 --> 00:35:46,830
+ال X طالعفال raw قلنا هو العمود اللى ما بين النقطة
+
+460
+00:35:46,830 --> 00:35:49,950
+البداية عندها ال magnetic field و الخط اللى مور
+
+461
+00:35:49,950 --> 00:35:52,070
+فيه الطيارة، الخط اللى مور فيه الطيارة هو طالع من
+
+462
+00:35:52,070 --> 00:35:55,930
+الورقة فعلى امتداده، احنا هو بيبدأ صحي من السفر
+
+463
+00:35:55,930 --> 00:35:59,510
+لكن على امتداده هي العمود عليه اللى هو ال raw اللى
+
+464
+00:35:59,510 --> 00:36:02,810
+هو بالتمام بسوء أربعة، واضح؟
+
+465
+00:36:13,970 --> 00:36:18,470
+عشان اجيب العمود هاي العمود اللى هو ال raw مابين
+
+466
+00:36:18,470 --> 00:36:21,150
+النقطة اللى بدأيسي عند المجلة الكتر دي هي قيمتها x
+
+467
+00:36:21,150 --> 00:36:27,570
+-3 وy4 وهي ال current ال filament اللى بيقول فيها
+
+468
+00:36:27,570 --> 00:36:35,220
+التيار فقيمة raw هي ال 4 واضحطب هيوصلت جاهزة مين
+
+469
+00:36:35,220 --> 00:36:41,460
+بيضل عليها اللي هي alpha 1 و alpha 2 alpha 2 سهلة
+
+470
+00:36:41,460 --> 00:36:44,960
+لأن alpha 2 اللي هي عند ال infinity فهتكون zero
+
+471
+00:36:44,960 --> 00:36:50,280
+alpha 1 ليه بدي ارجع ارسم الرسم هذي انا رسمت هي عن
+
+472
+00:36:50,280 --> 00:36:56,620
+هذي alpha 1
+
+473
+00:36:56,620 --> 00:37:03,190
+هي هنا alpha 1 هي المرسومة قدامكم اذا مش شايفينألف
+
+474
+00:37:03,190 --> 00:37:08,030
+و واحد هي مامتداد الخط و ألف و واحد هي مابين مابين
+
+475
+00:37:08,030 --> 00:37:14,090
+نقطة النقطة التي هي نقطة نقطة نقطة نقطة نقطة نقطة
+
+476
+00:37:14,090 --> 00:37:16,650
+نقطة نقطة نقطة نقطة نقطة نقطة نقطة نقطة نقطة نقطة
+
+477
+00:37:16,650 --> 00:37:18,730
+نقطة نقطة نقطة نقطة نقطة نقطة نقطة نقطة نقطة نقطة
+
+478
+00:37:18,730 --> 00:37:18,870
+نقطة نقطة نقطة نقطة نقطة نقطة نقطة نقطة نقطة نقطة
+
+479
+00:37:18,870 --> 00:37:20,270
+نقطة نقطة نقطة نقطة نقطة نقطة نقطة نقطة نقطة نقطة
+
+480
+00:37:20,270 --> 00:37:28,830
+نقطة نقطة نقطة نقطة نقطة نقطة نقطة
+
+481
+00:37:28,830 --> 00:37:33,690
+نهذه الزاوية ألفة اللي أنا بدور عليها ألفة واحد
+
+482
+00:37:33,690 --> 00:37:37,570
+اللي هنا جب تمامها اللي هي تلاتة على الوطر اللي هو
+
+483
+00:37:37,570 --> 00:37:43,490
+خمسة تمام اذا
+
+484
+00:37:43,490 --> 00:37:47,790
+هي عارفة كوصين ألف واحد كوصين ألف اتنين جب تمام ال
+
+485
+00:37:47,790 --> 00:37:51,150
+zero واحد جب تمام اللي هي ألف اتنين تلاتة على خمسة
+
+486
+00:37:51,960 --> 00:37:55,000
+بيضل عليّ اللي هي ال phi hat و اتجاه ال phi hat
+
+487
+00:37:55,000 --> 00:37:58,680
+إذا طلعتها عن التبسات هعرف أنه وين هي لأنه هي
+
+488
+00:37:58,680 --> 00:38:03,920
+اتجاه magnetic field الناتج من هذه النقطة فهيكون
+
+489
+00:38:03,920 --> 00:38:06,340
+اتجاه اللي هو z direction
+
+490
+00:38:12,060 --> 00:38:14,880
+أو أعمل اللي هي زي ما احنا شوفنا ال a row hat
+
+491
+00:38:14,880 --> 00:38:19,780
+قولنا هي a ال hat cross a row hat a ال hat في هذه
+
+492
+00:38:19,780 --> 00:38:22,660
+الحالة مين؟ ال current في اتجاه ال x direction a
+
+493
+00:38:22,660 --> 00:38:27,260
+ال hat اللي هي a x hat row hat مين هي ال z hat ف a
+
+494
+00:38:27,260 --> 00:38:30,520
+ال hat cross row hat هتعطينا المجلة الفيه في اتجاه
+
+495
+00:38:30,520 --> 00:38:31,560
+ال z direction
+
+496
+00:38:35,030 --> 00:38:38,530
+نجمع الاتنين مع بعض بيعطيني الـ total magnetic
+
+497
+00:38:38,530 --> 00:38:41,130
+field فهيكون عندى component في ال five direction و
+
+498
+00:38:41,130 --> 00:38:46,050
+واحدة في ال z direction المثل
+
+499
+00:38:46,050 --> 00:38:50,110
+اللى بعده هيجى مش من filament طويلة أسوأ أسمى ولا
+
+500
+00:38:50,110 --> 00:38:54,590
+final هتكون من filament عشكل دائرة filament عشكل
+
+501
+00:38:54,590 --> 00:38:59,210
+دائرة برضه line لازال انه IDL بس عشكل دائرة مش من
+
+502
+00:38:59,210 --> 00:39:02,890
+خط مستقيم يعنى ان انا بقوله لو كان عندى circular
+
+503
+00:39:03,350 --> 00:39:07,010
+Loop located at X تربيع زي Y تربيع بتسوى تسعة عامة
+
+504
+00:39:07,010 --> 00:39:10,890
+يعني انهم يلقوا في نقلة ميرول رقمتها تلاتة ال
+
+505
+00:39:10,890 --> 00:39:14,310
+circle located at X تربيع زي Y تربيع بتسوى تسعة
+
+506
+00:39:14,310 --> 00:39:17,710
+يعني ربع النار بتسوى تلاتة ال radius تبعها ال
+
+507
+00:39:17,710 --> 00:39:22,750
+circle Z بتسوى صفر يعني ال circle واقع دوام في ال
+
+508
+00:39:22,750 --> 00:39:27,680
+XY plane و ال radius تبعها بساوي تلاتةCarries a
+
+509
+00:39:27,680 --> 00:39:32,940
+direct current قيمته
+
+510
+00:39:32,940 --> 00:39:37,440
+10A along Phi hat Phi hat هي ال positive direction
+
+511
+00:39:37,440 --> 00:39:38,320
+من X ل Y
+
+512
+00:39:44,330 --> 00:39:49,990
+بتناقل magnet field عند النقطتين مرة عند X0 Y0 و
+
+513
+00:39:49,990 --> 00:39:56,190
+plus 4 و مرة عند 0 0 و minus 4 طبعا احنا مافيش
+
+514
+00:39:56,190 --> 00:39:59,390
+عندنا وقت كافي عشان نحلها بالتفصيل هحكيها على
+
+515
+00:39:59,390 --> 00:40:02,690
+السريع و انتوا بتحلوه في البيت و بتسلموه للقادة
+
+516
+00:40:02,690 --> 00:40:08,230
+القادمة DH بساوي I DL cross R على 4 by R cube بحدد
+
+517
+00:40:08,230 --> 00:40:11,510
+ال DL من هي ال DL اللي هي على ال loop مكان ال
+
+518
+00:40:11,510 --> 00:40:16,150
+currentDL متذكرين ايش بتساوي رو دي فاي ولان سيتو
+
+519
+00:40:16,150 --> 00:40:20,210
+فاي هات ال DL للcircle عبارة عن رو دي فاي اللى هو
+
+520
+00:40:20,210 --> 00:40:24,430
+القوص رو دي فاي فى جهة فاي هات وR اللى بتحددها 00
+
+521
+00:40:24,430 --> 00:40:28,490
+اتش اللى هى الاربع او الخمسة او ال minus اربعة
+
+522
+00:40:28,490 --> 00:40:32,510
+بجيب ال R اللى هى المسافة بين الفرق من بين R minus
+
+523
+00:40:32,510 --> 00:40:36,870
+R prime هى ال R ال R اللى هى ال رو رو هات و ال R
+
+524
+00:40:36,870 --> 00:40:40,630
+prime اللى هى 00 اتش او XYZ
+
+525
+00:40:43,940 --> 00:40:49,360
+بنحدد المسافة R بعد ما احدد المسافة R بجيب اللي هي
+
+526
+00:40:49,360 --> 00:40:54,080
+ال DL cross R طبعا قولنا المسافة بين R minus R
+
+527
+00:40:54,080 --> 00:40:56,260
+prime R اللي هي موقع النقطة باسمة ال magnetic
+
+528
+00:40:56,260 --> 00:41:00,460
+field minus R prime اللي هي موقع ال element بجيبله
+
+529
+00:41:00,460 --> 00:41:06,160
+cross product و بعود في ال DH في ال elements كلهم
+
+530
+00:41:06,160 --> 00:41:09,710
+يعني بعد ما اجمعهمبصير اندي اللي هو زي ما هو
+
+531
+00:41:09,710 --> 00:41:12,710
+اقسمهم ل two components واحدة component واحدة
+
+532
+00:41:12,710 --> 00:41:17,070
+component بكمل كل واحدة وبحصل على ال total
+
+533
+00:41:17,070 --> 00:41:23,570
+magnetic field طبعا من ال symmetry من ال symmetry
+
+534
+00:41:23,570 --> 00:41:27,740
+اذا طلعناكل element هيكون في element اقباله، صح؟
+
+535
+00:41:27,740 --> 00:41:30,320
+كل element هيكون في element اقباله، عندنا قلنا
+
+536
+00:41:30,320 --> 00:41:32,640
+هيطلع components اتنين، واحدة في تجاه الـR واحدة
+
+537
+00:41:32,640 --> 00:41:36,520
+في تجاه الـZ لو حطيت ال element لقباله اللي هنا،
+
+538
+00:41:36,520 --> 00:41:39,080
+هلاحظ برضه هيكون فيه two elements واحد في تجاه
+
+539
+00:41:39,080 --> 00:41:43,330
+الـZ واحد في تجاه الـRواحد element هنا هيعطيني
+
+540
+00:41:43,330 --> 00:41:47,190
+برضه دايما ال magnet فيه هيكون بزاوية زي هيك لفوق
+
+541
+00:41:47,190 --> 00:41:50,730
+واحدة component في ال z واحدة في ال rho يا هتكون
+
+542
+00:41:50,730 --> 00:41:53,430
+في ال z و minus rho فاللي في ال rho ال direction
+
+543
+00:41:53,430 --> 00:41:56,930
+كلهم هيروح ي cancel بعض مين هيضل اللي في ال z
+
+544
+00:41:56,930 --> 00:41:59,850
+direction فإذا من ال symmetry بقدر أخلص من مين
+
+545
+00:41:59,850 --> 00:42:03,370
+اللي ال rho component لأ تعب حالي و لأ أكملها هيضل
+
+546
+00:42:03,370 --> 00:42:06,430
+بس عندى اللي في ال z component واضح فمن ال
+
+547
+00:42:06,430 --> 00:42:10,140
+symmetry بس بتضل عندنا ال z componentو بعد هيك
+
+548
+00:42:10,140 --> 00:42:13,260
+بنعوض على قبل القدش على القيمة اللي هو قدرياها او
+
+549
+00:42:13,260 --> 00:42:15,800
+اللي عندها طالب من مجلة field أسوأ positive ولا
+
+550
+00:42:15,800 --> 00:42:16,220
+negative
+
+551
+00:42:19,700 --> 00:42:22,300
+المثال اللى بعده خلينى احنا بنقشه لقاءه القادر ان
+
+552
+00:42:22,300 --> 00:42:25,220
+شاء الله بس حله اللى هو تبع ال ring لإن المثالين
+
+553
+00:42:25,220 --> 00:42:28,560
+اللى بعد ال ring بيتمدوا عليه زى ما عملنا تبع ال
+
+554
+00:42:28,560 --> 00:42:30,460
+semi-infinite او يعني ال line اللى اللى قيله
+
+555
+00:42:30,460 --> 00:42:34,000
+definite line ال links كل الأمثل اللى عليه بعدها
+
+556
+00:42:34,000 --> 00:42:38,580
+كان محدد عليه تكترف القانون تبعه و بتحددى لل ..
+
+557
+00:42:38,580 --> 00:42:42,240
+نفس الحاجة لل ring الأمثل اللى بعده كلها معتمدة
+
+558
+00:42:42,240 --> 00:42:42,800
+عليه
+
diff --git a/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/I8ZXjFEyO9A_raw.json b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/I8ZXjFEyO9A_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..891428377e512ff0085124d0f2a4859a3d68c9bf
--- /dev/null
+++ b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/I8ZXjFEyO9A_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 4529, "start": 20.69, "end": 45.29, "text": "بسم الله الرحمن الرحيم السلام عليكم ورحمة الله وبركاته احنا اليوم ان شاء الله هنتبع واطينا في الكهر استاتيكية و هنتقل ل magnetostatic fields الشكتر 7 اللي بتحدث عن magnetostatic field فارجينا ال new field احنا كلنا مركزين على ال electric field و اليوم هنشوف ال magnetic field", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 21136, 37440, 25894, 24793, 4032, 2288, 35571, 3660, 21984, 4032, 26890, 4117, 9307, 3224, 1975, 5016, 8315, 45595, 20498, 16472, 13412, 16606, 21984, 8032, 29399, 3555, 3615, 4032, 41193, 1829, 8315, 8978, 33251, 3224, 2288, 44713, 9307, 1829, 4117, 10632, 4032, 8032, 29399, 4587, 1211, 5296, 15211, 555, 2399, 7909, 25124, 4117, 2655, 2288, 1614, 13672, 1829, 39894, 24401, 12984, 18871, 15211, 555, 2399, 2519, 6156, 9640, 7435, 1829, 8315, 2423, 777, 2519, 1975, 5016, 8315, 28242, 8315, 3714, 31747, 11622, 9957, 15844, 2423, 5210, 2519, 4032, 45595, 20498, 8032, 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0.9498697916666666}, {"start": 2472.71, "end": 2472.99, "word": " component", "probability": 0.25341796875}, {"start": 2472.99, "end": 2474.41, "word": " بكمل", "probability": 0.7508138020833334}, {"start": 2474.41, "end": 2474.61, "word": " كل", "probability": 0.93798828125}, {"start": 2474.61, "end": 2476.03, "word": " واحدة", "probability": 0.9729817708333334}, {"start": 2476.03, "end": 2476.51, "word": " وبحصل", "probability": 0.7608235677083334}, {"start": 2476.51, "end": 2476.67, "word": " على", "probability": 0.87255859375}, {"start": 2476.67, "end": 2476.81, "word": " ال", "probability": 0.82666015625}, {"start": 2476.81, "end": 2477.07, "word": " total", "probability": 0.83740234375}, {"start": 2477.07, "end": 2477.55, "word": " magnetic", "probability": 0.80859375}, {"start": 2477.55, "end": 2477.91, "word": " field", "probability": 0.837890625}, {"start": 2477.91, "end": 2478.47, "word": " طبعا", "probability": 0.9649658203125}, {"start": 2478.47, "end": 2478.63, "word": " من", "probability": 0.98291015625}, {"start": 2478.63, "end": 2478.79, "word": " ال", "probability": 0.828125}, {"start": 2478.79, "end": 2479.25, "word": " symmetry", "probability": 0.9580078125}, {"start": 2479.25, "end": 2481.65, "word": " من", "probability": 0.4033203125}, {"start": 2481.65, "end": 2483.23, "word": " ال", "probability": 0.82373046875}, {"start": 2483.23, "end": 2483.57, "word": " symmetry", "probability": 0.95849609375}, {"start": 2483.57, "end": 2483.77, "word": " اذا", "probability": 0.811279296875}, {"start": 2483.77, "end": 2484.33, "word": " طلعنا", "probability": 0.99267578125}], "temperature": 1.0}, {"id": 100, "seek": 250088, "start": 2484.66, "end": 2500.88, "text": "كل element هيكون في element اقباله، صح؟ كل element هيكون في element اقباله، عندنا قلنا هيطلع components اتنين، واحدة في تجاه الـR واحدة في تجاه الـZ لو حطيت ال element لقباله اللي هنا، هلاحظ برضه هيكون فيه two elements واحد في تجاه الـZ واحد في تجاه الـR", "tokens": [28820, 4478, 39896, 30544, 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direction كلهم هيروح ي cancel بعض مين هيضل اللي في ال z direction فإذا من ال symmetry بقدر أخلص من مين اللي ال rho component لأ تعب حالي و لأ أكملها هيضل بس عندى اللي في ال z component واضح فمن ال symmetry بس بتضل عندنا ال z component", "tokens": [14407, 24401, 4478, 34105, 39896, 3615, 9566, 1829, 22653, 4724, 43042, 3224, 11778, 47302, 15042, 2423, 2258, 7129, 8978, 3224, 39896, 30544, 4724, 11622, 995, 2407, 10632, 30767, 1829, 39896, 4117, 5296, 5172, 30543, 36764, 24401, 3660, 6542, 8978, 2423, 710, 36764, 24401, 3660, 8978, 2423, 20293, 35186, 8032, 2655, 30544, 8978, 2423, 710, 4032, 3175, 20293, 6156, 6027, 20292, 8978, 2423, 20293, 2423, 3513, 28242, 16095, 39896, 32887, 5016, 7251, 10373, 45030, 11242, 3714, 9957, 39896, 11242, 1211, 13672, 1829, 8978, 2423, 710, 3513, 6156, 28814, 15730, 9154, 2423, 25440, 4724, 28543, 2288, 5551, 9778, 1211, 9381, 9154, 3714, 9957, 13672, 1829, 2423, 20293, 6542, 5296, 10721, 37279, 3555, 11331, 6027, 1829, 4032, 5296, 10721, 5551, 24793, 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"end": 2523.59, "word": " بس", "probability": 0.96826171875}, {"start": 2523.59, "end": 2523.85, "word": " عندى", "probability": 0.6029052734375}, {"start": 2523.85, "end": 2523.91, "word": " اللي", "probability": 0.97900390625}, {"start": 2523.91, "end": 2524.17, "word": " في", "probability": 0.6357421875}, {"start": 2524.17, "end": 2524.29, "word": " ال", "probability": 0.84228515625}, {"start": 2524.29, "end": 2524.45, "word": " z", "probability": 0.99267578125}, {"start": 2524.45, "end": 2525.07, "word": " component", "probability": 0.98095703125}, {"start": 2525.07, "end": 2526.05, "word": " واضح", "probability": 0.9446614583333334}, {"start": 2526.05, "end": 2526.29, "word": " فمن", "probability": 0.73681640625}, {"start": 2526.29, "end": 2526.43, "word": " ال", "probability": 0.87548828125}, {"start": 2526.43, "end": 2526.79, "word": " symmetry", "probability": 0.9638671875}, {"start": 2526.79, "end": 2527.03, "word": " بس", "probability": 0.98046875}, {"start": 2527.03, "end": 2527.37, "word": " بتضل", "probability": 0.82470703125}, {"start": 2527.37, "end": 2527.69, "word": " عندنا", "probability": 0.84765625}, {"start": 2527.69, "end": 2527.89, "word": " ال", "probability": 0.93896484375}, {"start": 2527.89, "end": 2528.01, "word": " z", "probability": 0.98681640625}, {"start": 2528.01, "end": 2528.47, "word": " component", "probability": 0.953125}], "temperature": 1.0}, {"id": 102, "seek": 253621, "start": 2529.56, "end": 2536.22, "text": "و بعد هيك بنعوض على قبل القدش على القيمة اللي هو قدرياها او اللي عندها طالب من مجلة field أسوأ positive ولا negative", "tokens": [2407, 39182, 39896, 4117, 44945, 3615, 2407, 11242, 15844, 12174, 36150, 25062, 3215, 8592, 15844, 25062, 32640, 3660, 13672, 1829, 31439, 12174, 3215, 16572, 995, 11296, 1975, 2407, 13672, 1829, 43242, 11296, 23032, 6027, 3555, 9154, 3714, 7435, 37977, 2519, 5551, 3794, 2407, 10721, 3353, 49429, 3671], "avg_logprob": -0.35839842942853767, "compression_ratio": 1.3795620437956204, "no_speech_prob": 0.0, "words": [{"start": 2529.56, "end": 2529.74, "word": "و", "probability": 0.703125}, {"start": 2529.74, "end": 2529.94, "word": " بعد", "probability": 0.94482421875}, {"start": 2529.94, "end": 2530.14, "word": " هيك", "probability": 0.853515625}, {"start": 2530.14, "end": 2530.6, "word": " بنعوض", "probability": 0.8321533203125}, {"start": 2530.6, "end": 2530.76, "word": " على", "probability": 0.34033203125}, {"start": 2530.76, "end": 2531.02, "word": " قبل", "probability": 0.59814453125}, {"start": 2531.02, "end": 2531.36, "word": " القدش", "probability": 0.685302734375}, {"start": 2531.36, "end": 2531.48, "word": " على", "probability": 0.452392578125}, {"start": 2531.48, "end": 2531.9, "word": " القيمة", "probability": 0.807861328125}, {"start": 2531.9, "end": 2531.98, "word": " اللي", "probability": 0.7900390625}, {"start": 2531.98, "end": 2532.1, "word": " هو", "probability": 0.98388671875}, {"start": 2532.1, "end": 2532.86, "word": " قدرياها", "probability": 0.706982421875}, {"start": 2532.86, "end": 2533.26, "word": " او", "probability": 0.6749267578125}, {"start": 2533.26, "end": 2533.54, "word": " اللي", "probability": 0.951904296875}, {"start": 2533.54, "end": 2533.74, "word": " عندها", "probability": 0.992919921875}, {"start": 2533.74, "end": 2534.04, "word": " طالب", "probability": 0.9820963541666666}, {"start": 2534.04, "end": 2534.18, "word": " من", "probability": 0.344970703125}, {"start": 2534.18, "end": 2534.42, "word": " مجلة", "probability": 0.4800211588541667}, {"start": 2534.42, "end": 2534.8, "word": " field", "probability": 0.5146484375}, {"start": 2534.8, "end": 2535.22, "word": " أسوأ", "probability": 0.7713623046875}, {"start": 2535.22, "end": 2535.58, "word": " positive", "probability": 0.740234375}, {"start": 2535.58, "end": 2535.8, "word": " ولا", "probability": 0.88232421875}, {"start": 2535.8, "end": 2536.22, "word": " negative", "probability": 0.9892578125}], "temperature": 1.0}, {"id": 103, "seek": 256280, "start": 2539.7, "end": 2562.8, "text": "المثال اللى بعده خلينى احنا بنقشه لقاءه القادر ان شاء الله بس حله اللى هو تبع ال ring لإن المثالين اللى بعد ال ring بيتمدوا عليه زى ما عملنا تبع ال semi-infinite او يعني ال line اللى اللى قيله definite line ال links كل الأمثل اللى عليه بعدها كان محدد عليه تكترف القانون تبعه و بتحددى لل .. نفس الحاجة لل ring الأمثل اللى بعده كلها معتمدة عليه", "tokens": [45340, 12984, 6027, 13672, 7578, 39182, 3224, 16490, 1211, 9957, 7578, 1975, 5016, 8315, 44945, 4587, 8592, 3224, 5296, 4587, 16606, 3224, 25062, 18513, 2288, 16472, 13412, 16606, 21984, 4724, 3794, 11331, 1211, 3224, 13672, 7578, 31439, 6055, 3555, 3615, 2423, 4875, 5296, 28814, 1863, 9673, 12984, 6027, 9957, 13672, 7578, 39182, 2423, 4875, 4724, 36081, 2304, 3215, 14407, 47356, 30767, 7578, 19446, 6225, 42213, 8315, 6055, 3555, 3615, 2423, 12909, 12, 259, 5194, 642, 1975, 2407, 37495, 22653, 2423, 1622, 13672, 7578, 13672, 7578, 12174, 26895, 3224, 25131, 1622, 2423, 6123, 28242, 16247, 2304, 12984, 1211, 13672, 7578, 47356, 39182, 11296, 25961, 3714, 24401, 3215, 47356, 6055, 4117, 2655, 2288, 5172, 25062, 7649, 11536, 6055, 3555, 3615, 3224, 4032, 39894, 24401, 3215, 7578, 24976, 4386, 8717, 36178, 21542, 26108, 3660, 24976, 4875, 16247, 2304, 12984, 1211, 13672, 7578, 39182, 3224, 28242, 11296, 3714, 34268, 2304, 41891, 47356], "avg_logprob": -0.21476510587154618, "compression_ratio": 2.076642335766423, "no_speech_prob": 5.960464477539062e-07, "words": [{"start": 2539.7, "end": 2540.12, "word": "المثال", "probability": 0.8390299479166666}, {"start": 2540.12, "end": 2540.26, "word": " اللى", "probability": 0.87451171875}, {"start": 2540.26, "end": 2540.54, "word": " بعده", "probability": 0.8984375}, {"start": 2540.54, "end": 2540.92, "word": " خلينى", "probability": 0.7113037109375}, {"start": 2540.92, "end": 2541.12, "word": " احنا", "probability": 0.9031575520833334}, {"start": 2541.12, "end": 2541.58, "word": " بنقشه", "probability": 0.8839111328125}, {"start": 2541.58, "end": 2541.94, "word": " لقاءه", "probability": 0.8515625}, {"start": 2541.94, "end": 2542.22, "word": " القادر", "probability": 0.8699544270833334}, {"start": 2542.22, "end": 2542.3, "word": " ان", "probability": 0.70849609375}, {"start": 2542.3, "end": 2542.46, "word": " شاء", "probability": 0.9521484375}, {"start": 2542.46, "end": 2542.5, "word": " الله", "probability": 0.9306640625}, {"start": 2542.5, "end": 2542.7, "word": " بس", "probability": 0.864013671875}, {"start": 2542.7, "end": 2543.06, "word": " حله", "probability": 0.786865234375}, {"start": 2543.06, "end": 2543.26, "word": " اللى", "probability": 0.980224609375}, {"start": 2543.26, "end": 2543.4, "word": " هو", "probability": 0.95263671875}, {"start": 2543.4, "end": 2543.72, "word": " تبع", "probability": 0.8439127604166666}, {"start": 2543.72, "end": 2543.9, "word": " ال", "probability": 0.91455078125}, {"start": 2543.9, "end": 2544.2, "word": " ring", "probability": 0.935546875}, {"start": 2544.2, "end": 2544.62, "word": " لإن", "probability": 0.8018391927083334}, {"start": 2544.62, "end": 2545.22, "word": " المثالين", "probability": 0.9141845703125}, {"start": 2545.22, "end": 2545.46, "word": " اللى", "probability": 0.96923828125}, {"start": 2545.46, "end": 2545.7, "word": " بعد", "probability": 0.9072265625}, {"start": 2545.7, "end": 2545.92, "word": " ال", "probability": 0.98193359375}, {"start": 2545.92, "end": 2546.16, "word": " ring", "probability": 0.9912109375}, {"start": 2546.16, "end": 2546.64, "word": " بيتمدوا", "probability": 0.83955078125}, {"start": 2546.64, "end": 2546.92, "word": " عليه", "probability": 0.802734375}, {"start": 2546.92, "end": 2547.8, "word": " زى", "probability": 0.934814453125}, {"start": 2547.8, "end": 2547.88, "word": " ما", "probability": 0.9765625}, {"start": 2547.88, "end": 2548.2, "word": " عملنا", "probability": 0.9913736979166666}, {"start": 2548.2, "end": 2548.44, "word": " تبع", "probability": 0.9720052083333334}, {"start": 2548.44, "end": 2548.56, "word": " ال", "probability": 0.8037109375}, {"start": 2548.56, "end": 2548.74, "word": " semi", "probability": 0.748046875}, {"start": 2548.74, "end": 2549.28, "word": "-infinite", "probability": 0.8323974609375}, {"start": 2549.28, "end": 2549.58, "word": " او", "probability": 0.7315673828125}, {"start": 2549.58, "end": 2549.74, "word": " يعني", "probability": 0.782470703125}, {"start": 2549.74, "end": 2549.88, "word": " ال", "probability": 0.9482421875}, {"start": 2549.88, "end": 2550.08, "word": " line", "probability": 0.97509765625}, {"start": 2550.08, "end": 2550.22, "word": " اللى", "probability": 0.97802734375}, {"start": 2550.22, "end": 2550.36, "word": " اللى", "probability": 0.527099609375}, {"start": 2550.36, "end": 2550.46, "word": " قيله", "probability": 0.5557047526041666}, {"start": 2550.46, "end": 2550.74, "word": " definite", "probability": 0.86279296875}, {"start": 2550.74, "end": 2551.16, "word": " line", "probability": 0.841796875}, {"start": 2551.16, 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2556.82, "word": " تبعه", "probability": 0.9671630859375}, {"start": 2556.82, "end": 2556.98, "word": " و", "probability": 0.5693359375}, {"start": 2556.98, "end": 2557.54, "word": " بتحددى", "probability": 0.892822265625}, {"start": 2557.54, "end": 2557.76, "word": " لل", "probability": 0.208984375}, {"start": 2557.76, "end": 2558.58, "word": " ..", "probability": 0.76708984375}, {"start": 2558.58, "end": 2559.2, "word": " نفس", "probability": 0.761474609375}, {"start": 2559.2, "end": 2559.58, "word": " الحاجة", "probability": 0.9825846354166666}, {"start": 2559.58, "end": 2559.72, "word": " لل", "probability": 0.94189453125}, {"start": 2559.72, "end": 2560.04, "word": " ring", "probability": 0.98681640625}, {"start": 2560.04, "end": 2560.86, "word": " الأمثل", "probability": 0.855712890625}, {"start": 2560.86, "end": 2561.0, "word": " اللى", "probability": 0.969970703125}, {"start": 2561.0, "end": 2561.3, "word": " بعده", "probability": 0.945556640625}, {"start": 2561.3, "end": 2561.64, "word": " كلها", "probability": 0.9697265625}, {"start": 2561.64, "end": 2562.24, "word": " معتمدة", "probability": 0.8740234375}, {"start": 2562.24, "end": 2562.8, "word": " عليه", "probability": 0.91943359375}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2563.71525, "duration_after_vad": 2439.5549999999917}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/KxyN-qg3Hrg.srt b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/KxyN-qg3Hrg.srt
new file mode 100644
index 0000000000000000000000000000000000000000..a0145202d9f429fb2291078524f3ca062bef3339
--- /dev/null
+++ b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/KxyN-qg3Hrg.srt
@@ -0,0 +1,1742 @@
+1
+00:00:21,140 --> 00:00:23,560
+بسم الله الرحمن الرحيم السلام عليكم ورحمة الله
+
+2
+00:00:23,560 --> 00:00:26,100
+وبركاته  ونحن اليوم إن شاء الله سنتابع موضوعنا 
+
+3
+00:00:26,100 --> 00:00:29,620
+الذي هو electric field من المرة السابقة ووقفنا عند آخر 
+
+4
+00:00:29,620 --> 00:00:32,300
+مثال أنا قرأته سريعًا  بس إن شاء الله سنحله مرة
+
+5
+00:00:32,300 --> 00:00:35,460
+بالتفصيل الذي هو يحكي أنه فينا dielectric sphere
+
+6
+00:00:35,460 --> 00:00:38,400
+التي لها ال relative permittivity
+
+7
+00:00:38,400 --> 00:00:44,020
+epsilon 5 أو 7 من 10 سنرسم الشكل تبعنا  ال sphere
+
+8
+00:00:44,020 --> 00:00:47,540
+التي لها epsilon R
+
+9
+00:00:51,180 --> 00:00:58,820
+وعند ال center half point charge مقدارها اثنان
+
+10
+00:00:58,820 --> 00:01:04,140
+Pico column وعندنا 
+
+11
+00:01:04,140 --> 00:01:09,280
+ال radius أيضًا تبعها عشرة سنتيمترات ال radius يساوي
+
+12
+00:01:09,280 --> 00:01:15,900
+عشرة سنتيمترات أول حاجة طالبنا ال surface density of
+
+13
+00:01:15,900 --> 00:01:19,830
+polarization الذي هو ال rawP كما  نسميها
+
+14
+00:01:19,830 --> 00:01:24,650
+ال polarization ال surface polarization charges دي
+
+15
+00:01:24,650 --> 00:01:29,770
+نحن عرفناها بال polarization dot ar hat ar hat 
+
+16
+00:01:29,770 --> 00:01:35,650
+الذي هو باتجاه العمودي على ال surface تتذكرون أو
+
+17
+00:01:35,650 --> 00:01:39,030
+ar hat سميناه اتجاه العمودي على ال surface فهذه
+
+18
+00:01:39,030 --> 00:01:43,390
+سطحية لأنها من العمودي على ال surface ال ar hat
+
+19
+00:01:43,390 --> 00:01:45,570
+هو الذي يكون عمودي على ال surface في السطحية 
+
+20
+00:01:46,600 --> 00:01:49,780
+بالضبط من وجود ال polarization ال polarization
+
+21
+00:01:49,780 --> 00:01:52,560
+نحن قلنا تتناسب طرديًا مع ال electric field في ال
+
+22
+00:01:52,560 --> 00:01:57,660
+linear media ومعاملة ال ... إذا أنتم الذاكرين قلنا 
+
+23
+00:01:57,660 --> 00:02:00,700
+ال polarization تتناسب مع ال electric field ال 
+
+24
+00:02:00,700 --> 00:02:03,160
+electric field يحس ال polarization لأنه يعمل 
+
+25
+00:02:03,160 --> 00:02:07,560
+dipole ودرسناها كل واحدة من المعادلة تفاصيل فلما
+
+26
+00:02:07,560 --> 00:02:10,740
+يصبح أن الـ double نقدر نحس ال polarization هو
+
+27
+00:02:10,740 --> 00:02:13,860
+الـ variable volume ولأن أن الـ double و ال
+
+28
+00:02:13,860 --> 00:02:16,860
+polarization و ال electric field بينهم معامل التناسب 
+
+29
+00:02:16,860 --> 00:02:23,160
+هو susceptibility و Epsilon نقطة طب نحن نريد
+
+30
+00:02:23,160 --> 00:02:26,780
+معرفة ال electric field إذا عرفت ال electric field أعرف
+
+31
+00:02:26,780 --> 00:02:29,140
+ال polarization وإذا عرفت ال polarization أعرف مين 
+
+32
+00:02:29,140 --> 00:02:31,980
+الذي هو طلبها مني ال surface density و ال 
+
+33
+00:02:31,980 --> 00:02:35,040
+polarization طب E بالنسبة ل point of charge يعني
+
+34
+00:02:35,040 --> 00:02:37,870
+هو كل عندنا point of charge بس ال media بتاعتها
+
+35
+00:02:37,870 --> 00:02:40,650
+نعرف أن نبدلها عن ال epsilon node هي epsilon
+
+36
+00:02:40,650 --> 00:02:44,650
+بتاعة ال media هم أعطيني mean epsilon r و epsilon
+
+37
+00:02:44,650 --> 00:02:49,370
+ماذا تساوي epsilon node في epsilon r قلنا epsilon 
+
+38
+00:02:49,370 --> 00:02:51,870
+r معدومة الوحدة لأنها ال ratio بين ال epsilon
+
+39
+00:02:51,870 --> 00:02:55,490
+بتاعة ال media على epsilon node إذا E بتاعة ال 
+
+40
+00:02:55,490 --> 00:02:58,590
+point of charge التي عبارة عن Q بتاعة ال point of
+
+41
+00:02:58,590 --> 00:03:02,610
+charge على 4Y مش epsilon node ابسلون بتاعة ال 
+
+42
+00:03:02,610 --> 00:03:05,310
+media التي هي epsilon تعني من ماذا؟ أنا أسوء epsilon
+
+43
+00:03:05,310 --> 00:03:14,010
+نود في epsilon R في R تربيع R hat تمام؟  فندرس E طب
+
+44
+00:03:14,010 --> 00:03:17,190
+نريد أن نحصل على ال polarization ال polarization لن تكون
+
+45
+00:03:17,190 --> 00:03:22,110
+C في epsilon نود  جزء مع الطرف الذي مع الذي أسفل 
+
+46
+00:03:22,110 --> 00:03:28,030
+ستكون على ال Q طبعًا على 4 by epsilon R 
+
+47
+00:03:47,300 --> 00:03:53,820
+لأنني أشيل ال charge density سيكون
+
+48
+00:03:53,820 --> 00:03:58,460
+P.R hat سيظل عندي بس ال term داخل الذي عبارة عن
+
+49
+00:03:58,460 --> 00:04:04,300
+epsilon ر ناقص واحد Q على four by epsilon R في R
+
+50
+00:04:04,300 --> 00:04:09,040
+ثانية و ال R hat راح تمام ال R hat تمام يعني ماذا
+
+51
+00:04:09,040 --> 00:04:12,160
+السطحية التي حد هنا طب الجزء الثاني اشتعل من هنا
+
+52
+00:04:12,160 --> 00:04:16,280
+تقيم ال force التي على charge مقدارها ناقص أربعة 
+
+53
+00:04:16,280 --> 00:04:22,140
+column التي  مكانها على السطح اطل هنا على السطح
+
+54
+00:04:22,470 --> 00:04:26,630
+كمان point of charge مقدارها ناقص 4 بكورة أول 
+
+55
+00:04:26,630 --> 00:04:29,090
+حاجة نحصل على ال electric field بعد ال force لأن ال
+
+56
+00:04:29,090 --> 00:04:32,650
+force التي على هاي ال charge function تساوي Eq في
+
+57
+00:04:32,650 --> 00:04:38,890
+E إذا عرفت ال electric field التي في ال media أعرف 
+
+58
+00:04:38,890 --> 00:04:42,150
+ال force أنها ستكون هنا Eq في E و ماذا نحن حسبناها
+
+59
+00:04:42,150 --> 00:04:50,270
+مع بعضها ماذا ستكون Eq هي ناقص 4 بيكور سميتها ك Eq 
+
+60
+00:04:50,270 --> 00:05:00,240
+صغيرة الـ Q على 4Y نط في ي R في R تربيع R هذا هو
+
+61
+00:05:00,240 --> 00:05:06,200
+قيمة الـ Force يريد
+
+62
+00:05:06,200 --> 00:05:10,220
+Force with which the planes of  أضرر الـ Plate
+
+63
+00:05:10,220 --> 00:05:13,380
+Capacitor attract each other أضرر ال Plate
+
+64
+00:05:13,380 --> 00:05:19,720
+Capacitor  يعني هذه الـ Plane وهي أيضًا الآن هدول 
+
+65
+00:05:19,720 --> 00:05:26,490
+Two Planes واحد منهم عالية شحنة مجرة والثاني
+
+66
+00:05:26,490 --> 00:05:30,690
+عالية شحنة ثالثة فبالتأكيد في تجاذب بينهم فهو يريد مقدار
+
+67
+00:05:30,690 --> 00:05:36,890
+التجاذب الذي بين هدول two planes و plates also
+
+68
+00:05:36,890 --> 00:05:41,150
+determine the pressure on the surface of the plate
+
+69
+00:05:41,150 --> 00:05:44,250
+due to the field طبعًا  للحصول على ال force أول حاجة
+
+70
+00:05:44,250 --> 00:05:46,610
+نحصل على ال electric field و أخذته في ال electric field 
+
+71
+00:05:46,610 --> 00:05:49,500
+عن طريق Gauss law أنه بقدر أن نكون مقيمين في ال 
+
+72
+00:05:49,500 --> 00:05:52,000
+electric field الذي هو رايح من positive ل negative
+
+73
+00:05:52,000 --> 00:05:58,340
+بساوي raw S التي هي surface charge intensity على
+
+74
+00:05:58,340 --> 00:06:02,300
+ال Plate على اثنين ابسلون التي هي ال medium بين ال
+
+75
+00:06:02,300 --> 00:06:05,640
+two blades في An hat ومن An hat الذي هو العمودي
+
+76
+00:06:05,640 --> 00:06:11,240
+على ال blades اشتقيناها من Gauss law صحيح تتذكرينه داخل 
+
+77
+00:06:11,240 --> 00:06:15,630
+في الامتحان Gauss law فلذلك E ماذا تساوي رو أس التي 
+
+78
+00:06:15,630 --> 00:06:17,770
+هي ال charge density على ال surface على اثنين 
+
+79
+00:06:17,770 --> 00:06:21,270
+انصار معاهي unharmed هذا ال electric field طب
+
+80
+00:06:21,270 --> 00:06:27,050
+الفورس ماذا ستكون الفورس تكون ال charge ال total
+
+81
+00:06:27,050 --> 00:06:29,790
+charge في ال electric field فأنا عندي أنا
+
+82
+00:06:29,790 --> 00:06:33,270
+plane وكمان plate واحد منهم يؤثر على الثاني بالقوة 
+
+83
+00:06:33,270 --> 00:06:36,150
+بس أريد أن أحصل على ال total charge على ال plate الذي يبدأ
+
+84
+00:06:36,150 --> 00:06:40,910
+تتأثر بالقوة في ال electric field فبال total charge تساوي 
+
+85
+00:06:40,910 --> 00:06:44,080
+رو أس في ال area على افتراض ان ال area تعطي
+
+86
+00:06:44,080 --> 00:06:48,180
+surface تعطي S او A ليس مهم ماذا تسميها ممكن
+
+87
+00:06:48,180 --> 00:06:52,880
+تقولي اسمها فكيوش ستكون Raw S في ال letter P التي
+
+88
+00:06:52,880 --> 00:06:57,940
+أنا سميتها S فمن
+
+89
+00:06:57,940 --> 00:07:04,120
+ال letter P التي هو برعم Raw S على 2Y في A 
+
+90
+00:07:07,360 --> 00:07:11,480
+لو نحن افترضنا مثلًا هو ال X axis عمودي عليها يصبح 
+
+91
+00:07:11,480 --> 00:07:14,380
+An hat واضح علينا X hat عمودي عليها ال Y hat يحط
+
+92
+00:07:14,380 --> 00:07:17,240
+ماذا ماذا لكن لأنه نحن نأخذها بشكل عام نسميه An
+
+93
+00:07:17,240 --> 00:07:20,660
+hat لكن لو كان مثلًا قال لي انهم كانوا مرتبين بحيث
+
+94
+00:07:20,660 --> 00:07:23,900
+أن ال X axis كان عمودي على ال plates سيكون اتجاهه
+
+95
+00:07:23,900 --> 00:07:28,160
+An hat هو ربع عن Ax hat إذا مقدار القوة ماذا يريد
+
+96
+00:07:28,160 --> 00:07:35,140
+يساوي رؤس تربيع في ال surface area على اثنين
+
+97
+00:07:35,140 --> 00:07:41,180
+epsilon هذه القوة أو مقدار القوة هو ليس صلبًا بس 
+
+98
+00:07:41,180 --> 00:07:43,760
+القوة هو طالب ال pressure ال pressure بتعريف هو
+
+99
+00:07:43,760 --> 00:07:48,580
+force per unit area بتعريف ال pressure لو نسميه 
+
+100
+00:07:48,580 --> 00:07:54,160
+pressure يساوي force per unit area يعني هذه area
+
+101
+00:07:54,160 --> 00:07:59,860
+من؟ S إذا force على area ماذا ستكون؟ رو أس تقريبًا
+
+102
+00:07:59,860 --> 00:08:04,800
+على اثنين ابسلون هذه هي ال force طبعًا ال epsilon
+
+103
+00:08:04,800 --> 00:08:07,360
+هي التي تخبرنا عن ال permittivity بين ال two plates
+
+104
+00:08:07,790 --> 00:08:11,730
+وابسلون أقدرها بدلًا لأبسلون نوت أنها تساوي رو 
+
+105
+00:08:11,730 --> 00:08:17,170
+أس تربيع على اثنين ابسلون نوت في ابسلون R في اي
+
+106
+00:08:17,170 --> 00:08:21,830
+سبساح لحد هنا واضح دائمًا ال force و ال pressure 
+
+107
+00:08:21,830 --> 00:08:24,910
+مرتبطان ببعض أن ال pressure دائمًا force per unit 
+
+108
+00:08:24,910 --> 00:08:29,270
+area السؤال 
+
+109
+00:08:29,270 --> 00:08:32,850
+هذا أيضًا قريب من السؤال السابق أنه عندي ميزان مثل
+
+110
+00:08:32,850 --> 00:08:35,590
+ما أنتم شايفين أحد كفات الميزان هو عبارة عن ماذا 
+
+111
+00:08:35,590 --> 00:08:39,430
+capacitor two blades capacitor يعني بطريقة الماء
+
+112
+00:08:39,430 --> 00:08:46,370
+المعلق بالميزان هذه ال device نسميها electrometer
+
+113
+00:08:46,370 --> 00:08:50,130
+it is basically بين ال blades capacitor كما أنتم
+
+114
+00:08:50,130 --> 00:08:53,430
+شايفين بين ال blades capacitor with graduated
+
+115
+00:08:53,430 --> 00:08:57,910
+blades being suspended from a balance arm so that
+
+116
+00:08:57,910 --> 00:09:01,050
+the force on it is measurable in terms of the
+
+117
+00:09:01,050 --> 00:09:04,650
+weight يعني هو معلق قدرة المهالكة  ونقدر نقيسها
+
+118
+00:09:04,650 --> 00:09:08,550
+بدلاله الوزن يعني أعرف القوة التي بين ال two plates
+
+119
+00:09:08,550 --> 00:09:16,650
+ماذا دلالة الوزن الذي أنا أضعه على كفة الثانية if
+
+120
+00:09:16,650 --> 00:09:20,410
+S is the area of each plate shows that أن فرق 
+
+121
+00:09:20,410 --> 00:09:24,870
+الجهد الذي وضعناه هو V1 ناقص V2 يساوي 2FD
+
+122
+00:09:24,870 --> 00:09:28,710
+تربيع على epsilon نقطة S تحت الجذر طب نحن لكي 
+
+123
+00:09:28,710 --> 00:09:33,330
+نحصل على التي هي ال potential ماذا لزوم ال potential
+
+124
+00:09:33,330 --> 00:09:35,970
+مرتبط به بال electric field ال potential ماذا 
+
+125
+00:09:35,970 --> 00:09:42,890
+يساوي ال electric field يساوي V في D فح أو V
+
+126
+00:09:42,890 --> 00:09:47,570
+تساوي E على D ومن هي D؟ التي هي المسافة بين
+
+127
+00:09:47,570 --> 00:09:51,130
+الاثنين فأنا أول حاجة لازمة مني أن أحصل على هو ال electric
+
+128
+00:09:51,130 --> 00:09:54,550
+field لكي أقدر أن أحصل على ال potential فهذا الذي هو M
+
+129
+00:09:54,550 --> 00:09:57,550
+أول حاجة من ال force ونحن حسبناها مع بعض ال 
+
+130
+00:09:57,550 --> 00:10:01,990
+force فما المثال السادس؟ force تساوي رؤس تربيع
+
+131
+00:10:01,990 --> 00:10:07,170
+في S على 2 E نوت بالتالي أقدر أن أحصل على أن هي رؤس وهي
+
+132
+00:10:07,170 --> 00:10:15,610
+الـA في الـP رؤس من Gauss law هي diverge A أو ال 
+
+133
+00:10:15,610 --> 00:10:21,130
+clause Integra ل A ضد S تساوي ال clause بالتأكيد
+
+134
+00:10:21,130 --> 00:10:26,470
+حفظناها في Gauss law ماشي ال clause Integra ل A ضد
+
+135
+00:10:26,470 --> 00:10:31,130
+S تساوي ال clause charged 
+
+136
+00:10:33,690 --> 00:10:42,930
+رؤس في أس وهذه شحنة سطحية E في أس رؤس على ابسلون أه
+
+137
+00:10:42,930 --> 00:10:46,530
+الأس
+
+138
+00:10:46,530 --> 00:10:51,390
+يدخل مع أس فهي رؤس تساوي ابسلون E طبعًا هو ليس ماذا 
+
+139
+00:10:51,390 --> 00:10:53,750
+لأنه في أي مادية فهي مفترضة على ال space يعني أو
+
+140
+00:10:53,750 --> 00:10:57,470
+ممكن شيء أنا لم أقرأه كلها هي ال space موجودة في 
+
+141
+00:10:57,470 --> 00:11:03,540
+ال space ابسلون نوتر فعين رؤس تساوي E في epsilon 
+
+142
+00:11:03,540 --> 00:11:10,320
+note فهذا هو Gauss law إذا 
+
+143
+00:11:10,320 --> 00:11:14,140
+الفرصة التي حسبناها في المثال السابق التي هي رؤس
+
+144
+00:11:14,140 --> 00:11:18,600
+تدخل في s على 2 epsilon note تعطينا قيمة رؤس من 
+
+145
+00:11:18,600 --> 00:11:23,280
+رؤس أقدر أن أعرف من ماذا  E لأن E ماذا تساوي رؤس على 
+
+146
+00:11:23,280 --> 00:11:27,280
+epsilon note أو E ماذا تساوي vd على d إذا أنا
+
+147
+00:11:27,280 --> 00:11:28,820
+عرفت vd التي يريدها
+
+148
+00:11:37,130 --> 00:11:45,430
+قلنا رؤس ستساوي epsilon note في E و E تساوي VD على
+
+149
+00:11:45,430 --> 00:11:51,250
+D رؤس من المثال السابق يبقى ... يبقى ... يبقى عليها
+
+150
+00:11:51,250 --> 00:11:55,730
+تمرار عظم المثال السابق رؤس تساوي جزر التنبيه ب 2 
+
+151
+00:11:55,730 --> 00:12:02,230
+epsilon note F على S ستساوي epsilon note VD على D
+
+152
+00:12:02,230 --> 00:12:07,260
+لو ربعت الطرفين فصلت أو فيه D على طول هو الموضوع
+
+153
+00:12:07,260 --> 00:12:13,420
+الذي فندرسه يساوي D على Epsilon Note جزر 2 Epsilon
+
+154
+00:12:13,420 --> 00:12:17,960
+Note F على S ودخلت هدول داخل ال Integra وستكون
+
+155
+00:12:17,960 --> 00:12:26,580
+اندي الجزر تربيع 2D تربيع F على S Epsilon Note 
+
+156
+00:12:26,580 --> 00:12:32,580
+الذي هو مطلوب ال difference التي بين الأولى
+
+157
+00:12:32,580 --> 00:12:33,240
+والثانية 
+
+158
+00:12:39,040 --> 00:12:43,840
+دي جى ال continuity equation and relaxation time
+
+159
+00:12:43,840 --> 00:12:49,280
+ال continuity equation و ال relaxation time دي جى 
+
+160
+00:12:49,280 --> 00:12:54,320
+من التي هي التعريف دي أول حاجة ده ال current ال
+
+161
+00:12:54,320 --> 00:12:58,980
+charge current density surface current density جى
+
+162
+00:12:58,980 --> 00:13:02,600
+قلنا أن جى ماذا يساوي ال close integral لجى و
+
+163
+00:13:02,600 --> 00:13:05,620
+يقاس يساوي ال current لو أنا وضعت current out ماذا 
+
+164
+00:13:05,620 --> 00:13:08,280
+يعني الكمية ال charge التي تخرج من ال surface
+
+165
+00:13:08,280 --> 00:13:12,100
+وأعطيها إشارة سالبة لو current in كمية ال current
+
+166
+00:13:12,100 --> 00:13:14,160
+التي تخرج من ال surface وأعطيها إشارة موجبة 
+
+167
+00:13:14,160 --> 00:13:18,080
+فالأمر دي أن نحن تعرفنا أن جرم ما نحن نقوم به 
+
+168
+00:13:18,080 --> 00:13:22,420
+هو current density يعني ال close integral لجرم ال 
+
+169
+00:13:22,420 --> 00:13:26,220
+DS فعطينا طول التيار فحنا نأخذ I out ونقوم 
+
+170
+00:13:26,220 --> 00:13:29,500
+نحن مرضى نعرف أن أنا أقدر أكتب قيمة ال charge
+
+171
+00:13:29,500 --> 00:13:32,120
+التي ناقص Q in by dt
+
+172
+00:13:36,710 --> 00:13:45,310
+عرفنا أن جيه ماذا تساوي di by ds إذا كررنا إذا I 
+
+173
+00:13:45,310 --> 00:13:49,230
+out كما أنتم شايفين هي طبعًا close surface
+
+174
+00:13:49,230 --> 00:13:55,550
+integral لجيه ال DS نربطها  بتساوي أنها out ناقص dqn
+
+175
+00:13:55,550 --> 00:14:03,290
+by dt قصة نحن تناولنا هنا التي هي ال divergence
+
+176
+00:14:03,290 --> 00:14:04,430
+theorem التي تقول 
+
+177
+00:14:31,170 --> 00:14:37,830
+DVDVDVDVDVDVDVDV-D by Dt الـ QA لا أقدر أن أكتبها
+
+178
+00:14:37,830 --> 00:14:40,950
+برضه في دلالة Total Charge Density الـ Volume of
+
+179
+00:14:40,950 --> 00:14:46,330
+Charge Density Integral لRho V Db برضه Volume
+
+180
+00:14:46,330 --> 00:14:50,190
+Integral لو دخلت الـ Dt لم تؤثر على Volume
+
+181
+00:14:50,190 --> 00:14:53,570
+Integral بس أقدر أقولهم هي ناقص Integral لD Rho
+
+182
+00:14:53,570 -->
+
+201
+00:16:10,880 --> 00:16:18,800
+Law لو
+
+202
+00:16:18,800 --> 00:16:23,140
+احنا كان في عندنا نقطة في قلب الـ system تبعي في
+
+203
+00:16:23,140 --> 00:16:29,260
+أسطح conductor أو dielectricوها دي point charge
+
+204
+00:16:29,260 --> 00:16:33,380
+اللي حطيناها في الـ interior تبع الـ media بتاعتي ام
+
+205
+00:16:33,380 --> 00:16:36,760
+أوم سلوك بيقول هو الـ point form لـ أوم سلوك ماذا
+
+206
+00:16:36,760 --> 00:16:40,340
+ذاكرينه أن الـ point forms ايش بتساوي؟ J بتساوي
+
+207
+00:16:40,340 --> 00:16:44,960
+sigma E point
+
+208
+00:16:44,960 --> 00:16:50,020
+form لـ أوم سلوك أنه J current density بتساوي sigma
+
+209
+00:16:50,020 --> 00:16:55,400
+E طبعًا كمان عندنا من أوم سلوك نقدر نقول
+
+210
+00:17:03,140 --> 00:17:05,820
+هو حد divergence الطرفين اللي هو لا إيش هيكون؟
+
+211
+00:17:16,750 --> 00:17:19,270
+لو أخذنا الـ media أنها homogenous و linear ال
+
+212
+00:17:19,270 --> 00:17:21,390
+sigma بقدر أطلعها من الـ divergence لأنها ما تعتمدش
+
+213
+00:17:21,390 --> 00:17:24,550
+على الـ position يعني مش function في x و y و z فهي
+
+214
+00:17:24,550 --> 00:17:27,430
+الـ homogenous فهو مقدر يطلعها برة لو تعتمد على x و
+
+215
+00:17:27,430 --> 00:17:30,270
+y و z فهو مقدر يطلعها برة الـ divergence هاي حد سي
+
+216
+00:17:30,270 --> 00:17:35,250
+sigma divergence E بتساوي divergence J وهد إيش 
+
+217
+00:17:35,250 --> 00:17:41,230
+بتساوي رو V على ي sigma رو V على ي بتساوي
+
+218
+00:17:41,230 --> 00:17:44,850
+divergence E و الـ divergence E من الـ continuity
+
+219
+00:17:44,850 --> 00:17:46,030
+equation إيش بتساوي؟
+
+220
+00:17:52,130 --> 00:17:56,730
+هذه المعادلة صوت إيش؟ معادلة من الـ differential
+
+221
+00:17:56,730 --> 00:18:00,730
+equation فيها معدل الـ charge density لو أنا قعدت
+
+222
+00:18:00,730 --> 00:18:06,230
+أرتبها هتكون دي رو في على دي رو في إيش بتساوي؟ سالب
+
+223
+00:18:06,230 --> 00:18:13,570
+سيجما على ايبسلون في دي تي هذه اللي نكون منها حاجة
+
+224
+00:18:13,570 --> 00:18:20,220
+نسميها relaxation time لو أنا كملت طرفين هتكون لان
+
+225
+00:18:20,220 --> 00:18:27,660
+رو في على رو في نوب تساوي ماينوس هنا على إبسيلون في
+
+226
+00:18:27,660 --> 00:18:35,580
+وبالتالي بقدر أجيب اللي هو رو في بتساوي 
+
+227
+00:18:35,580 --> 00:18:42,220
+initial ات شارج لو
+
+228
+00:18:42,220 --> 00:18:44,180
+أخذنا الـ exponential بتعطينا
+
+229
+00:19:01,180 --> 00:19:05,140
+الزمن اللي لازم للـ charges احنا حطينا point of
+
+230
+00:19:05,140 --> 00:19:08,900
+charge في قلب الـ media وشوفنا إيش تأثير point of
+
+231
+00:19:08,900 --> 00:19:13,100
+charge في قلب الـ media بسيلها قعد التوزيع هذا هو
+
+232
+00:19:13,100 --> 00:19:16,980
+relaxation time الزمن اللي لازم لهي التشارج تسيلها
+
+233
+00:19:16,980 --> 00:19:20,100
+قعد التوزيع في قلب الـ media انتشار في قلب الـ media
+
+234
+00:19:20,100 --> 00:19:23,400
+تعريف
+
+235
+00:19:23,400 --> 00:19:27,540
+relaxation time احنا قلنا أن T بتساوي Tau ماذا
+
+236
+00:19:27,540 --> 00:19:31,440
+ذاكرين؟ زي اللي حكيت تشارج المكاسفات هذا القانون
+
+237
+00:19:31,440 --> 00:19:35,000
+RC law ده أنا نفس الحاجة أن T بتساوي الـ
+
+238
+00:19:35,000 --> 00:19:40,970
+relaxation time هتقل raw v لـ 37% من قيمة الـ initial
+
+239
+00:19:40,970 --> 00:19:46,310
+value لأن eights و minus و أحد بالـ 37% فـ 36.10%
+
+240
+00:19:46,310 --> 00:19:50,330
+فإذا الـ relaxation time هو الزمن اللي بتاخده الـ
+
+241
+00:19:50,330 --> 00:19:55,390
+charge عشان تسيلها توزية في داخل الـ material أنها
+
+242
+00:19:55,390 --> 00:20:02,770
+تنزل لقيمة مقدرها 36% من الـ initial value كمان
+
+243
+00:20:02,770 --> 00:20:06,930
+بعتمد لأن انتوا ملاحظين بعتمد على sigma عكسيًا يعني
+
+244
+00:20:06,930 --> 00:20:10,670
+إذا كبرت sigma وقت إيش تكبر sigma؟ الـ conductors
+
+245
+00:20:10,670 --> 00:20:14,790
+إذا كبرت sigma إيش بيصير لتاو؟ بتقل يعني على السريع
+
+246
+00:20:14,790 --> 00:20:18,150
+لأن شعر في الـ conductor لو قلت sigma الـ
+
+247
+00:20:18,150 --> 00:20:21,590
+conductivity وين بتقل كتير؟ في الـ insulators في الـ
+
+248
+00:20:21,590 --> 00:20:24,290
+dielectric بتقل سيجما إذا قلت سيجما إيش بيصير الـ
+
+249
+00:20:24,290 --> 00:20:28,850
+relaxation time بتوقف بيكبر يعني أن الـ charge في الـ
+
+250
+00:20:28,850 --> 00:20:31,990
+dielectric بطيء في الـ conductor سريع وهذا بيتناسب
+
+251
+00:20:31,990 --> 00:20:37,070
+مع اللي احنا بنحكيه الـ currents الـ
+
+252
+00:20:37,070 --> 00:20:40,010
+time constant مثلًا هم بيعطينا رسالة أنه عندي good
+
+253
+00:20:40,010 --> 00:20:45,690
+conductor اللي هو الكبر له سيجما 5.8 في 10 قوة 7
+
+254
+00:20:45,690 --> 00:20:53,260
+كبيرة 10 قوة 7 إشي يعني 58 ميجاموس يعني عكس الـ
+
+255
+00:20:53,260 --> 00:21:01,320
+Ohms مو برمتر لأنها سيجما إبسيلون ر ناخدها واحد
+
+256
+00:21:01,320 --> 00:21:05,780
+relative إبسيلون إذا هتكون relaxation time إبسيلون
+
+257
+00:21:05,780 --> 00:21:08,320
+هو عبارة عن إبسيلون relative إبسيلون نوت على سيجما
+
+258
+00:21:08,320 --> 00:21:13,200
+قال يفترض أن إبسيلون ر واحد يعني هو مفترض أنه الـ
+
+259
+00:21:13,200 --> 00:21:20,300
+spaceفهيكون قيمة sigma 1.53 في 10قوة ناقص 17
+
+260
+00:21:20,300 --> 00:21:24,240
+second لكن إذا أخذنا fused quartz هذه مادة
+
+261
+00:21:24,240 --> 00:21:29,560
+insulator sigma بتاعتها 10قوة ناقص 17 موز بيرميتر
+
+262
+00:21:29,560 --> 00:21:32,980
+طبعًا الإنسان قال إن هو الـ fused quartz هي نوع من
+
+263
+00:21:32,980 --> 00:21:37,200
+أنواع المواد العازلة sigma له 10قوة ناقص 17 ما لها
+
+264
+00:21:37,200 --> 00:21:40,220
+sigma بتاعته صغيرة كتير لأن هو مانه insulator للـ
+
+265
+00:21:40,220 --> 00:21:42,460
+quartz ولو إبسيلون من الأرض بتساوي خمسة
+
+266
+00:21:45,580 --> 00:21:49,400
+ما هي ممتازة فأسئل سمعار للـ cover واحد يعني بصراحة
+
+267
+00:21:49,400 --> 00:21:52,700
+يعني هنا الـ cover الناس يجب أن يقلوا 5.8×10⁷ و الـ
+
+268
+00:21:52,700 --> 00:21:55,740
+relative permittivity هي واحد فبتطلع معنى
+
+269
+00:21:55,740 --> 00:21:59,140
+relaxation time في الـ cover واحد تلاتة و خمسين مية
+
+270
+00:21:59,140 --> 00:22:03,020
+في عشر قط نقص اتاشر second يعني على السريع بيكون صار
+
+271
+00:22:03,020 --> 00:22:05,340
+عادة توزيع للـ charge في قلب الـ conductor اللي
+
+272
+00:22:05,340 --> 00:22:08,420
+حطفها الـ conductor بتوزع و بتروح على الـ surfaces
+
+273
+00:22:09,600 --> 00:22:13,400
+لكن الكوارث اللي قلنا sigma L مقالها قليلة صغيرة
+
+274
+00:22:13,400 --> 00:22:18,380
+عشان قوة ناقص 17 باللاحظ أنه عشان التوزيع بتشارج 51
+
+275
+00:22:18,380 --> 00:22:24,540
+يوم بطيء جدًا واضح؟
+
+276
+00:22:24,540 --> 00:22:28,840
+boundary conditions إيش هي الـ boundary conditions؟
+
+277
+00:22:28,840 --> 00:22:31,920
+boundary conditions هي بتدرس انتقال الموجات احنا
+
+278
+00:22:31,920 --> 00:22:34,760
+كلنا الهدف من الكهرومغناطيسية بعد ما تعرفنا كيف أقدر
+
+279
+00:22:34,760 --> 00:22:37,480
+أحسب الـ electric field في نقطة أحسب magnetic field
+
+280
+00:22:37,480 --> 00:22:41,180
+في نقطة أحسب الإن الـ electric field ناتج من الشعج
+
+281
+00:22:41,180 --> 00:22:44,420
+من الـ dye ولا الـ potential والاخرى اني اعرف لو
+
+282
+00:22:44,420 --> 00:22:47,640
+هذه الموجات اللي بتنتقل بتاعتي أسطح electric field
+
+283
+00:22:47,640 --> 00:22:51,580
+ولا magnetic field بتنقل قدر الـ media بتاعتي مش
+
+284
+00:22:51,580 --> 00:22:55,940
+هتظلها طول وقت في media واحدة أنا بقولها من مكان
+
+285
+00:22:55,940 --> 00:23:00,560
+لمكان هتمر في عدة medias احنا ببساطة بس هنشوف two
+
+286
+00:23:00,560 --> 00:23:02,900
+medias يعني مش هنشوف أكثر من media لكن هو ممكن
+
+287
+00:23:02,900 --> 00:23:08,260
+تتصادف عدة أنواع من الـ media الموجة بحد ذاتها عند
+
+288
+00:23:08,260 --> 00:23:12,020
+الـ boundary تحت الـ media لازم ما يتغيرش فيها إشي
+
+289
+00:23:12,020 --> 00:23:15,080
+لكن لما تدخل الـ media تكون فيها الـ media و هال
+
+290
+00:23:15,080 --> 00:23:17,700
+media هيكون فيه شوية اختلافات لكن عند الـ boundary
+
+291
+00:23:17,700 --> 00:23:21,740
+أنها continuous مش discrete في الموجة هي موجة يعني
+
+292
+00:23:21,740 --> 00:23:25,280
+زي ما أنا أكون هناك أعلى و طلعت نزلت تحت بصي ليش
+
+293
+00:23:25,280 --> 00:23:28,960
+discreteness عند الـ boundary لازم أكون نفس الحاجة
+
+294
+00:23:28,960 --> 00:23:32,220
+نفس الموجة شوية في الخصائص بتتغير كنت أعلى شوية و
+
+295
+00:23:32,220 --> 00:23:37,210
+نزلت بالنسبالك صرت أقصر ف نفس الشيء للموجة إذا
+
+296
+00:23:37,210 --> 00:23:40,690
+كنت من media لـ media حسيتها تغييرات لكن عند أطراف
+
+297
+00:23:40,690 --> 00:23:44,370
+عند الـ boundary بالتمام هتكون نفس الموجة فاحنا
+
+298
+00:23:44,370 --> 00:23:47,390
+بنستغل هذه الحاجة بمعرفتنا بعض خصائص عند الـ
+
+299
+00:23:47,390 --> 00:23:50,430
+boundary أنه إذا كنت عارفة خصائص الموجة في media
+
+300
+00:23:50,430 --> 00:23:53,430
+كيف أجيبها في الـ media التانية فالـ boundary
+
+301
+00:23:53,430 --> 00:23:57,590
+condition هي إيش الشروط اللي عند الـ boundary
+
+302
+00:23:57,590 --> 00:24:02,790
+between two media اللي لازم تتحقق عشان ما يصيرش أي
+
+303
+00:24:02,790 --> 00:24:08,340
+خلل للموجة هنتبع نشوف الـ boundary condition ما بين
+
+304
+00:24:08,340 --> 00:24:14,540
+dielectric و dielectric ايه اللي قيله epsilon الـ
+
+305
+00:24:14,540 --> 00:24:20,000
+relative epsilon واحد والتاني epsilon قاع تانين ما
+
+306
+00:24:20,000 --> 00:24:22,820
+بين conductor و dielectric ما بين conductor و free
+
+307
+00:24:22,820 --> 00:24:25,700
+space free space طبعًا حالة خاصة من الـ dielectric
+
+308
+00:24:25,700 --> 00:24:30,090
+يعني إذا عرفنا الثانية الثالثة حالة خاصة منها عشان
+
+309
+00:24:30,090 --> 00:24:32,750
+نعرف الـ boundary conditions احنا بنلجأ لـ Maxwell's
+
+310
+00:24:32,750 --> 00:24:34,950
+equations يعني مش هنقدر نطول boundary condition
+
+311
+00:24:34,950 --> 00:24:38,190
+بدون Maxwell's equation أن الـ two equations اللي هي
+
+312
+00:24:38,190 --> 00:24:41,730
+الـ close انتجرال لـ E دول DL بتساوي zero هم ذاكرين
+
+313
+00:24:41,730 --> 00:24:45,850
+هذه الـ conservative force و الـ close انتجرال لـ D
+
+314
+00:24:45,850 --> 00:24:53,890
+دول DS بتساوي Q enclosed معايا؟ طيب كمان بدي أكتب
+
+315
+00:24:53,890 --> 00:24:57,350
+الـ electric field ع شكل two components Electric
+
+316
+00:24:57,350 --> 00:25:01,930
+field تقوم بتحكي
+
+317
+00:25:01,930 --> 00:25:08,130
+طريقة E tangential plus E normal على الـ interface
+
+318
+00:25:21,940 --> 00:25:24,440
+اللي هو الـ surface بالتواري مشترك بين الجوال و
+
+319
+00:25:24,440 --> 00:25:27,740
+الطاولة هذا الـ interface هذا الـ boundary condition
+
+320
+00:25:27,740 --> 00:25:32,000
+واضح عنده
+
+321
+00:25:32,000 --> 00:25:34,800
+هيكون عندي two components للـelectric field واحدة
+
+322
+00:25:34,800 --> 00:25:38,300
+tangential لهذا الـ surface واحدة عمودية على هذا الـ
+
+323
+00:25:38,300 --> 00:25:43,920
+surface نبدأ
+
+324
+00:25:43,920 --> 00:25:47,520
+بالـ dielectric dielectric boundary condition زي ما
+
+325
+00:25:47,520 --> 00:25:50,280
+انتوا شايفين هي عندي two media زي الجوال والطاولة
+
+326
+00:25:50,280 --> 00:25:55,030
+اتنين dielectric هذه الـ surface الأول وهذه الـ
+
+327
+00:25:55,030 --> 00:26:00,750
+surface الثاني وهذه الـ
+
+328
+00:26:00,750 --> 00:26:03,890
+media الأولى وهذه ال media الثانية وهذه ال media
+
+329
+00:26:03,890 --> 00:26:05,650
+الثانية وهذه ال media الثانية وهذه ال media
+
+330
+00:26:05,650 --> 00:26:08,730
+الثانية وهذه ال media الثانية وهذه ال media
+
+331
+00:26:08,730 --> 00:26:10,970
+الثانية وهذه ال media الثانية وهذه ال media
+
+332
+00:26:10,970 --> 00:26:12,530
+الثانية وهذه ال media الثانية وهذه ال media
+
+333
+00:26:12,530 --> 00:26:12,890
+الثانية وهذه ال media الثانية وهذه ال media
+
+334
+00:26:12,890 --> 00:26:13,170
+الثانية وهذه ال media الثانية وهذه ال media
+
+335
+00:26:13,170 --> 00:26:14,570
+الثانية وهذه ال media الثانية وهذه ال media
+
+336
+00:26:14,570 --> 00:26:14,710
+الثانية وهذه ال media الثانية وهذه ال media
+
+337
+00:26:14,710 --> 00:26:15,790
+الثانية وهذه ال media الثانية وهذه ال media
+
+338
+00:26:15,790 --> 00:26:22,440
+الثانية وهذه ال media التمتوازي أطلع زي الجوال إيش
+
+339
+00:26:22,440 --> 00:26:28,600
+هيكون مستطيل لكن بشوفه أنا إيش كخط لو بطلع عليه
+
+340
+00:26:28,600 --> 00:26:32,000
+فهذه السرعة بتاعتنا انبعين كإنه خط بس هو في الواقع
+
+341
+00:26:32,000 --> 00:26:37,440
+عندي surface بين الـ two media عشان أعرف إيش بيصير
+
+342
+00:26:37,440 --> 00:26:41,220
+عند الـ boundary تقسمنا الـ electric field الأول هي
+
+343
+00:26:41,220 --> 00:26:47,670
+E1 وهي E2 E1 tangential component و normal component
+
+344
+00:26:47,670 --> 00:26:52,450
+و E2 نفس القضية tangential component للـ interface و
+
+345
+00:26:52,450 --> 00:26:55,890
+واحدة عمودية على الـ interface إذا E2 هي عندي الـ E
+
+346
+00:26:55,890 --> 00:27:00,890
+normal و E tangential E1 هي عندي E tangential و E
+
+347
+00:27:00,890 --> 00:27:03,330
+normal هستخدم
+
+348
+00:27:05,470 --> 00:27:07,650
+اللي هو Maxwell's equation بتقول الـ close
+
+349
+00:27:07,650 --> 00:27:12,530
+integral لـ E dot DL بتساوي 0 فهختار loop هذا loop
+
+350
+00:27:12,530 --> 00:27:15,870
+يعني الـ close integral أو الـ line integral هذي
+
+351
+00:27:15,870 --> 00:27:22,030
+بتقول لي أنه أي line لو أخدته close للـ FQ بتساوي 0
+
+352
+00:27:22,030 --> 00:27:28,990
+هاي الـ line بدنا ناخدها هاي الـ line integral هاخد
+
+353
+00:27:28,990 --> 00:27:32,070
+هذا الـ line أو الـ loop الـ imaginary loop اللي
+
+354
+00:27:32,070 --> 00:27:36,110
+هيكون بالنسبالي هاخد عليه الـ integration وهكامل
+
+355
+00:27:36,110 --> 00:27:39,750
+على كل واحدة من هدولة هنا هاي جزئية اللي كثرت كثير
+
+356
+00:27:39,750 --> 00:27:45,510
+منها يكون E tangential واحد E normal واحد هنا E
+
+357
+00:27:45,510 --> 00:27:50,530
+normal اثنين هنا مين E tangential اثنين E normal
+
+358
+00:27:50,530 --> 00:27:56,910
+اثنين E normal واحد E tangential واحد واضح؟ إذا
+
+359
+00:27:56,910 --> 00:28:00,650
+نكون جزئية من هدول الأجزاء هكاملها بالمشتقين هيكون
+
+360
+00:28:00,650 --> 00:28:06,330
+عندي E واحد tangential E1 tangential هي أحد الـ sides
+
+361
+00:28:06,330 --> 00:28:14,210
+تبعه Delta W للـ loop والارتفاع لو احده Delta H إذا
+
+362
+00:28:14,210 --> 00:28:19,870
+نقطعه Delta H ويلعب Delta ظهرنا فعندي من اللي هو
+
+363
+00:28:19,870 --> 00:28:23,830
+في الـ media الأولى من A لـ B هيكون E1 tangential
+
+364
+00:28:23,830 --> 00:28:32,130
+Delta W لاتجاه minus E1 normal Delta H لأن E1 Normal
+
+365
+00:28:32,130 --> 00:28:40,620
+اتجاه وين لأعلى E1 normal ΔH على 2 نفس القضية النورم
+
+366
+00:28:40,620 --> 00:28:44,480
+هنا عكسه يعني نورم اتجاه H هنا عكسه هيكون minus
+
+367
+00:28:44,480 --> 00:28:52,300
+E2 N ΔH على 2 بعدين التنجينتشارت برضه عكس اتجاهه
+
+368
+00:28:52,300 --> 00:28:58,160
+هيكون minus E2 tangential ΔW هنا اتجاه النورم تبع
+
+369
+00:28:58,160 --> 00:29:02,730
+الـ side الثاني نفس اتجاهه هيكون plus E2 normal مضبوط على
+
+370
+00:29:02,730 --> 00:29:11,970
+2 plus E1 normal مضبوط على 2 إذا طلعنا نلاحظ أن E1
+
+371
+00:29:11,970 --> 00:29:19,410
+normal مضبوط على 2 هنا مرة سالفة وهنا اثنين جبهة E2ن
+
+372
+00:29:19,410 --> 00:29:22,090
+الـ normal والـ component هنا سالفة وهنا اثنين جبهة
+
+373
+00:29:22,090 --> 00:29:26,850
+لما عندي الـ tangential component فإيش سواء عندي E1
+
+374
+00:29:26,850 --> 00:29:30,480
+tangential بيتساوى E2 tangential ماذا نستطيع أن
+
+375
+00:29:30,480 --> 00:29:33,820
+نقول؟ أن عند الـ boundary الـ tangential component
+
+376
+00:29:33,820 --> 00:29:37,980
+للـ electric field ما لها continuous لأنه لازم تكون
+
+377
+00:29:37,980 --> 00:29:41,580
+E1 tangential بتساوي E2 tangential إذا ال
+
+401
+00:31:14,640 --> 00:31:18,860
+ما لها discontinuous across the interface دي واحد
+
+402
+00:31:18,860 --> 00:31:22,240
+tangential بتساوي epsilon واحد أبسلونين تانين بـ D
+
+403
+00:31:22,240 --> 00:31:24,320
+تناير الـ Dungeon Shell إذا أنا عند الـ interface
+
+404
+00:31:24,320 --> 00:31:31,960
+الـ D منها مش ممكن يوصل الـ
+
+405
+00:31:31,960 --> 00:31:38,000
+Boundary Condition التاني بنا بنا نستخدم المعادلة
+
+406
+00:31:38,000 --> 00:31:40,840
+التانية اللي هي ال clause integral لـ D dot DS بسوء
+
+407
+00:31:40,840 --> 00:31:44,240
+Q and clause مين هيتستخدم؟ هيتستخدم اللي هم بيسموه
+
+408
+00:31:44,240 --> 00:31:48,300
+bull box بتعرفوا شو هو ال bull box؟ اللي هو صندوق
+
+409
+00:31:48,300 --> 00:31:50,120
+حربة الدواء ال bull box
+
+410
+00:31:55,980 --> 00:32:01,160
+طبعا أول حاجة عندي T1 و T2 لأن أنا cross ال T ل D
+
+411
+00:32:01,160 --> 00:32:04,860
+ل DS باخد tangential component من normal component
+
+412
+00:32:04,860 --> 00:32:09,660
+tangential component من normal component ل D ل 2
+
+413
+00:32:09,660 --> 00:32:13,560
+ببدأ أعمل ال integration على ال surface
+
+414
+00:32:19,170 --> 00:32:21,950
+اللي هي جزء الـ charge اللي enclosed في أندف الـ
+
+415
+00:32:21,950 --> 00:32:28,470
+surface قشبت يساوي ρو أس في دنت أس تمانش بساوي هذا
+
+416
+00:32:28,470 --> 00:32:33,790
+من الـ closed integral دي واحد نور في دنت دي أس
+
+417
+00:32:33,790 --> 00:32:38,230
+minus دي أنتنين نور في دي أس واللي على ال surface
+
+418
+00:32:38,230 --> 00:32:40,590
+الموازي هيكون بساوة صفر لأن ال product الـ dot
+
+419
+00:32:40,590 --> 00:32:45,530
+هيكون بساوة صفر دي فقط اللي معدت نورها على ال
+
+420
+00:32:45,530 --> 00:32:48,590
+surface هي اللي حدثهم بساوة صفر والباقي هيروح أس
+
+421
+00:32:49,430 --> 00:32:56,030
+هيظل عندي DN1-DN2 بتساوي رؤس إذا كانت رؤس بتساوي
+
+422
+00:32:56,030 --> 00:32:59,950
+Zero إذا كانت رؤس ال surface charge density بتساوي
+
+423
+00:32:59,950 --> 00:33:04,740
+Zero ساعتها بقدر أقول إنه ال norm component دي ربع
+
+424
+00:33:04,740 --> 00:33:07,240
+جوه احنا حسيتنا غير ال tangential component ال
+
+425
+00:33:07,240 --> 00:33:11,740
+normal component ل D بتكون continuous إذا أبسلون
+
+426
+00:33:11,740 --> 00:33:15,960
+لا تسوى zero بتكونش continuous بيكون الفرق بين ال
+
+427
+00:33:15,960 --> 00:33:23,090
+D norm عند ال interface بتسوى raw S لو كان طرق
+
+428
+00:33:23,090 --> 00:33:28,250
+أسئولنا بيساوي 0 هيكون D1 norm بيساوي D2 norm وD1
+
+429
+00:33:28,250 --> 00:33:33,030
+norm مش بيساوي Epsilon 1 E1 norm بيساوي Epsilon 2
+
+430
+00:33:33,030 --> 00:33:38,550
+E2 norm إذا عرفنا E tangential لل media E1
+
+431
+00:33:38,550 --> 00:33:44,930
+tangential وE1 norm وعرفنا E2 tangential وE2 norm
+
+432
+00:33:44,930 --> 00:33:47,650
+إيش عرفت؟ عرفت ال total electric field في ال media
+
+433
+00:33:47,650 --> 00:33:48,110
+الأولى
+
+434
+00:33:53,300 --> 00:33:57,720
+من ال two equations من ال clause integral لـ E ضد EL
+
+435
+00:33:57,720 --> 00:34:01,480
+ومن ال equation ال clause integral لـ D ضد DS واسمها
+
+436
+00:34:01,480 --> 00:34:07,640
+Q in clause اقدرت احسب ان ال total electric field
+
+437
+00:34:07,640 --> 00:34:09,640
+أسوا ال tangential components او ال normal
+
+438
+00:34:09,640 --> 00:34:14,600
+components طبعا لو عملنا ال surface اللى هى على طول
+
+439
+00:34:14,600 --> 00:34:18,020
+ال delta H لو أخدت اللى هو ال surface تبع السليندة
+
+440
+00:34:18,020 --> 00:34:21,060
+فأنا هيكون فيه عندي اللي هي ال tangential
+
+441
+00:34:21,060 --> 00:34:24,060
+component في ال surface هنا ولا تنجش ال component
+
+442
+00:34:24,060 --> 00:34:27,140
+في delta H على 2 يعني اللي هي مساحة القاعدة في
+
+443
+00:34:27,140 --> 00:34:30,360
+الارتفاع ال surface سريه هتكون محيط القاعدة في
+
+444
+00:34:30,360 --> 00:34:33,980
+الارتفاع نفس الأضياء في هذه جزئية مساحة القاعدة في
+
+445
+00:34:33,980 --> 00:34:37,420
+الارتفاع هيروحوا لـ 0 لأن في النهاية دلتا H تكون
+
+446
+00:34:37,420 --> 00:34:41,280
+ساوية تمام 0 عشان أكون بال time ended interface
+
+447
+00:34:41,280 --> 00:34:49,300
+فبظل عندي فقط D1 N minus D2 N بتثوره أصل هي جاية
+
+448
+00:34:49,300 --> 00:34:56,640
+من ال surface الدائرة اللي فوق والدائرة اللي تحت إن
+
+449
+00:34:56,640 --> 00:34:59,840
+ال surface هيكون الدائرة اللي فوق وال surface area
+
+450
+00:34:59,840 --> 00:35:04,480
+الجانبية بتاعة السيلندر والدائرة اللي تحت بس كل
+
+451
+00:35:04,480 --> 00:35:09,840
+اللي هيطلع من الدائرة .. من ال surface مساحة
+
+452
+00:35:09,840 --> 00:35:13,240
+الجانبية للسيلندر هيروح لصفر إنه في النهاية بدل
+
+453
+00:35:13,240 --> 00:35:17,160
+ذات تقشط روح لل zero فقط عندي فقط اللي هو ال
+
+454
+00:35:17,160 --> 00:35:18,100
+normal component
+
+455
+00:35:38,040 --> 00:35:41,840
+نفس الشيء في الدائرة اللي تحت اللي هيتقب ضقة اللي
+
+456
+00:35:41,840 --> 00:35:47,980
+هو ال normal component لل D هي D.Norm وفي الحادة
+
+457
+00:35:47,980 --> 00:35:53,820
+تجارب التنجينتشال ستكون Zero وهكذا نتفق أن D1
+
+458
+00:35:53,820 --> 00:35:56,500
+Normal minus D2 Normal تنقل نقل نقل نقل نقل نقل
+
+459
+00:35:56,500 --> 00:35:56,960
+نقل نقل نقل نقل نقل نقل نقل نقل نقل نقل نقل
+
+460
+00:35:56,960 --> 00:36:00,760
+نقل نقل نقل نقل
+
+461
+00:36:00,760 --> 00:36:02,200
+نقل نقل نقل نقل نقل نقل نقل نقل نقل نقل نقل
+
+462
+00:36:02,200 --> 00:36:10,780
+نقل نقل نقل نقل نقل نقل نقل نقل نقل نقل نقل
+
+463
+00:36:10,780 --> 00:36:12,060
+نقل نقل نقل نقل نقل نقل نقل نقل نقل نقل نقل
+
+464
+00:36:12,060 --> 00:36:17,190
+نقل نقل نقل نقالمساحة الجانبية لكن المساحة
+
+465
+00:36:17,190 --> 00:36:19,690
+الجانبية في النهاية هخليها 0 لأن هخلي delta H
+
+466
+00:36:19,690 --> 00:36:24,930
+بتروح لـ 0 تمام؟ إذا احنا استنتجنا إنه ال
+
+467
+00:36:24,930 --> 00:36:28,190
+tangential component لل electric field متساوي عند
+
+468
+00:36:28,190 --> 00:36:32,450
+ال interface ال tangential component لل D
+
+469
+00:36:32,450 --> 00:36:36,660
+discontinuous عند ال interface الـ Normal component
+
+470
+00:36:36,660 --> 00:36:40,960
+للـ D بتكون continuous فقط إذا كانت الرؤاس بتساوي
+
+471
+00:36:40,960 --> 00:36:46,140
+0 وساعتها بقدر أحسب ال tangential component لل
+
+472
+00:36:46,140 --> 00:36:47,480
+electric field
+
+473
+00:37:07,450 --> 00:37:11,330
+لللقاء القادم إن شاء الله هناخد بعض الأمثلة على ال
+
+474
+00:37:11,330 --> 00:37:14,370
+interface between two dialectic اللي هو خلصت
+
+475
+00:37:14,370 --> 00:37:17,790
+أشرحها اليوم هناخد أمثلة تثه لو أنا كنت عارفة بعض
+
+476
+00:37:17,790 --> 00:37:20,830
+القصاص بتركيب في أحد ال facets أو في أحد ال media
+
+477
+00:37:20,830 --> 00:37:23,110
+كيف أجيبه في ال media التانية
diff --git a/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/R4EBPdgiKoM_postprocess.srt b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/R4EBPdgiKoM_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..12871404b92242eb4f81605e1866880fbca42cae
--- /dev/null
+++ b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/R4EBPdgiKoM_postprocess.srt
@@ -0,0 +1,1860 @@
+1
+00:00:21,310 --> 00:00:23,630
+بسم الله الرحمن الرحيم السلام عليكم و رحمة الله و
+
+2
+00:00:23,630 --> 00:00:27,810
+بركاته احنا ان شاء الله المحاضرة هي هنتبع ال
+
+3
+00:00:27,810 --> 00:00:30,750
+differential elements اللي بدناها قبل العيد احنا
+
+4
+00:00:30,750 --> 00:00:33,050
+حكيناها ك division و cylindrical coordinate شفنا
+
+5
+00:00:33,050 --> 00:00:37,310
+ال dl و شفنا ال ds و ال dv و وصلنا ان ال dl و ال
+
+6
+00:00:37,310 --> 00:00:41,570
+ds vectors و ال dv مالها scalar ضال علينا اللي هو
+
+7
+00:00:41,570 --> 00:00:44,290
+cylindrical coordinate فال cylindrical coordinate
+
+8
+00:00:44,290 --> 00:00:49,710
+ال element بيكون زي هيكي بهذا الشكل القطع اللي زال
+
+9
+00:00:49,710 --> 00:00:59,040
+أمامناهيكون عندنا three different points هيتجاه
+
+10
+00:00:59,040 --> 00:01:03,380
+الار سفريكال كواردنات انا لما انتقل من shell لو
+
+11
+00:01:03,380 --> 00:01:06,280
+انا اتخيلت كل space تبعي spheres اتخيلنا كل
+
+12
+00:01:06,280 --> 00:01:09,020
+cylinder اتخيلنا كل space كل cylinders اتخيلنا
+
+13
+00:01:09,020 --> 00:01:13,140
+spheres لما انتقل من shell ل shell انا من ار لار
+
+14
+00:01:13,140 --> 00:01:18,710
+تانية الانتقال هذا بعطيني DRكمان ان لما انتقل من
+
+15
+00:01:18,710 --> 00:01:22,650
+theta ل theta هيكون في عندي تغير في theta هيكون في
+
+16
+00:01:22,650 --> 00:01:27,590
+عندي دي theta كمان في ال D phi لما انتقل من
+
+17
+00:01:27,590 --> 00:01:30,830
+الزاوية عندي phi معينة ده phi تانية هيكون في عندي
+
+18
+00:01:30,830 --> 00:01:34,070
+D phi بتولد عن هيك هذا ال element اللي قدامنا
+
+19
+00:01:34,070 --> 00:01:39,890
+التغير في phi والتغير في theta والتغير في R فهيكون
+
+20
+00:01:39,890 --> 00:01:46,730
+عندى في أطول زي هذا الطولمن هنا لهنا هذا الطول هو
+
+21
+00:01:46,730 --> 00:01:50,290
+بساطة انتقال من شلة لشلة يعني هيكون ايش طوله؟ دي R
+
+22
+00:01:50,290 --> 00:01:55,870
+هذا الطول هو مقابل لمين؟ لـDθ هذا لما انتقلت من
+
+23
+00:01:55,870 --> 00:02:00,190
+ثتة معينة لثتة تانية من ثتة واحد لثتة اتنين فصار
+
+24
+00:02:00,190 --> 00:02:04,190
+عندي D ثتا القسم مقابل لأي زاوية ايش بيكون؟ الطول
+
+25
+00:02:04,190 --> 00:02:08,750
+النصف القطر في الزاوية النصف القطر عنا ايش بيمته؟
+
+26
+00:02:08,750 --> 00:02:13,150
+R في D ثتا فإذا هذا ال links ايش هيكون؟ R D ثتا
+
+27
+00:02:13,670 --> 00:02:17,070
+دلين ديمين اللي هو ال links اللي في هذا الاتجاه
+
+28
+00:02:17,070 --> 00:02:22,490
+هذا الاتجاه مش بيساوي هو لو انا طلعت على اسقاطه
+
+29
+00:02:22,490 --> 00:02:27,190
+هيكون هذا اسقاطهطول نصف القطر من قبل لهذا القوس ده
+
+30
+00:02:27,190 --> 00:02:31,050
+قوس لزاوية المقابلة إليه زاوية المقابلة إليه دي
+
+31
+00:02:31,050 --> 00:02:34,630
+فاي أنا كنت عيد فاي معينة وانت قعدت لفاي تانية بس
+
+32
+00:02:34,630 --> 00:02:37,810
+هذا الإسقاط هو عبارة عن مين إذا طلعت نصف القطر R
+
+33
+00:02:37,810 --> 00:02:42,170
+بعمله إسقاطين واحد على اتجاه ال Z واحد على اتجاه
+
+34
+00:02:42,170 --> 00:02:47,880
+ال XYZ الاتجاه ال Z هو R sin θاللي في اتجاه ال X Y
+
+35
+00:02:47,880 --> 00:02:53,340
+Z في ال plan يعني X Y Z هيكون R Sine Theta فهذا
+
+36
+00:02:53,340 --> 00:02:57,180
+هيكون طوله R Sine Theta و هذه هتكون اغارة عن R
+
+37
+00:02:57,180 --> 00:03:01,520
+Sine Theta D Phi R Sine Theta D Phi اذا عندي انا
+
+38
+00:03:01,520 --> 00:03:05,700
+ال three element changes او يعني links of changes
+
+39
+00:03:05,700 --> 00:03:15,200
+بيدي او DR او R D Theta او R Sine Theta D Phiفازن
+
+40
+00:03:15,200 --> 00:03:17,760
+ال differential displacement ال DL اللى هى vector
+
+41
+00:03:17,760 --> 00:03:22,040
+هيكون عندى اتجاه ال R اللى هو زى ما شوفناه قبل هدا
+
+42
+00:03:22,040 --> 00:03:29,740
+هو اتجاه ال R عند D R R hat اتجاه ال R هاي R hat
+
+43
+00:03:29,740 --> 00:03:35,440
+هاي R واحد R ثانى هاي D R واتجاهها اتجاه ال R hat
+
+44
+00:03:35,440 --> 00:03:39,020
+اللى هو اتجاه الكتر فانا هناك عند ال element هذا
+
+45
+00:03:39,020 --> 00:03:43,420
+اللى هو عبارة عن مين R D ستة واتجاهه اتجاه اللى
+
+46
+00:03:43,420 --> 00:03:49,150
+وسطه hatالـ element الأخير هو هذا الـ element هذا
+
+47
+00:03:49,150 --> 00:03:53,530
+الأسقطمار هذا عمارة عن أمر الـ sin θ دي θ في الـ
+
+48
+00:03:53,530 --> 00:04:03,510
+defined تجاهه و تجاه الهوايب فاتي باضي نجي
+
+49
+00:04:03,510 --> 00:04:07,410
+لـ surfaces الـ surfaces طبعا طبعا بتحيطها كل يعني
+
+50
+00:04:07,410 --> 00:04:09,290
+كل واحد من هدولة هعتبره surface
+
+51
+00:04:15,100 --> 00:04:19,220
+هذه الـ surface و كمان ال surface اللي فوق كل واحد
+
+52
+00:04:19,220 --> 00:04:23,400
+من هدول ال surfaces له قيمة و له اتجاه اذا كده
+
+53
+00:04:23,400 --> 00:04:28,280
+قلنا ال links دي ال مع long vector و ال surfaces
+
+54
+00:04:28,280 --> 00:04:32,620
+vector الاتجاه ده بقى عمودي على ال surface و برا
+
+55
+00:04:32,620 --> 00:04:34,640
+ال volume يعني لو انا ال surface تبع المحيط في
+
+56
+00:04:34,640 --> 00:04:38,740
+الطبق هيكون ال norm اللي طالع من الطبق هو اتجاه ال
+
+57
+00:04:38,740 --> 00:04:42,000
+surfaceفكل واحد من هدول ال surfaces طب احنا عارفين
+
+58
+00:04:42,000 --> 00:04:44,680
+نقول كل واحدة من هدول الأحوال يعني مثلا لو أخدت
+
+59
+00:04:44,680 --> 00:04:47,840
+هدا ال surface ها surface هبقى بيقولنا إيش بيساوي
+
+60
+00:04:47,840 --> 00:04:52,720
+DM وهيبقى بيقولنا إيش بيبقى بيساوي RDθ فإذا
+
+61
+00:04:52,720 --> 00:04:58,220
+المساحة دي إيش هتكون RDθ في R هتكون R تربية Dθ
+
+62
+00:04:58,220 --> 00:05:01,540
+وإيش الاتجاه هون بيكون إذا هذا هو الاتجاه ال R
+
+63
+00:05:01,540 --> 00:05:06,380
+وهذا الاتجاه هو ال θ فاتجاه العمودي عليه هيكون مين
+
+64
+00:05:06,380 --> 00:05:10,690
+هو Phi hatهذا ال surface هيكون النور طبعا هو في
+
+65
+00:05:10,690 --> 00:05:14,930
+تجاه ال pi hat نقول هيك طالب ال pi hat موزر هذا في
+
+66
+00:05:14,930 --> 00:05:20,970
+تجاه ال pi hat انا
+
+67
+00:05:20,970 --> 00:05:28,750
+بقيت اللي هو r d theta و dr هذا اللي هو في تجاه ال
+
+68
+00:05:28,750 --> 00:05:32,590
+theta و هذا في تجاه ال r فاللي عمودي عليها هيكون
+
+69
+00:05:32,590 --> 00:05:36,590
+مين اللي هو ال pi hat نيجي لل surface التاني مثلا
+
+70
+00:05:38,630 --> 00:05:42,790
+عندها انا اخد ال surface من هنا هذا ال surface
+
+71
+00:05:42,790 --> 00:05:49,650
+هتطلع هنا rdθ و هتطلع هنا يبقى عبارة عن rsinθdφ
+
+72
+00:05:49,650 --> 00:05:53,250
+فعندى التغيرات او الاتجاه التعطي اتجاه ال θ و
+
+73
+00:05:53,250 --> 00:05:57,350
+اتجاه ال ف هت او الاتجاه التعطي فوان بيكون هذا ال
+
+74
+00:05:57,350 --> 00:06:01,550
+normal عليا اتجاه ال r هت تمام فازال ارى هتكون
+
+75
+00:06:01,550 --> 00:06:04,050
+عندى r تربيع sinθdθdφ
+
+76
+00:06:21,310 --> 00:06:26,410
+YRθRsinθ⁻⁻ فالارية هي عبارة عن R ترقية sinθDθ⁻⁻
+
+77
+00:06:26,410 --> 00:06:31,190
+اتجاه R hat اخر الارية اللي هتكون يندي واحد منهم
+
+78
+00:06:31,190 --> 00:06:37,250
+هو DR والتاني R ثالث sinθ⁻⁻R هيكون اتجاهنا θ hat
+
+79
+00:06:42,970 --> 00:06:46,830
+بعدين احنا قلنا ال surface differential area هي
+
+80
+00:06:46,830 --> 00:06:50,050
+عبارة عن vector اللي هي نقدار اللي هي اتجاهه فممكن
+
+81
+00:06:50,050 --> 00:06:52,690
+تكون اللي هو احد هدول ال surfaces اللي هي مثلا هذا
+
+82
+00:06:52,690 --> 00:06:57,250
+ال surface بقعة ربيع sin θ dθ dφ و اتجاهه ارهار او
+
+83
+00:06:57,250 --> 00:07:00,430
+هذا ال surface اللي هو R sin θ dr dφ و اتجاهه θ
+
+84
+00:07:00,430 --> 00:07:05,750
+hat او ال surface هذا اللي هو عبارة عن R dθ dr و
+
+85
+00:07:05,750 --> 00:07:11,440
+اتجاهه 5 هتDifferential Volume ببساطة بحصل ضرب
+
+86
+00:07:11,440 --> 00:07:16,440
+التلك اطول اذا رجعنا للقطع بتاعتنا ال volume مش
+
+87
+00:07:16,440 --> 00:07:20,280
+هيكون حصل ضرب طول في العرض في الارتفاع يعني هيكون
+
+88
+00:07:20,280 --> 00:07:30,940
+DR في RDθ في RsinθDπ اذا
+
+89
+00:07:30,940 --> 00:07:36,240
+هيكون R تربية SinθDRDθDπ وزي ما قلنا ال volume هو
+
+90
+00:07:36,240 --> 00:07:41,920
+quantity هو scalarبناخد أمثلة على الأشياء اللي
+
+91
+00:07:41,920 --> 00:07:45,040
+احنا شفناها على المحاضرات الماضية بنحط على جانب ال
+
+92
+00:07:45,040 --> 00:07:50,460
+elements كلهم بتاعة ال Cartesian و الcyclic و
+
+93
+00:07:50,460 --> 00:07:54,080
+الcyclical و الcyclical و الcyclical و الcyclical
+
+94
+00:07:54,080 --> 00:07:54,640
+و الcyclical و الcyclical و الcyclical و
+
+95
+00:07:54,640 --> 00:07:58,140
+الcyclical و الcyclical و الcyclical و الcyclical
+
+96
+00:07:58,140 --> 00:08:02,160
+و الcyclical و الcyclical و الcyclical و
+
+97
+00:08:02,160 --> 00:08:08,080
+الcyclical و الcyclical و الcyclical و الcyclical
+
+98
+00:08:08,080 --> 00:08:09,630
+و الcyclical و الcyclical و الcyclical و الcyx hat
+
+99
+00:08:09,630 --> 00:08:15,790
+زي ال dy y hat زي ال dz زدها هذا ال mean
+
+100
+00:08:15,790 --> 00:08:19,610
+differential links ال area ال area أثرش في ال
+
+101
+00:08:19,610 --> 00:08:23,290
+Cartesian لإن انا هتكون dx مثلا و dy بتجاه زدها
+
+102
+00:08:23,290 --> 00:08:31,470
+يعني دي ايه؟ هتكون احد يا dx dy بتجاه زدها او dx
+
+103
+00:08:31,470 --> 00:08:44,510
+dz بتجاه y hatDX DY DX DX DX DX DX DX DX DX DX DX
+
+104
+00:08:44,510 --> 00:08:45,530
+DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX
+
+105
+00:08:45,530 --> 00:08:55,110
+DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX
+
+106
+00:08:55,110 --> 00:08:55,410
+DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX
+
+107
+00:08:55,410 --> 00:08:55,570
+DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX
+
+108
+00:08:55,570 --> 00:08:58,530
+DX DX DX DX DX DX DX
+
+109
+00:09:03,590 --> 00:09:09,090
+دلها الـ cylindrical الـ
+
+110
+00:09:09,090 --> 00:09:11,270
+cylindrical coordinate أخدناها برضه قبل الليل دي
+
+111
+00:09:11,270 --> 00:09:16,330
+اللي
+
+112
+00:09:16,330 --> 00:09:24,390
+هو ال DL دلها ال DL vector هتكون دي رو رو hat زي
+
+113
+00:09:24,390 --> 00:09:31,380
+ال رو في الفيزا ال DZ Z hat المشترك بين كارتيزيا و
+
+114
+00:09:31,380 --> 00:09:35,840
+الصفري كان هو Z coordinate بيضلوا ال Z هو نفس ال Z
+
+115
+00:09:35,840 --> 00:09:44,940
+هنا في عندنا ان هو ال area و ال area قبلنا DA رو
+
+116
+00:09:44,940 --> 00:09:53,220
+D Pi DZ تجاه رو hat كمان D رو DZ تجاه رو Pi hat
+
+117
+00:10:22,970 --> 00:10:24,370
+D5D0D5D0D6D6D6D6D6D6D6D6D6D6D6D6D6D6D6D6D6D6D6D6D6D6D6D6D6D6D6D6D6
+
+118
+00:10:34,740 --> 00:10:44,520
+و اخر واحدة دي ار سان سيتا دي فيهات
+
+119
+00:10:53,080 --> 00:10:56,780
+دى هى بـ three elements يجى بعدين لنا اللى هو ال
+
+120
+00:10:56,780 --> 00:11:00,720
+area والـ area اللى قلناه حصل طرد طولين ولم ننسى
+
+121
+00:11:00,720 --> 00:11:11,720
+الاتجاه NPS يعني هتساوي R تربيع sin θ dθ dφ اتجاه
+
+122
+00:11:11,720 --> 00:11:21,760
+Rها او هتكون R sin θ dr dφ اتجاه روح θها او هتكون
+
+123
+00:11:40,080 --> 00:11:45,900
+نبدأ في الأسئلة كما تشاهدون فهذا المثال ليس واضح
+
+124
+00:11:45,900 --> 00:11:47,060
+الشكل اللي أمامنا
+
+125
+00:11:52,130 --> 00:11:57,150
+السلندر يتعامل مع الـ cylindrical coordinate في
+
+126
+00:11:57,150 --> 00:11:59,190
+حالة السلندر لازم يتعامل مع الـ cylindrical
+
+127
+00:11:59,190 --> 00:12:00,010
+coordinate
+
+128
+00:12:09,880 --> 00:12:13,720
+consider ال object اللى قدامنا و بده نحسب ال
+
+129
+00:12:13,720 --> 00:12:16,020
+distance احنا عشان نحسب ال distance احنا اخدنا ال
+
+130
+00:12:16,020 --> 00:12:20,600
+links ال differential links يعني اخدنا DL فى كل
+
+131
+00:12:20,600 --> 00:12:23,680
+اتجار عشان اطول ال distance ايش بدي اعمل؟ بدي اعمل
+
+132
+00:12:23,680 --> 00:12:27,260
+integration انا مثلا اخد جزء يعني مثلا يجى و يطلب
+
+133
+00:12:27,260 --> 00:12:30,780
+منا اللى هو ال distance ما بين ال B و ال C ال
+
+134
+00:12:30,780 --> 00:12:33,960
+distance ما بين ال B و ال C عشان اجيب ال distance
+
+135
+00:12:33,960 --> 00:12:37,380
+انا عارفة ال DL عارفة ال DL فى هذا الاتجار احنا
+
+136
+00:12:37,380 --> 00:12:41,490
+بكتبها مع بعض عشان هو ال DLعشان أحصل على الطول كله
+
+137
+00:12:41,490 --> 00:12:46,050
+مش بس هو بدي أكامل، معايا؟ بس أول ما أعمل أي حاجة
+
+138
+00:12:46,050 --> 00:12:49,650
+أول خطوة بدي أعملها أن النقاط اللي هتكتبلنا يوم هي
+
+139
+00:12:49,650 --> 00:12:54,210
+نقاط معلها بال Cartesian Coordinates يعني عند ال A
+
+140
+00:12:54,210 --> 00:13:00,270
+كتبها تبدلت ال X Y Z 5 0 0 و ال B ابدلت ال X Y Z X
+
+141
+00:13:00,270 --> 00:13:06,170
+0 Y 5 Z 0 و ال C برضه عبارة عن 0 5 10 و ال D نفس
+
+142
+00:13:06,170 --> 00:13:11,360
+الحاجةأول خطوة بنعملها ان نحول من ال Cartesian لل
+
+143
+00:13:11,360 --> 00:13:13,980
+cylindrical coordinate، مين بيبقى تعملها المهمة؟
+
+144
+00:13:13,980 --> 00:13:18,260
+بس مش حابسين نتعامل مع بعض، سهل، نتعامل مع بعض،
+
+145
+00:13:18,260 --> 00:13:24,560
+تلقوا هم
+
+146
+00:13:24,560 --> 00:13:29,540
+إسراء، هدين،
+
+147
+00:13:29,540 --> 00:13:34,160
+اذا احنا اللي بدنا نعمله؟ان نحسب ال distance عشان
+
+148
+00:13:34,160 --> 00:13:36,800
+نحسبها ممتاز احنا اول حاجة اش نعرف ايش ال
+
+149
+00:13:36,800 --> 00:13:38,700
+coordinate تبع ال cylindrical coordinate ايش فيه
+
+150
+00:13:38,700 --> 00:13:45,700
+عندنا رو و فاي و زد ال
+
+151
+00:13:45,700 --> 00:13:51,000
+رو احنا بتذكر ايه اش هم ده ده اش هم ده تلتها نتذكر
+
+152
+00:13:51,000 --> 00:13:54,600
+مع بعض عشان ما نخبطش و نحفظ يعني خلينا نفهم اكتر و
+
+153
+00:13:54,600 --> 00:13:57,920
+نحفظ احنا عندنا ال cylinder فيه عندنا هو القاعدة
+
+154
+00:13:57,920 --> 00:14:02,130
+بتاعتها اللي هي الدائرة اللي تحتهاوالدائرة بتحتوي
+
+155
+00:14:02,130 --> 00:14:07,290
+على اتنين من الكواردنات اللي هي ال raw و الفارق
+
+156
+00:14:07,290 --> 00:14:11,390
+ايش هي ال raw قلناها ال raw هو اكبر عن ايه مكمونة
+
+157
+00:14:11,390 --> 00:14:15,170
+تجاه ال X و تجاه ال Z فهيكون جزر الترابير بس مافيه
+
+158
+00:14:15,170 --> 00:14:21,170
+شيء في ال Z بل بس واحد في ال X و في ال Y X Y Z فال
+
+159
+00:14:21,170 --> 00:14:23,450
+cylinder بتاعتى او ال raw اللي هو ال radius تبع
+
+160
+00:14:23,450 --> 00:14:26,070
+الدائرة عشان يكون منتخبط ال radius تبع الدائرة
+
+161
+00:14:26,070 --> 00:14:29,190
+وشوفناها كمان مع بعض ان ال raw انها كمبونة تجاه ال
+
+162
+00:14:29,190 --> 00:14:32,870
+X واحد تجاه ال Zهيكون هذا الطولة تغير عن X تربيه
+
+163
+00:14:32,870 --> 00:14:36,450
+زائد Y تربيه تحت الجزر زي ما أخدنا ال distances
+
+164
+00:14:36,450 --> 00:14:39,750
+هيكون ال component تجاه X هيكون ال component تجاه
+
+165
+00:14:39,750 --> 00:14:42,950
+X تربيه تغير و Y تربيه تحت الجزر تربيه هذين
+
+166
+00:14:42,950 --> 00:14:49,130
+يتقرروا هذين يتقرروا هذين يتقرروا هذين يتقرروا
+
+167
+00:14:49,130 --> 00:14:54,750
+هذين يتقرروا هذين يتقرروا هذين يتقرروا هذين
+
+168
+00:14:54,750 --> 00:14:54,870
+يتقرروا هذين يتقرروا هذين يتقرروا هذين يتقرروا
+
+169
+00:14:54,870 --> 00:14:56,900
+يتقرروا هذين يتقرروا هذين ياللي هو ال Y والمجاور
+
+170
+00:14:56,900 --> 00:15:07,580
+لها له X فهي تكون فقشة عن inverse ال Y على X فهي
+
+171
+00:15:07,580 --> 00:15:14,740
+نفس ال Z الحقيقية فخلّينا نحوّل النقاط و ندّل نقطة
+
+172
+00:15:14,740 --> 00:15:20,960
+C خلّي البساوة .. ليش عم تتفت على البساوة؟ هو الصح
+
+173
+00:15:20,960 --> 00:15:21,680
+أنك تتفت عليها
+
+174
+00:15:24,700 --> 00:15:33,040
+خمسة عشرين جزر خمسة عشرين خمسة درس خمس درس خمس درس
+
+175
+00:15:33,040 --> 00:15:36,460
+خمس درس خمس درس خمس درس خمس درس خمس درس خمس درس
+
+176
+00:15:36,460 --> 00:15:38,240
+خمس درس خمس درس خمس درس خمس درس خمس درس خمس درس
+
+177
+00:15:38,240 --> 00:15:39,200
+خمس درس خمس درس خمس درس خمس درس خمس درس خمس درس
+
+178
+00:15:39,200 --> 00:15:49,080
+خمس درس خمس درس خمس درس خمس درس خمس درس خمس
+
+179
+00:15:49,080 --> 00:15:57,480
+درس خمس درس خمالنقطة الاخرى هي نقطة
+
+180
+00:15:57,480 --> 00:16:01,700
+نفسنا احنا نقطة
+
+181
+00:16:01,700 --> 00:16:05,460
+نفسنا هنا وقع ايش ممكنها الـ5 تكون؟ الـ5 تأتي من
+
+182
+00:16:05,460 --> 00:16:08,760
+الـ0 و بتلف لك و باقى ده النقطة ايش كانت في النقطة
+
+183
+00:16:08,760 --> 00:16:17,600
+باقى؟ باق أفين نزل النقطة بـ0
+
+184
+00:16:17,600 --> 00:16:19,600
+5 0
+
+185
+00:16:30,190 --> 00:16:49,730
+خمسة تمام نروح
+
+186
+00:16:49,730 --> 00:16:52,030
+خمسة نرفع التانية inverse
+
+187
+00:17:00,280 --> 00:17:08,100
+بعدين بيخوذ الدايمة X عشان هذا القرن P كل نقطة مضت
+
+188
+00:17:08,100 --> 00:17:09,880
+بجانبها 100 ملتقى شوية
+
+189
+00:17:24,120 --> 00:17:27,140
+طبعا يعني احنا شايفين اللي هو cylinder ما بين الـ0
+
+190
+00:17:27,140 --> 00:17:31,560
+و الـPi على 2 فأكيد اي نقطة واقعة في هذا البلان
+
+191
+00:17:31,560 --> 00:17:35,700
+اللي هو Y بال X axis هتكون 5 اتساوة 0 و أي بلان
+
+192
+00:17:35,700 --> 00:17:40,200
+على ال Y axis هتكون 5 اتساوة وPi على 2
+
+193
+00:17:59,930 --> 00:18:03,850
+ظلنا مين؟ مصر
+
+194
+00:18:13,220 --> 00:18:15,980
+ممتازا اول خطوة قلنا احنا من انه احنا cylindrical
+
+195
+00:18:15,980 --> 00:18:19,020
+فاسهلنا نروح من ال kartesian ل ال cylindrical
+
+196
+00:18:19,020 --> 00:18:22,660
+coordinate فحولنا نقطة كل نقطة من اللي هو ال
+
+197
+00:18:22,660 --> 00:18:25,860
+kartesian ل ال cylindrical نبدأ بأول ال distance
+
+198
+00:18:25,860 --> 00:18:30,120
+بسيطة يعني ساعدت فيها هي بده طول من B ل C ايش هنا
+
+199
+00:18:30,120 --> 00:18:37,380
+DL دي ال دي ال دي ال دي ال دي ال دي ال دي ال دي ال
+
+200
+00:18:37,380 --> 00:18:42,800
+دي ال
+
+201
+00:18:42,800 --> 00:18:42,920
+دي ال دي ال دي ال دي ال دي ال دي ال دي ال دي ال دي
+
+202
+00:18:42,920 --> 00:18:46,340
+ال دي ال دي ال دي ال دي ال دي ال دي ال دزائد دي رو
+
+203
+00:18:46,340 --> 00:18:52,120
+رو هابز زائد
+
+204
+00:18:52,120 --> 00:19:00,180
+رو دي فاي فاي هاب زائد هي دي زد زد هابز حالينا
+
+205
+00:19:00,180 --> 00:19:03,320
+نطلع على ال element تبعنا احنا هو يعني على هذا ال
+
+206
+00:19:03,320 --> 00:19:08,850
+axis او على هذا القولإذا طلعت قلت إنه إيش فيه بي
+
+207
+00:19:08,850 --> 00:19:11,690
+والسي بالcylindrical حتى لو طلعنا على ال Cartesian
+
+208
+00:19:11,690 --> 00:19:14,250
+هلنا نطلع على ال cylindrical ال cylindrical هي
+
+209
+00:19:14,250 --> 00:19:20,970
+نقطة بي وهي نقطة سي هل اتغيرت ال raw؟ ال raw خمسة
+
+210
+00:19:20,970 --> 00:19:27,490
+ماتغيرتش يعني دي raw إيش بيساوي؟ Zero كمان
+
+211
+00:19:27,490 --> 00:19:33,290
+ال five هل اتغيرت ال five؟ إذا دي five مالها؟ Zero
+
+212
+00:19:34,010 --> 00:19:39,750
+من يظل عندنا zz بالفعل تغيرات من 0 ل10 فإذا دي ال
+
+213
+00:19:39,750 --> 00:19:43,830
+element اللي هنا دي ال vector بيحطه هنا عليه
+
+214
+00:19:43,830 --> 00:19:51,410
+vector عشان نميزه احنا بساوي ال element
+
+215
+00:19:51,410 --> 00:19:55,170
+اللي على هذا ال links اللي هو بالدنيا لو أخدت أنا
+
+216
+00:19:55,170 --> 00:20:04,100
+element الحاجة اللي بتتغير هنا فقطDL == DZZH هيطير
+
+217
+00:20:04,100 --> 00:20:08,440
+في هذا الطول او هو بده ال distance بدوش ال DL فازا
+
+218
+00:20:08,440 --> 00:20:13,520
+بده اكمل اقول L ايش فهتساوي L التكامل من اللي هو
+
+219
+00:20:13,520 --> 00:20:17,560
+الدرجة التي تتغيرها من Zero لعشرة اذا انت عاملة
+
+220
+00:20:17,560 --> 00:20:24,400
+Zero لعشرة DZZH هتساوي
+
+221
+00:20:24,400 --> 00:20:32,660
+Zمن صفر لعشرة زرد هات اذا الحكومة الجواب عبارة عن
+
+222
+00:20:32,660 --> 00:20:38,160
+عشرة زرد هات اذا ال distance اللي ليه ال pc هي
+
+223
+00:20:38,160 --> 00:20:45,580
+عبارة عن عشرة زرد هات طبعا فضل ان شاء الله فالحد
+
+224
+00:20:45,580 --> 00:20:50,660
+يعمل ال distance CD انا بتفكر هنا يلا
+
+225
+00:20:54,540 --> 00:20:58,840
+كله هيطلع على فرصة فانا فيها بده إشي لع الصبورة
+
+226
+00:20:58,840 --> 00:21:05,720
+فيها بده حاجة من الصبورة فبقى أسم سحبنيها فلاقيتها
+
+227
+00:21:05,720 --> 00:21:10,180
+مين هو بده substance اللي هى CD ايه ال CD ايه ال
+
+228
+00:21:10,180 --> 00:21:15,280
+CD فهذا اللي بيبنيها ايه
+
+229
+00:21:15,280 --> 00:21:20,060
+اللي هى ال CD فهي
+
+230
+00:21:20,060 --> 00:21:33,170
+ال C هي 55 على 8 أعشر والـ D يعني 5 0 0 10 تمام
+
+231
+00:21:33,170 --> 00:21:41,470
+هتكتب ال D L D L D L تولدها تساوي نفس اللي كتبتها
+
+232
+00:21:41,470 --> 00:21:47,630
+زميلتنا تولد D Rho Rho Hat زائد Rho D Phi Phi Hat
+
+233
+00:21:47,630 --> 00:21:53,270
+زائد D زيت زيت Hatطبعا انا بكتبلكم ياها بشكل عام
+
+234
+00:21:53,270 --> 00:21:56,250
+انا بدي شوي شوي تعرفوا و تأكدوا مين اللي بتغير بس
+
+235
+00:21:56,250 --> 00:22:00,390
+احنا نطب شكل عام مع بعض نشوف انه انا عندنا اذا
+
+236
+00:22:00,390 --> 00:22:04,490
+طلعته هذا ال plan هذا ال plan اللي هو موازن لل XY
+
+237
+00:22:04,490 --> 00:22:10,470
+plan قاعد عن Z ايش بتساوي؟ Z بتساوي عشرة، Z ثابتة،
+
+238
+00:22:10,470 --> 00:22:14,050
+عشرة عشرة هذا ال plan تخيلنا الستوانة بتاعتنا
+
+239
+00:22:14,050 --> 00:22:18,750
+الستوانة بتاعتنا هذه ثابتة عن Z ده عشرة، اذا زد
+
+240
+00:22:18,750 --> 00:22:22,810
+ماتغيرتش، اذا ليه زد ايش بتساوي؟ Zeroايش كمان هنا
+
+241
+00:22:22,810 --> 00:22:27,710
+على هذا القوس رو ثابتة رو ثابتة ضمس خمسة لو انا
+
+242
+00:22:27,710 --> 00:22:31,630
+غيرت من قوس لقوس تاني بتتغير رو لكن احنا ضالين على
+
+243
+00:22:31,630 --> 00:22:36,590
+نفس القوس فعندي رو ثابتة اذا دي رو ثابتة اذا ده
+
+244
+00:22:36,590 --> 00:22:40,850
+عندي القوس من قبل لو انا اخدت اي element هذا ال
+
+245
+00:22:40,850 --> 00:22:45,250
+element ايش هيكون هذا عبارة عني هذه دي فاي وهذه
+
+246
+00:22:45,250 --> 00:22:49,550
+اللي هي رو هيكون رو دي فاي اذا اللي ضال عندي رو دي
+
+247
+00:22:49,550 --> 00:22:55,810
+فاي فاي هاتفانا اللي ضابط اتغير لأن الزاوية اتغيرت
+
+248
+00:22:55,810 --> 00:23:03,750
+من الـ 0 لـ pi على 2 هو بده من C ل D يعني ان
+
+249
+00:23:03,750 --> 00:23:07,810
+الزاوية اتغيرت من pi على 2 ل 0 او اذا طلعنا للناس
+
+250
+00:23:07,810 --> 00:23:11,650
+لان انا اتكلمكم تمام اذا L هو افكار مطلوب ال
+
+251
+00:23:11,650 --> 00:23:14,090
+distance يعني انا بخليكم تكتبوا ال vector L بس هو
+
+252
+00:23:14,090 --> 00:23:16,910
+بده ال distance فهي بس المقدار L يعني روزن فيه
+
+253
+00:23:16,910 --> 00:23:20,790
+عشان تكون دقيقين مع السؤال هو بده ال L دي L اللي
+
+254
+00:23:20,790 --> 00:23:26,270
+هي ك scalarDL بتساوي رو دي فاي بس هى هو اللى بدنا
+
+255
+00:23:26,270 --> 00:23:31,750
+قل التكامل رو
+
+256
+00:23:31,750 --> 00:23:35,690
+دي فاي مش ال displacement و بده ال distance ال
+
+257
+00:23:35,690 --> 00:23:39,170
+distance قولنا scalar رو دي فاي فعندنا قل اشبه
+
+258
+00:23:39,170 --> 00:23:46,770
+تساوي قل التكامل قبل اللى قل و كتب هنا مش DL إذا
+
+259
+00:23:46,770 --> 00:23:51,470
+كتبتي DL بتكميشي قل التكاملDL هو ال element زى ما
+
+260
+00:23:51,470 --> 00:23:56,010
+انت شايفها ده ال element هذا ال DL L هو كل الطول
+
+261
+00:23:56,010 --> 00:24:03,890
+فكل الطول مش معروف تكامل ف Y اللى هي من باية على
+
+262
+00:24:03,890 --> 00:24:06,410
+اتنين من ها distance فخلاص تفعلها من ها distance
+
+263
+00:24:06,410 --> 00:24:16,010
+من باية على اتنين ل Zero تمام فانت كامل روح دبل
+
+264
+00:24:16,010 --> 00:24:20,290
+سابقة تطلع على براه و بقيمتها قداش روحفهذا ال
+
+265
+00:24:20,290 --> 00:24:25,410
+links خمسة خمسة خمسة خمسة خمسة خمسة خمسة خمسة خمسة
+
+266
+00:24:25,410 --> 00:24:26,290
+خمسة خمسة خمسة خمسة خمسة خمسة خمسة خمسة خمسة خمسة
+
+267
+00:24:26,290 --> 00:24:35,290
+خمسة خمسة خمسة خمسة خمسة خمسة خمسة خمسة خمسة خمسة
+
+268
+00:24:35,290 --> 00:24:36,810
+خمسة خمسة خمسة خمسة خمسة خمسة خمسة خمسة خمسة خمسة
+
+269
+00:24:36,810 --> 00:24:40,210
+خمسة خمسة خمسة خمسة خمسة خمسة خمسة خمسة خمسة
+
+270
+00:24:40,210 --> 00:24:43,670
+خمسة
+
+271
+00:24:43,670 --> 00:24:52,470
+خمسة خمسة خمسة خمسة خمسة خمسيلا لبعده بكنا surface
+
+272
+00:24:52,470 --> 00:25:00,330
+بعدها ال surface area A,B,C,D مين بقى يا عملنا
+
+273
+00:25:00,330 --> 00:25:09,570
+إياها؟ يلا احنا .. احنا عايزين نحوها بقى
+
+274
+00:25:09,570 --> 00:25:17,770
+احنا احنا كتبنا ال surface
+
+275
+00:25:17,770 --> 00:25:24,540
+area اللي هي AD C
+
+276
+00:25:24,540 --> 00:25:27,600
+A
+
+277
+00:25:27,600 --> 00:25:32,780
+D على
+
+278
+00:25:32,780 --> 00:25:36,640
+وجه هذا السليندر يعني لو احنا طلعنا هاي بس هي مش
+
+279
+00:25:36,640 --> 00:25:42,780
+سليندر كاملة هذا هو ال area اللي انا بدي اسمه
+
+280
+00:25:42,780 --> 00:25:44,560
+قانون ال area
+
+281
+00:25:50,520 --> 00:25:54,480
+بنشوف مين اللي بتغير و مين السابت عشان انا دي ال
+
+282
+00:25:54,480 --> 00:25:59,200
+هو انا اخد قطع على هذا قطع عجزه قطع صغيرة اش اللي
+
+283
+00:25:59,200 --> 00:26:03,900
+هيكون اللي متغير فيها اندي فاي بتتغير من zero ل
+
+284
+00:26:03,900 --> 00:26:08,540
+five على اتنين والزت اللي بتتغير من zero لعشرة مين
+
+285
+00:26:08,540 --> 00:26:12,320
+اللي سابت على هذا ال surface رو رو ست على خمسة اذا
+
+286
+00:26:12,320 --> 00:26:17,790
+محاخد مين انا اللي هي رو دي five دي زت رابعىرو دي
+
+287
+00:26:17,790 --> 00:26:28,810
+فاي دي زد ال
+
+288
+00:26:28,810 --> 00:26:33,930
+area اللى اختارناها رو دي فاي دي زد لإن انا لو
+
+289
+00:26:33,930 --> 00:26:37,570
+أخدت اي قطعة على هذا ال surface هيكون في عند
+
+290
+00:26:37,570 --> 00:26:42,410
+التغير في اتجاه اللى هو ال 5 هو رو دي فاي و هو
+
+291
+00:26:42,410 --> 00:26:44,730
+اتجاه الزد اللى هو دي زد
+
+292
+00:26:55,670 --> 00:27:01,110
+طبعا إذا إحنا بنا نكامل ال five بتروح من zero ل
+
+293
+00:27:01,110 --> 00:27:07,610
+five على اتنين و ال z بتروح من zero ل عشر رقصها
+
+294
+00:27:07,610 --> 00:27:17,370
+بتاعنا قداشه حمسة دي five بس احنا دي five دي zطب
+
+295
+00:27:17,370 --> 00:27:22,490
+اذا ال area ايش اللي هتكون ال area التكامل اذا ال
+
+296
+00:27:22,490 --> 00:27:25,370
+total area هي ال differential area ال differential
+
+297
+00:27:25,370 --> 00:27:29,150
+area هو جزء على ال surface عشان اجيب كل ال surface
+
+298
+00:27:29,150 --> 00:27:32,690
+بتقعة كاملة فعندي هيكون في التكاملها من zero
+
+299
+00:27:32,690 --> 00:27:37,930
+double ال integral فعندي في تكامل على في و في
+
+300
+00:27:37,930 --> 00:27:44,490
+تكامل على z هنحط انه في بتروح في بتروح من zero لبي
+
+301
+00:27:44,490 --> 00:27:51,970
+على اتنينوعندي ال Z بتروح من 0 ل 10 ان كان تطلع
+
+302
+00:27:51,970 --> 00:27:59,410
+الحمص لبرا ال Phi هكملها من E Phi ل E Z تكامل ل
+
+303
+00:27:59,410 --> 00:28:04,230
+Diesel خلّي بس تقبل Integral يعني حتى لو ال Diesel
+
+304
+00:28:04,230 --> 00:28:09,970
+بينه بس انت ماكملتيش إيش لسه يعني عيد نفس ال ..
+
+305
+00:28:19,830 --> 00:28:25,390
+هيكون عندى تكامل ال Z هيطلع Z تكمل من 0 ل 10 قيمة
+
+306
+00:28:25,390 --> 00:28:29,430
+عشرة وال D Phi هتكون Phi تكملها من 0 ل Pi على 2
+
+307
+00:28:29,430 --> 00:28:32,650
+هيكون من Pi على 2 لذا هى الجواب هيكون خمسة في Pi
+
+308
+00:28:32,650 --> 00:28:40,390
+على 2 في اللى هو عشرة اتجاه الورق الهاتف هيكون
+
+309
+00:28:40,390 --> 00:28:45,110
+عندى خمسة في خمسة خمسة عشرين Pi فهى Pi تلاتة
+
+310
+00:28:45,110 --> 00:28:48,650
+واربعة عشرينية ممتاز ممتاز جدا
+
+311
+00:28:57,230 --> 00:29:08,350
+في حد كمان هيبقى واضح
+
+312
+00:29:08,350 --> 00:29:11,770
+ما اللي بنعمله؟ انا اتعمدت ان اكتر ما بدا وكنت بس
+
+313
+00:29:11,770 --> 00:29:14,770
+شوية المفروض مع التمرين انكوا تصيروا فاهمين انه ده
+
+314
+00:29:14,770 --> 00:29:16,830
+هي التغيرات و ده دلقوس
+
+315
+00:29:20,630 --> 00:29:25,290
+اللي هي قاعدة
+
+316
+00:29:25,290 --> 00:29:28,950
+قاعدة السلندر اللي قدامنا أو هو جزء من السلندر
+
+317
+00:29:28,950 --> 00:29:32,270
+الشكل اللي قدامنا القاعدة بتاعة ايش اللي بتغير
+
+318
+00:29:32,270 --> 00:29:37,250
+فيها هل دي z بتتغير زت ثابت على مين على zero زت
+
+319
+00:29:37,250 --> 00:29:40,870
+ثابت على مين اللي بتتغيرها ال raw بتتغير لو انا
+
+320
+00:29:40,870 --> 00:29:46,650
+أخدت element عليها ال raw هيتغير من zero ل 5ومن
+
+321
+00:29:46,650 --> 00:29:53,530
+هنا فاية بتتغير اللى هناخده اسم مين اللى هو رو دى
+
+322
+00:29:53,530 --> 00:30:00,550
+فاية دى رو واتجاهه اللى هو سنة هالكامل
+
+323
+00:30:00,550 --> 00:30:06,070
+اذا ال a إيش هتساوي اللى بتطلع تغيره هالكامل
+
+324
+00:30:06,070 --> 00:30:11,670
+فالفاية بتتغير مين بتغير ال رو بتتغير ال رو بتتغير
+
+325
+00:30:11,670 --> 00:30:16,130
+ليش تطلع عند ال رو دى رو عند الفايةبتغير من zero ل
+
+326
+00:30:16,130 --> 00:30:18,850
+five على اتنين اذا اولا خلينا نعمل انتقال انتقال
+
+327
+00:30:18,850 --> 00:30:22,550
+انتقال
+
+328
+00:30:22,550 --> 00:30:23,770
+انتقال انتقال انتقال انتقال انتقال انتقال انتقال
+
+329
+00:30:23,770 --> 00:30:23,870
+انتقال انتقال انتقال انتقال انتقال انتقال انتقال
+
+330
+00:30:23,870 --> 00:30:24,690
+انتقال انتقال انتقال انتقال انتقال انتقال انتقال
+
+331
+00:30:24,690 --> 00:30:24,730
+انتقال انتقال انتقال انتقال انتقال انتقال انتقال
+
+332
+00:30:24,730 --> 00:30:34,230
+انتقال انتقال انتقال انتقال انتقال
+
+333
+00:30:43,510 --> 00:30:47,190
+عندى الـ Phi هكملها من 0 ل π على 2 حتى تعطينا قداش
+
+334
+00:30:47,190 --> 00:30:51,750
+بي على 2 و ال row دى رقش هتعطينا row تربيه على 2
+
+335
+00:30:51,750 --> 00:31:00,170
+روه دى روه هتعطينا روه تربيه على 2 روه
+
+336
+00:31:00,170 --> 00:31:07,390
+تربيه على 2 زدها اذا هتصير 25 على 4 في بي
+
+337
+00:31:16,760 --> 00:31:22,100
+ممتاز اخر حاجة مين بحب يعملها اللي هو ال volume ال
+
+338
+00:31:22,100 --> 00:31:27,780
+volume
+
+339
+00:31:27,780 --> 00:31:30,540
+حصل ضرب التلات ال franchises اللي هو ايش اللي
+
+340
+00:31:30,540 --> 00:31:37,580
+هيكون هي دي ان رو دي رو دي فاي دي زد دي رو دي فاي
+
+341
+00:31:37,580 --> 00:31:41,600
+دي زد ان ال رو بتتغير من و لا وين من زي رو لخمسة
+
+342
+00:31:41,950 --> 00:31:45,890
+والـ 5 من 0 ل 5 على 2، لأ ال volume ولا يمكن، هو
+
+343
+00:31:45,890 --> 00:31:50,590
+مش vector of volume، ال volume مولا scalar I don't
+
+344
+00:31:50,590 --> 00:31:55,050
+know if that makes more sense فعم،
+
+345
+00:31:55,050 --> 00:31:58,090
+اذا V أشف هالساعة و أنت كان في ال triple integral،
+
+346
+00:31:58,090 --> 00:32:01,970
+V أقلت بV، أقلت بV، في ال triple integral ال rho
+
+347
+00:32:01,970 --> 00:32:07,250
+من 0 ل 5 و ال 5 من 0 ل 5 على 2 و ال z من 0 ل 10
+
+348
+00:32:22,550 --> 00:32:29,990
+الزد نطلعها عشرة والفا يبقى على اثنين والزد عشرة
+
+349
+00:32:29,990 --> 00:32:35,430
+ونضغ علينا الهيروتن بي على اتنين
+
+350
+00:32:54,670 --> 00:32:57,930
+طبعا واضح اش اللى احنا استخدنا منه من انه عرفنا ال
+
+351
+00:32:57,930 --> 00:33:00,450
+differential links ال differential area و ال
+
+352
+00:33:00,450 --> 00:33:03,830
+differential volume اني بقدر اطول اى links اى
+
+353
+00:33:03,830 --> 00:33:07,530
+distance فيه ال space و اقدر اطول اى area و اقدر
+
+354
+00:33:07,530 --> 00:33:08,650
+اطول اى volume
+
+355
+00:33:21,420 --> 00:33:29,300
+هي المثال التاني المثال
+
+356
+00:33:33,000 --> 00:33:37,360
+المثال هنا جزء من سفير احنا المثال السابق كان جزء
+
+357
+00:33:37,360 --> 00:33:41,900
+من سلمدة قلت هانشوف هذا جزء من سفير هذا الجزء من
+
+358
+00:33:41,900 --> 00:33:45,420
+السفير بقول لي التالي عنه بقول يا دي النتفة اللي
+
+359
+00:33:45,420 --> 00:33:48,160
+شغلينها يعني هاي لو تخيلنا احنا عندنا بطيخة و واحد
+
+360
+00:33:48,160 --> 00:33:51,040
+قطعها كتعرفوا كيف يبيعوا البطيخ قطعها هيك النتفة
+
+361
+00:33:51,040 --> 00:33:54,680
+صغيرة و بطولها عشان يفرج البيئة الشخصة دي حمره ولا
+
+362
+00:33:54,680 --> 00:34:00,460
+دي هو الجزء هذا بس طلعنا عليه هنلاقي انه قيلنا ان
+
+363
+00:34:00,460 --> 00:34:09,290
+Rر تتغير من قيمة تلاتة لخمسة يعني دي ر بتروح من
+
+364
+00:34:09,290 --> 00:34:16,390
+قيمة تلاتة لخمسة ثتا بتبدأ من ستين لتسين يعني هذا
+
+365
+00:34:16,390 --> 00:34:21,610
+المفروض تبقى على ال X Y plane مثلا من ستين لتسين
+
+366
+00:34:21,610 --> 00:34:26,610
+بعدين عندي فاي اللي هو هذا اتجاه الفاي فاي بتتحرك
+
+367
+00:34:26,610 --> 00:34:32,680
+من خمسة واربعين لعند هذه النقطة لستينإذا عنده a من
+
+368
+00:34:32,680 --> 00:34:37,340
+تلاتة لخمسة ثتا من ستين لتسعين و five من خمسة
+
+369
+00:34:37,340 --> 00:34:41,600
+واربعين لستين
+
+370
+00:34:41,600 --> 00:34:48,340
+أول حاجة طالب مننا distance dh distance dh هي حاب
+
+371
+00:34:48,340 --> 00:34:52,620
+تجرب نفس الحاجة نفس اللي عملنا distance dh دي حاجة
+
+372
+00:34:52,620 --> 00:34:53,160
+هتجربه
+
+373
+00:35:02,520 --> 00:35:07,160
+لو طلعنا على ال DH قداش قيمة R عند هذا ال shell
+
+374
+00:35:07,160 --> 00:35:10,620
+هدول اتخيلوهم ال shell اللى بوقع عليها نفس ال
+
+375
+00:35:10,620 --> 00:35:14,660
+shell اللى هو ال differential AEHD و ال shell
+
+376
+00:35:14,660 --> 00:35:18,960
+التانى اللى وراها اللى بوقع عليه ال BFGC Shell ورا
+
+377
+00:35:18,960 --> 00:35:23,740
+shell عند ال shell الصغيرة R بتتغير اهي انا ك
+
+378
+00:35:23,740 --> 00:35:31,420
+shell طب اتغيرت R قداش قيمة R هنااللي قداش؟ R قداش
+
+379
+00:35:31,420 --> 00:35:35,880
+قيمة R؟ تلاتة اللي براها خمسة فاحنا هلاقيتها أصلا
+
+380
+00:35:35,880 --> 00:35:39,160
+بوقعين على ال chill اللي عندها R قداش قيمتها تلاتة
+
+381
+00:35:39,160 --> 00:35:43,300
+اذا احنا هلاقيتها متأكدين ان R سابت هنا مين بتغير
+
+382
+00:35:43,300 --> 00:35:50,040
+هو بده distance DH تلعب ال DH هنا θتة تغيرت؟ لأ
+
+383
+00:35:50,040 --> 00:35:53,540
+احنا قولنا θتة عند ال plan اللي فوق ثتة قيمتها
+
+384
+00:35:53,540 --> 00:35:56,200
+ستين و ال plan التحتاني تسعين احنا في ال plan
+
+385
+00:35:56,200 --> 00:36:02,120
+التحتانيطب إذا هنا R ثابتة و θ ثابتة ثتا ثابتة على
+
+386
+00:36:02,120 --> 00:36:05,660
+تسعين و R ثابتة على تلاتة مين اللي بتغير؟ five
+
+387
+00:36:05,660 --> 00:36:11,000
+بتتغير من خمسة و أربعين لستين طب إيش هنا ال links
+
+388
+00:36:11,000 --> 00:36:13,160
+اللي هنا؟ ميذكرين إيش ال links اللي هنا؟ لو أنا
+
+389
+00:36:13,160 --> 00:36:19,100
+أخدت مادات هذا المسقط تبع ال R ال radius R في sin
+
+390
+00:36:19,100 --> 00:36:23,220
+theta أنا أسقطه ع ال z axis R كو sin theta وع ال x
+
+391
+00:36:23,220 --> 00:36:26,660
+y plane قولنا R sin theta فالقفص إيش بيكون؟
+
+392
+00:36:53,620 --> 00:36:56,760
+RsinθDθRsinθDθRsinθDθRsinθDθRsinθDθRsinθDθصين سيتا
+
+393
+00:36:56,760 --> 00:37:03,480
+دي سيتا فاي هاف خلاص
+
+394
+00:37:03,480 --> 00:37:08,120
+انسى هذا الحكيم مين اللي قولنا بتغير R ثابت طبعا
+
+395
+00:37:08,120 --> 00:37:14,560
+بتقدر تطلع R وصين سيتا قولنا R ثلاثة وثيتا تسعين
+
+396
+00:37:14,560 --> 00:37:18,380
+ففقدر أطلعهم برا ال Integral R أطول عودة عن R
+
+397
+00:37:18,380 --> 00:37:24,710
+ثلاثة مش مشكلة فاي اللي هي منبتروح انه بيطول من 45
+
+398
+00:37:24,710 --> 00:37:33,710
+ل 60 اذا
+
+399
+00:37:33,710 --> 00:37:44,450
+ايش هينكون عندي R تلاتة وعندي
+
+400
+00:37:44,450 --> 00:37:48,870
+اللي هي ال 5 بتتحرك
+
+401
+00:37:48,870 --> 00:37:58,450
+قيمتها من 45لأ الستين مش هيساوي لنا بيكمل وخلاص
+
+402
+00:37:58,450 --> 00:38:03,450
+فعل دي فعل هي فعل و لا لأ هيكون عندى تلاتة افتحها
+
+403
+00:38:03,450 --> 00:38:07,910
+تلاتة و افتحها post فاللي هي الفعل هتتحرك من ستين
+
+404
+00:38:07,910 --> 00:38:10,490
+درجة لخمس و .. من خمس و أربعين درجة لستين درجة
+
+405
+00:38:10,490 --> 00:38:13,870
+الفرق بينهم هو type five بس عشان أنا مابحث عفوظش
+
+406
+00:38:13,870 --> 00:38:17,380
+بتحولها ل radialالأسئلة الأولى اللى حولهم هو ال
+
+407
+00:38:17,380 --> 00:38:20,680
+radian 45 و 60 اول افضل افضل افضل افضل افضل افضل
+
+408
+00:38:20,680 --> 00:38:22,260
+افضل افضل افضل افضل افضل افضل افضل افضل افضل افضل
+
+409
+00:38:22,260 --> 00:38:23,840
+افضل افضل افضل افضل افضل افضل افضل افضل افضل افضل
+
+410
+00:38:23,840 --> 00:38:23,880
+افضل افضل افضل افضل افضل افضل افضل افضل افضل افضل
+
+411
+00:38:23,880 --> 00:38:23,920
+افضل افضل افضل افضل افضل افضل افضل افضل افضل افضل
+
+412
+00:38:23,920 --> 00:38:27,340
+افضل افضل
+
+413
+00:38:27,340 --> 00:38:31,200
+افضل
+
+414
+00:38:31,200 --> 00:38:40,140
+افضل
+
+415
+00:38:40,140 --> 00:38:44,740
+اف
+
+416
+00:38:55,820 --> 00:39:02,700
+ممتاز ممتاز فى حد تانى محب يجرب لسه حلنا الجزء
+
+417
+00:39:02,700 --> 00:39:05,940
+الاول عنه واخدنا اللى هو ال differential links
+
+418
+00:39:05,940 --> 00:39:10,800
+اللى هو ال R Sine theta D Pi Pi hat فانه هو الوحيد
+
+419
+00:39:10,800 --> 00:39:17,520
+اللى بضيع فى حاجة تمام هشوف الجزء التانى FGأنا بس
+
+420
+00:39:17,520 --> 00:39:28,260
+ساعدكم، مين يطلع؟ يالا كده يا سرعة خل
+
+421
+00:39:28,260 --> 00:39:31,240
+حاجة شوية حلوة، طب و الله أنا كانت فكرة أمشي في
+
+422
+00:39:31,240 --> 00:39:35,580
+الموضوع، طب مش غلط، احنا بعد العيد خليني أفجي،
+
+423
+00:39:35,580 --> 00:39:37,820
+أفجي، خليني نرجع على أفجي، هون أفجي، هاي اللي
+
+424
+00:39:37,820 --> 00:39:40,800
+بقالك، هاي اللي بقالك، مين بتغيرتيه؟هذه الـ shell
+
+425
+00:39:40,800 --> 00:39:45,840
+اللي برا R ثابتة فيها ولا متغيرة؟ هنا أنا ماسكة
+
+426
+00:39:45,840 --> 00:39:50,820
+طبّة ثابتة، ثابتة، قداش قيمتها؟ خمسة، خمسة احنا
+
+427
+00:39:50,820 --> 00:39:54,060
+هذه جزء من الـ shell الجوانية، من الطبّة الجوانية،
+
+428
+00:39:54,060 --> 00:39:57,040
+خيالنا أننا نمسك بلّوننا، و ببعد، بمسك البلّون
+
+429
+00:39:57,040 --> 00:40:01,240
+الأكبر، صح؟ اتغيرت قيمة R على البلّون الكبير، اذا
+
+430
+00:40:01,240 --> 00:40:06,780
+هنا R ثابتة، على هذا الجزء من الطبّة التي تعطيه،
+
+431
+00:40:06,780 --> 00:40:10,690
+قيمة R فيها خمسةبعد كمان هلاقيتها في هنا تغيرت على
+
+432
+00:40:10,690 --> 00:40:14,670
+هذا الطول احنا في قولنا عند هذه النقطة كم تقيمتها
+
+433
+00:40:14,670 --> 00:40:19,370
+45 وعند هذه النقطة 60 أسوأ هنا ولا هنا في اداش
+
+434
+00:40:19,370 --> 00:40:23,770
+قيمتها 60 اذا في سابطة و او سابطة مين اللي اتغير
+
+435
+00:40:23,770 --> 00:40:27,750
+ستة ستة ايش قيمة هذا ال links حيث انه اتغير في هذا
+
+436
+00:40:27,750 --> 00:40:32,070
+ال links هيكون اللي هو احد جزئية هيكون قيمة ال
+
+437
+00:40:32,070 --> 00:40:38,330
+radius R D ستة R D ستةاللي هي أي واحد فيهم لو
+
+438
+00:40:38,330 --> 00:40:44,690
+طلعنا نعدي L هيكون R D θ θ hat اذا دي L فهيكون دي
+
+439
+00:40:44,690 --> 00:40:48,130
+R Zero لأن R ثابتة على خمسة و دي Phi Zero لأنها
+
+440
+00:40:48,130 --> 00:40:52,990
+ثابتة على اللي هو الستين على طول اذا بدأ اقول L
+
+441
+00:40:52,990 --> 00:40:56,030
+ايش بيها تساوي ال vector خلاص اختيها vector كام ل
+
+442
+00:40:56,030 --> 00:41:00,490
+L ال vector روحتي عليها ثانية R اللي قيمتها خمسة
+
+443
+00:41:01,440 --> 00:41:09,340
+مضت كامل ل θ من 60 ل
+
+444
+00:41:09,340 --> 00:41:14,560
+90 60 يعني بقى على تلاتة؟ بقى على تلاتة و 90 هي
+
+445
+00:41:14,560 --> 00:41:21,180
+بقى على تلاتة بدء θ ثلاثة تلاتة تلاتة تلاتة تلاتة
+
+446
+00:41:21,180 --> 00:41:24,520
+تلاتة
+
+447
+00:41:41,650 --> 00:41:45,030
+ممتاز نشوف ال surface area و لا احنا خلاص وقتنا
+
+448
+00:41:45,030 --> 00:41:50,210
+يعطيكوا العافية و انتوا دي اكم تكملوا هاي الأمثلة
+
+449
+00:41:50,210 --> 00:41:54,280
+و محطوطوا أرقام الأمثلة زى ما انتوا شايفينهمال
+
+450
+00:41:54,280 --> 00:41:58,240
+practice exercise فانا بدي اياكم تحلوهم و تتأكدوا
+
+451
+00:41:58,240 --> 00:42:01,960
+انكم فاهمين كل هذه النقات عشان اللقاء القادم ان
+
+452
+00:42:01,960 --> 00:42:09,640
+شاء الله هنكمل فيه ال chapter هنقلها اللي هو ال
+
+453
+00:42:09,640 --> 00:42:11,280
+line و ال curve و ال contour
+
+454
+00:42:15,570 --> 00:42:18,730
+اللي هي اللي بسميهم ال line integral و ال curve
+
+455
+00:42:18,730 --> 00:42:22,090
+integral او ال contour integral كلهم بنفس المعنى و
+
+456
+00:42:22,090 --> 00:42:24,970
+هنشوف اللي هو ال surface integral و ال volume
+
+457
+00:42:24,970 --> 00:42:28,330
+integral او اللي يعني بيسموهم ال waffle integral
+
+458
+00:42:28,330 --> 00:42:33,610
+بالكتسار او ال contour integral هاي ال line او ال
+
+459
+00:42:33,610 --> 00:42:37,150
+contour او ال curve integral و هنشوف اللي هو ال
+
+460
+00:42:37,150 --> 00:42:40,530
+surface integral او ال closed contour و بعدين ال
+
+461
+00:42:40,530 --> 00:42:44,470
+surface integral و ال volume integralمع بعض اللقاء
+
+462
+00:42:44,470 --> 00:42:46,990
+القادم ان شاء الله فاندي أكترجوا الأشياء اللي
+
+463
+00:42:46,990 --> 00:42:51,150
+أخدناها مع بعض و اللقاء القادم بترفعوا ع هيكل هم
+
+464
+00:42:51,150 --> 00:42:54,510
+الكاتلة المادة ان شاء الله اللي حكينا عنها يعطيكوا
+
+465
+00:42:54,510 --> 00:42:54,870
+العرش
+
diff --git a/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/R4EBPdgiKoM_raw.srt b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/R4EBPdgiKoM_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..0c081603c20de5294d86a7d643f9c7026ddbb8dc
--- /dev/null
+++ b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/R4EBPdgiKoM_raw.srt
@@ -0,0 +1,1924 @@
+1
+00:00:21,310 --> 00:00:23,630
+بسم الله الرحمن الرحيم السلام عليكم و رحمة الله و
+
+2
+00:00:23,630 --> 00:00:27,810
+بركاته احنا ان شاء الله المحاضرة هي هنتبع ال
+
+3
+00:00:27,810 --> 00:00:30,750
+differential elements اللي بدناها قبل العيد احنا
+
+4
+00:00:30,750 --> 00:00:33,050
+حكيناها ك division و cylindrical coordinate شفنا
+
+5
+00:00:33,050 --> 00:00:37,310
+ال dl و شفنا ال ds و ال dv و وصلنا ان ال dl و ال
+
+6
+00:00:37,310 --> 00:00:41,570
+ds vectors و ال dv مالها scalar ضال علينا اللي هو
+
+7
+00:00:41,570 --> 00:00:44,290
+cylindrical coordinate فال cylindrical coordinate
+
+8
+00:00:44,290 --> 00:00:49,710
+ال element بيكون زي هيكي بهذا الشكل القطع اللي زال
+
+9
+00:00:49,710 --> 00:00:59,040
+أمامناهيكون عندنا three different points هيتجاه
+
+10
+00:00:59,040 --> 00:01:03,380
+الار سفريكال كواردنات انا لما انتقل من shell لو
+
+11
+00:01:03,380 --> 00:01:06,280
+انا اتخيلت كل space تبعي spheres اتخيلنا كل
+
+12
+00:01:06,280 --> 00:01:09,020
+cylinder اتخيلنا كل space كل cylinders اتخيلنا
+
+13
+00:01:09,020 --> 00:01:13,140
+spheres لما انتقل من shell ل shell انا من ار لار
+
+14
+00:01:13,140 --> 00:01:18,710
+تانية الانتقال هذا بعطيني DRكمان ان لما انتقل من
+
+15
+00:01:18,710 --> 00:01:22,650
+theta ل theta هيكون في عندي تغير في theta هيكون في
+
+16
+00:01:22,650 --> 00:01:27,590
+عندي دي theta كمان في ال D phi لما انتقل من
+
+17
+00:01:27,590 --> 00:01:30,830
+الزاوية عندي phi معينة ده phi تانية هيكون في عندي
+
+18
+00:01:30,830 --> 00:01:34,070
+D phi بتولد عن هيك هذا ال element اللي قدامنا
+
+19
+00:01:34,070 --> 00:01:39,890
+التغير في phi والتغير في theta والتغير في R فهيكون
+
+20
+00:01:39,890 --> 00:01:46,730
+عندى في أطول زي هذا الطولمن هنا لهنا هذا الطول هو
+
+21
+00:01:46,730 --> 00:01:50,290
+بساطة انتقال من شلة لشلة يعني هيكون ايش طوله؟ دي R
+
+22
+00:01:50,290 --> 00:01:55,870
+هذا الطول هو مقابل لمين؟ لـDθ هذا لما انتقلت من
+
+23
+00:01:55,870 --> 00:02:00,190
+ثتة معينة لثتة تانية من ثتة واحد لثتة اتنين فصار
+
+24
+00:02:00,190 --> 00:02:04,190
+عندي D ثتا القسم مقابل لأي زاوية ايش بيكون؟ الطول
+
+25
+00:02:04,190 --> 00:02:08,750
+النصف القطر في الزاوية النصف القطر عنا ايش بيمته؟
+
+26
+00:02:08,750 --> 00:02:13,150
+R في D ثتا فإذا هذا ال links ايش هيكون؟ R D ثتا
+
+27
+00:02:13,670 --> 00:02:17,070
+دلين ديمين اللي هو ال links اللي في هذا الاتجاه
+
+28
+00:02:17,070 --> 00:02:22,490
+هذا الاتجاه مش بيساوي هو لو انا طلعت على اسقاطه
+
+29
+00:02:22,490 --> 00:02:27,190
+هيكون هذا اسقاطهطول نصف القطر من قبل لهذا القوس ده
+
+30
+00:02:27,190 --> 00:02:31,050
+قوس لزاوية المقابلة إليه زاوية المقابلة إليه دي
+
+31
+00:02:31,050 --> 00:02:34,630
+فاي أنا كنت عيد فاي معينة وانت قعدت لفاي تانية بس
+
+32
+00:02:34,630 --> 00:02:37,810
+هذا الإسقاط هو عبارة عن مين إذا طلعت نصف القطر R
+
+33
+00:02:37,810 --> 00:02:42,170
+بعمله إسقاطين واحد على اتجاه ال Z واحد على اتجاه
+
+34
+00:02:42,170 --> 00:02:47,880
+ال XYZ الاتجاه ال Z هو R sin θاللي في اتجاه ال X Y
+
+35
+00:02:47,880 --> 00:02:53,340
+Z في ال plan يعني X Y Z هيكون R Sine Theta فهذا
+
+36
+00:02:53,340 --> 00:02:57,180
+هيكون طوله R Sine Theta و هذه هتكون اغارة عن R
+
+37
+00:02:57,180 --> 00:03:01,520
+Sine Theta D Phi R Sine Theta D Phi اذا عندي انا
+
+38
+00:03:01,520 --> 00:03:05,700
+ال three element changes او يعني links of changes
+
+39
+00:03:05,700 --> 00:03:15,200
+بيدي او DR او R D Theta او R Sine Theta D Phiفازن
+
+40
+00:03:15,200 --> 00:03:17,760
+ال differential displacement ال DL اللى هى vector
+
+41
+00:03:17,760 --> 00:03:22,040
+هيكون عندى اتجاه ال R اللى هو زى ما شوفناه قبل هدا
+
+42
+00:03:22,040 --> 00:03:29,740
+هو اتجاه ال R عند D R R hat اتجاه ال R هاي R hat
+
+43
+00:03:29,740 --> 00:03:35,440
+هاي R واحد R ثانى هاي D R واتجاهها اتجاه ال R hat
+
+44
+00:03:35,440 --> 00:03:39,020
+اللى هو اتجاه الكتر فانا هناك عند ال element هذا
+
+45
+00:03:39,020 --> 00:03:43,420
+اللى هو عبارة عن مين R D ستة واتجاهه اتجاه اللى
+
+46
+00:03:43,420 --> 00:03:49,150
+وسطه hatالـ element الأخير هو هذا الـ element هذا
+
+47
+00:03:49,150 --> 00:03:53,530
+الأسقطمار هذا عمارة عن أمر الـ sin θ دي θ في الـ
+
+48
+00:03:53,530 --> 00:04:03,510
+defined تجاهه و تجاه الهوايب فاتي باضي نجي
+
+49
+00:04:03,510 --> 00:04:07,410
+لـ surfaces الـ surfaces طبعا طبعا بتحيطها كل يعني
+
+50
+00:04:07,410 --> 00:04:09,290
+كل واحد من هدولة هعتبره surface
+
+51
+00:04:15,100 --> 00:04:19,220
+هذه الـ surface و كمان ال surface اللي فوق كل واحد
+
+52
+00:04:19,220 --> 00:04:23,400
+من هدول ال surfaces له قيمة و له اتجاه اذا كده
+
+53
+00:04:23,400 --> 00:04:28,280
+قلنا ال links دي ال مع long vector و ال surfaces
+
+54
+00:04:28,280 --> 00:04:32,620
+vector الاتجاه ده بقى عمودي على ال surface و برا
+
+55
+00:04:32,620 --> 00:04:34,640
+ال volume يعني لو انا ال surface تبع المحيط في
+
+56
+00:04:34,640 --> 00:04:38,740
+الطبق هيكون ال norm اللي طالع من الطبق هو اتجاه ال
+
+57
+00:04:38,740 --> 00:04:42,000
+surfaceفكل واحد من هدول ال surfaces طب احنا عارفين
+
+58
+00:04:42,000 --> 00:04:44,680
+نقول كل واحدة من هدول الأحوال يعني مثلا لو أخدت
+
+59
+00:04:44,680 --> 00:04:47,840
+هدا ال surface ها surface هبقى بيقولنا إيش بيساوي
+
+60
+00:04:47,840 --> 00:04:52,720
+DM وهيبقى بيقولنا إيش بيبقى بيساوي RDθ فإذا
+
+61
+00:04:52,720 --> 00:04:58,220
+المساحة دي إيش هتكون RDθ في R هتكون R تربية Dθ
+
+62
+00:04:58,220 --> 00:05:01,540
+وإيش الاتجاه هون بيكون إذا هذا هو الاتجاه ال R
+
+63
+00:05:01,540 --> 00:05:06,380
+وهذا الاتجاه هو ال θ فاتجاه العمودي عليه هيكون مين
+
+64
+00:05:06,380 --> 00:05:10,690
+هو Phi hatهذا ال surface هيكون النور طبعا هو في
+
+65
+00:05:10,690 --> 00:05:14,930
+تجاه ال pi hat نقول هيك طالب ال pi hat موزر هذا في
+
+66
+00:05:14,930 --> 00:05:20,970
+تجاه ال pi hat انا
+
+67
+00:05:20,970 --> 00:05:28,750
+بقيت اللي هو r d theta و dr هذا اللي هو في تجاه ال
+
+68
+00:05:28,750 --> 00:05:32,590
+theta و هذا في تجاه ال r فاللي عمودي عليها هيكون
+
+69
+00:05:32,590 --> 00:05:36,590
+مين اللي هو ال pi hat نيجي لل surface التاني مثلا
+
+70
+00:05:38,630 --> 00:05:42,790
+عندها انا اخد ال surface من هنا هذا ال surface
+
+71
+00:05:42,790 --> 00:05:49,650
+هتطلع هنا rdθ و هتطلع هنا يبقى عبارة عن rsinθdφ
+
+72
+00:05:49,650 --> 00:05:53,250
+فعندى التغيرات او الاتجاه التعطي اتجاه ال θ و
+
+73
+00:05:53,250 --> 00:05:57,350
+اتجاه ال ف هت او الاتجاه التعطي فوان بيكون هذا ال
+
+74
+00:05:57,350 --> 00:06:01,550
+normal عليا اتجاه ال r هت تمام فازال ارى هتكون
+
+75
+00:06:01,550 --> 00:06:04,050
+عندى r تربيع sinθdθdφ
+
+76
+00:06:21,310 --> 00:06:26,410
+YRθRsinθ⁻⁻ فالارية هي عبارة عن R ترقية sinθDθ⁻⁻
+
+77
+00:06:26,410 --> 00:06:31,190
+اتجاه R hat اخر الارية اللي هتكون يندي واحد منهم
+
+78
+00:06:31,190 --> 00:06:37,250
+هو DR والتاني R ثالث sinθ⁻⁻R هيكون اتجاهنا θ hat
+
+79
+00:06:42,970 --> 00:06:46,830
+بعدين احنا قلنا ال surface differential area هي
+
+80
+00:06:46,830 --> 00:06:50,050
+عبارة عن vector اللي هي نقدار اللي هي اتجاهه فممكن
+
+81
+00:06:50,050 --> 00:06:52,690
+تكون اللي هو احد هدول ال surfaces اللي هي مثلا هذا
+
+82
+00:06:52,690 --> 00:06:57,250
+ال surface بقعة ربيع sin θ dθ dφ و اتجاهه ارهار او
+
+83
+00:06:57,250 --> 00:07:00,430
+هذا ال surface اللي هو R sin θ dr dφ و اتجاهه θ
+
+84
+00:07:00,430 --> 00:07:05,750
+hat او ال surface هذا اللي هو عبارة عن R dθ dr و
+
+85
+00:07:05,750 --> 00:07:11,440
+اتجاهه 5 هتDifferential Volume ببساطة بحصل ضرب
+
+86
+00:07:11,440 --> 00:07:16,440
+التلك اطول اذا رجعنا للقطع بتاعتنا ال volume مش
+
+87
+00:07:16,440 --> 00:07:20,280
+هيكون حصل ضرب طول في العرض في الارتفاع يعني هيكون
+
+88
+00:07:20,280 --> 00:07:30,940
+DR في RDθ في RsinθDπ اذا
+
+89
+00:07:30,940 --> 00:07:36,240
+هيكون R تربية SinθDRDθDπ وزي ما قلنا ال volume هو
+
+90
+00:07:36,240 --> 00:07:41,920
+quantity هو scalarبناخد أمثلة على الأشياء اللي
+
+91
+00:07:41,920 --> 00:07:45,040
+احنا شفناها على المحاضرات الماضية بنحط على جانب ال
+
+92
+00:07:45,040 --> 00:07:50,460
+elements كلهم بتاعة ال Cartesian و الcyclic و
+
+93
+00:07:50,460 --> 00:07:54,080
+الcyclical و الcyclical و الcyclical و الcyclical
+
+94
+00:07:54,080 --> 00:07:54,640
+و الcyclical و الcyclical و الcyclical و
+
+95
+00:07:54,640 --> 00:07:58,140
+الcyclical و الcyclical و الcyclical و الcyclical
+
+96
+00:07:58,140 --> 00:08:02,160
+و الcyclical و الcyclical و الcyclical و
+
+97
+00:08:02,160 --> 00:08:08,080
+الcyclical و الcyclical و الcyclical و الcyclical
+
+98
+00:08:08,080 --> 00:08:08,080
+و الcyclical و الcyclical و الcyclical و
+
+99
+00:08:08,080 --> 00:08:08,080
+الcyclical و الcyclical و الcyclical و الcyclical
+
+100
+00:08:08,080 --> 00:08:09,630
+و الcyclical و الcyclical و الcyclical و الcyx hat
+
+101
+00:08:09,630 --> 00:08:15,790
+زي ال dy y hat زي ال dz زدها هذا ال mean
+
+102
+00:08:15,790 --> 00:08:19,610
+differential links ال area ال area أثرش في ال
+
+103
+00:08:19,610 --> 00:08:23,290
+Cartesian لإن انا هتكون dx مثلا و dy بتجاه زدها
+
+104
+00:08:23,290 --> 00:08:31,470
+يعني دي ايه؟ هتكون احد يا dx dy بتجاه زدها او dx
+
+105
+00:08:31,470 --> 00:08:44,510
+dz بتجاه y hatDX DY DX DX DX DX DX DX DX DX DX DX
+
+106
+00:08:44,510 --> 00:08:45,530
+DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX
+
+107
+00:08:45,530 --> 00:08:55,110
+DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX
+
+108
+00:08:55,110 --> 00:08:55,410
+DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX
+
+109
+00:08:55,410 --> 00:08:55,410
+DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX
+
+110
+00:08:55,410 --> 00:08:55,410
+DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX
+
+111
+00:08:55,410 --> 00:08:55,410
+DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX
+
+112
+00:08:55,410 --> 00:08:55,410
+DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX
+
+113
+00:08:55,410 --> 00:08:55,410
+DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX
+
+114
+00:08:55,410 --> 00:08:55,570
+DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX
+
+115
+00:08:55,570 --> 00:08:55,570
+DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX
+
+116
+00:08:55,570 --> 00:08:55,570
+DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX
+
+117
+00:08:55,570 --> 00:08:55,570
+DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX
+
+118
+00:08:55,570 --> 00:08:58,530
+DX DX DX DX DX DX DX
+
+119
+00:09:03,590 --> 00:09:09,090
+دلها الـ cylindrical الـ
+
+120
+00:09:09,090 --> 00:09:11,270
+cylindrical coordinate أخدناها برضه قبل الليل دي
+
+121
+00:09:11,270 --> 00:09:16,330
+اللي
+
+122
+00:09:16,330 --> 00:09:24,390
+هو ال DL دلها ال DL vector هتكون دي رو رو hat زي
+
+123
+00:09:24,390 --> 00:09:31,380
+ال رو في الفيزا ال DZ Z hat المشترك بين كارتيزيا و
+
+124
+00:09:31,380 --> 00:09:35,840
+الصفري كان هو Z coordinate بيضلوا ال Z هو نفس ال Z
+
+125
+00:09:35,840 --> 00:09:44,940
+هنا في عندنا ان هو ال area و ال area قبلنا DA رو
+
+126
+00:09:44,940 --> 00:09:53,220
+D Pi DZ تجاه رو hat كمان D رو DZ تجاه رو Pi hat
+
+127
+00:10:22,970 --> 00:10:24,370
+D5D0D5D0D6D6D6D6D6D6D6D6D6D6D6D6D6D6D6D6D6D6D6D6D6D6D6D6D6D6D6D6D6
+
+128
+00:10:34,740 --> 00:10:44,520
+و اخر واحدة دي ار سان سيتا دي فيهات
+
+129
+00:10:53,080 --> 00:10:56,780
+دى هى بـ three elements يجى بعدين لنا اللى هو ال
+
+130
+00:10:56,780 --> 00:11:00,720
+area والـ area اللى قلناه حصل طرد طولين ولم ننسى
+
+131
+00:11:00,720 --> 00:11:11,720
+الاتجاه NPS يعني هتساوي R تربيع sin θ dθ dφ اتجاه
+
+132
+00:11:11,720 --> 00:11:21,760
+Rها او هتكون R sin θ dr dφ اتجاه روح θها او هتكون
+
+133
+00:11:40,080 --> 00:11:45,900
+نبدأ في الأسئلة كما تشاهدون فهذا المثال ليس واضح
+
+134
+00:11:45,900 --> 00:11:47,060
+الشكل اللي أمامنا
+
+135
+00:11:52,130 --> 00:11:57,150
+السلندر يتعامل مع الـ cylindrical coordinate في
+
+136
+00:11:57,150 --> 00:11:59,190
+حالة السلندر لازم يتعامل مع الـ cylindrical
+
+137
+00:11:59,190 --> 00:12:00,010
+coordinate
+
+138
+00:12:09,880 --> 00:12:13,720
+consider ال object اللى قدامنا و بده نحسب ال
+
+139
+00:12:13,720 --> 00:12:16,020
+distance احنا عشان نحسب ال distance احنا اخدنا ال
+
+140
+00:12:16,020 --> 00:12:20,600
+links ال differential links يعني اخدنا DL فى كل
+
+141
+00:12:20,600 --> 00:12:23,680
+اتجار عشان اطول ال distance ايش بدي اعمل؟ بدي اعمل
+
+142
+00:12:23,680 --> 00:12:27,260
+integration انا مثلا اخد جزء يعني مثلا يجى و يطلب
+
+143
+00:12:27,260 --> 00:12:30,780
+منا اللى هو ال distance ما بين ال B و ال C ال
+
+144
+00:12:30,780 --> 00:12:33,960
+distance ما بين ال B و ال C عشان اجيب ال distance
+
+145
+00:12:33,960 --> 00:12:37,380
+انا عارفة ال DL عارفة ال DL فى هذا الاتجار احنا
+
+146
+00:12:37,380 --> 00:12:41,490
+بكتبها مع بعض عشان هو ال DLعشان أحصل على الطول كله
+
+147
+00:12:41,490 --> 00:12:46,050
+مش بس هو بدي أكامل، معايا؟ بس أول ما أعمل أي حاجة
+
+148
+00:12:46,050 --> 00:12:49,650
+أول خطوة بدي أعملها أن النقاط اللي هتكتبلنا يوم هي
+
+149
+00:12:49,650 --> 00:12:54,210
+نقاط معلها بال Cartesian Coordinates يعني عند ال A
+
+150
+00:12:54,210 --> 00:13:00,270
+كتبها تبدلت ال X Y Z 5 0 0 و ال B ابدلت ال X Y Z X
+
+151
+00:13:00,270 --> 00:13:06,170
+0 Y 5 Z 0 و ال C برضه عبارة عن 0 5 10 و ال D نفس
+
+152
+00:13:06,170 --> 00:13:11,360
+الحاجةأول خطوة بنعملها ان نحول من ال Cartesian لل
+
+153
+00:13:11,360 --> 00:13:13,980
+cylindrical coordinate، مين بيبقى تعملها المهمة؟
+
+154
+00:13:13,980 --> 00:13:18,260
+بس مش حابسين نتعامل مع بعض، سهل، نتعامل مع بعض،
+
+155
+00:13:18,260 --> 00:13:24,560
+تلقوا هم
+
+156
+00:13:24,560 --> 00:13:29,540
+إسراء، هدين،
+
+157
+00:13:29,540 --> 00:13:34,160
+اذا احنا اللي بدنا نعمله؟ان نحسب ال distance عشان
+
+158
+00:13:34,160 --> 00:13:36,800
+نحسبها ممتاز احنا اول حاجة اش نعرف ايش ال
+
+159
+00:13:36,800 --> 00:13:38,700
+coordinate تبع ال cylindrical coordinate ايش فيه
+
+160
+00:13:38,700 --> 00:13:45,700
+عندنا رو و فاي و زد ال
+
+161
+00:13:45,700 --> 00:13:51,000
+رو احنا بتذكر ايه اش هم ده ده اش هم ده تلتها نتذكر
+
+162
+00:13:51,000 --> 00:13:54,600
+مع بعض عشان ما نخبطش و نحفظ يعني خلينا نفهم اكتر و
+
+163
+00:13:54,600 --> 00:13:57,920
+نحفظ احنا عندنا ال cylinder فيه عندنا هو القاعدة
+
+164
+00:13:57,920 --> 00:14:02,130
+بتاعتها اللي هي الدائرة اللي تحتهاوالدائرة بتحتوي
+
+165
+00:14:02,130 --> 00:14:07,290
+على اتنين من الكواردنات اللي هي ال raw و الفارق
+
+166
+00:14:07,290 --> 00:14:11,390
+ايش هي ال raw قلناها ال raw هو اكبر عن ايه مكمونة
+
+167
+00:14:11,390 --> 00:14:15,170
+تجاه ال X و تجاه ال Z فهيكون جزر الترابير بس مافيه
+
+168
+00:14:15,170 --> 00:14:21,170
+شيء في ال Z بل بس واحد في ال X و في ال Y X Y Z فال
+
+169
+00:14:21,170 --> 00:14:23,450
+cylinder بتاعتى او ال raw اللي هو ال radius تبع
+
+170
+00:14:23,450 --> 00:14:26,070
+الدائرة عشان يكون منتخبط ال radius تبع الدائرة
+
+171
+00:14:26,070 --> 00:14:29,190
+وشوفناها كمان مع بعض ان ال raw انها كمبونة تجاه ال
+
+172
+00:14:29,190 --> 00:14:32,870
+X واحد تجاه ال Zهيكون هذا الطولة تغير عن X تربيه
+
+173
+00:14:32,870 --> 00:14:36,450
+زائد Y تربيه تحت الجزر زي ما أخدنا ال distances
+
+174
+00:14:36,450 --> 00:14:39,750
+هيكون ال component تجاه X هيكون ال component تجاه
+
+175
+00:14:39,750 --> 00:14:42,950
+X تربيه تغير و Y تربيه تحت الجزر تربيه هذين
+
+176
+00:14:42,950 --> 00:14:49,130
+يتقرروا هذين يتقرروا هذين يتقرروا هذين يتقرروا
+
+177
+00:14:49,130 --> 00:14:54,750
+هذين يتقرروا هذين يتقرروا هذين يتقرروا هذين
+
+178
+00:14:54,750 --> 00:14:54,870
+يتقرروا هذين يتقرروا هذين يتقرروا هذين يتقرروا
+
+179
+00:14:54,870 --> 00:14:54,870
+هذين يتقرروا هذين يتقرروا هذين يتقرروا هذين
+
+180
+00:14:54,870 --> 00:14:56,900
+يتقرروا هذين يتقرروا هذين ياللي هو ال Y والمجاور
+
+181
+00:14:56,900 --> 00:15:07,580
+لها له X فهي تكون فقشة عن inverse ال Y على X فهي
+
+182
+00:15:07,580 --> 00:15:14,740
+نفس ال Z الحقيقية فخلّينا نحوّل النقاط و ندّل نقطة
+
+183
+00:15:14,740 --> 00:15:20,960
+C خلّي البساوة .. ليش عم تتفت على البساوة؟ هو الصح
+
+184
+00:15:20,960 --> 00:15:21,680
+أنك تتفت عليها
+
+185
+00:15:24,700 --> 00:15:33,040
+خمسة عشرين جزر خمسة عشرين خمسة درس خمس درس خمس درس
+
+186
+00:15:33,040 --> 00:15:36,460
+خمس درس خمس درس خمس درس خمس درس خمس درس خمس درس
+
+187
+00:15:36,460 --> 00:15:38,240
+خمس درس خمس درس خمس درس خمس درس خمس درس خمس درس
+
+188
+00:15:38,240 --> 00:15:38,240
+خمس درس خمس درس خمس درس خمس درس خمس درس خمس درس
+
+189
+00:15:38,240 --> 00:15:39,200
+خمس درس خمس درس خمس درس خمس درس خمس درس خمس درس
+
+190
+00:15:39,200 --> 00:15:49,080
+خمس درس خمس درس خمس درس خمس درس خمس درس خمس
+
+191
+00:15:49,080 --> 00:15:57,480
+درس خمس درس خمالنقطة الاخرى هي نقطة
+
+192
+00:15:57,480 --> 00:16:01,700
+نفسنا احنا نقطة
+
+193
+00:16:01,700 --> 00:16:05,460
+نفسنا هنا وقع ايش ممكنها الـ5 تكون؟ الـ5 تأتي من
+
+194
+00:16:05,460 --> 00:16:08,760
+الـ0 و بتلف لك و باقى ده النقطة ايش كانت في النقطة
+
+195
+00:16:08,760 --> 00:16:17,600
+باقى؟ باق أفين نزل النقطة بـ0
+
+196
+00:16:17,600 --> 00:16:19,600
+5 0
+
+197
+00:16:30,190 --> 00:16:49,730
+خمسة تمام نروح
+
+198
+00:16:49,730 --> 00:16:52,030
+خمسة نرفع التانية inverse
+
+199
+00:17:00,280 --> 00:17:08,100
+بعدين بيخوذ الدايمة X عشان هذا القرن P كل نقطة مضت
+
+200
+00:17:08,100 --> 00:17:09,880
+بجانبها 100 ملتقى شوية
+
+201
+00:17:24,120 --> 00:17:27,140
+طبعا يعني احنا شايفين اللي هو cylinder ما بين الـ0
+
+202
+00:17:27,140 --> 00:17:31,560
+و الـPi على 2 فأكيد اي نقطة واقعة في هذا البلان
+
+203
+00:17:31,560 --> 00:17:35,700
+اللي هو Y بال X axis هتكون 5 اتساوة 0 و أي بلان
+
+204
+00:17:35,700 --> 00:17:40,200
+على ال Y axis هتكون 5 اتساوة وPi على 2
+
+205
+00:17:59,930 --> 00:18:03,850
+ظلنا مين؟ مصر
+
+206
+00:18:13,220 --> 00:18:15,980
+ممتازا اول خطوة قلنا احنا من انه احنا cylindrical
+
+207
+00:18:15,980 --> 00:18:19,020
+فاسهلنا نروح من ال kartesian ل ال cylindrical
+
+208
+00:18:19,020 --> 00:18:22,660
+coordinate فحولنا نقطة كل نقطة من اللي هو ال
+
+209
+00:18:22,660 --> 00:18:25,860
+kartesian ل ال cylindrical نبدأ بأول ال distance
+
+210
+00:18:25,860 --> 00:18:30,120
+بسيطة يعني ساعدت فيها هي بده طول من B ل C ايش هنا
+
+211
+00:18:30,120 --> 00:18:37,380
+DL دي ال دي ال دي ال دي ال دي ال دي ال دي ال دي ال
+
+212
+00:18:37,380 --> 00:18:42,800
+دي ال
+
+213
+00:18:42,800 --> 00:18:42,920
+دي ال دي ال دي ال دي ال دي ال دي ال دي ال دي ال دي
+
+214
+00:18:42,920 --> 00:18:42,920
+ال دي ال دي ال دي ال دي ال دي ال دي ال دي ال دي ال
+
+215
+00:18:42,920 --> 00:18:42,920
+دي ال دي ال دي ال دي ال دي ال دي ال دي ال دي ال دي
+
+216
+00:18:42,920 --> 00:18:46,340
+ال دي ال دي ال دي ال دي ال دي ال دي ال دزائد دي رو
+
+217
+00:18:46,340 --> 00:18:52,120
+رو هابز زائد
+
+218
+00:18:52,120 --> 00:19:00,180
+رو دي فاي فاي هاب زائد هي دي زد زد هابز حالينا
+
+219
+00:19:00,180 --> 00:19:03,320
+نطلع على ال element تبعنا احنا هو يعني على هذا ال
+
+220
+00:19:03,320 --> 00:19:08,850
+axis او على هذا القولإذا طلعت قلت إنه إيش فيه بي
+
+221
+00:19:08,850 --> 00:19:11,690
+والسي بالcylindrical حتى لو طلعنا على ال Cartesian
+
+222
+00:19:11,690 --> 00:19:14,250
+هلنا نطلع على ال cylindrical ال cylindrical هي
+
+223
+00:19:14,250 --> 00:19:20,970
+نقطة بي وهي نقطة سي هل اتغيرت ال raw؟ ال raw خمسة
+
+224
+00:19:20,970 --> 00:19:27,490
+ماتغيرتش يعني دي raw إيش بيساوي؟ Zero كمان
+
+225
+00:19:27,490 --> 00:19:33,290
+ال five هل اتغيرت ال five؟ إذا دي five مالها؟ Zero
+
+226
+00:19:34,010 --> 00:19:39,750
+من يظل عندنا zz بالفعل تغيرات من 0 ل10 فإذا دي ال
+
+227
+00:19:39,750 --> 00:19:43,830
+element اللي هنا دي ال vector بيحطه هنا عليه
+
+228
+00:19:43,830 --> 00:19:51,410
+vector عشان نميزه احنا بساوي ال element
+
+229
+00:19:51,410 --> 00:19:55,170
+اللي على هذا ال links اللي هو بالدنيا لو أخدت أنا
+
+230
+00:19:55,170 --> 00:20:04,100
+element الحاجة اللي بتتغير هنا فقطDL == DZZH هيطير
+
+231
+00:20:04,100 --> 00:20:08,440
+في هذا الطول او هو بده ال distance بدوش ال DL فازا
+
+232
+00:20:08,440 --> 00:20:13,520
+بده اكمل اقول L ايش فهتساوي L التكامل من اللي هو
+
+233
+00:20:13,520 --> 00:20:17,560
+الدرجة التي تتغيرها من Zero لعشرة اذا انت عاملة
+
+234
+00:20:17,560 --> 00:20:24,400
+Zero لعشرة DZZH هتساوي
+
+235
+00:20:24,400 --> 00:20:32,660
+Zمن صفر لعشرة زرد هات اذا الحكومة الجواب عبارة عن
+
+236
+00:20:32,660 --> 00:20:38,160
+عشرة زرد هات اذا ال distance اللي ليه ال pc هي
+
+237
+00:20:38,160 --> 00:20:45,580
+عبارة عن عشرة زرد هات طبعا فضل ان شاء الله فالحد
+
+238
+00:20:45,580 --> 00:20:50,660
+يعمل ال distance CD انا بتفكر هنا يلا
+
+239
+00:20:54,540 --> 00:20:58,840
+كله هيطلع على فرصة فانا فيها بده إشي لع الصبورة
+
+240
+00:20:58,840 --> 00:21:05,720
+فيها بده حاجة من الصبورة فبقى أسم سحبنيها فلاقيتها
+
+241
+00:21:05,720 --> 00:21:10,180
+مين هو بده substance اللي هى CD ايه ال CD ايه ال
+
+242
+00:21:10,180 --> 00:21:15,280
+CD فهذا اللي بيبنيها ايه
+
+243
+00:21:15,280 --> 00:21:20,060
+اللي هى ال CD فهي
+
+244
+00:21:20,060 --> 00:21:33,170
+ال C هي 55 على 8 أعشر والـ D يعني 5 0 0 10 تمام
+
+245
+00:21:33,170 --> 00:21:41,470
+هتكتب ال D L D L D L تولدها تساوي نفس اللي كتبتها
+
+246
+00:21:41,470 --> 00:21:47,630
+زميلتنا تولد D Rho Rho Hat زائد Rho D Phi Phi Hat
+
+247
+00:21:47,630 --> 00:21:53,270
+زائد D زيت زيت Hatطبعا انا بكتبلكم ياها بشكل عام
+
+248
+00:21:53,270 --> 00:21:56,250
+انا بدي شوي شوي تعرفوا و تأكدوا مين اللي بتغير بس
+
+249
+00:21:56,250 --> 00:22:00,390
+احنا نطب شكل عام مع بعض نشوف انه انا عندنا اذا
+
+250
+00:22:00,390 --> 00:22:04,490
+طلعته هذا ال plan هذا ال plan اللي هو موازن لل XY
+
+251
+00:22:04,490 --> 00:22:10,470
+plan قاعد عن Z ايش بتساوي؟ Z بتساوي عشرة، Z ثابتة،
+
+252
+00:22:10,470 --> 00:22:14,050
+عشرة عشرة هذا ال plan تخيلنا الستوانة بتاعتنا
+
+253
+00:22:14,050 --> 00:22:18,750
+الستوانة بتاعتنا هذه ثابتة عن Z ده عشرة، اذا زد
+
+254
+00:22:18,750 --> 00:22:22,810
+ماتغيرتش، اذا ليه زد ايش بتساوي؟ Zeroايش كمان هنا
+
+255
+00:22:22,810 --> 00:22:27,710
+على هذا القوس رو ثابتة رو ثابتة ضمس خمسة لو انا
+
+256
+00:22:27,710 --> 00:22:31,630
+غيرت من قوس لقوس تاني بتتغير رو لكن احنا ضالين على
+
+257
+00:22:31,630 --> 00:22:36,590
+نفس القوس فعندي رو ثابتة اذا دي رو ثابتة اذا ده
+
+258
+00:22:36,590 --> 00:22:40,850
+عندي القوس من قبل لو انا اخدت اي element هذا ال
+
+259
+00:22:40,850 --> 00:22:45,250
+element ايش هيكون هذا عبارة عني هذه دي فاي وهذه
+
+260
+00:22:45,250 --> 00:22:49,550
+اللي هي رو هيكون رو دي فاي اذا اللي ضال عندي رو دي
+
+261
+00:22:49,550 --> 00:22:55,810
+فاي فاي هاتفانا اللي ضابط اتغير لأن الزاوية اتغيرت
+
+262
+00:22:55,810 --> 00:23:03,750
+من الـ 0 لـ pi على 2 هو بده من C ل D يعني ان
+
+263
+00:23:03,750 --> 00:23:07,810
+الزاوية اتغيرت من pi على 2 ل 0 او اذا طلعنا للناس
+
+264
+00:23:07,810 --> 00:23:11,650
+لان انا اتكلمكم تمام اذا L هو افكار مطلوب ال
+
+265
+00:23:11,650 --> 00:23:14,090
+distance يعني انا بخليكم تكتبوا ال vector L بس هو
+
+266
+00:23:14,090 --> 00:23:16,910
+بده ال distance فهي بس المقدار L يعني روزن فيه
+
+267
+00:23:16,910 --> 00:23:20,790
+عشان تكون دقيقين مع السؤال هو بده ال L دي L اللي
+
+268
+00:23:20,790 --> 00:23:26,270
+هي ك scalarDL بتساوي رو دي فاي بس هى هو اللى بدنا
+
+269
+00:23:26,270 --> 00:23:31,750
+قل التكامل رو
+
+270
+00:23:31,750 --> 00:23:35,690
+دي فاي مش ال displacement و بده ال distance ال
+
+271
+00:23:35,690 --> 00:23:39,170
+distance قولنا scalar رو دي فاي فعندنا قل اشبه
+
+272
+00:23:39,170 --> 00:23:46,770
+تساوي قل التكامل قبل اللى قل و كتب هنا مش DL إذا
+
+273
+00:23:46,770 --> 00:23:51,470
+كتبتي DL بتكميشي قل التكاملDL هو ال element زى ما
+
+274
+00:23:51,470 --> 00:23:56,010
+انت شايفها ده ال element هذا ال DL L هو كل الطول
+
+275
+00:23:56,010 --> 00:24:03,890
+فكل الطول مش معروف تكامل ف Y اللى هي من باية على
+
+276
+00:24:03,890 --> 00:24:06,410
+اتنين من ها distance فخلاص تفعلها من ها distance
+
+277
+00:24:06,410 --> 00:24:16,010
+من باية على اتنين ل Zero تمام فانت كامل روح دبل
+
+278
+00:24:16,010 --> 00:24:20,290
+سابقة تطلع على براه و بقيمتها قداش روحفهذا ال
+
+279
+00:24:20,290 --> 00:24:25,410
+links خمسة خمسة خمسة خمسة خمسة خمسة خمسة خمسة خمسة
+
+280
+00:24:25,410 --> 00:24:26,290
+خمسة خمسة خمسة خمسة خمسة خمسة خمسة خمسة خمسة خمسة
+
+281
+00:24:26,290 --> 00:24:35,290
+خمسة خمسة خمسة خمسة خمسة خمسة خمسة خمسة خمسة خمسة
+
+282
+00:24:35,290 --> 00:24:36,810
+خمسة خمسة خمسة خمسة خمسة خمسة خمسة خمسة خمسة خمسة
+
+283
+00:24:36,810 --> 00:24:40,210
+خمسة خمسة خمسة خمسة خمسة خمسة خمسة خمسة خمسة
+
+284
+00:24:40,210 --> 00:24:43,670
+خمسة
+
+285
+00:24:43,670 --> 00:24:52,470
+خمسة خمسة خمسة خمسة خمسة خمسيلا لبعده بكنا surface
+
+286
+00:24:52,470 --> 00:25:00,330
+بعدها ال surface area A,B,C,D مين بقى يا عملنا
+
+287
+00:25:00,330 --> 00:25:09,570
+إياها؟ يلا احنا .. احنا عايزين نحوها بقى
+
+288
+00:25:09,570 --> 00:25:17,770
+احنا احنا كتبنا ال surface
+
+289
+00:25:17,770 --> 00:25:24,540
+area اللي هي AD C
+
+290
+00:25:24,540 --> 00:25:27,600
+A
+
+291
+00:25:27,600 --> 00:25:32,780
+D على
+
+292
+00:25:32,780 --> 00:25:36,640
+وجه هذا السليندر يعني لو احنا طلعنا هاي بس هي مش
+
+293
+00:25:36,640 --> 00:25:42,780
+سليندر كاملة هذا هو ال area اللي انا بدي اسمه
+
+294
+00:25:42,780 --> 00:25:44,560
+قانون ال area
+
+295
+00:25:50,520 --> 00:25:54,480
+بنشوف مين اللي بتغير و مين السابت عشان انا دي ال
+
+296
+00:25:54,480 --> 00:25:59,200
+هو انا اخد قطع على هذا قطع عجزه قطع صغيرة اش اللي
+
+297
+00:25:59,200 --> 00:26:03,900
+هيكون اللي متغير فيها اندي فاي بتتغير من zero ل
+
+298
+00:26:03,900 --> 00:26:08,540
+five على اتنين والزت اللي بتتغير من zero لعشرة مين
+
+299
+00:26:08,540 --> 00:26:12,320
+اللي سابت على هذا ال surface رو رو ست على خمسة اذا
+
+300
+00:26:12,320 --> 00:26:17,790
+محاخد مين انا اللي هي رو دي five دي زت رابعىرو دي
+
+301
+00:26:17,790 --> 00:26:28,810
+فاي دي زد ال
+
+302
+00:26:28,810 --> 00:26:33,930
+area اللى اختارناها رو دي فاي دي زد لإن انا لو
+
+303
+00:26:33,930 --> 00:26:37,570
+أخدت اي قطعة على هذا ال surface هيكون في عند
+
+304
+00:26:37,570 --> 00:26:42,410
+التغير في اتجاه اللى هو ال 5 هو رو دي فاي و هو
+
+305
+00:26:42,410 --> 00:26:44,730
+اتجاه الزد اللى هو دي زد
+
+306
+00:26:55,670 --> 00:27:01,110
+طبعا إذا إحنا بنا نكامل ال five بتروح من zero ل
+
+307
+00:27:01,110 --> 00:27:07,610
+five على اتنين و ال z بتروح من zero ل عشر رقصها
+
+308
+00:27:07,610 --> 00:27:17,370
+بتاعنا قداشه حمسة دي five بس احنا دي five دي zطب
+
+309
+00:27:17,370 --> 00:27:22,490
+اذا ال area ايش اللي هتكون ال area التكامل اذا ال
+
+310
+00:27:22,490 --> 00:27:25,370
+total area هي ال differential area ال differential
+
+311
+00:27:25,370 --> 00:27:29,150
+area هو جزء على ال surface عشان اجيب كل ال surface
+
+312
+00:27:29,150 --> 00:27:32,690
+بتقعة كاملة فعندي هيكون في التكاملها من zero
+
+313
+00:27:32,690 --> 00:27:37,930
+double ال integral فعندي في تكامل على في و في
+
+314
+00:27:37,930 --> 00:27:44,490
+تكامل على z هنحط انه في بتروح في بتروح من zero لبي
+
+315
+00:27:44,490 --> 00:27:51,970
+على اتنينوعندي ال Z بتروح من 0 ل 10 ان كان تطلع
+
+316
+00:27:51,970 --> 00:27:59,410
+الحمص لبرا ال Phi هكملها من E Phi ل E Z تكامل ل
+
+317
+00:27:59,410 --> 00:28:04,230
+Diesel خلّي بس تقبل Integral يعني حتى لو ال Diesel
+
+318
+00:28:04,230 --> 00:28:09,970
+بينه بس انت ماكملتيش إيش لسه يعني عيد نفس ال ..
+
+319
+00:28:19,830 --> 00:28:25,390
+هيكون عندى تكامل ال Z هيطلع Z تكمل من 0 ل 10 قيمة
+
+320
+00:28:25,390 --> 00:28:29,430
+عشرة وال D Phi هتكون Phi تكملها من 0 ل Pi على 2
+
+321
+00:28:29,430 --> 00:28:32,650
+هيكون من Pi على 2 لذا هى الجواب هيكون خمسة في Pi
+
+322
+00:28:32,650 --> 00:28:40,390
+على 2 في اللى هو عشرة اتجاه الورق الهاتف هيكون
+
+323
+00:28:40,390 --> 00:28:45,110
+عندى خمسة في خمسة خمسة عشرين Pi فهى Pi تلاتة
+
+324
+00:28:45,110 --> 00:28:48,650
+واربعة عشرينية ممتاز ممتاز جدا
+
+325
+00:28:57,230 --> 00:29:08,350
+في حد كمان هيبقى واضح
+
+326
+00:29:08,350 --> 00:29:11,770
+ما اللي بنعمله؟ انا اتعمدت ان اكتر ما بدا وكنت بس
+
+327
+00:29:11,770 --> 00:29:14,770
+شوية المفروض مع التمرين انكوا تصيروا فاهمين انه ده
+
+328
+00:29:14,770 --> 00:29:16,830
+هي التغيرات و ده دلقوس
+
+329
+00:29:20,630 --> 00:29:25,290
+اللي هي قاعدة
+
+330
+00:29:25,290 --> 00:29:28,950
+قاعدة السلندر اللي قدامنا أو هو جزء من السلندر
+
+331
+00:29:28,950 --> 00:29:32,270
+الشكل اللي قدامنا القاعدة بتاعة ايش اللي بتغير
+
+332
+00:29:32,270 --> 00:29:37,250
+فيها هل دي z بتتغير زت ثابت على مين على zero زت
+
+333
+00:29:37,250 --> 00:29:40,870
+ثابت على مين اللي بتتغيرها ال raw بتتغير لو انا
+
+334
+00:29:40,870 --> 00:29:46,650
+أخدت element عليها ال raw هيتغير من zero ل 5ومن
+
+335
+00:29:46,650 --> 00:29:53,530
+هنا فاية بتتغير اللى هناخده اسم مين اللى هو رو دى
+
+336
+00:29:53,530 --> 00:30:00,550
+فاية دى رو واتجاهه اللى هو سنة هالكامل
+
+337
+00:30:00,550 --> 00:30:06,070
+اذا ال a إيش هتساوي اللى بتطلع تغيره هالكامل
+
+338
+00:30:06,070 --> 00:30:11,670
+فالفاية بتتغير مين بتغير ال رو بتتغير ال رو بتتغير
+
+339
+00:30:11,670 --> 00:30:16,130
+ليش تطلع عند ال رو دى رو عند الفايةبتغير من zero ل
+
+340
+00:30:16,130 --> 00:30:18,850
+five على اتنين اذا اولا خلينا نعمل انتقال انتقال
+
+341
+00:30:18,850 --> 00:30:22,550
+انتقال
+
+342
+00:30:22,550 --> 00:30:22,550
+انتقال انتقال انتقال انتقال انتقال انتقال انتقال
+
+343
+00:30:22,550 --> 00:30:23,770
+انتقال انتقال انتقال انتقال انتقال انتقال انتقال
+
+344
+00:30:23,770 --> 00:30:23,870
+انتقال انتقال انتقال انتقال انتقال انتقال انتقال
+
+345
+00:30:23,870 --> 00:30:23,870
+انتقال انتقال انتقال انتقال انتقال انتقال انتقال
+
+346
+00:30:23,870 --> 00:30:24,690
+انتقال انتقال انتقال انتقال انتقال انتقال انتقال
+
+347
+00:30:24,690 --> 00:30:24,730
+انتقال انتقال انتقال انتقال انتقال انتقال انتقال
+
+348
+00:30:24,730 --> 00:30:34,230
+انتقال انتقال انتقال انتقال انتقال
+
+349
+00:30:43,510 --> 00:30:47,190
+عندى الـ Phi هكملها من 0 ل π على 2 حتى تعطينا قداش
+
+350
+00:30:47,190 --> 00:30:51,750
+بي على 2 و ال row دى رقش هتعطينا row تربيه على 2
+
+351
+00:30:51,750 --> 00:31:00,170
+روه دى روه هتعطينا روه تربيه على 2 روه
+
+352
+00:31:00,170 --> 00:31:07,390
+تربيه على 2 زدها اذا هتصير 25 على 4 في بي
+
+353
+00:31:16,760 --> 00:31:22,100
+ممتاز اخر حاجة مين بحب يعملها اللي هو ال volume ال
+
+354
+00:31:22,100 --> 00:31:27,780
+volume
+
+355
+00:31:27,780 --> 00:31:30,540
+حصل ضرب التلات ال franchises اللي هو ايش اللي
+
+356
+00:31:30,540 --> 00:31:37,580
+هيكون هي دي ان رو دي رو دي فاي دي زد دي رو دي فاي
+
+357
+00:31:37,580 --> 00:31:41,600
+دي زد ان ال رو بتتغير من و لا وين من زي رو لخمسة
+
+358
+00:31:41,950 --> 00:31:45,890
+والـ 5 من 0 ل 5 على 2، لأ ال volume ولا يمكن، هو
+
+359
+00:31:45,890 --> 00:31:50,590
+مش vector of volume، ال volume مولا scalar I don't
+
+360
+00:31:50,590 --> 00:31:55,050
+know if that makes more sense فعم،
+
+361
+00:31:55,050 --> 00:31:58,090
+اذا V أشف هالساعة و أنت كان في ال triple integral،
+
+362
+00:31:58,090 --> 00:32:01,970
+V أقلت بV، أقلت بV، في ال triple integral ال rho
+
+363
+00:32:01,970 --> 00:32:07,250
+من 0 ل 5 و ال 5 من 0 ل 5 على 2 و ال z من 0 ل 10
+
+364
+00:32:22,550 --> 00:32:29,990
+الزد نطلعها عشرة والفا يبقى على اثنين والزد عشرة
+
+365
+00:32:29,990 --> 00:32:35,430
+ونضغ علينا الهيروتن بي على اتنين
+
+366
+00:32:54,670 --> 00:32:57,930
+طبعا واضح اش اللى احنا استخدنا منه من انه عرفنا ال
+
+367
+00:32:57,930 --> 00:33:00,450
+differential links ال differential area و ال
+
+368
+00:33:00,450 --> 00:33:03,830
+differential volume اني بقدر اطول اى links اى
+
+369
+00:33:03,830 --> 00:33:07,530
+distance فيه ال space و اقدر اطول اى area و اقدر
+
+370
+00:33:07,530 --> 00:33:08,650
+اطول اى volume
+
+371
+00:33:21,420 --> 00:33:29,300
+هي المثال التاني المثال
+
+372
+00:33:33,000 --> 00:33:37,360
+المثال هنا جزء من سفير احنا المثال السابق كان جزء
+
+373
+00:33:37,360 --> 00:33:41,900
+من سلمدة قلت هانشوف هذا جزء من سفير هذا الجزء من
+
+374
+00:33:41,900 --> 00:33:45,420
+السفير بقول لي التالي عنه بقول يا دي النتفة اللي
+
+375
+00:33:45,420 --> 00:33:48,160
+شغلينها يعني هاي لو تخيلنا احنا عندنا بطيخة و واحد
+
+376
+00:33:48,160 --> 00:33:51,040
+قطعها كتعرفوا كيف يبيعوا البطيخ قطعها هيك النتفة
+
+377
+00:33:51,040 --> 00:33:54,680
+صغيرة و بطولها عشان يفرج البيئة الشخصة دي حمره ولا
+
+378
+00:33:54,680 --> 00:34:00,460
+دي هو الجزء هذا بس طلعنا عليه هنلاقي انه قيلنا ان
+
+379
+00:34:00,460 --> 00:34:09,290
+Rر تتغير من قيمة تلاتة لخمسة يعني دي ر بتروح من
+
+380
+00:34:09,290 --> 00:34:16,390
+قيمة تلاتة لخمسة ثتا بتبدأ من ستين لتسين يعني هذا
+
+381
+00:34:16,390 --> 00:34:21,610
+المفروض تبقى على ال X Y plane مثلا من ستين لتسين
+
+382
+00:34:21,610 --> 00:34:26,610
+بعدين عندي فاي اللي هو هذا اتجاه الفاي فاي بتتحرك
+
+383
+00:34:26,610 --> 00:34:32,680
+من خمسة واربعين لعند هذه النقطة لستينإذا عنده a من
+
+384
+00:34:32,680 --> 00:34:37,340
+تلاتة لخمسة ثتا من ستين لتسعين و five من خمسة
+
+385
+00:34:37,340 --> 00:34:41,600
+واربعين لستين
+
+386
+00:34:41,600 --> 00:34:48,340
+أول حاجة طالب مننا distance dh distance dh هي حاب
+
+387
+00:34:48,340 --> 00:34:52,620
+تجرب نفس الحاجة نفس اللي عملنا distance dh دي حاجة
+
+388
+00:34:52,620 --> 00:34:53,160
+هتجربه
+
+389
+00:35:02,520 --> 00:35:07,160
+لو طلعنا على ال DH قداش قيمة R عند هذا ال shell
+
+390
+00:35:07,160 --> 00:35:10,620
+هدول اتخيلوهم ال shell اللى بوقع عليها نفس ال
+
+391
+00:35:10,620 --> 00:35:14,660
+shell اللى هو ال differential AEHD و ال shell
+
+392
+00:35:14,660 --> 00:35:18,960
+التانى اللى وراها اللى بوقع عليه ال BFGC Shell ورا
+
+393
+00:35:18,960 --> 00:35:23,740
+shell عند ال shell الصغيرة R بتتغير اهي انا ك
+
+394
+00:35:23,740 --> 00:35:31,420
+shell طب اتغيرت R قداش قيمة R هنااللي قداش؟ R قداش
+
+395
+00:35:31,420 --> 00:35:35,880
+قيمة R؟ تلاتة اللي براها خمسة فاحنا هلاقيتها أصلا
+
+396
+00:35:35,880 --> 00:35:39,160
+بوقعين على ال chill اللي عندها R قداش قيمتها تلاتة
+
+397
+00:35:39,160 --> 00:35:43,300
+اذا احنا هلاقيتها متأكدين ان R سابت هنا مين بتغير
+
+398
+00:35:43,300 --> 00:35:50,040
+هو بده distance DH تلعب ال DH هنا θتة تغيرت؟ لأ
+
+399
+00:35:50,040 --> 00:35:53,540
+احنا قولنا θتة عند ال plan اللي فوق ثتة قيمتها
+
+400
+00:35:53,540 --> 00:35:56,200
+ستين و ال plan التحتاني تسعين احنا في ال plan
+
+401
+00:35:56,200 --> 00:36:02,120
+التحتانيطب إذا هنا R ثابتة و θ ثابتة ثتا ثابتة على
+
+402
+00:36:02,120 --> 00:36:05,660
+تسعين و R ثابتة على تلاتة مين اللي بتغير؟ five
+
+403
+00:36:05,660 --> 00:36:11,000
+بتتغير من خمسة و أربعين لستين طب إيش هنا ال links
+
+404
+00:36:11,000 --> 00:36:13,160
+اللي هنا؟ ميذكرين إيش ال links اللي هنا؟ لو أنا
+
+405
+00:36:13,160 --> 00:36:19,100
+أخدت مادات هذا المسقط تبع ال R ال radius R في sin
+
+406
+00:36:19,100 --> 00:36:23,220
+theta أنا أسقطه ع ال z axis R كو sin theta وع ال x
+
+407
+00:36:23,220 --> 00:36:26,660
+y plane قولنا R sin theta فالقفص إيش بيكون؟
+
+408
+00:36:53,620 --> 00:36:56,760
+RsinθDθRsinθDθRsinθDθRsinθDθRsinθDθRsinθDθصين سيتا
+
+409
+00:36:56,760 --> 00:37:03,480
+دي سيتا فاي هاف خلاص
+
+410
+00:37:03,480 --> 00:37:08,120
+انسى هذا الحكيم مين اللي قولنا بتغير R ثابت طبعا
+
+411
+00:37:08,120 --> 00:37:14,560
+بتقدر تطلع R وصين سيتا قولنا R ثلاثة وثيتا تسعين
+
+412
+00:37:14,560 --> 00:37:18,380
+ففقدر أطلعهم برا ال Integral R أطول عودة عن R
+
+413
+00:37:18,380 --> 00:37:24,710
+ثلاثة مش مشكلة فاي اللي هي منبتروح انه بيطول من 45
+
+414
+00:37:24,710 --> 00:37:33,710
+ل 60 اذا
+
+415
+00:37:33,710 --> 00:37:44,450
+ايش هينكون عندي R تلاتة وعندي
+
+416
+00:37:44,450 --> 00:37:48,870
+اللي هي ال 5 بتتحرك
+
+417
+00:37:48,870 --> 00:37:58,450
+قيمتها من 45لأ الستين مش هيساوي لنا بيكمل وخلاص
+
+418
+00:37:58,450 --> 00:38:03,450
+فعل دي فعل هي فعل و لا لأ هيكون عندى تلاتة افتحها
+
+419
+00:38:03,450 --> 00:38:07,910
+تلاتة و افتحها post فاللي هي الفعل هتتحرك من ستين
+
+420
+00:38:07,910 --> 00:38:10,490
+درجة لخمس و .. من خمس و أربعين درجة لستين درجة
+
+421
+00:38:10,490 --> 00:38:13,870
+الفرق بينهم هو type five بس عشان أنا مابحث عفوظش
+
+422
+00:38:13,870 --> 00:38:17,380
+بتحولها ل radialالأسئلة الأولى اللى حولهم هو ال
+
+423
+00:38:17,380 --> 00:38:20,680
+radian 45 و 60 اول افضل افضل افضل افضل افضل افضل
+
+424
+00:38:20,680 --> 00:38:22,260
+افضل افضل افضل افضل افضل افضل افضل افضل افضل افضل
+
+425
+00:38:22,260 --> 00:38:23,840
+افضل افضل افضل افضل افضل افضل افضل افضل افضل افضل
+
+426
+00:38:23,840 --> 00:38:23,880
+افضل افضل افضل افضل افضل افضل افضل افضل افضل افضل
+
+427
+00:38:23,880 --> 00:38:23,920
+افضل افضل افضل افضل افضل افضل افضل افضل افضل افضل
+
+428
+00:38:23,920 --> 00:38:27,340
+افضل افضل
+
+429
+00:38:27,340 --> 00:38:31,200
+افضل
+
+430
+00:38:31,200 --> 00:38:40,140
+افضل
+
+431
+00:38:40,140 --> 00:38:44,740
+اف
+
+432
+00:38:55,820 --> 00:39:02,700
+ممتاز ممتاز فى حد تانى محب يجرب لسه حلنا الجزء
+
+433
+00:39:02,700 --> 00:39:05,940
+الاول عنه واخدنا اللى هو ال differential links
+
+434
+00:39:05,940 --> 00:39:10,800
+اللى هو ال R Sine theta D Pi Pi hat فانه هو الوحيد
+
+435
+00:39:10,800 --> 00:39:17,520
+اللى بضيع فى حاجة تمام هشوف الجزء التانى FGأنا بس
+
+436
+00:39:17,520 --> 00:39:28,260
+ساعدكم، مين يطلع؟ يالا كده يا سرعة خل
+
+437
+00:39:28,260 --> 00:39:31,240
+حاجة شوية حلوة، طب و الله أنا كانت فكرة أمشي في
+
+438
+00:39:31,240 --> 00:39:35,580
+الموضوع، طب مش غلط، احنا بعد العيد خليني أفجي،
+
+439
+00:39:35,580 --> 00:39:37,820
+أفجي، خليني نرجع على أفجي، هون أفجي، هاي اللي
+
+440
+00:39:37,820 --> 00:39:40,800
+بقالك، هاي اللي بقالك، مين بتغيرتيه؟هذه الـ shell
+
+441
+00:39:40,800 --> 00:39:45,840
+اللي برا R ثابتة فيها ولا متغيرة؟ هنا أنا ماسكة
+
+442
+00:39:45,840 --> 00:39:50,820
+طبّة ثابتة، ثابتة، قداش قيمتها؟ خمسة، خمسة احنا
+
+443
+00:39:50,820 --> 00:39:54,060
+هذه جزء من الـ shell الجوانية، من الطبّة الجوانية،
+
+444
+00:39:54,060 --> 00:39:57,040
+خيالنا أننا نمسك بلّوننا، و ببعد، بمسك البلّون
+
+445
+00:39:57,040 --> 00:40:01,240
+الأكبر، صح؟ اتغيرت قيمة R على البلّون الكبير، اذا
+
+446
+00:40:01,240 --> 00:40:06,780
+هنا R ثابتة، على هذا الجزء من الطبّة التي تعطيه،
+
+447
+00:40:06,780 --> 00:40:10,690
+قيمة R فيها خمسةبعد كمان هلاقيتها في هنا تغيرت على
+
+448
+00:40:10,690 --> 00:40:14,670
+هذا الطول احنا في قولنا عند هذه النقطة كم تقيمتها
+
+449
+00:40:14,670 --> 00:40:19,370
+45 وعند هذه النقطة 60 أسوأ هنا ولا هنا في اداش
+
+450
+00:40:19,370 --> 00:40:23,770
+قيمتها 60 اذا في سابطة و او سابطة مين اللي اتغير
+
+451
+00:40:23,770 --> 00:40:27,750
+ستة ستة ايش قيمة هذا ال links حيث انه اتغير في هذا
+
+452
+00:40:27,750 --> 00:40:32,070
+ال links هيكون اللي هو احد جزئية هيكون قيمة ال
+
+453
+00:40:32,070 --> 00:40:38,330
+radius R D ستة R D ستةاللي هي أي واحد فيهم لو
+
+454
+00:40:38,330 --> 00:40:44,690
+طلعنا نعدي L هيكون R D θ θ hat اذا دي L فهيكون دي
+
+455
+00:40:44,690 --> 00:40:48,130
+R Zero لأن R ثابتة على خمسة و دي Phi Zero لأنها
+
+456
+00:40:48,130 --> 00:40:52,990
+ثابتة على اللي هو الستين على طول اذا بدأ اقول L
+
+457
+00:40:52,990 --> 00:40:56,030
+ايش بيها تساوي ال vector خلاص اختيها vector كام ل
+
+458
+00:40:56,030 --> 00:41:00,490
+L ال vector روحتي عليها ثانية R اللي قيمتها خمسة
+
+459
+00:41:01,440 --> 00:41:09,340
+مضت كامل ل θ من 60 ل
+
+460
+00:41:09,340 --> 00:41:14,560
+90 60 يعني بقى على تلاتة؟ بقى على تلاتة و 90 هي
+
+461
+00:41:14,560 --> 00:41:21,180
+بقى على تلاتة بدء θ ثلاثة تلاتة تلاتة تلاتة تلاتة
+
+462
+00:41:21,180 --> 00:41:24,520
+تلاتة
+
+463
+00:41:41,650 --> 00:41:45,030
+ممتاز نشوف ال surface area و لا احنا خلاص وقتنا
+
+464
+00:41:45,030 --> 00:41:50,210
+يعطيكوا العافية و انتوا دي اكم تكملوا هاي الأمثلة
+
+465
+00:41:50,210 --> 00:41:54,280
+و محطوطوا أرقام الأمثلة زى ما انتوا شايفينهمال
+
+466
+00:41:54,280 --> 00:41:58,240
+practice exercise فانا بدي اياكم تحلوهم و تتأكدوا
+
+467
+00:41:58,240 --> 00:42:01,960
+انكم فاهمين كل هذه النقات عشان اللقاء القادم ان
+
+468
+00:42:01,960 --> 00:42:09,640
+شاء الله هنكمل فيه ال chapter هنقلها اللي هو ال
+
+469
+00:42:09,640 --> 00:42:11,280
+line و ال curve و ال contour
+
+470
+00:42:15,570 --> 00:42:18,730
+اللي هي اللي بسميهم ال line integral و ال curve
+
+471
+00:42:18,730 --> 00:42:22,090
+integral او ال contour integral كلهم بنفس المعنى و
+
+472
+00:42:22,090 --> 00:42:24,970
+هنشوف اللي هو ال surface integral و ال volume
+
+473
+00:42:24,970 --> 00:42:28,330
+integral او اللي يعني بيسموهم ال waffle integral
+
+474
+00:42:28,330 --> 00:42:33,610
+بالكتسار او ال contour integral هاي ال line او ال
+
+475
+00:42:33,610 --> 00:42:37,150
+contour او ال curve integral و هنشوف اللي هو ال
+
+476
+00:42:37,150 --> 00:42:40,530
+surface integral او ال closed contour و بعدين ال
+
+477
+00:42:40,530 --> 00:42:44,470
+surface integral و ال volume integralمع بعض اللقاء
+
+478
+00:42:44,470 --> 00:42:46,990
+القادم ان شاء الله فاندي أكترجوا الأشياء اللي
+
+479
+00:42:46,990 --> 00:42:51,150
+أخدناها مع بعض و اللقاء القادم بترفعوا ع هيكل هم
+
+480
+00:42:51,150 --> 00:42:54,510
+الكاتلة المادة ان شاء الله اللي حكينا عنها يعطيكوا
+
+481
+00:42:54,510 --> 00:42:54,870
+العرش
+
diff --git a/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/SXNt5y2mt6I.srt b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/SXNt5y2mt6I.srt
new file mode 100644
index 0000000000000000000000000000000000000000..2d86e0667ba9c738dea39358ad267fb2a70e7e41
--- /dev/null
+++ b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/SXNt5y2mt6I.srt
@@ -0,0 +1,679 @@
+1
+00:00:20,650 --> 00:00:22,710
+بسم الله الرحمن الرحيم السلام عليكم ورحمة الله
+
+2
+00:00:22,710 --> 00:00:26,130
+وبركاته إحنا اليوم إن شاء الله هنتابع موضوعنا اللي 
+
+3
+00:00:26,130 --> 00:00:29,090
+هو الـfield في المادة يعني every field in the
+
+4
+00:00:29,090 --> 00:00:34,090
+materials إحنا المحاضرة الماضية شفنا كيف إنّه الـD
+
+5
+00:00:34,090 --> 00:00:42,070
+و الـE بيرتبطوا بعلاقة اللي هي Epsilon ED بيساوي
+
+6
+00:00:42,070 --> 00:00:46,010
+Epsilon E قلنا طبيعة هذه العلاقة ممكن أقول عنها
+
+7
+00:00:46,010 --> 00:00:50,310
+Linear Homogenous حسب إيش هي الـEpsilon هذه أو ممكن 
+
+8
+00:00:50,310 --> 00:00:53,990
+أقول عنها non-linear, non-homogeneous, anisotropic
+
+9
+00:00:53,990 --> 00:00:56,970
+و هكذا قلنا إيش اللي بيحددها، الأشياء هي إيش في
+
+10
+00:00:56,970 --> 00:01:01,810
+وضعية الـD، الـEpsilon بتاعتنا، أول حاجة ممكن نقول إنّ الـD
+
+11
+00:01:01,810 --> 00:01:05,490
+إذا كانت تتناسب طرديًا مع الـE أو Linear ليه بنقول عنها 
+
+12
+00:01:05,490 --> 00:01:09,270
+Linear؟ يعني زي ما اتفقنا ما فيش عندنا E تربيع أو E قوه
+
+13
+00:01:10,700 --> 00:01:14,800
+لأنّ ممكن يكون العلاقة فيها terms أعلى، لكن مثلًا هي
+
+14
+00:01:14,800 --> 00:01:17,640
+كده، إحنا بنحكي عن Linear، بتصير non-linear
+
+15
+00:01:17,640 --> 00:01:20,580
+بيصير عندنا مثلًا الـfield جاية من الـlaser، high
+
+16
+00:01:20,580 --> 00:01:23,540
+intensity laser، فبيصير عندنا E، E تربيع، و الآخَر، 
+
+17
+00:01:23,540 --> 00:01:28,100
+يعني الـpolarization بتصير بتتناسب مع Chi P, 
+
+18
+00:01:28,440 --> 00:01:32,720
+Chi E, Chi E تربيع و الآخَر، هذا الـLinearity قلنا
+
+19
+00:01:32,720 --> 00:01:37,580
+إذا الـD تتناسب مع الـE فقط، كمان قلنا إذا إبسلون أو 
+
+20
+00:01:37,580 --> 00:01:41,700
+سيجما في حالة الـJ، يتساوى سيجما E ويتساوى D 
+
+21
+00:01:41,700 --> 00:01:51,220
+يتساوى إبسلون E يتساوى D يتساوى إبسلون E يتساوى D
+
+22
+00:01:51,220 --> 00:01:55,660
+يتساوى إبسلون E يتساوى إبسلون E يتساوى سيجما E
+
+23
+00:01:55,660 --> 00:01:59,460
+يتساوى إبسلون E يتساوى سيجما E يتساوى إبسلون E
+
+24
+00:01:59,460 --> 00:01:59,720
+يتساوى إبسلون E يتساوى إبسلون E يتساوى إبسلون E
+
+25
+00:01:59,720 --> 00:02:00,100
+يتساوى إبسلون E يتسا
+
+26
+00:02:06,020 --> 00:02:09,420
+معادلة مقلاقتها الـE-linear، الكلام اللي نقدر نقول 
+
+27
+00:02:09,420 --> 00:02:13,400
+عنها هو homogenous إذا كانت أسواء epsilon ولا
+
+28
+00:02:13,400 --> 00:02:17,820
+sigma باعتمدوش على الـvector space يعني باعتمدوش
+
+29
+00:02:17,820 --> 00:02:20,980
+على x و y و z يعني في كل نقطة من الـspace بنلاقيها
+
+30
+00:02:20,980 --> 00:02:24,600
+نفس القيمة بكون homogenous لو كانت بتختلف حسب
+
+31
+00:02:24,600 --> 00:02:28,000
+موقعها حسب الـvector space بنسميها inhomogeneous
+
+32
+00:02:28,000 --> 00:02:36,200
+كمان إحنا قلنا إنّ الـD U E ممكن تكون isotropic إذا 
+
+33
+00:02:36,200 --> 00:02:41,100
+بتعتمدش على الـdirection يعني إذا كانت إذا اتجاهها
+
+34
+00:02:41,100 --> 00:02:44,100
+بهذا الاتجاه بتكون قيمتها مختلفة عن هذا الاتجاه
+
+35
+00:02:44,100 --> 00:02:48,180
+بتكون anisotropic لكن إذا كانت في أي اتجاه لو
+
+36
+00:02:48,180 --> 00:02:52,480
+قستها في أي direction يبقى نفس القيمة بتكون
+
+37
+00:02:52,480 --> 00:02:53,120
+isotropic
+
+38
+00:02:57,200 --> 00:02:59,920
+طبعًا إذا إحنا بنحكي عن isotropic اللي هو قلنا إيش
+
+39
+00:02:59,920 --> 00:03:02,900
+قلنا في الـisotropic إنّها بتعتمد على الاتجاه
+
+40
+00:03:02,900 --> 00:03:08,980
+بيكون الـE و الـD و الـB مش parallel، إحنا معناه لما يكون نفس
+
+41
+00:03:08,980 --> 00:03:12,880
+الاتجاه معناه إنّه الـE if it is isotropic و الـD بيكونوا 
+
+42
+00:03:12,880 --> 00:03:15,620
+في نفس الاتجاه، الـE و الـG بيكونوا في نفس الاتجاه
+
+43
+00:03:23,500 --> 00:03:28,400
+matrix matrix اللي بتوضح للاعتمادية على الـ
+
+44
+00:03:28,400 --> 00:03:33,540
+direction زي ما إحنا هنشوف هنا، عند DXاش هتكون مش 
+
+45
+00:03:33,540 --> 00:03:36,980
+في نفس الاتجاه EX في لها components في اتجاه الـEY
+
+46
+00:03:36,980 --> 00:03:43,170
+و EZ، عند DXاش هتكون إبسلون XXEX plus epsilon xy ey
+
+47
+00:03:43,170 --> 00:03:48,390
+plus epsilon xz ez، طبعًا طبيعة الـmaterials بتختلف
+
+48
+00:03:48,390 --> 00:03:52,390
+أو تصلف الـcrystalline material حسب مين السفر في
+
+49
+00:03:52,390 --> 00:03:56,830
+هدول ومين المسافر فيهم، يعني بتكون symmetric مثلًا
+
+50
+00:03:56,830 --> 00:04:00,870
+هدول الـmaterials بتكونوا symmetric إذا كانوا الـ
+
+51
+00:04:00,870 --> 00:04:06,630
+exz بتساوي الـepsilon xz بتساوي الـzx بتكون 
+
+52
+00:04:06,630 --> 00:04:09,970
+symmetric، الـepsilon xy بتساوي الـepsilon
+
+53
+00:04:35,940 --> 00:04:37,340
+YZYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
+
+54
+00:04:39,330 --> 00:04:42,070
+طبعًا كل حاجة زي ما حكيت مسميات، يعني أنتم ممكن
+
+55
+00:04:42,070 --> 00:04:45,630
+تلاقوهم في كتب متعددة للـmaterials اللي بيصنفوا
+
+56
+00:04:45,630 --> 00:04:50,630
+طبيعة الاستجابة للـelectric field حسب مين فدولة
+
+57
+00:04:50,630 --> 00:04:53,130
+يعني هم بيدرسوهم في المختبرات و بيحسبوا قيم الـ
+
+58
+00:04:53,130 --> 00:04:55,430
+excellence و برضه ممكن يحسبوا رياضيًا..
+
+59
+00:04:55,430 --> 00:04:59,570
+mathematically ويتقانوهم في بعض مين فيهم سفر ومين 
+
+60
+00:04:59,570 --> 00:05:03,010
+فيهم السفر، إذا في عندهم سالب يعني بيساوي بعض
+
+61
+00:05:03,010 --> 00:05:07,920
+بس سالب، إيش طبيعة المادة وهكذا هذه هي جزء من 
+
+62
+00:05:07,920 --> 00:05:12,120
+تعريف اللي هي الـmaterials حسب هل هي symmetric و
+
+63
+00:05:12,120 --> 00:05:15,640
+لا antisymmetric، إيش هم الـzero من فيهم، الـzero من
+
+64
+00:05:15,640 --> 00:05:21,800
+فيهم، الـzero من هدول الـcomponents هكذا 
+
+65
+00:05:21,800 --> 00:05:26,100
+أنا بمقدر أقول إنّكم فاهمين إيش العلاقة دي و
+
+66
+00:05:26,100 --> 00:05:30,920
+اكسل او ايه؟ إذا مش دائماً diverse
+
+67
+00:05:34,550 --> 00:05:40,750
+دي اللي بتساوي روه دائماً هي بقدر أقول إنّه تاجرش دي
+
+68
+00:05:40,750 --> 00:05:47,150
+بتساوي روه على إبسلون؟ مش دائماً واضح؟
+
+69
+00:05:47,150 --> 00:05:52,710
+ليه؟ لأنّ هنا دي بادر إبسلون دي مش دائماً بقدر أطلع 
+
+70
+00:05:52,710 --> 00:05:56,130
+إبسلون، الـdivergence وقت إش بقدرش أطلعها؟ لما تكون
+
+71
+00:05:56,130 --> 00:05:59,850
+هي مالها؟ بتعتمد على X و Y و Z إنّها inhomogeneous لأنّها
+
+72
+00:05:59,850 --> 00:06:03,590
+بيصير هي تفاضل two components، لكن إذا كانت Linear 
+
+73
+00:06:03,590 --> 00:06:08,530
+أو Homogeneous بقدر أطلّها من الـDifferential فإذا 
+
+74
+00:06:08,530 --> 00:06:14,290
+مش دائماً هذا الحكيم بتطبق لهذا الحكيم فقط في 
+
+75
+00:06:14,290 --> 00:06:17,090
+الـFree Space كنا بسهولة نقول الـdivergence بتساويها 
+
+76
+00:06:17,090 --> 00:06:18,850
+على الـEpsilon نقطة، إحنا عارفين الـEpsilon نقطة
+
+77
+00:06:18,850 --> 00:06:22,290
+مالها، constant، اللي هي بتاعة الـSpace لكن لو 
+
+78
+00:06:22,290 --> 00:06:25,150
+بدّي أحكي عن الـmaterial، بدّي أكون حذرة إيش طبيعة
+
+79
+00:06:25,150 --> 00:06:28,690
+الـmaterial قبل ما أقول إنّ الـEpsilon بقدر أطلّها
+
+80
+00:06:28,690 --> 00:06:30,190
+من قلب الـDifferential؟
+
+81
+00:06:40,440 --> 00:06:43,520
+هذا اللي أنا حكيته يعني إنّه للـmaterials بدّي أكون
+
+82
+00:06:43,520 --> 00:06:47,760
+حذرة إيش طبيعة المادة قبل ما أحكي عن العلاقات اللي
+
+83
+00:06:47,760 --> 00:06:51,280
+تربط المادة بالـelectric field، لكن لو إحنا بنحكي 
+
+84
+00:06:51,280 --> 00:06:55,120
+على free space ببساطة بحكي على الـepsilon not
+
+85
+00:06:55,120 --> 00:06:59,660
+العلاقات كلّها اللي درسناها لـfree space بتنطبق على 
+
+86
+00:06:59,660 --> 00:07:03,160
+الـmaterial space كليتها الفرقية إنّي بستبدل
+
+87
+00:07:03,160 --> 00:07:06,680
+epsilon not بـepsilon يعني الفرصة اللي متذكرينها 
+
+88
+00:07:06,680 --> 00:07:11,820
+لما حكينا على الـfree space ماذا تساوي الـforce؟
+
+89
+00:07:11,820 --> 00:07:16,160
+تذكرينها؟ بين two charges following force اكيو
+
+90
+00:07:16,160 --> 00:07:21,380
+واحد اكيو تنين على four by epsilon not صح في R
+
+91
+00:07:21,380 --> 00:07:26,080
+تربيع في R هذا أو R بيكتروا على RQ أو يعني هاخدوا
+
+92
+00:07:26,080 --> 00:07:30,760
+اكتروا عشان في الـR ليه الـR minus R تربيع تمام؟
+
+93
+00:07:30,760 --> 00:07:36,980
+لكن في الـ.. هذه في الـfree space، في الـmaterial
+
+94
+00:07:36,980 --> 00:07:45,470
+space إيش بتصير؟ الـQ1 و الـQ2 على 4Y إبسلون R تربيع 
+
+95
+00:07:45,470 --> 00:07:50,050
+في R تقريبًا، طبعًا إبسلون إيش قلنا عنها إحنا هي
+
+96
+00:07:50,050 --> 00:07:53,730
+إبسلون نط في إبسلون R، متذكرين قلنا إبسلون R هي 
+
+97
+00:07:53,730 --> 00:07:56,610
+relative permittivity اللي بتساوي إبسلون على إبسلون
+
+98
+00:07:56,610 --> 00:08:02,260
+نط، إبسلون بقدر أكتبها بهذا الشكل بدل إبسلون نوت
+
+99
+00:08:02,260 --> 00:08:04,880
+باستخدام إبسلون بتاعة الـmaterial باستخدام
+
+100
+00:08:04,880 --> 00:08:07,020
+permittivity بتاعة الـfree space باستخدام
+
+101
+00:08:07,020 --> 00:08:09,900
+permittivity بتاعة الـmaterial اللي هي بتساوي
+
+102
+00:08:09,900 --> 00:08:13,200
+إبسلون نوت في إبسلون R، إبسلون R إنّها relative
+
+103
+00:08:13,200 --> 00:08:16,480
+permittivity للـmaterial، نفس الشيء لـ الـtotal
+
+104
+00:08:16,480 --> 00:08:19,860
+energy، الـtotal energy كانت عندنا نص الـintegral
+
+105
+00:08:19,860 --> 00:08:23,700
+لـإبسلون E تربيع EV بدل إبسلون بستخدمها إبسلون نوت
+
+106
+00:08:23,700 --> 00:08:32,960
+إبسلون R، واضح؟ في أي استفسار لحد هنا؟ نشوف مثال إن
+
+107
+00:08:32,960 --> 00:08:37,660
+قضيت electrical cube of side L، يعني عندك cube وكل
+
+108
+00:08:37,660 --> 00:08:43,360
+side له thing to I ونقعد at the origin، يعني الـ
+
+109
+00:08:43,360 --> 00:08:48,350
+center تبعه بالتوازي مع الـorigin، السينتر تبع الـ
+
+110
+00:08:48,350 --> 00:08:51,890
+cube at the origin واضح؟ إذا السينتر تبعه at the
+
+111
+00:08:51,890 --> 00:08:56,270
+origin يعني عندي X فيها L على 2 و -X فيها L 
+
+112
+00:08:56,270 --> 00:09:01,530
+على 2، Y فيها L على 2 و -Y -L على 2، و Z
+
+113
+00:09:01,530 --> 00:09:06,110
+عندي L على 2 و -L على 2 لأنّه عارف من الـcenter
+
+114
+00:09:06,110 --> 00:09:11,310
+has a radial polarization given by P بساوي R hat 
+
+115
+00:09:11,310 --> 00:09:14,370
+الـpolarization متذكرينها اللي هي 
+
+116
+00:09:30,200 --> 00:09:32,580
+عرفنا المحاضرة الماضية عن الـbounded charges في
+
+117
+00:09:32,580 --> 00:09:35,840
+عندنا surface و في عندنا volume bounded charges، الـ
+
+118
+00:09:35,840 --> 00:09:38,600
+surface قلنا الـcharge density بتاعته بيساوي الـ
+
+119
+00:09:38,600 --> 00:09:43,000
+polarization في الـnormal على الـsurface، متذكرين الـ
+
+120
+00:09:43,000 --> 00:09:47,100
+surface بقول P dot الـnormal على الـsurface، فإحنا 
+
+121
+00:09:47,100 --> 00:09:51,040
+بناخد واحد من الـsides بتاعة الـcube، بناخد واحد من 
+
+122
+00:09:51,040 --> 00:09:54,820
+الـside مثلًا الـside اللي على الـx axis اللي واقف 
+
+123
+00:09:54,820 --> 00:10:00,220
+مثلًا بناخد عند x بتساوي L على 2، اللي الـside اللي 
+
+124
+00:10:00,220 --> 00:10:03,260
+واقف عند L على 2، إيش اللي عمودي عليه هيكون اللي هو 
+
+125
+00:10:03,260 --> 00:10:07,220
+الـnormal اللي واقف على الـX-axis، إيش بدّه يكون الـ
+
+126
+00:10:07,220 --> 00:10:11,480
+sites بتاعه؟ اللي هي الـY و الـZ، صح؟ إذا العمود
+
+127
+00:10:11,480 --> 00:10:13,900
+اللي عليه يمينه بدّه يكون X hat، اللي عند الـ
+
+128
+00:10:13,900 --> 00:10:18,060
+positive X بتساوي L على 2، الـsites بتاعه بيكونوا
+
+129
+00:10:18,060 --> 00:10:23,420
+Y و Z، فهيكون الـnormal إيه؟ X hat، فعندي AR
+
+130
+00:10:23,420 --> 00:10:31,430
+vector dot X hat إيش هيضل عنده؟ AX، صح؟ لأنّ AX X
+
+131
+00:10:31,430 --> 00:10:36,310
+hat dot x hat هتكون AX، إذا الـcharge density الـ
+
+132
+00:10:36,310 --> 00:10:41,230
+surface density لواحد من الـsurfaces هي AX لو بدأنا 
+
+133
+00:10:41,230 --> 00:10:45,670
+نكملها من هو، لو إنّ الـX أو يعني قيمة متأسفة قيمة الـ
+
+134
+00:10:45,670 --> 00:10:48,610
+X عندها اللحظة إيش بتساوي؟ قلع على اتنين لأنّ أخذنا 
+
+135
+00:10:48,610 --> 00:10:53,130
+الـsurface اللي عندها قلع على اتنين صحيح؟ تمام، الـ
+
+136
+00:10:53,130 --> 00:10:56,390
+total charge إيش بدّها تساوي؟ الـintegral رو دي أس
+
+137
+00:10:57,140 --> 00:11:01,500
+بدّي أكامل الـintegral لـraw دي أصل and كل واحدة من
+
+138
+00:11:01,500 --> 00:11:05,240
+هدول الـsize هيكون قيمة الـsurface charge density
+
+139
+00:11:05,240 --> 00:11:10,490
+A قلع على اتنين إذا بدّي أضربها في ستة و DS مين هتكون
+
+140
+00:11:10,490 --> 00:11:13,110
+التكامل على الـlinks من -قلع على اتنين لـ +
+
+141
+00:11:13,110 --> 00:11:17,010
+قلع على اتنين إنّه كل surface أنا باخد كل surface بجيب
+
+142
+00:11:17,010 --> 00:11:21,430
+الـtotal charge لكل surface اللي هي التكامل رو دي أس 
+
+143
+00:11:21,430 --> 00:11:26,610
+و بضربها في ستة اللي هي ست أوجه المكعب، فكونت
+
+144
+00:11:26,610 --> 00:11:29,090
+ستة تكامل من -قلع على اتنين لـ قلع على اتنين تكامل 
+
+145
+00:11:29,090 --> 00:11:32,780
+من -قلع على اتنين لـ قلع على اتنين، رو دي رو دي أصلي
+
+146
+00:11:32,780 --> 00:11:35,520
+هي point of charge surface point of charge دي وي 
+
+147
+00:11:35,520 --> 00:11:39,660
+دي زد إذا كملنا على هذا الجزء وضربته في ستة قلنا 
+
+148
+00:11:39,660 --> 00:11:42,900
+لأنّه عندي ست أوجه بيطلع معايا إنّ surface of charge 
+
+149
+00:11:42,900 --> 00:11:46,260
+بتساوي تلاتة A قلت Q هيجنسه على surface of charge 
+
+150
+00:11:46,260 --> 00:11:49,580
+بس في عندنا كمان volume of charge، إيش عرفنا الـ
+
+151
+00:11:49,580 --> 00:11:53,120
+point volume of charge هي -diverse P، يعني أنا
+
+152
+00:11:53,120 --> 00:12:00,210
+إيش بدّي أساوي؟ بدّي أفاضل d by dxx hat dot P ذائق d 
+
+153
+00:12:00,210 --> 00:12:05,590
+by dy y hat dot P وهكذا إيش هيصير إنّ دي xx فمين
+
+154
+00:12:05,590 --> 00:12:14,230
+للـX ذائق d by dy للـY واضح هنا 
+
+155
+00:12:14,230 --> 00:12:20,610
+الـraw P فعمل P تساوي و -ده درجة P تساوي و
+
+156
+00:12:20,610 --> 00:12:23,190
+-d by dx x hat
+
+157
+00:12:36,000 --> 00:12:43,640
+ماذا بقي؟ إيه؟ constant طبعًا
+
+158
+00:12:43,640 --> 00:12:47,240
+من dot الـproduct هذه dot تمامي، بيظل x، إيش هيكون
+
+159
+00:12:47,240 --> 00:12:53,680
+-A dx by dx، واحد dot الـproduct الـy هذين 
+
+160
+00:12:53,680 --> 00:12:55,900
+هيظل معه بس هذي هيكون zero
+
+161
+00:13:06,330 --> 00:13:12,220
+واضح؟ إذا الـvolume charge density هتكون -
+
+162
+00:13:12,220 --> 00:13:15,720
+ثلاثة A، بيدي الـtotal charge هكامل على الـvolume 
+
+163
+00:13:15,720 --> 00:13:19,040
+هتعطيني -ثلاثة A cubed لأنّ الـvolume إيش 
+
+164
+00:13:19,040 --> 00:13:22,640
+بيساوي الطول في العرض في الارتفاع، ألف ألف ألف
+
+165
+00:13:22,640 --> 00:13:25,240
+هتعطيني طول الـcube، إذا بتطلعنا نلاقي إنّ الـ
+
+166
+00:13:25,240 --> 00:13:30,660
+surface تلاتة A قلت Q و الـvolume -ثلاثة A و 
+
+167
+00:13:30,660 --> 00:13:34,240
+هذا أثبتناه المحاضرة الماضية إنّه مالها؟ الـ
+
+168
+00:13:34,240 --> 00:13:38,660
+dielectric مالها الـtotal charge بتساوي صفر لأنّه 
+
+169
+00:13:38,660 --> 00:13:42,100
+مالها neutral هو صح، في له polarization وفي له
+
+170
+00:13:42,100 --> 00:13:45,620
+bound
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/SXNt5y2mt6I_postprocess.srt b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/SXNt5y2mt6I_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..8edd5dbbbab61fcec673dcced1330c3087d1d82e
--- /dev/null
+++ b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/SXNt5y2mt6I_postprocess.srt
@@ -0,0 +1,792 @@
+1
+00:00:20,650 --> 00:00:22,710
+بسم الله الرحمن الرحيم السلام عليكم ورحمة الله
+
+2
+00:00:22,710 --> 00:00:26,130
+وبركاته احنا اليوم ان شاء الله هنتبع موضوعنا اللي
+
+3
+00:00:26,130 --> 00:00:29,090
+هو ال field في المادة يعني every field in the
+
+4
+00:00:29,090 --> 00:00:34,090
+materials احنا المحاضرة الماضية شوفنا كيف انه ال D
+
+5
+00:00:34,090 --> 00:00:42,070
+و E برتبطوا بعلاقة اللي هي Epsilon ED بيسوي
+
+6
+00:00:42,070 --> 00:00:46,010
+Epsilon E قولنا طبيعة هاي العلاقة ممكن اقول عنها
+
+7
+00:00:46,010 --> 00:00:50,310
+Linear هموجنس حسب ايش هي ال Epsilon هاي او ممكن
+
+8
+00:00:50,310 --> 00:00:53,990
+اقول عنها non-linear, non-homogeneous, anisotropic
+
+9
+00:00:53,990 --> 00:00:56,970
+وها كذا قولنا ايش اللي بيحددلها الأشياء هي ايش في
+
+10
+00:00:56,970 --> 00:01:01,810
+وضعية D ال Epsilon بتاعتنا اول حاجة ممكن نقول ان D
+
+11
+00:01:01,810 --> 00:01:05,490
+اذا كانت ناسب قرضيا مع E او Linear ليه بنقول عنها
+
+12
+00:01:05,490 --> 00:01:09,270
+Linear يعني زي ما اتفقنا مافيش عندنا E تربيع او EQ
+
+13
+00:01:10,700 --> 00:01:14,800
+لأن ممكن يكون العلاقة فيها terms أعلى، لكن مثلا هي
+
+14
+00:01:14,800 --> 00:01:17,640
+كده، احنا بنحكي عن linear، مقتش بيصير non-linear
+
+15
+00:01:17,640 --> 00:01:20,580
+بيصير عندنا مثلا ال field جاية من ال laser، high
+
+16
+00:01:20,580 --> 00:01:23,540
+intensity laser، فبيصير عندنا E E و تربية و الأخر،
+
+17
+00:01:23,540 --> 00:01:28,100
+يعني الباقي ال polarization بتصير بتتنسب مع Chi P,
+
+18
+00:01:28,440 --> 00:01:32,720
+Chi E, Chi E تربية و الأخرهذا الـ Linearity قلنا
+
+19
+00:01:32,720 --> 00:01:37,580
+إذا D تتناسب مع E فقط كمان قلنا إذا إبسلون أو
+
+20
+00:01:37,580 --> 00:01:41,700
+سيجما في حالة الـ J يتساوى سيجما E و يتساوى D
+
+21
+00:01:41,700 --> 00:01:51,220
+يتساوى إبسلون E يتساوى D يتساوى إبسلون E يتساوى D
+
+22
+00:01:51,220 --> 00:01:55,660
+يتساوى إبسلون E يتساوى إبسلون E يتساوى سيجما E
+
+23
+00:01:55,660 --> 00:01:59,460
+يتساوى إبسلون E يتساوى سيجما E يتساوى إبسلون E
+
+24
+00:01:59,460 --> 00:01:59,720
+يتساوى إبسلون E يتساوى إبسلون E يتساوى إبسلون E
+
+25
+00:01:59,720 --> 00:02:00,100
+يتساوى إبسلون E يتسا
+
+26
+00:02:06,020 --> 00:02:09,420
+معادلة مقلاقتها ال E-linear الكلام اللي نقدر نقول
+
+27
+00:02:09,420 --> 00:02:13,400
+عنها هو homogenous إذا كانت أسواء epsilon ولا
+
+28
+00:02:13,400 --> 00:02:17,820
+sigma باعتمدوش على ال vector space يعني باعتمدوش
+
+29
+00:02:17,820 --> 00:02:20,980
+على x و y و z يعني في كل نقطة من ال space بنلاقيها
+
+30
+00:02:20,980 --> 00:02:24,600
+نفس القيمة بكون homogenous لو كانت بتختلف حسب
+
+31
+00:02:24,600 --> 00:02:28,000
+موقعها حسب ال vector space بنسميها inhomogeneous
+
+32
+00:02:28,000 --> 00:02:36,200
+كمان احنا قلنا ان ال DUEممكن تكون isotropic إذا
+
+33
+00:02:36,200 --> 00:02:41,100
+بتعتمدش على ال direction يعني إذا كانت إذا اتجاهها
+
+34
+00:02:41,100 --> 00:02:44,100
+بهذا الاتجاه بتكون قيمتها مختلفة عن هذا الاتجاه
+
+35
+00:02:44,100 --> 00:02:48,180
+بتكون an isotropic لكن إذا كانت في أي اتجاه لو
+
+36
+00:02:48,180 --> 00:02:52,480
+قستها في أي direction يبقى نفس القيمة بتكون
+
+37
+00:02:52,480 --> 00:02:53,120
+isotropic
+
+38
+00:02:57,200 --> 00:02:59,920
+طبعا اذا احنا بنحكي عن isotropic اللي هو قلنا ايش
+
+39
+00:02:59,920 --> 00:03:02,900
+قلنا في ال isotropic انها بتعتمد على الاتجاه
+
+40
+00:03:02,900 --> 00:03:08,980
+بيكونه E وD وB مش parallel احنا معناه لما يكون نفس
+
+41
+00:03:08,980 --> 00:03:12,880
+الاتجاه معناه انه E if it is isotropic وD بيكونوا
+
+42
+00:03:12,880 --> 00:03:15,620
+في نفس الاتجاه E وG بيكونوا في نفس الاتجاه
+
+43
+00:03:23,500 --> 00:03:28,400
+ماتريكس ماتريكس اللى بتوضح للاعتمادية على ال
+
+44
+00:03:28,400 --> 00:03:33,540
+direction زى ما احنا هنشوف هنا عند DXاش هتكون مش
+
+45
+00:03:33,540 --> 00:03:36,980
+في نفس الاتجاه EX فيلها components في اتجاه ال EY
+
+46
+00:03:36,980 --> 00:03:43,170
+و EZ عند DXاش هتكون يبسلون XXEXplus epsilon xy ey
+
+47
+00:03:43,170 --> 00:03:48,390
+plus epsilon xz ez طبعا طبيعة ال materials بتختلف
+
+48
+00:03:48,390 --> 00:03:52,390
+أو تصلف ال crystalline material حسب مين السفر في
+
+49
+00:03:52,390 --> 00:03:56,830
+هدولة ومين المسافر فيهم يعني بتكون symmetric مثلا
+
+50
+00:03:56,830 --> 00:04:00,870
+هدولة ال materials بتكونوا symmetric إذا كانوا ال
+
+51
+00:04:00,870 --> 00:04:06,630
+exz بتساوي ال epsilon xz بتساوي ال zx بتكون
+
+52
+00:04:06,630 --> 00:04:09,970
+symmetric ال epsilon xy بتساوي ال epsilon
+
+53
+00:04:35,940 --> 00:04:37,340
+YZYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
+
+54
+00:04:39,330 --> 00:04:42,070
+طبعا كل حاجة زي ما حكيت مسميات، يعني أنتم ممكن
+
+55
+00:04:42,070 --> 00:04:45,630
+تلاقوهم في كتب متعددة لل materials اللي بيصنفوا
+
+56
+00:04:45,630 --> 00:04:50,630
+طبيعة الاستجابة ل electric field حسب مين فدولة
+
+57
+00:04:50,630 --> 00:04:53,130
+يعني هم بدرسوهم في المختبرات و بيحسبوا قيم ال
+
+58
+00:04:53,130 --> 00:04:55,430
+excellence و برضه ممكن يحسبوا رياضي ..
+
+59
+00:04:55,430 --> 00:04:59,570
+mathematically و يتقانوهم في بعض مين فيهم سفر و
+
+60
+00:04:59,570 --> 00:05:03,010
+مين فيهم السفر، إذا في عندهم سوالب يعني بيسووا بعض
+
+61
+00:05:03,010 --> 00:05:07,920
+بس سالب، إيش طبيعة المادة و هكذاهذه هي جزء من
+
+62
+00:05:07,920 --> 00:05:12,120
+تعريف اللي هي ال materials حسب هل هي symmetric و
+
+63
+00:05:12,120 --> 00:05:15,640
+لا antisymmetric ايش هم ال zero من فيهم ال zero من
+
+64
+00:05:15,640 --> 00:05:21,800
+فيهم ال zero من هدول ال components هكذا
+
+65
+00:05:21,800 --> 00:05:26,100
+انا بمقدر اقول انه سانا فاهمين ايش العلاقة دي و
+
+66
+00:05:26,100 --> 00:05:30,920
+اكسل او ايه اذا مش دائما diverse
+
+67
+00:05:34,550 --> 00:05:40,750
+دى اللى بتساوي روه دائما هى بقدر اقول انه تاجرش دى
+
+68
+00:05:40,750 --> 00:05:47,150
+بتساوي روه على إبسلون مش دائما واضح؟
+
+69
+00:05:47,150 --> 00:05:52,710
+ليش؟ لإن هنا دى بادر إبسلون دى مش دائما بقدر يطلع
+
+70
+00:05:52,710 --> 00:05:56,130
+إبسلون ال divergence وقت إش بقدرش يطلعها لما تكون
+
+71
+00:05:56,130 --> 00:05:59,850
+هى مالها بتعتمد على X وY وZ ان هو genus لإنها
+
+72
+00:05:59,850 --> 00:06:03,590
+بيصير هى تفاضل two componentsلكن إذا كانت Linear
+
+73
+00:06:03,590 --> 00:06:08,530
+أو Homogeneous بقدر أطلّها من الـDifferential فإذا
+
+74
+00:06:08,530 --> 00:06:14,290
+مش دائما هذا الحكيم بتبسط لهذا الحكيم فقط في
+
+75
+00:06:14,290 --> 00:06:17,090
+الـFree Space كنا بسهولة نقول الـdiversity بتثوره
+
+76
+00:06:17,090 --> 00:06:18,850
+على الـEpsilon نقطة، إحنا عارفين الـEpsilon نقطة
+
+77
+00:06:18,850 --> 00:06:22,290
+مالها، constant، اللي هي تاعة الـSpace لكن لو
+
+78
+00:06:22,290 --> 00:06:25,150
+بدحكي عن الـmaterial، بدكون حذرة إيش طبيعة
+
+79
+00:06:25,150 --> 00:06:28,690
+الـmaterial قبل ما أقول إن الـEpsilon بقدر أطلّها
+
+80
+00:06:28,690 --> 00:06:30,190
+من قلب الـDifferential؟
+
+81
+00:06:40,440 --> 00:06:43,520
+هذا اللي انا حكيته يعني انه لل materials بدأ اكون
+
+82
+00:06:43,520 --> 00:06:47,760
+حذرة ايش طبيعة المادة قبل ما احكي عن العلاقات اللي
+
+83
+00:06:47,760 --> 00:06:51,280
+تربط المادة بال electric field لكن لو احنا بنحكي
+
+84
+00:06:51,280 --> 00:06:55,120
+على free space بساطة بحكي على ال epsilon not
+
+85
+00:06:55,120 --> 00:06:59,660
+العلاقات كلها اللي درسناها ل free space بتنطبق على
+
+86
+00:06:59,660 --> 00:07:03,160
+ال material space كليتها الفرقية اني بستبدل
+
+87
+00:07:03,160 --> 00:07:06,680
+epsilon not ب epsilon يعني الفرصة اللي متذكرينها
+
+88
+00:07:06,680 --> 00:07:11,820
+لما حكينا على ال free spaceماذا تسوي ال force؟
+
+89
+00:07:11,820 --> 00:07:16,160
+تذكرينها؟ بين two charges following force اكيو
+
+90
+00:07:16,160 --> 00:07:21,380
+واحد اكيو تنين على four by epsilon not صح في R
+
+91
+00:07:21,380 --> 00:07:26,080
+تربية في R هذا او R بيكتروا على RQ او يعني هاخدوا
+
+92
+00:07:26,080 --> 00:07:30,760
+اكتروا عشان في الار ليه ال R minus R براية تمام؟
+
+93
+00:07:30,760 --> 00:07:36,980
+لكن في ال .. هذه في ال free space في ال material
+
+94
+00:07:36,980 --> 00:07:45,470
+space ايش بتصير؟الـ Q1 و Q2 على 4Y إبسلون R تربيع
+
+95
+00:07:45,470 --> 00:07:50,050
+في R تقريبًا طبعًا إبسلون إيش قلنا علفناها إحنا هي
+
+96
+00:07:50,050 --> 00:07:53,730
+إبسلون نط في إبسلون R متذاكرين قلنا إبسلون R هي
+
+97
+00:07:53,730 --> 00:07:56,610
+relative permittivity اللي بتسوى إبسلون على إبسلون
+
+98
+00:07:56,610 --> 00:08:02,260
+نطأبسلون بقدر اكتبها بهذا الشكل بدل ابسلون نوت
+
+99
+00:08:02,260 --> 00:08:04,880
+باستخدام ابسلون بتاعة ال material باستخدام
+
+100
+00:08:04,880 --> 00:08:07,020
+permittivity بتاعة ال free space باستخدام
+
+101
+00:08:07,020 --> 00:08:09,900
+permittivity بتاعة ال material اللي هي بتساوي
+
+102
+00:08:09,900 --> 00:08:13,200
+ابسلون نوت في ابسلون R ابسلون R ان هي relative
+
+103
+00:08:13,200 --> 00:08:16,480
+permittivity لالمaterial نفس الاشي ل ال total
+
+104
+00:08:16,480 --> 00:08:19,860
+energy ال total energy كانت عندنا نص الintegral
+
+105
+00:08:19,860 --> 00:08:23,700
+لأبسلون E تربيه EV بدل ابسلون بستخدمها ابسلون نوت
+
+106
+00:08:23,700 --> 00:08:32,960
+ابسلون Rواضح؟ في أي استفسار لحد هنا؟ نشوف مثال إن
+
+107
+00:08:32,960 --> 00:08:37,660
+قضيت electrical cube of side L، يعني عندك cube وكل
+
+108
+00:08:37,660 --> 00:08:43,360
+side له thing to I ونقعد at the origin، يعني ال
+
+109
+00:08:43,360 --> 00:08:48,350
+center تبعه بالترابع مع ال originالسينتر تبع ال
+
+110
+00:08:48,350 --> 00:08:51,890
+cube at the origin باضح؟ إذا السينتر تبعه at the
+
+111
+00:08:51,890 --> 00:08:56,270
+origin يعني عندي X فيها L على 2 و minus X فيها L
+
+112
+00:08:56,270 --> 00:09:01,530
+على 2 Y فيها L على 2 و minus Y minus L على 2 و زد
+
+113
+00:09:01,530 --> 00:09:06,110
+عندي L على 2 و minus L على 2 لأنه عارف من السينتر
+
+114
+00:09:06,110 --> 00:09:11,310
+has a radial polarization given by P بساوية R hat
+
+115
+00:09:11,310 --> 00:09:14,370
+ال polarization ماتينياها اللي هي
+
+116
+00:09:30,200 --> 00:09:32,580
+عرفنا المحاضر الماضي عن الـ bounded charges في
+
+117
+00:09:32,580 --> 00:09:35,840
+عندنا surface و في عندنا volume bounded charges ال
+
+118
+00:09:35,840 --> 00:09:38,600
+surface قولنا ال charge density بتاع التقاشية ال
+
+119
+00:09:38,600 --> 00:09:43,000
+polarization في ال normal على ال surfaceمتذكرين ال
+
+120
+00:09:43,000 --> 00:09:47,100
+surface بقول P dot ال normal على ال surface فاحنا
+
+121
+00:09:47,100 --> 00:09:51,040
+ناخد واحد من ال sides بتاعة ال cube ناخد واحد من
+
+122
+00:09:51,040 --> 00:09:54,820
+ال side مثلا ال side اللي على ال x axis اللي واقف
+
+123
+00:09:54,820 --> 00:10:00,220
+مثلا ناخد عند x بتساوي L على 2 اللي ال side اللي
+
+124
+00:10:00,220 --> 00:10:03,260
+واقف عند L على 2 ايش اللي عمودي عليه هيكون اللي هو
+
+125
+00:10:03,260 --> 00:10:07,220
+ال normاللي وقف على ال X-axis، إيش بده يكون ال
+
+126
+00:10:07,220 --> 00:10:11,480
+sites بتاعه؟ اللي هي ال Y و ال Z، صح؟ إذا العمود
+
+127
+00:10:11,480 --> 00:10:13,900
+اللي علي يميني بده يكون X hat، اللي عند ال
+
+128
+00:10:13,900 --> 00:10:18,060
+positive X بتساوية L على 2، ال sites بتاعه يكونوا
+
+129
+00:10:18,060 --> 00:10:23,420
+Y و Z، فهيكون ال normal إيه؟ X hat، فعندي AR
+
+130
+00:10:23,420 --> 00:10:31,430
+vector dot X hat إيش هيضل عنديه؟ A X، صح؟لأن a x x
+
+131
+00:10:31,430 --> 00:10:36,310
+hat dot x hat هتكون ax إذا ال charge density ال
+
+132
+00:10:36,310 --> 00:10:41,230
+surface density لواحد من ال surfaces هي ax لو بدأ
+
+133
+00:10:41,230 --> 00:10:45,670
+أكملها من هو لوان ال x أو يعني قيمة متأسفة قيمة ال
+
+134
+00:10:45,670 --> 00:10:48,610
+x عندها اللحظة إيش بتساوي قلع على اتنين لأن حاخدنا
+
+135
+00:10:48,610 --> 00:10:53,130
+ال surface اللي عندها قلع على اتنين صحيح؟ تمام ال
+
+136
+00:10:53,130 --> 00:10:56,390
+total charge إيش بدها تساوي ال integral رو دي أس
+
+137
+00:10:57,140 --> 00:11:01,500
+بدي أكامل ال integral ل raw دي أصل and كل واحدة من
+
+138
+00:11:01,500 --> 00:11:05,240
+هدول ال size هيكون قيمة ال surface charge density
+
+139
+00:11:05,240 --> 00:11:10,490
+A فئة على اتنينأذا بدروحها في ستة و DS مين هتكون
+
+140
+00:11:10,490 --> 00:11:13,110
+التكامل على ال links من minus ألعة اتنين ل plus
+
+141
+00:11:13,110 --> 00:11:17,010
+ألعة اتنين انه كل surface انا باخد كل surface بجيب
+
+142
+00:11:17,010 --> 00:11:21,430
+ال total charge لكل surface اللي هي التكامل روه DS
+
+143
+00:11:21,430 --> 00:11:26,610
+و بدروحها في ستة اللي هي ست أو جهلة المكعب فكونت
+
+144
+00:11:26,610 --> 00:11:29,090
+ستة تكامل من minus ألعة اتنين ل ألعة اتنين تكامل
+
+145
+00:11:29,090 --> 00:11:32,780
+من minus ألعة اتنين ل ألعة اتنينرو دي رو بي أصلي
+
+146
+00:11:32,780 --> 00:11:35,520
+هي point of charge surface point of charge دي وي
+
+147
+00:11:35,520 --> 00:11:39,660
+دي زد إذا كملنا على هذا الجزء وضربته في ستة قلنا
+
+148
+00:11:39,660 --> 00:11:42,900
+لإنه عندي ست أوجه بطلع معايا إن surface of charge
+
+149
+00:11:42,900 --> 00:11:46,260
+بتاو تلاتة A قل ال Q هيجنسه على surface of charge
+
+150
+00:11:46,260 --> 00:11:49,580
+بس في عندنا كمان volume of charge إيش عرفنا ال
+
+151
+00:11:49,580 --> 00:11:53,120
+point volume of charge هي minus diverse B يعني أنا
+
+152
+00:11:53,120 --> 00:12:00,210
+إيش بدي أسوي بدي أفاضل d by dxx hat dot b ذائق d
+
+153
+00:12:00,210 --> 00:12:05,590
+by dy y hat dot b و هكذا ايش هيصير ان دي xx فمين
+
+154
+00:12:05,590 --> 00:12:14,230
+لل x ذائق d by dy لل y واضح هنا
+
+155
+00:12:14,230 --> 00:12:20,610
+ال raw b فعمل b تسوى و minus ده درجة b تسوى و
+
+156
+00:12:20,610 --> 00:12:23,190
+minus d by dx x hat
+
+157
+00:12:36,000 --> 00:12:43,640
+ماذا بيقف ايه؟ constant طبعا
+
+158
+00:12:43,640 --> 00:12:47,240
+من dot ال product هذي dot تمامي بيظل x ايش هيكون
+
+159
+00:12:47,240 --> 00:12:53,680
+minus a dx by dx واحد ال dot ال product ال y هذين
+
+160
+00:12:53,680 --> 00:12:55,900
+هيظل معاه بس هذي هيكون zero
+
+161
+00:13:06,330 --> 00:13:12,220
+واضح؟أذا ال volume charge density هتكون minus
+
+162
+00:13:12,220 --> 00:13:15,720
+ثلاثة a بيدي ال total charge هكامل على ال volume
+
+163
+00:13:15,720 --> 00:13:19,040
+هتعطيني minus ثلاثة a cubed لإن ال volume إيش
+
+164
+00:13:19,040 --> 00:13:22,640
+بيساوي الطول في العرض في الارتفاع ألف ألف ألب
+
+165
+00:13:22,640 --> 00:13:25,240
+هتعطيني أقل ال cube إذا بتطلعنا نلاقي أن ال
+
+166
+00:13:25,240 --> 00:13:30,660
+surfaceتلاتة A قلت Q و ال volume minus ثلاثة A و
+
+167
+00:13:30,660 --> 00:13:34,240
+هذا أثبتناه المحاضرة الماضية أنه ماله ال
+
+168
+00:13:34,240 --> 00:13:38,660
+dielectric ماله ال total charge بتساوي سفر لأنه
+
+169
+00:13:38,660 --> 00:13:42,100
+ماله neutral هو صح صلّه polarization و صلّه فيه
+
+170
+00:13:42,100 --> 00:13:45,620
+pound surface polarized charge و في عندى pound
+
+171
+00:13:45,620 --> 00:13:49,140
+volume من pound يعني معناه مالها مربوطة يعني في
+
+172
+00:13:49,140 --> 00:13:52,120
+النهاية مافيش عندى أنا total charge ال total
+
+173
+00:13:52,120 --> 00:13:55,710
+charge سفر و هذا احنا أثبتناه بالتي استخدمتها من
+
+174
+00:13:55,710 --> 00:13:58,630
+الـ divergence theorem إذا ما الذاكرين وطلعت برضه
+
+175
+00:13:58,630 --> 00:14:02,870
+معنى بتساوي 0 الـ dielectric sphere اللي هي
+
+176
+00:14:02,870 --> 00:14:06,690
+epsilon r ال relative permittivity 5 و 7 و 10 و ال
+
+177
+00:14:06,690 --> 00:14:09,930
+radius تبعها 10 سانتي اللي هي pointed charge اتنين
+
+178
+00:14:09,930 --> 00:14:15,290
+بيكوكولوم عادة على ال center تبعهابتمام؟ بدنا ال
+
+179
+00:14:15,290 --> 00:14:18,150
+surface density of polarization charged on the
+
+180
+00:14:18,150 --> 00:14:20,990
+surface of the sphere و بعدين ال force اللي
+
+181
+00:14:20,990 --> 00:14:27,250
+exerted على charge on a 4 minus 4 column point
+
+182
+00:14:27,250 --> 00:14:32,400
+charge placed on the sphereأول حاجة هو طالب مننا
+
+183
+00:14:32,400 --> 00:14:34,620
+ايش ال density of polarization charged on the
+
+184
+00:14:34,620 --> 00:14:40,200
+surface sphere بده هذه ال raw اللي هي P dot A R
+
+185
+00:14:40,200 --> 00:14:43,440
+hat او P dot R hat بده اجيب P بده اجيب ال diagonal
+
+186
+00:14:43,440 --> 00:14:46,860
+moment مش معطينيها مش معطيني ال polarization عشان
+
+187
+00:14:46,860 --> 00:14:49,680
+اجيب polarization بده اجيب مين E اذا جبت ال
+
+188
+00:14:49,680 --> 00:14:51,760
+electric field بده اجيب ال polarization ان ال
+
+189
+00:14:51,760 --> 00:14:54,060
+polarization ايه ايش العلاقة بينهم it's a
+
+190
+00:14:54,060 --> 00:14:58,130
+stability في epsilon naughtفأول حاجة بجيب ال
+
+191
+00:14:58,130 --> 00:15:01,110
+electric field اللي هو ناتج عن اللي هي ال
+
+192
+00:15:01,110 --> 00:15:05,330
+dielectric sphere اللي لها point of charge placed
+
+193
+00:15:05,330 --> 00:15:08,650
+at its center بحسب اللي هي ال electric field من
+
+194
+00:15:08,650 --> 00:15:11,530
+هذه ال point of charge و بعدين بقى أجيب اللي هو
+
+195
+00:15:11,530 --> 00:15:16,530
+surface charge density و بعدين بستخدم كولوم laws
+
+196
+00:15:16,530 --> 00:15:20,190
+عشان أجيب ال force واضح؟ و اللقاء القادم إحنا
+
+197
+00:15:20,190 --> 00:15:26,450
+بنكمل الموضوع اللي أمامنا أنه إن شاء اللهوحلقات
+
+198
+00:15:26,450 --> 00:15:27,210
+ومقامارات
+
diff --git a/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/SXNt5y2mt6I_raw.json b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/SXNt5y2mt6I_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..2866569462c9143d514cffb0a60b1ed112d59ef6
--- /dev/null
+++ b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/SXNt5y2mt6I_raw.json
@@ -0,0 +1 @@
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new file mode 100644
index 0000000000000000000000000000000000000000..8edd5dbbbab61fcec673dcced1330c3087d1d82e
--- /dev/null
+++ b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/SXNt5y2mt6I_raw.srt
@@ -0,0 +1,792 @@
+1
+00:00:20,650 --> 00:00:22,710
+بسم الله الرحمن الرحيم السلام عليكم ورحمة الله
+
+2
+00:00:22,710 --> 00:00:26,130
+وبركاته احنا اليوم ان شاء الله هنتبع موضوعنا اللي
+
+3
+00:00:26,130 --> 00:00:29,090
+هو ال field في المادة يعني every field in the
+
+4
+00:00:29,090 --> 00:00:34,090
+materials احنا المحاضرة الماضية شوفنا كيف انه ال D
+
+5
+00:00:34,090 --> 00:00:42,070
+و E برتبطوا بعلاقة اللي هي Epsilon ED بيسوي
+
+6
+00:00:42,070 --> 00:00:46,010
+Epsilon E قولنا طبيعة هاي العلاقة ممكن اقول عنها
+
+7
+00:00:46,010 --> 00:00:50,310
+Linear هموجنس حسب ايش هي ال Epsilon هاي او ممكن
+
+8
+00:00:50,310 --> 00:00:53,990
+اقول عنها non-linear, non-homogeneous, anisotropic
+
+9
+00:00:53,990 --> 00:00:56,970
+وها كذا قولنا ايش اللي بيحددلها الأشياء هي ايش في
+
+10
+00:00:56,970 --> 00:01:01,810
+وضعية D ال Epsilon بتاعتنا اول حاجة ممكن نقول ان D
+
+11
+00:01:01,810 --> 00:01:05,490
+اذا كانت ناسب قرضيا مع E او Linear ليه بنقول عنها
+
+12
+00:01:05,490 --> 00:01:09,270
+Linear يعني زي ما اتفقنا مافيش عندنا E تربيع او EQ
+
+13
+00:01:10,700 --> 00:01:14,800
+لأن ممكن يكون العلاقة فيها terms أعلى، لكن مثلا هي
+
+14
+00:01:14,800 --> 00:01:17,640
+كده، احنا بنحكي عن linear، مقتش بيصير non-linear
+
+15
+00:01:17,640 --> 00:01:20,580
+بيصير عندنا مثلا ال field جاية من ال laser، high
+
+16
+00:01:20,580 --> 00:01:23,540
+intensity laser، فبيصير عندنا E E و تربية و الأخر،
+
+17
+00:01:23,540 --> 00:01:28,100
+يعني الباقي ال polarization بتصير بتتنسب مع Chi P,
+
+18
+00:01:28,440 --> 00:01:32,720
+Chi E, Chi E تربية و الأخرهذا الـ Linearity قلنا
+
+19
+00:01:32,720 --> 00:01:37,580
+إذا D تتناسب مع E فقط كمان قلنا إذا إبسلون أو
+
+20
+00:01:37,580 --> 00:01:41,700
+سيجما في حالة الـ J يتساوى سيجما E و يتساوى D
+
+21
+00:01:41,700 --> 00:01:51,220
+يتساوى إبسلون E يتساوى D يتساوى إبسلون E يتساوى D
+
+22
+00:01:51,220 --> 00:01:55,660
+يتساوى إبسلون E يتساوى إبسلون E يتساوى سيجما E
+
+23
+00:01:55,660 --> 00:01:59,460
+يتساوى إبسلون E يتساوى سيجما E يتساوى إبسلون E
+
+24
+00:01:59,460 --> 00:01:59,720
+يتساوى إبسلون E يتساوى إبسلون E يتساوى إبسلون E
+
+25
+00:01:59,720 --> 00:02:00,100
+يتساوى إبسلون E يتسا
+
+26
+00:02:06,020 --> 00:02:09,420
+معادلة مقلاقتها ال E-linear الكلام اللي نقدر نقول
+
+27
+00:02:09,420 --> 00:02:13,400
+عنها هو homogenous إذا كانت أسواء epsilon ولا
+
+28
+00:02:13,400 --> 00:02:17,820
+sigma باعتمدوش على ال vector space يعني باعتمدوش
+
+29
+00:02:17,820 --> 00:02:20,980
+على x و y و z يعني في كل نقطة من ال space بنلاقيها
+
+30
+00:02:20,980 --> 00:02:24,600
+نفس القيمة بكون homogenous لو كانت بتختلف حسب
+
+31
+00:02:24,600 --> 00:02:28,000
+موقعها حسب ال vector space بنسميها inhomogeneous
+
+32
+00:02:28,000 --> 00:02:36,200
+كمان احنا قلنا ان ال DUEممكن تكون isotropic إذا
+
+33
+00:02:36,200 --> 00:02:41,100
+بتعتمدش على ال direction يعني إذا كانت إذا اتجاهها
+
+34
+00:02:41,100 --> 00:02:44,100
+بهذا الاتجاه بتكون قيمتها مختلفة عن هذا الاتجاه
+
+35
+00:02:44,100 --> 00:02:48,180
+بتكون an isotropic لكن إذا كانت في أي اتجاه لو
+
+36
+00:02:48,180 --> 00:02:52,480
+قستها في أي direction يبقى نفس القيمة بتكون
+
+37
+00:02:52,480 --> 00:02:53,120
+isotropic
+
+38
+00:02:57,200 --> 00:02:59,920
+طبعا اذا احنا بنحكي عن isotropic اللي هو قلنا ايش
+
+39
+00:02:59,920 --> 00:03:02,900
+قلنا في ال isotropic انها بتعتمد على الاتجاه
+
+40
+00:03:02,900 --> 00:03:08,980
+بيكونه E وD وB مش parallel احنا معناه لما يكون نفس
+
+41
+00:03:08,980 --> 00:03:12,880
+الاتجاه معناه انه E if it is isotropic وD بيكونوا
+
+42
+00:03:12,880 --> 00:03:15,620
+في نفس الاتجاه E وG بيكونوا في نفس الاتجاه
+
+43
+00:03:23,500 --> 00:03:28,400
+ماتريكس ماتريكس اللى بتوضح للاعتمادية على ال
+
+44
+00:03:28,400 --> 00:03:33,540
+direction زى ما احنا هنشوف هنا عند DXاش هتكون مش
+
+45
+00:03:33,540 --> 00:03:36,980
+في نفس الاتجاه EX فيلها components في اتجاه ال EY
+
+46
+00:03:36,980 --> 00:03:43,170
+و EZ عند DXاش هتكون يبسلون XXEXplus epsilon xy ey
+
+47
+00:03:43,170 --> 00:03:48,390
+plus epsilon xz ez طبعا طبيعة ال materials بتختلف
+
+48
+00:03:48,390 --> 00:03:52,390
+أو تصلف ال crystalline material حسب مين السفر في
+
+49
+00:03:52,390 --> 00:03:56,830
+هدولة ومين المسافر فيهم يعني بتكون symmetric مثلا
+
+50
+00:03:56,830 --> 00:04:00,870
+هدولة ال materials بتكونوا symmetric إذا كانوا ال
+
+51
+00:04:00,870 --> 00:04:06,630
+exz بتساوي ال epsilon xz بتساوي ال zx بتكون
+
+52
+00:04:06,630 --> 00:04:09,970
+symmetric ال epsilon xy بتساوي ال epsilon
+
+53
+00:04:35,940 --> 00:04:37,340
+YZYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
+
+54
+00:04:39,330 --> 00:04:42,070
+طبعا كل حاجة زي ما حكيت مسميات، يعني أنتم ممكن
+
+55
+00:04:42,070 --> 00:04:45,630
+تلاقوهم في كتب متعددة لل materials اللي بيصنفوا
+
+56
+00:04:45,630 --> 00:04:50,630
+طبيعة الاستجابة ل electric field حسب مين فدولة
+
+57
+00:04:50,630 --> 00:04:53,130
+يعني هم بدرسوهم في المختبرات و بيحسبوا قيم ال
+
+58
+00:04:53,130 --> 00:04:55,430
+excellence و برضه ممكن يحسبوا رياضي ..
+
+59
+00:04:55,430 --> 00:04:59,570
+mathematically و يتقانوهم في بعض مين فيهم سفر و
+
+60
+00:04:59,570 --> 00:05:03,010
+مين فيهم السفر، إذا في عندهم سوالب يعني بيسووا بعض
+
+61
+00:05:03,010 --> 00:05:07,920
+بس سالب، إيش طبيعة المادة و هكذاهذه هي جزء من
+
+62
+00:05:07,920 --> 00:05:12,120
+تعريف اللي هي ال materials حسب هل هي symmetric و
+
+63
+00:05:12,120 --> 00:05:15,640
+لا antisymmetric ايش هم ال zero من فيهم ال zero من
+
+64
+00:05:15,640 --> 00:05:21,800
+فيهم ال zero من هدول ال components هكذا
+
+65
+00:05:21,800 --> 00:05:26,100
+انا بمقدر اقول انه سانا فاهمين ايش العلاقة دي و
+
+66
+00:05:26,100 --> 00:05:30,920
+اكسل او ايه اذا مش دائما diverse
+
+67
+00:05:34,550 --> 00:05:40,750
+دى اللى بتساوي روه دائما هى بقدر اقول انه تاجرش دى
+
+68
+00:05:40,750 --> 00:05:47,150
+بتساوي روه على إبسلون مش دائما واضح؟
+
+69
+00:05:47,150 --> 00:05:52,710
+ليش؟ لإن هنا دى بادر إبسلون دى مش دائما بقدر يطلع
+
+70
+00:05:52,710 --> 00:05:56,130
+إبسلون ال divergence وقت إش بقدرش يطلعها لما تكون
+
+71
+00:05:56,130 --> 00:05:59,850
+هى مالها بتعتمد على X وY وZ ان هو genus لإنها
+
+72
+00:05:59,850 --> 00:06:03,590
+بيصير هى تفاضل two componentsلكن إذا كانت Linear
+
+73
+00:06:03,590 --> 00:06:08,530
+أو Homogeneous بقدر أطلّها من الـDifferential فإذا
+
+74
+00:06:08,530 --> 00:06:14,290
+مش دائما هذا الحكيم بتبسط لهذا الحكيم فقط في
+
+75
+00:06:14,290 --> 00:06:17,090
+الـFree Space كنا بسهولة نقول الـdiversity بتثوره
+
+76
+00:06:17,090 --> 00:06:18,850
+على الـEpsilon نقطة، إحنا عارفين الـEpsilon نقطة
+
+77
+00:06:18,850 --> 00:06:22,290
+مالها، constant، اللي هي تاعة الـSpace لكن لو
+
+78
+00:06:22,290 --> 00:06:25,150
+بدحكي عن الـmaterial، بدكون حذرة إيش طبيعة
+
+79
+00:06:25,150 --> 00:06:28,690
+الـmaterial قبل ما أقول إن الـEpsilon بقدر أطلّها
+
+80
+00:06:28,690 --> 00:06:30,190
+من قلب الـDifferential؟
+
+81
+00:06:40,440 --> 00:06:43,520
+هذا اللي انا حكيته يعني انه لل materials بدأ اكون
+
+82
+00:06:43,520 --> 00:06:47,760
+حذرة ايش طبيعة المادة قبل ما احكي عن العلاقات اللي
+
+83
+00:06:47,760 --> 00:06:51,280
+تربط المادة بال electric field لكن لو احنا بنحكي
+
+84
+00:06:51,280 --> 00:06:55,120
+على free space بساطة بحكي على ال epsilon not
+
+85
+00:06:55,120 --> 00:06:59,660
+العلاقات كلها اللي درسناها ل free space بتنطبق على
+
+86
+00:06:59,660 --> 00:07:03,160
+ال material space كليتها الفرقية اني بستبدل
+
+87
+00:07:03,160 --> 00:07:06,680
+epsilon not ب epsilon يعني الفرصة اللي متذكرينها
+
+88
+00:07:06,680 --> 00:07:11,820
+لما حكينا على ال free spaceماذا تسوي ال force؟
+
+89
+00:07:11,820 --> 00:07:16,160
+تذكرينها؟ بين two charges following force اكيو
+
+90
+00:07:16,160 --> 00:07:21,380
+واحد اكيو تنين على four by epsilon not صح في R
+
+91
+00:07:21,380 --> 00:07:26,080
+تربية في R هذا او R بيكتروا على RQ او يعني هاخدوا
+
+92
+00:07:26,080 --> 00:07:30,760
+اكتروا عشان في الار ليه ال R minus R براية تمام؟
+
+93
+00:07:30,760 --> 00:07:36,980
+لكن في ال .. هذه في ال free space في ال material
+
+94
+00:07:36,980 --> 00:07:45,470
+space ايش بتصير؟الـ Q1 و Q2 على 4Y إبسلون R تربيع
+
+95
+00:07:45,470 --> 00:07:50,050
+في R تقريبًا طبعًا إبسلون إيش قلنا علفناها إحنا هي
+
+96
+00:07:50,050 --> 00:07:53,730
+إبسلون نط في إبسلون R متذاكرين قلنا إبسلون R هي
+
+97
+00:07:53,730 --> 00:07:56,610
+relative permittivity اللي بتسوى إبسلون على إبسلون
+
+98
+00:07:56,610 --> 00:08:02,260
+نطأبسلون بقدر اكتبها بهذا الشكل بدل ابسلون نوت
+
+99
+00:08:02,260 --> 00:08:04,880
+باستخدام ابسلون بتاعة ال material باستخدام
+
+100
+00:08:04,880 --> 00:08:07,020
+permittivity بتاعة ال free space باستخدام
+
+101
+00:08:07,020 --> 00:08:09,900
+permittivity بتاعة ال material اللي هي بتساوي
+
+102
+00:08:09,900 --> 00:08:13,200
+ابسلون نوت في ابسلون R ابسلون R ان هي relative
+
+103
+00:08:13,200 --> 00:08:16,480
+permittivity لالمaterial نفس الاشي ل ال total
+
+104
+00:08:16,480 --> 00:08:19,860
+energy ال total energy كانت عندنا نص الintegral
+
+105
+00:08:19,860 --> 00:08:23,700
+لأبسلون E تربيه EV بدل ابسلون بستخدمها ابسلون نوت
+
+106
+00:08:23,700 --> 00:08:32,960
+ابسلون Rواضح؟ في أي استفسار لحد هنا؟ نشوف مثال إن
+
+107
+00:08:32,960 --> 00:08:37,660
+قضيت electrical cube of side L، يعني عندك cube وكل
+
+108
+00:08:37,660 --> 00:08:43,360
+side له thing to I ونقعد at the origin، يعني ال
+
+109
+00:08:43,360 --> 00:08:48,350
+center تبعه بالترابع مع ال originالسينتر تبع ال
+
+110
+00:08:48,350 --> 00:08:51,890
+cube at the origin باضح؟ إذا السينتر تبعه at the
+
+111
+00:08:51,890 --> 00:08:56,270
+origin يعني عندي X فيها L على 2 و minus X فيها L
+
+112
+00:08:56,270 --> 00:09:01,530
+على 2 Y فيها L على 2 و minus Y minus L على 2 و زد
+
+113
+00:09:01,530 --> 00:09:06,110
+عندي L على 2 و minus L على 2 لأنه عارف من السينتر
+
+114
+00:09:06,110 --> 00:09:11,310
+has a radial polarization given by P بساوية R hat
+
+115
+00:09:11,310 --> 00:09:14,370
+ال polarization ماتينياها اللي هي
+
+116
+00:09:30,200 --> 00:09:32,580
+عرفنا المحاضر الماضي عن الـ bounded charges في
+
+117
+00:09:32,580 --> 00:09:35,840
+عندنا surface و في عندنا volume bounded charges ال
+
+118
+00:09:35,840 --> 00:09:38,600
+surface قولنا ال charge density بتاع التقاشية ال
+
+119
+00:09:38,600 --> 00:09:43,000
+polarization في ال normal على ال surfaceمتذكرين ال
+
+120
+00:09:43,000 --> 00:09:47,100
+surface بقول P dot ال normal على ال surface فاحنا
+
+121
+00:09:47,100 --> 00:09:51,040
+ناخد واحد من ال sides بتاعة ال cube ناخد واحد من
+
+122
+00:09:51,040 --> 00:09:54,820
+ال side مثلا ال side اللي على ال x axis اللي واقف
+
+123
+00:09:54,820 --> 00:10:00,220
+مثلا ناخد عند x بتساوي L على 2 اللي ال side اللي
+
+124
+00:10:00,220 --> 00:10:03,260
+واقف عند L على 2 ايش اللي عمودي عليه هيكون اللي هو
+
+125
+00:10:03,260 --> 00:10:07,220
+ال normاللي وقف على ال X-axis، إيش بده يكون ال
+
+126
+00:10:07,220 --> 00:10:11,480
+sites بتاعه؟ اللي هي ال Y و ال Z، صح؟ إذا العمود
+
+127
+00:10:11,480 --> 00:10:13,900
+اللي علي يميني بده يكون X hat، اللي عند ال
+
+128
+00:10:13,900 --> 00:10:18,060
+positive X بتساوية L على 2، ال sites بتاعه يكونوا
+
+129
+00:10:18,060 --> 00:10:23,420
+Y و Z، فهيكون ال normal إيه؟ X hat، فعندي AR
+
+130
+00:10:23,420 --> 00:10:31,430
+vector dot X hat إيش هيضل عنديه؟ A X، صح؟لأن a x x
+
+131
+00:10:31,430 --> 00:10:36,310
+hat dot x hat هتكون ax إذا ال charge density ال
+
+132
+00:10:36,310 --> 00:10:41,230
+surface density لواحد من ال surfaces هي ax لو بدأ
+
+133
+00:10:41,230 --> 00:10:45,670
+أكملها من هو لوان ال x أو يعني قيمة متأسفة قيمة ال
+
+134
+00:10:45,670 --> 00:10:48,610
+x عندها اللحظة إيش بتساوي قلع على اتنين لأن حاخدنا
+
+135
+00:10:48,610 --> 00:10:53,130
+ال surface اللي عندها قلع على اتنين صحيح؟ تمام ال
+
+136
+00:10:53,130 --> 00:10:56,390
+total charge إيش بدها تساوي ال integral رو دي أس
+
+137
+00:10:57,140 --> 00:11:01,500
+بدي أكامل ال integral ل raw دي أصل and كل واحدة من
+
+138
+00:11:01,500 --> 00:11:05,240
+هدول ال size هيكون قيمة ال surface charge density
+
+139
+00:11:05,240 --> 00:11:10,490
+A فئة على اتنينأذا بدروحها في ستة و DS مين هتكون
+
+140
+00:11:10,490 --> 00:11:13,110
+التكامل على ال links من minus ألعة اتنين ل plus
+
+141
+00:11:13,110 --> 00:11:17,010
+ألعة اتنين انه كل surface انا باخد كل surface بجيب
+
+142
+00:11:17,010 --> 00:11:21,430
+ال total charge لكل surface اللي هي التكامل روه DS
+
+143
+00:11:21,430 --> 00:11:26,610
+و بدروحها في ستة اللي هي ست أو جهلة المكعب فكونت
+
+144
+00:11:26,610 --> 00:11:29,090
+ستة تكامل من minus ألعة اتنين ل ألعة اتنين تكامل
+
+145
+00:11:29,090 --> 00:11:32,780
+من minus ألعة اتنين ل ألعة اتنينرو دي رو بي أصلي
+
+146
+00:11:32,780 --> 00:11:35,520
+هي point of charge surface point of charge دي وي
+
+147
+00:11:35,520 --> 00:11:39,660
+دي زد إذا كملنا على هذا الجزء وضربته في ستة قلنا
+
+148
+00:11:39,660 --> 00:11:42,900
+لإنه عندي ست أوجه بطلع معايا إن surface of charge
+
+149
+00:11:42,900 --> 00:11:46,260
+بتاو تلاتة A قل ال Q هيجنسه على surface of charge
+
+150
+00:11:46,260 --> 00:11:49,580
+بس في عندنا كمان volume of charge إيش عرفنا ال
+
+151
+00:11:49,580 --> 00:11:53,120
+point volume of charge هي minus diverse B يعني أنا
+
+152
+00:11:53,120 --> 00:12:00,210
+إيش بدي أسوي بدي أفاضل d by dxx hat dot b ذائق d
+
+153
+00:12:00,210 --> 00:12:05,590
+by dy y hat dot b و هكذا ايش هيصير ان دي xx فمين
+
+154
+00:12:05,590 --> 00:12:14,230
+لل x ذائق d by dy لل y واضح هنا
+
+155
+00:12:14,230 --> 00:12:20,610
+ال raw b فعمل b تسوى و minus ده درجة b تسوى و
+
+156
+00:12:20,610 --> 00:12:23,190
+minus d by dx x hat
+
+157
+00:12:36,000 --> 00:12:43,640
+ماذا بيقف ايه؟ constant طبعا
+
+158
+00:12:43,640 --> 00:12:47,240
+من dot ال product هذي dot تمامي بيظل x ايش هيكون
+
+159
+00:12:47,240 --> 00:12:53,680
+minus a dx by dx واحد ال dot ال product ال y هذين
+
+160
+00:12:53,680 --> 00:12:55,900
+هيظل معاه بس هذي هيكون zero
+
+161
+00:13:06,330 --> 00:13:12,220
+واضح؟أذا ال volume charge density هتكون minus
+
+162
+00:13:12,220 --> 00:13:15,720
+ثلاثة a بيدي ال total charge هكامل على ال volume
+
+163
+00:13:15,720 --> 00:13:19,040
+هتعطيني minus ثلاثة a cubed لإن ال volume إيش
+
+164
+00:13:19,040 --> 00:13:22,640
+بيساوي الطول في العرض في الارتفاع ألف ألف ألب
+
+165
+00:13:22,640 --> 00:13:25,240
+هتعطيني أقل ال cube إذا بتطلعنا نلاقي أن ال
+
+166
+00:13:25,240 --> 00:13:30,660
+surfaceتلاتة A قلت Q و ال volume minus ثلاثة A و
+
+167
+00:13:30,660 --> 00:13:34,240
+هذا أثبتناه المحاضرة الماضية أنه ماله ال
+
+168
+00:13:34,240 --> 00:13:38,660
+dielectric ماله ال total charge بتساوي سفر لأنه
+
+169
+00:13:38,660 --> 00:13:42,100
+ماله neutral هو صح صلّه polarization و صلّه فيه
+
+170
+00:13:42,100 --> 00:13:45,620
+pound surface polarized charge و في عندى pound
+
+171
+00:13:45,620 --> 00:13:49,140
+volume من pound يعني معناه مالها مربوطة يعني في
+
+172
+00:13:49,140 --> 00:13:52,120
+النهاية مافيش عندى أنا total charge ال total
+
+173
+00:13:52,120 --> 00:13:55,710
+charge سفر و هذا احنا أثبتناه بالتي استخدمتها من
+
+174
+00:13:55,710 --> 00:13:58,630
+الـ divergence theorem إذا ما الذاكرين وطلعت برضه
+
+175
+00:13:58,630 --> 00:14:02,870
+معنى بتساوي 0 الـ dielectric sphere اللي هي
+
+176
+00:14:02,870 --> 00:14:06,690
+epsilon r ال relative permittivity 5 و 7 و 10 و ال
+
+177
+00:14:06,690 --> 00:14:09,930
+radius تبعها 10 سانتي اللي هي pointed charge اتنين
+
+178
+00:14:09,930 --> 00:14:15,290
+بيكوكولوم عادة على ال center تبعهابتمام؟ بدنا ال
+
+179
+00:14:15,290 --> 00:14:18,150
+surface density of polarization charged on the
+
+180
+00:14:18,150 --> 00:14:20,990
+surface of the sphere و بعدين ال force اللي
+
+181
+00:14:20,990 --> 00:14:27,250
+exerted على charge on a 4 minus 4 column point
+
+182
+00:14:27,250 --> 00:14:32,400
+charge placed on the sphereأول حاجة هو طالب مننا
+
+183
+00:14:32,400 --> 00:14:34,620
+ايش ال density of polarization charged on the
+
+184
+00:14:34,620 --> 00:14:40,200
+surface sphere بده هذه ال raw اللي هي P dot A R
+
+185
+00:14:40,200 --> 00:14:43,440
+hat او P dot R hat بده اجيب P بده اجيب ال diagonal
+
+186
+00:14:43,440 --> 00:14:46,860
+moment مش معطينيها مش معطيني ال polarization عشان
+
+187
+00:14:46,860 --> 00:14:49,680
+اجيب polarization بده اجيب مين E اذا جبت ال
+
+188
+00:14:49,680 --> 00:14:51,760
+electric field بده اجيب ال polarization ان ال
+
+189
+00:14:51,760 --> 00:14:54,060
+polarization ايه ايش العلاقة بينهم it's a
+
+190
+00:14:54,060 --> 00:14:58,130
+stability في epsilon naughtفأول حاجة بجيب ال
+
+191
+00:14:58,130 --> 00:15:01,110
+electric field اللي هو ناتج عن اللي هي ال
+
+192
+00:15:01,110 --> 00:15:05,330
+dielectric sphere اللي لها point of charge placed
+
+193
+00:15:05,330 --> 00:15:08,650
+at its center بحسب اللي هي ال electric field من
+
+194
+00:15:08,650 --> 00:15:11,530
+هذه ال point of charge و بعدين بقى أجيب اللي هو
+
+195
+00:15:11,530 --> 00:15:16,530
+surface charge density و بعدين بستخدم كولوم laws
+
+196
+00:15:16,530 --> 00:15:20,190
+عشان أجيب ال force واضح؟ و اللقاء القادم إحنا
+
+197
+00:15:20,190 --> 00:15:26,450
+بنكمل الموضوع اللي أمامنا أنه إن شاء اللهوحلقات
+
+198
+00:15:26,450 --> 00:15:27,210
+ومقامارات
+
diff --git a/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/T2PklTp3S9c_postprocess.srt b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/T2PklTp3S9c_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..071646e8c6189c228cf044fb65febe0296decb06
--- /dev/null
+++ b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/T2PklTp3S9c_postprocess.srt
@@ -0,0 +1,2180 @@
+1
+00:00:20,670 --> 00:00:23,810
+بسم الله الرحمن الرحيم السلام عليكم ورحمة الله
+
+2
+00:00:23,810 --> 00:00:27,110
+وبركاته احنا اليوم ان شاء الله هنشوف أمثلة مباشرة
+
+3
+00:00:27,110 --> 00:00:29,890
+عن boundary condition problems هنشوف الطريقتين
+
+4
+00:00:29,890 --> 00:00:33,730
+هنشوف كيف لو يكون ال potential بس function واحد من
+
+5
+00:00:33,730 --> 00:00:36,290
+المتغيرات كيف انه بنعمل بال integration ونحصل على
+
+6
+00:00:36,290 --> 00:00:39,910
+نتائجو طبعا بيستعمل ال boundary conditions و
+
+7
+00:00:39,910 --> 00:00:42,230
+الحالة التانية انه هنشوف كيف ال separation
+
+8
+00:00:42,230 --> 00:00:44,530
+variable المعناه بيكون potential بعتمد على ال X و
+
+9
+00:00:44,530 --> 00:00:48,550
+ال Y و ال Z هنبدأ بالمثال اللي قدامنا المثال اللي
+
+10
+00:00:48,550 --> 00:00:51,530
+أمامنا يقول ان فيه اللي current carrying
+
+11
+00:00:51,530 --> 00:00:54,450
+components in high voltage power equipment must
+
+12
+00:00:54,450 --> 00:00:57,390
+يكون يعني ما يكون يعني ان ال components بتحمل
+
+13
+00:00:57,390 --> 00:01:01,310
+طيارات في high voltage لازم نبردها الطريقة اللي
+
+14
+00:01:01,310 --> 00:01:03,950
+بحكي عنها بيسموها ال electrohydronic
+
+15
+00:01:06,130 --> 00:01:10,470
+power أو يعني pump, electro hydronic pump ليه EHD؟
+
+16
+00:01:10,470 --> 00:01:13,490
+هذه بتستخدم عشان تعمل cooling لاللي هي ال
+
+17
+00:01:13,490 --> 00:01:16,930
+components في ال high voltageالفكرة بتاعتها انه
+
+18
+00:01:16,930 --> 00:01:20,910
+بيكون فينا electronic .. يعني الشحنات بتصدر من
+
+19
+00:01:20,910 --> 00:01:26,030
+يعني بسلها استحداث في أحد ال electrode و بتروح ال
+
+20
+00:01:26,030 --> 00:01:29,730
+electrode التاني و هي بتحرك و بتنقل الحرارة فبتبرد
+
+21
+00:01:29,730 --> 00:01:32,770
+ال electrical components طب عندنا معناه الفين
+
+22
+00:01:32,770 --> 00:01:36,050
+different charges مثلا بحكي عن charges او يعني
+
+23
+00:01:36,050 --> 00:01:41,660
+توليد للشحناتفي عندي free charges هو معطينا ان ال
+
+24
+00:01:41,660 --> 00:01:44,720
+charge density قيمتها روزيرو وانها uniform يعني لا
+
+25
+00:01:44,720 --> 00:01:48,060
+بتعتمد على X ولا V ولا Z كونستان قيمتها خمس و
+
+26
+00:01:48,060 --> 00:01:53,280
+عشرين ميلي كولوم بميتر اكيورو V not اللي هي عند Z
+
+27
+00:01:53,280 --> 00:01:58,600
+equal zero اتنين و عشر كيلو فولت او V عند ال D
+
+28
+00:01:58,600 --> 00:02:02,120
+بسوا زيرو اذا هذه هي الاستوانة اللي بتمثل ال
+
+29
+00:02:02,120 --> 00:02:08,070
+electro hydrodynamics pump اش طالب منها؟طالب مننا
+
+30
+00:02:08,070 --> 00:02:13,430
+ان نجيب ال retention و ال voltage طبعا و ال
+
+31
+00:02:13,430 --> 00:02:19,050
+electric field و ال total charge نبدأ في انه احنا
+
+32
+00:02:19,050 --> 00:02:21,930
+ع طرفنا كلها انه في different charges اذا ال
+
+33
+00:02:21,930 --> 00:02:24,550
+charge معناها لا تسوى zero اذا بستخدمي لبلاس
+
+34
+00:02:24,550 --> 00:02:29,910
+equation اللي بمعنى ان دل التطبيع V بتسوى equation
+
+35
+00:02:29,910 --> 00:02:33,210
+بمعنى ان رو V لا تسوى Zero لما بيكون Zero قولنا
+
+36
+00:02:33,210 --> 00:02:36,450
+بنسميه لبلاس بس هم equationsإذا بنستخدم بسهولة
+
+37
+00:02:36,450 --> 00:02:40,290
+equation لإن دلتر بيع V بيسوا minus رو V على
+
+38
+00:02:40,290 --> 00:02:44,150
+إبسلون إحنا قلنا رو V ما لها constant، uniform إذا
+
+39
+00:02:44,150 --> 00:02:47,350
+بقدر أعوض عن رو V برا 0 إيش ال boundary conditions
+
+40
+00:02:47,350 --> 00:02:50,150
+اللي استعملنا اللي أنا حكيتهم معاكم، قرأتهم معاكم
+
+41
+00:02:50,150 --> 00:02:55,830
+and V at Z equals 0 بتسوا V نول و V at Z equals D
+
+42
+00:02:55,830 --> 00:02:59,130
+بتسوا 0 وكمان حاجة بلاحظها إن ال potential ماله
+
+43
+00:02:59,130 --> 00:03:02,910
+بقت متفقت على ال Z direction لا ال component في ال
+
+44
+00:03:02,910 --> 00:03:06,600
+raw ولا في ال Phiيعني لا كمبونات في اتجاه ال raw
+
+45
+00:03:06,600 --> 00:03:09,640
+ولا كمبونات في اتجاه ال fire ال potential هيكون ما
+
+46
+00:03:09,640 --> 00:03:12,840
+بين ال two electrodes هيكون ما بين ال z equal zero
+
+47
+00:03:12,840 --> 00:03:15,700
+و ال z equal d ال potential ما بين هدول المقاطين
+
+48
+00:03:15,700 --> 00:03:19,760
+اذا بقيت فقط على ال z direction اذا هذه المعلومات
+
+49
+00:03:19,760 --> 00:03:22,700
+صارت معنا ان نحط بيها بسوء equation بتقول ان دل
+
+50
+00:03:22,700 --> 00:03:28,710
+تربيع v بتسوي minus rho v على epsilonطبعا قولنا V
+
+51
+00:03:28,710 --> 00:03:32,350
+مالها بتعتمد فقط على Z وD التربية في ال
+
+52
+00:03:32,350 --> 00:03:34,850
+cylindrical coordinate احنا شوفنا المحاضرة الماضية
+
+53
+00:03:34,850 --> 00:03:38,750
+في component بتعتمد على ال raw واحدة بتعتمد على ال
+
+54
+00:03:38,750 --> 00:03:42,730
+Phi والثانية بتعتمد على ال Z دي V بي دي رو زيرو دي
+
+55
+00:03:42,730 --> 00:03:46,750
+V بي دي Phi زيرو ميبضل ان دي تانية V بي دي Z تربية
+
+56
+00:03:46,750 --> 00:03:50,920
+اذا انت تتبسط المعادلة اللي امامنالأ دي تربيه V
+
+57
+00:03:50,920 --> 00:03:55,300
+على دي تربيه Z بيساومها نصره نض على إبسرون، إبسرون
+
+58
+00:03:55,300 --> 00:03:58,600
+اللي هي ال dialectic أو ال dialectic constant
+
+59
+00:03:58,600 --> 00:04:00,440
+لمين، لالميديا
+
+60
+00:04:05,500 --> 00:04:11,060
+أول حاجة بنكامل أول مرة عند D2V by DZ تربيع بيساوي
+
+61
+00:04:11,060 --> 00:04:14,660
+some constant لإن بدأ أكامل بيصير DV by DZ ايش
+
+62
+00:04:14,660 --> 00:04:20,180
+بتساوي minus rho naught على Y زي Z زائد some
+
+63
+00:04:20,180 --> 00:04:24,060
+constant لإن واحنا مش عاملها محددة ال integration
+
+64
+00:04:24,060 --> 00:04:27,460
+and to remind يازم بحطلها اللي هو ال constant
+
+65
+00:04:27,460 --> 00:04:30,540
+الأول اللي هذا بتحدثه من وين من بعض ال condition
+
+66
+00:04:30,980 --> 00:04:35,580
+بكامل كمان مرة dv by dz بتساوي some constant
+
+67
+00:04:35,580 --> 00:04:40,020
+multiplied by z زاد عنظر constant عشان تعطيني v
+
+68
+00:04:40,020 --> 00:04:44,740
+بتساوي minus rho0 z تربيع على اتنين ابسلون زاد a z
+
+69
+00:04:44,740 --> 00:04:47,760
+زاد b اذا a و b منهم بدنا نحددهم في ال boundary كل
+
+70
+00:04:47,760 --> 00:04:50,780
+شئ دعوني اكتر المعادلة لان انا اقصد فيها عشان نفكر
+
+71
+00:04:50,780 --> 00:04:54,440
+الصلاة التانية اذا v لحد الايشة as function of z
+
+72
+00:04:54,440 --> 00:05:03,610
+عشان تساوي minus rho0 v z تربيععلى اتنين ابسلون
+
+73
+00:05:03,610 --> 00:05:10,130
+زائد a زائد a في z زائد b هذه هي المعادلة طبعا
+
+74
+00:05:10,130 --> 00:05:13,350
+احنا اتفقنا ان ال a و ال b طبعا ال solution هذا مش
+
+75
+00:05:13,350 --> 00:05:17,970
+كامل اذا تركت الحل بهذا الشكل لأي انسان هذا يتبقى
+
+76
+00:05:17,970 --> 00:05:22,170
+على اي استوانة مالهوش علاقة بالاستوانة اللي عندها
+
+77
+00:05:22,170 --> 00:05:27,570
+ال potential z equals zeroو عن Z equal D بيسووا
+
+78
+00:05:27,570 --> 00:05:33,370
+Zero هذا يعني بيحقق عدد لنهائي من الحلول إيش
+
+79
+00:05:33,370 --> 00:05:37,110
+مابعوض عن A و B بيعطيني حل A و B ممكن يكونوا أي
+
+80
+00:05:37,110 --> 00:05:40,430
+رقم لكن عشان تطبق هذا ال solution لل
+
+81
+00:05:40,430 --> 00:05:45,110
+electrohydraulic بعمل بتاعتنا لازم أستخدم ال
+
+82
+00:05:45,110 --> 00:05:50,370
+boundary conditions إذا بدي أطبق عن Z equal Zero D
+
+83
+00:05:50,370 --> 00:05:55,310
+at Zero إيش أنها بيسووا Zeroهذه بتروح وهذه بتروح
+
+84
+00:05:55,310 --> 00:05:58,310
+بالضبع النبي إذا أول حاجة السنتج النبي إيش بتساوي
+
+85
+00:05:58,310 --> 00:06:06,590
+V0 و V عند D إيش ما بتساوي Zero إذا ناقص Raw Not D
+
+86
+00:06:06,590 --> 00:06:15,810
+تربيع على 2 Epsilon زائد A في D زائد B بتساوي Zero
+
+87
+00:06:15,810 --> 00:06:19,670
+الطبيعي عارفين اللي هى V0 طلعلنا من يجيب A إذا A
+
+88
+00:06:19,670 --> 00:06:26,710
+إيش بتساوي Raw Not D تربيععلى اتنين ابسلون مايكس
+
+89
+00:06:26,710 --> 00:06:28,430
+بيه مينيا مايكس مايكس بيه موت
+
+90
+00:06:40,630 --> 00:06:44,450
+أذا نستخدم ال boundary conditions و بقدر أجيب قيم
+
+91
+00:06:44,450 --> 00:06:49,310
+a و b و أعوض عنهم ايه زى ما انتوا شايفين طلعت معنى
+
+92
+00:06:49,310 --> 00:06:55,510
+b تسوى v0 و a rho0 d على 2 epsilon-v0 على d طبعا
+
+93
+00:06:55,510 --> 00:07:00,510
+لو دخلنا fd هنا هتصبح rho0dd على 2 epsilon-v0 على
+
+94
+00:07:00,510 --> 00:07:03,480
+dواضح؟ طب اتبنى ال electric field احنا قلنا من
+
+95
+00:07:03,480 --> 00:07:06,120
+ذاكر ال electric field يا من gas يا من carbon يا
+
+96
+00:07:06,120 --> 00:07:09,780
+من ال potential احنا هذا المثال واضح انه مقدرش
+
+97
+00:07:09,780 --> 00:07:11,960
+استخدم الا ال potential مقدرش الا بال potential
+
+98
+00:07:11,960 --> 00:07:14,780
+يعني مافيش مجال احل هذا المثال ال electric field
+
+99
+00:07:14,780 --> 00:07:16,600
+على طريق ال potential عشان هيك جيبنا ال potential
+
+100
+00:07:16,600 --> 00:07:21,930
+ال electric field هي سوى minus grade Vطب هنا قلنا
+
+101
+00:07:21,930 --> 00:07:25,170
+فى ماله function فقط فى الـ z ال gradient اللى هى
+
+102
+00:07:25,170 --> 00:07:29,870
+برضه تتبع ال raw وعال فعل وعال z ال two components
+
+103
+00:07:29,870 --> 00:07:32,970
+ال other two components هيكون لل zero هتضللنا مين
+
+104
+00:07:32,970 --> 00:07:37,710
+minus dv by dz زدها إذا انتجاه ال electric field
+
+105
+00:07:37,710 --> 00:07:43,490
+هو في اتجاه ال z direction and father إيش هتعطينا
+
+106
+00:07:43,490 --> 00:07:49,360
+raw knot z على إبسلونو طبعا فيه ناقص فبتصير هي
+
+107
+00:07:49,360 --> 00:07:52,620
+plus minus a في زد لها طبعا إيه اللي هي هذا
+
+108
+00:07:52,620 --> 00:07:57,960
+القيمة، بطلت يعني undefined لو عوضنا بتعطينا اللي
+
+109
+00:07:57,960 --> 00:08:02,520
+هي قيمة ال electric بده ال net force و ال pressure
+
+110
+00:08:02,520 --> 00:08:10,540
+طبعا ال force اللي بتساوي ال integral لQ في Eالـ Q
+
+111
+00:08:10,540 --> 00:08:19,740
+علينا ميه؟ الـ Q علينا ميه؟ الـ Q علينا
+
+112
+00:08:19,740 --> 00:08:20,800
+ميه؟ الـ Q علينا ميه؟ الـ Q علينا ميه؟ الـ Q علينا
+
+113
+00:08:20,800 --> 00:08:21,100
+ميه؟ الـ Q علينا ميه؟ الـ Q علينا ميه؟ الـ Q علينا
+
+114
+00:08:21,100 --> 00:08:21,660
+ميه؟ الـ Q علينا ميه؟ الـ Q علينا ميه؟ الـ Q علينا
+
+115
+00:08:21,660 --> 00:08:21,880
+ميه؟ الـ Q علينا ميه؟ الـ Q علينا ميه؟ الـ Q علينا
+
+116
+00:08:21,880 --> 00:08:23,400
+ميه؟ الـ Q علينا ميه؟ الـ Q علينا ميه؟ الـ Q علينا
+
+117
+00:08:23,400 --> 00:08:24,880
+ميه؟ الـ Q علينا ميه؟ الـ Q علينا ميه؟ الـ Q علينا
+
+118
+00:08:24,880 --> 00:08:31,040
+ميه؟ الـ Q علينا ميه؟ الـ Q
+
+119
+00:08:31,040 --> 00:08:38,460
+علينا ميه؟ الـ Q علينا ميه؟ الـ Q علينا ميه
+
+120
+00:08:41,100 --> 00:08:46,520
+عند الـ integral لدى S و لأنه لا تعتمد E على لا رو
+
+121
+00:08:46,520 --> 00:08:50,000
+ولا فاي فبقدر أخد ال DS لحالها دي S اللي هي فيها
+
+122
+00:08:50,000 --> 00:08:54,580
+الاعتمادية على رو والفاي و بقول ان التكامل ل E DZ
+
+123
+00:08:54,580 --> 00:08:58,620
+وجدت من و من Zero ل D طبعا DS بتعطينا S بس لو
+
+124
+00:08:58,620 --> 00:09:00,740
+أحطتها في دالة ال رو والفاي ففي النهاية هتعطيني ال
+
+125
+00:09:00,740 --> 00:09:04,600
+S limits تعانها لازم أحضر عندي رو نوت في S وهي
+
+126
+00:09:04,600 --> 00:09:07,660
+هكمل E DZ بتدعوض عن ال E و كامل
+
+127
+00:09:10,900 --> 00:09:16,080
+هذه هتعطينا V نض على D تكملها هتعطينا في Z رو نض
+
+128
+00:09:16,080 --> 00:09:20,100
+على ي في Z هتعطينا رو نض على ي في Z تربيع على 2
+
+129
+00:09:20,100 --> 00:09:24,380
+الterm الأخرش هتعطيني minus rho على ي في D على 2
+
+130
+00:09:24,380 --> 00:09:29,220
+في Z يعني هيكون في عندى تربيع الاعتمادية تربيعية
+
+131
+00:09:29,220 --> 00:09:33,660
+طبعا زى ما انتوا شايفين هي الاعتمادية تربيعية
+
+132
+00:09:33,660 --> 00:09:39,120
+وطبعا اتعود من Zero ل D في تجاه Z hatإذا عوضنا عن
+
+133
+00:09:39,120 --> 00:09:43,600
+D عن Z بتساوي D و طرحنا منها عن Z equals 0 فالـ
+
+134
+00:09:43,600 --> 00:09:46,740
+Zero كله هذا term ساو سفر لأن كل term تتمد على Z
+
+135
+00:09:46,740 --> 00:09:52,400
+دل بس اللي تتمد على D فإذا عوضنا على D بنحصل على
+
+136
+00:09:52,400 --> 00:09:56,960
+قيمة ال force واضح؟ في أي السفسار لحد هنا؟
+
+137
+00:10:02,440 --> 00:10:05,380
+البريشار قلنا هو ال force per unit area ماعليه ال
+
+138
+00:10:05,380 --> 00:10:10,100
+SMF على S و طبعا البريشار ماله ال quantity is
+
+139
+00:10:10,100 --> 00:10:12,320
+scalar ال quantity فباخد المجنيده تطلع ال force
+
+140
+00:10:12,320 --> 00:10:17,040
+per unit area فتعطينى اللى رو نود V نود فهم يعطينا
+
+141
+00:10:17,040 --> 00:10:21,480
+قيمة رو نود و V نود قداش قيمهم و بحصل على البريشار
+
+142
+00:10:21,480 --> 00:10:25,640
+بيه ال newton per meter تلبيه واضح؟ في عياه
+
+143
+00:10:25,640 --> 00:10:33,180
+استفسار؟ فهذا السؤال الأول السؤال التانىيعني ما
+
+144
+00:10:33,180 --> 00:10:36,700
+شاء الله واضح مش اي سلسلة تمام امتازة السؤال
+
+145
+00:10:36,700 --> 00:10:41,520
+التانى هى مبدأ اللى هى Xerox Machine Xerographic
+
+146
+00:10:41,520 --> 00:10:44,340
+Copying Machine او Xerox Machine باختصار مسئول
+
+147
+00:10:44,340 --> 00:10:48,460
+عنها الفكرة انتوا زى ما شايفين فى عندى هو photo
+
+148
+00:10:48,460 --> 00:10:53,400
+conductive وفى عندى اللى هو two plates اتنين ما هم
+
+149
+00:10:53,400 --> 00:10:58,380
+grounded وطبعا هذا ماخده كسبيل مثل X directionإن
+
+150
+00:10:58,380 --> 00:11:01,600
+ال limits تعمل photographic ال photo conductor من
+
+151
+00:11:01,600 --> 00:11:05,680
+zero ل A و الفراغ اللي فيه في ال photo conductor
+
+152
+00:11:05,680 --> 00:11:08,840
+عندنا من A ل D، بيكون دايما مشحون ال photo
+
+153
+00:11:08,840 --> 00:11:13,390
+conductor بستفت شعج ع سبيل المثالمش اللي بيصير انه
+
+154
+00:11:13,390 --> 00:11:16,690
+لما نحط القماش عشان نعملها copying بيصير
+
+155
+00:11:16,690 --> 00:11:19,770
+combination هاي العملية هنا ما بين ال positive و
+
+156
+00:11:19,770 --> 00:11:23,990
+ال negative charges وبالتالي لما يحطوا الحبر بياخد
+
+157
+00:11:23,990 --> 00:11:27,970
+تسخن ال .. الماد ال .. ال .. النسخة اللي انا بتاخد
+
+158
+00:11:27,970 --> 00:11:32,810
+منها ال copy و الحبر بياخد اللي هيالـ form أو يعني
+
+159
+00:11:32,810 --> 00:11:37,110
+بتشكل حسب اللي هي المعلومات اللي موجودة على النسخة
+
+160
+00:11:37,110 --> 00:11:41,430
+الأصلية وبعد هيك بيروح و بيمور عليه الورق الأبيض و
+
+161
+00:11:41,430 --> 00:11:45,890
+بياخد النسخة و بيعمل النسخة إيش اللي طاروا من هذا؟
+
+162
+00:11:45,890 --> 00:11:50,910
+هذه هي الفكرة إحنا بدنا نقرر أو نحدد we want to
+
+163
+00:11:50,910 --> 00:11:56,370
+determineالصورة هي أقرألكم إيها بالإنقليزي، الصورة
+
+164
+00:11:56,370 --> 00:12:01,150
+تتطور من بورينج، بورينج يعني انه بروشه، a charged
+
+165
+00:12:01,150 --> 00:12:03,290
+black powder over the surface of the
+
+166
+00:12:03,290 --> 00:12:05,850
+photoconductor هو اللي بعت الإشارة الموجبة، the
+
+167
+00:12:05,850 --> 00:12:08,270
+electric field attracts the charged powder which
+
+168
+00:12:08,270 --> 00:12:11,310
+is later transferred to the paper and melted to
+
+169
+00:12:11,310 --> 00:12:14,330
+form a permanent imageWe want to terminal the
+
+170
+00:12:14,330 --> 00:12:17,110
+electric field below and above the surface of the
+
+171
+00:12:17,110 --> 00:12:19,310
+photoconductor.يعني بدنا ال electric field في هذه
+
+172
+00:12:19,310 --> 00:12:22,310
+ال region من 0 ل A و ال electric field above ال
+
+173
+00:12:22,310 --> 00:12:26,130
+photoconductor هي من A ل D بدنا electric field في
+
+174
+00:12:26,130 --> 00:12:29,610
+ال two regions عندنا ال boundary conditions واضح
+
+175
+00:12:29,610 --> 00:12:32,710
+اننا في عندنا boundary عند ال A في عندنا واضح في
+
+176
+00:12:32,710 --> 00:12:36,850
+ايش ال charge density في raw surface charge يعني
+
+177
+00:12:36,850 --> 00:12:43,290
+ال D normalمعناها بتسوي السفر DM1-DM2 نورما بتساوي
+
+178
+00:12:43,290 --> 00:12:47,470
+رؤس فى عنا surface of charge فى عنا ال region عنا
+
+179
+00:12:47,470 --> 00:12:51,750
+عند X equals 0 ال potential بتساوي سفر وعنا ال X
+
+180
+00:12:51,750 --> 00:12:54,150
+بالساوية دى برضه potential بتساوي زيرو لإنه ماعنهم
+
+181
+00:12:54,150 --> 00:12:57,710
+التنتين إجراندوا إذا إحنا عنا عارفين كل المعلومات
+
+182
+00:12:57,710 --> 00:13:01,830
+من الرسمة إنه عندي عند ال interface مابين اللى هو
+
+183
+00:13:01,830 --> 00:13:03,790
+ال photo conductor
+
+184
+00:13:06,330 --> 00:13:11,050
+another dialectic لو Y1 أن في رؤس service charge
+
+185
+00:13:11,050 --> 00:13:16,010
+أن ال potentials عند ال zero و D هم عارفينطبعا
+
+186
+00:13:16,010 --> 00:13:19,150
+واضح لنا أن ال potential هيكون اعتمادية وين؟ على
+
+187
+00:13:19,150 --> 00:13:22,270
+ال X يعني ال potential هي هاي ال two plates فال X
+
+188
+00:13:22,270 --> 00:13:24,390
+هيكون ال difference بين ال potential بين ال two
+
+189
+00:13:24,390 --> 00:13:28,850
+plates مش هيكون في اتجاهات تانية في ال Y و ال Z
+
+190
+00:13:28,850 --> 00:13:33,050
+فهتكون فقط الاعتمادية على X تقرأ على المثال السابق
+
+191
+00:13:33,050 --> 00:13:37,250
+بس الاعتمادية على X وكمان ال free charge صفر لأن
+
+192
+00:13:37,250 --> 00:13:39,670
+هي surface charge على ال boundary لكن ال free
+
+193
+00:13:39,670 --> 00:13:44,430
+charge مالها صفرفزرنا دلتر بيه V بتسوى تنين V by
+
+194
+00:13:44,430 --> 00:13:48,550
+DX التربية بتسوى Zero نفس الحاجة بتكامل أول مرة و
+
+195
+00:13:48,550 --> 00:13:51,550
+أكامل تاني مرة طبعا المثال هدنا ال feature بتسوى
+
+196
+00:13:51,550 --> 00:13:55,610
+Zero فأخدنا مين اللي هي ال class أول مرة بتكامل
+
+197
+00:13:55,610 --> 00:13:59,830
+بتعطينا A المرة اللي بعدها التفاضل التكامل أولا دي
+
+198
+00:13:59,830 --> 00:14:03,170
+V by DX مش بتعطيني constant A المرة اللي بعدها إيش
+
+199
+00:14:03,170 --> 00:14:07,350
+بيصير V بتسوى Ax زائد B واضح هذا ال integration
+
+200
+00:14:07,350 --> 00:14:11,090
+مافيش لكوا أي مشكلةكل السؤال هي أن أعرف كيف أصيغي
+
+201
+00:14:11,090 --> 00:14:14,350
+ال potential، المثال الأولاني، بتطلع ال blades
+
+202
+00:14:14,350 --> 00:14:17,830
+هنا، هنا ال charger بتنتج وهنا بتروح، اذا اعتمادية
+
+203
+00:14:17,830 --> 00:14:19,730
+على هذا ال axis ال potential، بين هدولة ال two
+
+204
+00:14:19,730 --> 00:14:23,690
+blades، هنا عمللياهم بعد الشكل اعتمادية على ال x
+
+205
+00:14:23,690 --> 00:14:27,710
+-axis، انتهت القصة، فشي على ال z و ال y، اذا سهل
+
+206
+00:14:27,710 --> 00:14:31,520
+جدا، هنا by double integrationنحدد الـ two regions
+
+207
+00:14:31,520 --> 00:14:34,200
+أنها potential في الـ photoconductor اللي هي من 0
+
+208
+00:14:34,200 --> 00:14:39,380
+ل A و 1 من A لفوق ل D فإذا عندي two potentials
+
+209
+00:14:39,380 --> 00:14:42,520
+واحد اللي هو بنطبق على ال region for X أقل من A
+
+210
+00:14:42,520 --> 00:14:46,780
+والتاني في ال region X أكبر من A for X أكبر من A
+
+211
+00:14:46,780 --> 00:14:50,480
+هو نعطيها أبسلون واحد أه صح يعني X أكبر من A
+
+212
+00:14:50,480 --> 00:14:53,760
+أبسلون واحد فعشان هيك بسميهم واحد يعني عشان تتناسب
+
+213
+00:14:53,760 --> 00:14:57,380
+مع ال Epsilon تبعها فإذا V واحد بيساوي A واحد X
+
+214
+00:14:57,380 --> 00:15:07,040
+سائد B واحدالتانية V2 بتسوأ A2 X أقل من A وطبعا كل
+
+215
+00:15:07,040 --> 00:15:11,420
+هدول ال constants A1, A2, B1, B2 بنجيبهم من ال
+
+216
+00:15:11,420 --> 00:15:15,280
+boundary conditions اول two boundary conditions
+
+217
+00:15:15,280 --> 00:15:20,320
+احنا حكيناهم اللي هي V1 دنيا ال D بتسوأ Zero و V2
+
+218
+00:15:20,320 --> 00:15:25,540
+ليش هاللي اتحلمناهم V1 و V2 لأن V1اللي هي في هال
+
+219
+00:15:25,540 --> 00:15:30,660
+region فأكيد V1 اللي لازم تكون عند D بصوة صفر و V2
+
+220
+00:15:30,660 --> 00:15:33,660
+في هال region V2 هي اللي عند ال zero بصوة صفر
+
+221
+00:15:33,660 --> 00:15:37,440
+واضح؟ احنا قولنا بشكل عام ال potential عند X equal
+
+222
+00:15:37,440 --> 00:15:40,580
+zero صفر و potential عند X equal D بصوة صفر
+
+223
+00:15:40,810 --> 00:15:45,430
+أتحدثناهم قولنا سميناها D1 في ال region A أكبر من
+
+224
+00:15:45,430 --> 00:15:52,170
+X أكبر من A V1 سميناها و for X أقل من A سميناها V2
+
+225
+00:15:52,170 --> 00:15:57,870
+فإذا عيلنا V1 and X بتساوي D بتساوي 0 و V2 عند X
+
+226
+00:15:57,870 --> 00:16:03,410
+equal 0 بتساوي 0 لو عوضنا إيش بيصير V1 بتساوي 0
+
+227
+00:16:03,410 --> 00:16:10,130
+عوض عن X0 D إذا V1 إيش بتساوي minus A1 في D
+
+228
+00:16:28,470 --> 00:16:35,030
+بتساوي a1d بزاق بي واحد اذا بي واحد بتساوي ماينوس
+
+229
+00:16:35,030 --> 00:16:41,310
+a واحد في دي كمان في تنين عند ال zeroبتساوى zero
+
+230
+00:16:41,310 --> 00:16:43,050
+بتساوى B2
+
+231
+00:16:49,260 --> 00:16:52,560
+لسه احنا ماخلصماش كل المجاهيين، احنا قدرنا نجيب
+
+232
+00:16:52,560 --> 00:16:55,720
+بعضهم، عرفنا ان P اتنين بالسوء zero، هاي عرفنا
+
+233
+00:16:55,720 --> 00:17:00,320
+واحد، والتاني جيبنا العلاقة من A واحد وP واحد لإي
+
+234
+00:17:00,320 --> 00:17:03,580
+واحد وثمان اثنان اي واحد دي، لازمني اعرف يا A واحد
+
+235
+00:17:03,580 --> 00:17:06,660
+يا P واحد، اذا عرفت A واحد باعرف P واحد، اذا عرفت
+
+236
+00:17:06,660 --> 00:17:09,580
+P واحد باعرف A واحد، ومن كمان A تنين، لسه هدول
+
+237
+00:17:09,580 --> 00:17:14,180
+المجاهيينكمان قولنا في كمان واحدة boundary
+
+238
+00:17:14,180 --> 00:17:16,980
+condition كمان قولنا ال normal component ل D
+
+239
+00:17:16,980 --> 00:17:21,640
+بيتساو مين ال surface charge density اذا D 1 N
+
+240
+00:17:21,640 --> 00:17:26,220
+minus D 2 N بتساوي رقص عند مين عند X بتساوي اين
+
+241
+00:17:26,220 --> 00:17:29,480
+عند بالتمام ال interface بين اللي هو ال photo
+
+242
+00:17:29,480 --> 00:17:36,240
+conductor و ال dielectric اللي فوق اذا معناه بدأ
+
+243
+00:17:36,240 --> 00:17:40,440
+اجيب ال D ادول اللي احنا عملناهم على الصدورة
+
+244
+00:17:43,460 --> 00:17:48,220
+عشان أجيب ال D بدي أجيب ال E كيف بدي أجيب ال E؟ ال
+
+245
+00:17:48,220 --> 00:17:52,700
+E هي عبارة عن دل ال V فإيش هيكون؟ عندي ال D بتسوء
+
+246
+00:17:52,700 --> 00:17:58,420
+Epsilon E و E قولنا بتسوء منص دل ال V و ال V إحنا
+
+247
+00:17:58,420 --> 00:18:01,580
+قولنا بعد مدة على مينة؟ ال X إذا هتكون DV by DX
+
+248
+00:18:01,580 --> 00:18:07,920
+فعندي منص Epsilon دل ال V رؤس بتسوء D1n منص D2n
+
+249
+00:18:07,920 --> 00:18:16,280
+D1n إيش هتكون؟ Epsilon 1 E1nوD2 هتكون E2E2N
+
+250
+00:18:16,280 --> 00:18:20,120
+وبالتالي بقدر اجيبهم من تفاضل اللي هي ال vote
+
+251
+00:18:20,120 --> 00:18:26,860
+potential DB1 by DX و DB2 by DX طب لو انا فضلت V1
+
+252
+00:18:26,860 --> 00:18:34,000
+ايش بتساوي بشكل عام V1 بتساوي A1 X ذات V1 و V2
+
+253
+00:18:34,000 --> 00:18:38,640
+بتساوي A2 X ذات V2 التفاضل هو بالنسبة ل X من A1 و
+
+254
+00:18:38,640 --> 00:18:42,730
+A2بعد النتيجة زى ما انتوا شايفين اذا رؤس ايش بيبقى
+
+255
+00:18:42,730 --> 00:18:46,510
+تساوي مغنى ايسون واحد اي واحد زاد ايسون اتنين
+
+256
+00:18:46,510 --> 00:18:54,330
+اتنين اي واحد اتنين
+
+257
+00:18:54,330 --> 00:18:58,810
+اتنين اتنين اتنين اتنين اتنين اتنين اتنين اتنين
+
+258
+00:18:58,810 --> 00:18:59,230
+اتنين اتنين اتنين اتنين اتنين اتنين اتنين اتنين
+
+259
+00:18:59,230 --> 00:18:59,250
+اتنين اتنين اتنين اتنين اتنين اتنين اتنين اتنين
+
+260
+00:18:59,250 --> 00:19:02,330
+اتنين اتنين اتنين اتنين اتنين اتنين اتنين اتنين
+
+261
+00:19:02,330 --> 00:19:06,070
+اتنين اتنين اتنين اتنين اتنين اتنين ات
+
+262
+00:19:09,100 --> 00:19:11,900
+أحنا أهالي الرابعة المعادلة الرابعة لدينا أربعة
+
+263
+00:19:11,900 --> 00:19:14,540
+مجاهير فهنا أربعة معادلات عند ال potential عند ال
+
+264
+00:19:14,540 --> 00:19:17,360
+zero قلنا بيساوي zero potential عند ال D بيساوي
+
+265
+00:19:17,360 --> 00:19:20,380
+zero قلنا ال normal component لدى D عند ال
+
+266
+00:19:20,380 --> 00:19:23,340
+interface بيساوي رقص و ال potential نفسه عند ال A
+
+267
+00:19:23,340 --> 00:19:26,260
+أشمال لازم يكون continuous فعند ال potential عند
+
+268
+00:19:26,260 --> 00:19:28,660
+ال A لازم يكون متساوي فهنا المعادلة اللى أنا
+
+269
+00:19:28,660 --> 00:19:32,120
+ماكتبتاش لسه اللى هي V واحد عند X بيساوي A هساوي V
+
+270
+00:19:32,120 --> 00:19:38,290
+تنين عند X بيساوي A اللى هى هذهV1 عند X بالساوية L
+
+271
+00:19:38,290 --> 00:19:43,730
+هي A1 في X عوضنا عن X ب A زائد B1 بتساوية A8 في L
+
+272
+00:19:43,730 --> 00:19:50,240
+فعنا هي واحدةوهي معادلة وهي تالتة ورابعين عندي
+
+273
+00:19:50,240 --> 00:19:53,440
+اتقاعد ال B2 بأعوض عنها بالساوة 0 خلاص احنا
+
+274
+00:19:53,440 --> 00:19:59,420
+عارفينها في عند ال B1 مربوطة ب A1 بدلالة D بقدر
+
+275
+00:19:59,420 --> 00:20:03,480
+أعوض عنها هنا فاش بجيب علاقة بين مين ومين من A2
+
+276
+00:20:03,480 --> 00:20:09,660
+وA1 بأعوض عن واحدة منهم هنا بأعوض عن مثلا A1 او A2
+
+277
+00:20:09,660 --> 00:20:13,060
+نعملهم بالتفصيل واضحش اللي صار القصار أول حاجة
+
+278
+00:20:13,060 --> 00:20:17,720
+احنا عرفنا ال B1 بدلالة A1لعوضناها هذه اللي هي من
+
+279
+00:20:17,720 --> 00:20:24,940
+V1 at A بيساوي V2 at N لعوضناها عن V1 بيجيب علاقة
+
+280
+00:20:24,940 --> 00:20:29,460
+A2 ب A1 يعني هاي اللي هي من ال normal component لل
+
+281
+00:20:29,460 --> 00:20:34,960
+D تربط A1 و A2 بعوض عن A2 او A1 بجيب واحدة منهم
+
+282
+00:20:34,960 --> 00:20:39,320
+خلاص يعني انتهت صار معروفة عند ال A2 او ال A1
+
+283
+00:20:39,320 --> 00:20:42,960
+ابدات الرؤس epsilon 1 epsilon 2 صارت معروفة عرفنا
+
+284
+00:20:42,960 --> 00:20:49,490
+A1 بنعرف A2بنعرف اللي هو P1، واضح؟ اذا معناه انه
+
+285
+00:20:49,490 --> 00:20:51,890
+بقدر اجيب اللي هي ال electric field و هذا دائما
+
+286
+00:20:51,890 --> 00:20:54,990
+لازم نطبه ل E1 و E2 اللي هي E1 ايش اللي قولنا
+
+287
+00:20:54,990 --> 00:21:02,410
+بتساوي minus del E1 هتكون E1 D1 دي فيها E1 E1 هي
+
+288
+00:21:02,410 --> 00:21:07,470
+minus del V هي minus DV by DX اللي هي قولنا ايش
+
+289
+00:21:07,470 --> 00:21:08,710
+هتساوي بساطة E1
+
+290
+00:21:11,340 --> 00:21:16,340
+-A1 في اتجاه ال X-axis و E2 ايش هتكون minus A2 في
+
+291
+00:21:16,340 --> 00:21:20,640
+X hat و هدول احنا طلعهم فبنعود عنهم في المعادلة
+
+292
+00:21:20,640 --> 00:21:26,380
+وبالتالي بحصل على E1 و E2 واضح؟ تمام اذا كل هاي
+
+293
+00:21:26,380 --> 00:21:29,740
+قضية الجبرة بس الواحد دي تتحقق من ال configuration
+
+294
+00:21:29,740 --> 00:21:32,580
+تبع ال problem بتاعته وين ال electric field وين ال
+
+295
+00:21:32,580 --> 00:21:35,600
+potential اتجاهه وين ال boundary conditions وبتمتي
+
+296
+00:21:35,600 --> 00:21:41,560
+الحلتمام هي كده احنا شوفنا مثالين واحد على ال بصة
+
+297
+00:21:41,560 --> 00:21:47,080
+equation واحد على ال plus equation نشوف كمان مثال
+
+298
+00:21:47,080 --> 00:21:52,140
+ايش المثال هنا راح لمثال باكمد على الفاية احنا
+
+299
+00:21:52,140 --> 00:21:56,260
+الأمثل شوفناهم يا بتلدوا على ال z يا على ال x برضه
+
+300
+00:21:56,260 --> 00:21:59,840
+لازالت variable واحد خلنا نشوف السؤال عندي ال semi
+
+301
+00:21:59,840 --> 00:22:03,750
+infinite conducting planesعندي semi-infinite ايش
+
+302
+00:22:03,750 --> 00:22:10,290
+معناه انه بتده بس في نص ال globe نص الاسباسي فمثلا
+
+303
+00:22:10,290 --> 00:22:14,770
+عندنا ال plane الأولاني قاعد في equal zero يعني في
+
+304
+00:22:14,770 --> 00:22:20,070
+equal zero و من الرسمة واضح بمتد في اتجاه ال X و
+
+305
+00:22:20,070 --> 00:22:28,870
+ال Z بستر X و زر من اتجاهين واضح؟ بالتاني هو يعني
+
+306
+00:22:28,870 --> 00:22:36,950
+في equal five على ستة1 and x and φ equal 0 وقلنا
+
+307
+00:22:36,950 --> 00:22:41,730
+فى تدرون من ال X من ال روح المطابقة على ال X و
+
+308
+00:22:41,730 --> 00:22:46,630
+بتلف لحته Y 1 فى 0 هتكون على ال X axis فى على 6
+
+309
+00:22:46,630 --> 00:22:50,450
+طبعا ما بين ال X و ال Y هى شايفين ال X component و
+
+310
+00:22:50,450 --> 00:22:54,730
+هى ال Y axis و هى ال Z axis نعطينا قيم ال
+
+311
+00:22:54,730 --> 00:22:59,450
+potential على كل واحد من هدولة ال blends الأولانى
+
+312
+00:23:00,540 --> 00:23:04,260
+الـ Plane هذا اللي هو من اللي زمان قد حكينا عن فاي
+
+313
+00:23:04,260 --> 00:23:07,480
+equal zero هو semi-infinite لأنه semi-infinite
+
+314
+00:23:07,480 --> 00:23:11,540
+بروحش لقى ال minus x لو بروح من ال minus x ل plus
+
+315
+00:23:11,540 --> 00:23:15,580
+x بصير infinite هذا الـ Plane لكن هو semi-infinite
+
+316
+00:23:15,580 --> 00:23:18,900
+لأنه بروح من minus z ل plus z و فقط في ال positive
+
+317
+00:23:18,900 --> 00:23:23,710
+x axis هاي ال semi-infiniteقيمة ال potential عند
+
+318
+00:23:23,710 --> 00:23:30,630
+هذا ال plan بتسوى 0 and 5 بتسوى
+
+319
+00:23:30,630 --> 00:23:34,730
+باي على ستة اللي هو ال plan التاني قيمة ال
+
+320
+00:23:34,730 --> 00:23:40,210
+potential 100 volt بده يانا برضه نحصل V أو E اذا
+
+321
+00:23:40,210 --> 00:23:42,710
+عرفنا V دايما زي ما انتوا عارفين بنقدر نجيب ال E
+
+322
+00:23:42,710 --> 00:23:45,870
+طبعا احنا بنقدر نستخدم هنا من ال cylindrical
+
+323
+00:23:45,870 --> 00:23:49,850
+coordinateلأنه فيه اعتمادية على ال file اعتمادية
+
+324
+00:23:49,850 --> 00:23:53,840
+على ال file فيه ال desert axis و فيه ال drawأولا
+
+325
+00:23:53,840 --> 00:23:57,420
+باعتمد على ال row بتنشغل محدد يعني فاي equal zero
+
+326
+00:23:57,420 --> 00:24:00,660
+و فاي باي على تنسيق باعتمد على مين على فاي ال
+
+327
+00:24:00,660 --> 00:24:03,060
+boundary condition حتى يتسهل و لا اعتمادية
+
+328
+00:24:03,060 --> 00:24:06,020
+اعتمادية على فاي واحدة عند ال zero واحدة عند ال
+
+329
+00:24:06,020 --> 00:24:11,340
+باي على ستة اذا دي التربيع V بتتبسط لمين واحد على
+
+330
+00:24:11,340 --> 00:24:15,320
+رو تربيع دي تانية V باي دي فاية تربيع بتساوي اش
+
+331
+00:24:15,320 --> 00:24:20,850
+سفر مش free charges مش هبصيرتي free chargesبتنال
+
+332
+00:24:20,850 --> 00:24:24,010
+كامل طبعا ال raw تربيع اللى تسوى zero واضح فيه قلو
+
+333
+00:24:24,010 --> 00:24:27,590
+radius فإذا ما بقدر أدب فيها بتروح فبصير عند ال D
+
+334
+00:24:27,590 --> 00:24:31,350
+V by D Phi إيش بتسوى constant كمان مرة أكامل V إيش
+
+335
+00:24:31,350 --> 00:24:39,190
+بتسوى ال constant في Phi زائد another constant V
+
+336
+00:24:39,190 --> 00:24:45,710
+بيبقى تسوى A Phi زائد B تمام؟ في حاجة مهمة إنه
+
+337
+00:24:45,710 --> 00:24:50,900
+دايما عند ال raw equal to zero فيه gapand ال raw
+
+338
+00:24:50,900 --> 00:24:53,960
+هيوحط لكيها في الرسمة في النجاب دي عشان ال
+
+339
+00:24:53,960 --> 00:24:58,040
+insulation يعني عشان مايصيرش ال potential يعني
+
+340
+00:24:58,040 --> 00:25:01,180
+عشان يفصل ال two potentials مايصيرش دي قاعدة
+
+341
+00:25:01,180 --> 00:25:05,200
+استوزيع لل potential ففي NDL gap صغيرة كتير لادرش
+
+342
+00:25:05,200 --> 00:25:08,260
+ان احنا بنهملها بس هي موجودة بتعمل زي insulation
+
+343
+00:25:08,260 --> 00:25:09,840
+بين ال two plates
+
+344
+00:25:14,690 --> 00:25:16,870
+هيجيبنا ال potential و طبعا هنا بس بنحط ال powder
+
+345
+00:25:16,870 --> 00:25:19,790
+conditions إيش ال powder conditions عندنا فا يكل
+
+346
+00:25:19,790 --> 00:25:23,050
+زيرو ال potential بيساوي زيرو and فا يكل ماي على
+
+347
+00:25:23,050 --> 00:25:26,670
+ستة ال potential بيساوي مية إيه معوض؟ إذا أنا عند
+
+348
+00:25:26,670 --> 00:25:31,530
+فا يكل زيرو بيحط بي إيش بيساوي سفر هيخلص من بي إيش
+
+349
+00:25:31,530 --> 00:25:35,730
+طبعا إن ال potential بيساوي إيه فا؟فاي نوت بشكل
+
+350
+00:25:35,730 --> 00:25:38,230
+عام الهي باية على ستة ال note ها دي يعني some
+
+351
+00:25:38,230 --> 00:25:41,670
+constant V note إيش بتساوي إيه في نوت يعني بمعنى
+
+352
+00:25:41,670 --> 00:25:45,290
+إيه عرفناها ساعة V note اللي هي مية على في نوت
+
+353
+00:25:45,290 --> 00:25:49,110
+اللي هي باية على ستة إذا بشكل عام V إيش بتساوي V
+
+354
+00:25:49,110 --> 00:25:52,400
+نوت على في نوت في في هدولة عارفينهمفاية نوت مية
+
+355
+00:25:52,400 --> 00:25:55,680
+وفاية نوت باية على ستة لك او في سؤال تانى قال لي
+
+356
+00:25:55,680 --> 00:25:59,800
+باية مثلا هذا فاية بيساوي باية اتنين بقدر استخدمها
+
+357
+00:25:59,800 --> 00:26:03,100
+للعلاقة يعني نتذكرها انها V بتساوي ال constant
+
+358
+00:26:03,100 --> 00:26:06,580
+potential على قيمة الزاوية اللى عندها معاك فقيمة
+
+359
+00:26:06,580 --> 00:26:10,380
+ال potential في فاية اذا V بتتناسب تقريبا مع فاية
+
+360
+00:26:10,380 --> 00:26:14,340
+محل ال potential تظهر مين بدناه ايه ايه ال minus
+
+361
+00:26:14,340 --> 00:26:18,220
+ده V بتمت على فاية ناخد ال component بتاعة فاية
+
+362
+00:26:18,220 --> 00:26:23,450
+الواحد على رو دي بي بي فاية و فاية هاتلو اتفضلنا
+
+363
+00:26:23,450 --> 00:26:26,570
+بالنسبة للفا إيش بيظل عندنا ال constant V0 على فاي
+
+364
+00:26:26,570 --> 00:26:32,310
+نوت اللي هي 100 على 4 على 6 واحد على رو في V0 على
+
+365
+00:26:32,310 --> 00:26:35,550
+فاي نوت في تجاه الفاي نوت معود بيعطينا قيمة ال
+
+366
+00:26:35,550 --> 00:26:41,650
+potential وقيمة ال equilibrium and النقطةواحد ده
+
+367
+00:26:41,650 --> 00:26:45,670
+بتاعت متعمين على theta ده عندى two coins ال coin
+
+368
+00:26:45,670 --> 00:26:48,970
+الأولانى طبعا ال coins اللى حددتهم بزاوية الرقص
+
+369
+00:26:48,970 --> 00:26:52,930
+بيسموها زاوية رقص المخرض اللى هى الأولى ال two
+
+370
+00:26:52,930 --> 00:26:58,090
+conducting coins الأولانى زاوية رقصه اللى هى theta
+
+371
+00:26:58,090 --> 00:27:02,650
+واحد باية العشرةوالتانى اللى هو سيرة الدنيا باي
+
+372
+00:27:02,650 --> 00:27:07,410
+على ستة نفس القضية عند ال zero فيه gap عشان
+
+373
+00:27:07,410 --> 00:27:11,210
+مايصيرش فيه touch بين ال two plates ففي عندنا
+
+374
+00:27:11,210 --> 00:27:15,150
+insulation gap من الهوى، gap صغيرة، صغيرة كتير
+
+375
+00:27:15,150 --> 00:27:18,070
+لازرش اللى بنهيملها، لازرش في عندها اي conditions
+
+376
+00:27:18,070 --> 00:27:22,090
+الحاجة اللى بيعطيناياها ان عند باي على أشرك بتنشر
+
+377
+00:27:22,090 --> 00:27:25,640
+قيمة two سفر هي groundedيعني حتى لو مش كاتبها
+
+378
+00:27:25,640 --> 00:27:30,620
+هديمها لها grounded وعندي V على ستة V نود هم
+
+379
+00:27:30,620 --> 00:27:34,040
+يعطينا قداش كيمة V نود اللي هي خمسين Volt واضح بده
+
+380
+00:27:34,040 --> 00:27:40,080
+طبعات V وE between the two conesطبعا اللى واضح لنا
+
+381
+00:27:40,080 --> 00:27:42,400
+ان ال potential بقت نضع على θ لان اي اللى بتنش على
+
+382
+00:27:42,400 --> 00:27:45,740
+عين θ واحد بساوة صفر وعين ثتر اتنين بساوة V0 اذا
+
+383
+00:27:45,740 --> 00:27:47,700
+اللى بتنش على عين ثتر اتنين بساوة V0 اذا اللى بتنش
+
+384
+00:27:47,700 --> 00:27:48,180
+على عين ثتر اتنين بساوة V0 اذا اللى بتنش على عين
+
+385
+00:27:48,180 --> 00:27:50,240
+ثتر اتنين بساوة V0 اذا اللى بتنش على عين ثتر اتنين
+
+386
+00:27:50,240 --> 00:27:52,480
+بساوة V0 اذا اللى بتنش على عين ثتر اتنين بساوة V0
+
+387
+00:27:52,480 --> 00:27:56,740
+اذا اللى بتنش على عين ثتر اتنين
+
+388
+00:27:56,740 --> 00:28:06,470
+بساوة V0 اذا اللى بتنش على عين ثتر اتنين بسأول
+
+389
+00:28:06,470 --> 00:28:11,150
+تكامل أشبط يعني sin θ dv by d θ بيسوء constant هذا
+
+390
+00:28:11,150 --> 00:28:15,470
+ال constant مش هيصير dv بتسوء ال constant على sin
+
+391
+00:28:15,470 --> 00:28:19,550
+θ d θ يعني صار عندى d θ على sin θ التكامل عشان
+
+392
+00:28:19,550 --> 00:28:25,770
+كمان مرةأول تجامل طبعا ال Vandori احنا حكينا عنها
+
+393
+00:28:25,770 --> 00:28:29,870
+مافيش اي مشكلة لو قلنا Zeta R0 Zeta 0 excluded
+
+394
+00:28:29,870 --> 00:28:33,590
+عشان ان بتعمل insulation ضربنا بقعة ربيع سنة و ستة
+
+395
+00:28:33,590 --> 00:28:37,850
+بيضل هدش كده أول مرة إيش بيعطيني constantتعريف
+
+396
+00:28:37,850 --> 00:28:41,170
+مرة؟ بعمل separation of variable لإن مش هقدر أكامل
+
+397
+00:28:41,170 --> 00:28:44,550
+و هو مابيش .. فبقسم على sin θ و بدروف في dθ فبصير
+
+398
+00:28:44,550 --> 00:28:49,850
+عندى dv سواء تكمل dθ على sin θ و هدي إيش بقدر
+
+399
+00:28:49,850 --> 00:28:53,550
+أسويها اللي هي باستخدام ال trick ليش ضعيف الزاوية
+
+400
+00:28:53,940 --> 00:28:58,520
+قانون ضعف الزاوية عارفينهم؟ sin ضعف الزاوية او two
+
+401
+00:28:58,520 --> 00:29:02,120
+theta ايش بيسوي اتنين sin theta cosine theta يعني
+
+402
+00:29:02,120 --> 00:29:05,800
+عملي الزاوية theta اذا بتصير اتنين sin النص theta
+
+403
+00:29:05,800 --> 00:29:08,840
+cosine النص theta ليش فدي اعمل هيك؟ لإن واحدة من
+
+404
+00:29:08,840 --> 00:29:15,580
+هدولة تفاضل التانيةلو ضربت انا ال bust و المقام او
+
+405
+00:29:15,580 --> 00:29:21,460
+يعني قسمت على cos θ و ضربت في cos θ عشان مايصيرش
+
+406
+00:29:21,460 --> 00:29:23,820
+اي خلل هاي ال trip كلنا ساخناها عشان نعملها ده ال
+
+407
+00:29:23,820 --> 00:29:27,280
+integration لو ضربت في cosine و قسمت على cosine
+
+408
+00:29:27,280 --> 00:29:31,820
+هاي بتصير ايش؟ cosine تربية وهي ايش بتصير؟ tan اذا
+
+409
+00:29:31,820 --> 00:29:35,400
+بيصير عامد ال cosine تربية θ على اتنين في tan θ
+
+410
+00:29:35,400 --> 00:29:40,330
+على اتنين معايا ولا اكتب على اللوح؟الـ cos تربيعش
+
+411
+00:29:40,330 --> 00:29:44,210
+هي c كان واحد على cos عند دي ستة على .. بتصير c
+
+412
+00:29:44,210 --> 00:29:48,390
+كان تربيع ستة على اتنين على تان ستة بتعرف ان فضل
+
+413
+00:29:48,390 --> 00:29:54,930
+تان ستة هي c كان تربيع فصرت هاي dx على x صح؟ طبعا،
+
+414
+00:29:54,930 --> 00:29:58,410
+اذا أول حاجة قولنا ال sign ستة هي أبارع اتنين cos
+
+415
+00:29:58,410 --> 00:30:02,070
+ستة على اتنين sign ستة على اتنين ضربنا في cos ستة
+
+416
+00:30:02,070 --> 00:30:05,530
+على اتنين وقسمنا في cos ستة على اتنين صارت cos
+
+417
+00:30:05,530 --> 00:30:08,790
+تربيع ستة على اتنين وهي صارت تان ستة على اتنين
+
+418
+00:30:20,240 --> 00:30:26,320
+D ثتا على sin ثتا يقولنا اتنين sin ثتا على اتنين
+
+419
+00:30:26,320 --> 00:30:31,100
+cosine ثتا على اتنين هذا كله بالضبط في cosine ثتا
+
+420
+00:30:31,100 --> 00:30:34,900
+على اتنين واسمه على cosine ثتا على اتنين
+
+421
+00:30:40,080 --> 00:30:45,240
+عندي sin 6 على 2 على cos 6 على 2 هتعطيني ت 6 على 2
+
+422
+00:30:45,240 --> 00:30:52,720
+و cos تربيه 6 على 2 سو a على 2 التكامل 1 على cos
+
+423
+00:30:52,720 --> 00:31:00,640
+اللي هو c كانت تربيه 6 على 2 دي 3 على ت 6 على 2
+
+424
+00:31:00,640 --> 00:31:07,960
+بضل إنه هاد ال X يعني أخليها 6 على 2 اتنين واضح؟
+
+425
+00:31:11,910 --> 00:31:21,730
+فإذا صارت dx على x وبالتالي بحصل على ..
+
+426
+00:31:21,730 --> 00:31:28,550
+فبتصير a ln θ tan θ على 2 زائد some constant طبعا
+
+427
+00:31:28,550 --> 00:31:32,090
+إحنا خلاص كوصلنا لل potential بدأ أحط اللي هي ال
+
+428
+00:31:32,090 --> 00:31:34,890
+boundary condition قلنا على θ equal 0 ال potential
+
+429
+00:31:34,890 --> 00:31:43,250
+بيساوي 0 tan ال 0 قداشمقابل الـ 0 مقابل الـ 0
+
+430
+00:31:43,250 --> 00:31:52,730
+مقابل الـ
+
+431
+00:31:52,730 --> 00:32:03,730
+0
+
+432
+00:32:05,290 --> 00:32:07,730
+بس هو مش بيعطينا عند ال zero، احنا ليش مدورة على
+
+433
+00:32:07,730 --> 00:32:10,570
+zero، اتقش ال conditions تاولنا، عند ال pi على
+
+434
+00:32:10,570 --> 00:32:13,550
+عشرة، احنا قولنا ال zero هي بنستستيها، ليش اللي
+
+435
+00:32:13,550 --> 00:32:17,450
+هال insulation؟ ان واحدة عدل ال pi على عشرة، اللي
+
+436
+00:32:17,450 --> 00:32:20,150
+عندها ال potential بيساوي zero، والتانية pi على ال
+
+437
+00:32:20,150 --> 00:32:23,550
+six اللي عندها potential لينو، بنعوض عليهم، اذا
+
+438
+00:32:23,550 --> 00:32:26,690
+عندنا ال potential أول حاجة عند مين؟ أكتبهم
+
+439
+00:32:57,680 --> 00:33:01,700
+بس بنعود عند النقطات اللي أمامنا
+
+440
+00:33:05,310 --> 00:33:12,390
+على عشرة اللي هي بالساوية عندها سفر a لان تاني غير
+
+441
+00:33:12,390 --> 00:33:18,210
+عشر باي على عشرين زائد
+
+442
+00:33:18,210 --> 00:33:24,230
+بي و المرة التانية اللي عند ال باي على ستة اللي هي
+
+443
+00:33:24,230 --> 00:33:31,650
+الساوية خمسين ساوية a لان باي على ستة اتنين اللي
+
+444
+00:33:31,650 --> 00:33:32,290
+هي اتناشر
+
+445
+00:33:35,240 --> 00:33:42,280
+bye على معاشر زائدبنعمل معادلتين طبعا وجهينين بقدر
+
+446
+00:33:42,280 --> 00:33:46,680
+أعود و أستخدم ال calculator و أجيب الناتج تبعي هو
+
+447
+00:33:46,680 --> 00:33:50,620
+طبعا بيخليهم 6 2 6 1 عشان انه في النهاية انت بتقدر
+
+448
+00:33:50,620 --> 00:33:57,440
+تخلي الحل تبعك لأي زرع لأي 6 1 6 2 فاحنا لو خلناهم
+
+449
+00:33:57,440 --> 00:34:01,280
+دلت 6 1 6 2 مافيش اي مشكلة عندنا يعني بتطلعنا
+
+450
+00:34:01,280 --> 00:34:06,380
+solution اللي هي V بتسوء A لن مثلا الحالة الأولى
+
+451
+00:34:06,380 --> 00:34:10,960
+عند 6 equals 0 A بيش بتسوء minusهي الحالة اللي
+
+452
+00:34:10,960 --> 00:34:15,260
+بيبقى هذه بشكل عام لو بيخدنا الشكل العام اللي
+
+453
+00:34:15,260 --> 00:34:21,240
+بيبقى بي بيبقى بي
+
+454
+00:34:21,240 --> 00:34:26,460
+بيبقى
+
+455
+00:34:26,460 --> 00:34:27,620
+بي بيبقى بي بيبقى بي بيبقى بي بيبقى بي بيبقى بي
+
+456
+00:34:27,620 --> 00:34:27,680
+بيبقى بيبقى بيبقى بيبقى بيبقى بيبقى بيبقى بيبقى
+
+457
+00:34:27,680 --> 00:34:27,740
+بيبقى بيبقى بيبقى بيبقى بيبقى بيبقى بيبقى بيبقى
+
+458
+00:34:27,740 --> 00:34:38,060
+بيبقى بيبقى بيبقى ب
+
+459
+00:34:38,410 --> 00:34:47,590
+فتساوي خمسين او V0 مثلا V0 هتساوي A لان فتا تنين
+
+460
+00:34:47,590 --> 00:34:54,390
+على اثنين زائد B اليمين minus A لان فتا واحد على
+
+461
+00:34:54,390 --> 00:35:02,810
+اثنين فتساوي A لان فتا تنين على فتا واحد اذا ايه
+
+462
+00:35:02,810 --> 00:35:08,050
+ايش هتساوي V0 على لان
+
+463
+00:35:10,350 --> 00:35:15,090
+بعد ذلك احنا عرفنا ال B ابدلالة ال A وعرفنا ال A
+
+464
+00:35:15,090 --> 00:35:19,610
+بقدر ارجع وضع ال A اللى هى B لضع لانسى 2 على ساتة
+
+465
+00:35:19,610 --> 00:35:24,030
+واحد بقدر اذا اكتب ال potential بشكل عام ابدلالة
+
+466
+00:35:24,030 --> 00:35:29,310
+اللى هو ال A و ال B اللى هى B لضت لانسى 6 على 2
+
+467
+00:35:29,310 --> 00:35:33,130
+على تان ستة واحد على اتنين على لان ستة اتنين على
+
+468
+00:35:33,130 --> 00:35:37,930
+تان ستة اتنين على تان ستة واحد على اتنينانا ال 10
+
+469
+00:35:37,930 --> 00:35:44,250
+ضيعتها او انت كنت ساكتين لن تم تلتة واحدة على
+
+470
+00:35:44,250 --> 00:35:51,010
+اتنين انا لن ما ضيعتها لن تم تلتة واحدة على اتنين
+
+471
+00:35:51,010 --> 00:36:03,010
+فاول شيء ايه؟ من هنا انا جادي واضح لن تم دنيا ضاعة
+
+472
+00:36:03,010 --> 00:36:12,210
+على اتناش زي اتنينأحنا V0 يعني لن تان فتة تمين على
+
+473
+00:36:12,210 --> 00:36:21,810
+اتنين زي بي وقلنا بي من هي من هي minus A
+
+474
+00:36:21,810 --> 00:36:29,150
+لن تان فتة واحد على اتنين وبالتالي V0 ايش هتساوي
+
+475
+00:36:29,150 --> 00:36:34,570
+او A يعني بنقدر نقول انه A بيساوي V0 على فدولة تان
+
+476
+00:36:34,570 --> 00:36:41,390
+لن و لنالفئة الاسفة بينهم هتكون لن تان ثانية ثانية
+
+477
+00:36:41,390 --> 00:36:56,790
+اتنين على اتنين على اتن
+
+478
+00:36:56,790 --> 00:37:01,170
+بيتا واحدة اتن بيتا واحدة على اتن بيتا واحدة على
+
+479
+00:37:01,170 --> 00:37:04,430
+اتن بيتا
+
+480
+00:37:04,430 --> 00:37:11,700
+واحدة على اتن بيتا واحدة على اتنلن تان ثتا اتنين
+
+481
+00:37:11,700 --> 00:37:17,680
+على اتنين على تان ثتا واحد على اتنين وبالتالي بقى
+
+482
+00:37:17,680 --> 00:37:25,360
+درجة بيش بتسوي minus a equal هذا الكلام بيقلو تان
+
+483
+00:37:25,360 --> 00:37:29,580
+ثتا واحد على تان لن تان
+
+484
+00:37:38,160 --> 00:37:48,100
+طب V إيش بتساوي؟ A times theta 1 على 2 و أقدر أحسب
+
+485
+00:37:48,100 --> 00:37:52,380
+اللي هو قيمة ال potential بنعوض عنهم بيطلع معنا
+
+486
+00:37:52,380 --> 00:37:55,200
+المفترة اللي ماتش فيها بتعتمد على N times theta
+
+487
+00:37:55,200 --> 00:38:00,560
+بقى كله constants E إيش بتساوي؟ minus دلن ال V لإن
+
+488
+00:38:00,560 --> 00:38:04,640
+طبعا كل هذا بنرجح في النهاية بنعوض عن هنا عن Aنعوض
+
+489
+00:38:04,640 --> 00:38:08,100
+عن A و بنعوض عن B فبتظهر لنا ten theta على اتنين
+
+490
+00:38:08,100 --> 00:38:11,940
+قعدت بس ترتيب بسيط وصير معنا اللي هو المقدار الأهم
+
+491
+00:38:11,940 --> 00:38:15,100
+بي قلنا بيساومها ناس A لان ten theta واحد على
+
+492
+00:38:15,100 --> 00:38:18,860
+اتنين لو عوضنا عنه تطينا A لان ten theta على اتنين
+
+493
+00:38:18,860 --> 00:38:23,560
+على ten theta واحد على اتنين و هكذا واضح أه؟أذا V
+
+494
+00:38:23,560 --> 00:38:27,360
+سمنا عارفينها بنجيب E ليه minus دل ال V وطبعا
+
+495
+00:38:27,360 --> 00:38:31,420
+اعتمادية على ال theta هذا ال coordinate بأخد ال
+
+496
+00:38:31,420 --> 00:38:33,960
+theta component فال gradient بتعطينا theta hat
+
+497
+00:38:33,960 --> 00:38:39,060
+minus 1 على r dv by d theta لو أنا فضلت هذا
+
+498
+00:38:39,060 --> 00:38:42,400
+المقدار طبعا مين اللي بعتمد على كل ال theta بس هذه
+
+499
+00:38:42,400 --> 00:38:45,460
+اللي فوق فده كله بيكون len على len
+
+500
+00:38:58,950 --> 00:39:06,210
+الجزء التاني مستمر بالنسبة لي هذه عبارة عن
+
+501
+00:39:17,590 --> 00:39:25,190
+تان ثتا على اتنين minus نفس الكلام D0 على length
+
+502
+00:39:25,190 --> 00:39:29,330
+تان ثتا على اتنين على اتنين تان ثتا اتنين على
+
+503
+00:39:29,330 --> 00:39:34,490
+اتنين على تان ثتا واحد على اتنين مضروف في مين في
+
+504
+00:39:34,490 --> 00:39:38,910
+اللي هو length تان ثتا واحد حقرتها على اتنين هذا
+
+505
+00:39:38,910 --> 00:39:44,040
+كله constant من النقطة فتفاضوا بثوث زفرمين بيظل
+
+506
+00:39:44,040 --> 00:39:47,460
+هنا تفاضل هذا جزء اللي هو V0 على لن تنفذ 2 على 2
+
+507
+00:39:47,460 --> 00:39:56,940
+على تنفذ 1 على 2 لن اشتفظ له 1 DX على X اشتفظ له
+
+508
+00:39:56,940 --> 00:40:04,500
+DX يكان تربيه ثتا على 2 في نص على تنفذه طب اطلع
+
+509
+00:40:04,500 --> 00:40:06,380
+معناه اللي انت شايفينه
+
+510
+00:40:11,500 --> 00:40:15,840
+هتكون E بيتساوى minus A على R طبعا احنا بنقوله هذا
+
+511
+00:40:15,840 --> 00:40:18,420
+زى ما رسمتلكم ايه كده بقولكم ايه على الورق بقدر
+
+512
+00:40:18,420 --> 00:40:22,400
+كله افضله بيطلع معايا انه E بتساوى minus B ند على
+
+513
+00:40:22,400 --> 00:40:26,560
+R sin θ ل N tan θ اتنين على اتنين على تان ستة واحد
+
+514
+00:40:26,560 --> 00:40:28,540
+اتنين ستة hat واضح
+
+515
+00:40:32,850 --> 00:40:36,970
+طبعا ال secant تربيه اللى هى sin على cosine على ال
+
+516
+00:40:36,970 --> 00:40:40,470
+secant تربيه واحد على cosine تربيه اللى هى ال
+
+517
+00:40:40,470 --> 00:40:44,010
+trick اللى استخدمناها على التان ايش بيصير التان؟
+
+518
+00:40:44,010 --> 00:40:47,850
+sin على cosine فعشان هيك بيضلنا بس اللى هى ال
+
+519
+00:40:47,850 --> 00:40:50,670
+cosine اللى أمامنا هال DX على X زى ما اتفقنا
+
+520
+00:40:50,670 --> 00:40:54,590
+فبتعطينا اللى هى secant تربيه على التان وبالتالي
+
+521
+00:40:54,590 --> 00:41:00,480
+بيضلنا المفضل اللى أمامنابنعوض عن الأرقام لان طول
+
+522
+00:41:00,480 --> 00:41:04,620
+الوقت نستخدم V0 و θ1 و θ2 بيعطينا قيمة ال
+
+523
+00:41:04,620 --> 00:41:07,920
+potential اللى هو طالبه قيمة ال potential هو قيمة
+
+524
+00:41:07,920 --> 00:41:10,240
+ال electric field بعوض عن الأرقام الموجودة عندى و
+
+525
+00:41:10,240 --> 00:41:14,600
+مش بيعطينا قيمة R لان هو semi infiniteو .. او يعني
+
+526
+00:41:14,600 --> 00:41:17,280
+مش ايه لأ قداش ال radius تبع ال coin و قداش كلمة
+
+527
+00:41:17,280 --> 00:41:21,500
+ال .. طبعا هو function of θ و R ناتج ال electric
+
+528
+00:41:21,500 --> 00:41:25,840
+field زي ما انتش فيه بيطلع function of R و θ لو
+
+529
+00:41:25,840 --> 00:41:28,220
+بيعطينا نقطة محددة ايه يعني النقطة المحددة
+
+530
+00:41:28,220 --> 00:41:31,840
+بيجيبالك ان هو طبعا بدنا ال electric field فلاحظنا
+
+531
+00:41:31,840 --> 00:41:35,800
+بعد التفاضل اللي عملناه انه بيطلع ان ال E من وين
+
+532
+00:41:35,800 --> 00:41:39,360
+اشت ال R من اللي هي ال gradient بيطلع ال electric
+
+533
+00:41:39,360 --> 00:41:44,060
+field function of R و θ ال potentialفقط function
+
+534
+00:41:44,060 --> 00:41:49,700
+of θ لكن الectric field فهي function of two points
+
+535
+00:41:49,700 --> 00:41:54,480
+R وθ هذا اللي هو ال separation of variables اللي
+
+536
+00:41:54,480 --> 00:41:57,400
+هناخده اللي قادم ان شاء الله هنا عندنا زي ما انتوا
+
+537
+00:41:57,400 --> 00:42:02,540
+شايفين ان اللي هو المتوازن الاضلاع وعندنا ال
+
+538
+00:42:02,540 --> 00:42:07,820
+conditions على كل surface وبدنا نجيب ال potential
+
+539
+00:42:07,820 --> 00:42:11,600
+فواضح انه فينا potential بين اللي هو ال plate اللي
+
+540
+00:42:11,600 --> 00:42:11,960
+على ال
+
+541
+00:42:20,920 --> 00:42:29,930
+عن طريق الاسئلة الاسئلة الاسئلة هيبالتالي هذا
+
+542
+00:42:29,930 --> 00:42:33,710
+هنحتاج two variables x و y وبالتالي لازم نحل ال
+
+543
+00:42:33,710 --> 00:42:37,250
+potential في two dimensions و نعمل ان هي
+
+544
+00:42:37,250 --> 00:42:40,950
+separation of variables فخلي هذا للقاء القادم ان
+
+545
+00:42:40,950 --> 00:42:45,410
+شاء الله وبنخلص second chapter لقاء القادم
+
diff --git a/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/T2PklTp3S9c_raw.json b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/T2PklTp3S9c_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..4420c079677250cda368a341e9febec5200eacba
--- /dev/null
+++ b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/T2PklTp3S9c_raw.json
@@ -0,0 +1 @@
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0.79315185546875}, {"start": 653.08, "end": 653.22, "word": " ما", "probability": 0.55224609375}, {"start": 653.22, "end": 653.4, "word": " هم", "probability": 0.54248046875}, {"start": 653.4, "end": 653.92, "word": " grounded", "probability": 0.88037109375}, {"start": 653.92, "end": 654.74, "word": " وطبعا", "probability": 0.966796875}, {"start": 654.74, "end": 654.96, "word": " هذا", "probability": 0.452392578125}, {"start": 654.96, "end": 655.44, "word": " ماخده", "probability": 0.84210205078125}, {"start": 655.44, "end": 655.96, "word": " كسبيل", "probability": 0.7744140625}, {"start": 655.96, "end": 656.28, "word": " مثل", "probability": 0.7666015625}, {"start": 656.28, "end": 656.54, "word": " X", "probability": 0.7138671875}, {"start": 656.54, "end": 657.06, "word": " direction", "probability": 0.60546875}], "temperature": 1.0}, {"id": 27, "seek": 67108, "start": 658.04, "end": 671.08, "text": "إن ال limits تعمل photographic ال photo conductor من zero ل A و الفراغ اللي فيه في ال photo conductor عندنا من A ل D، بيكون دايما مشحون ال photo conductor بستفت شعج ع سبيل المثال", "tokens": [28814, 1863, 2423, 10406, 6055, 25957, 1211, 8348, 299, 2423, 5052, 29957, 9154, 4018, 5296, 316, 4032, 27188, 2288, 5718, 118, 13672, 1829, 8978, 3224, 8978, 2423, 5052, 29957, 43242, 8315, 9154, 316, 5296, 413, 12399, 4724, 1829, 30544, 11778, 47302, 15042, 37893, 5016, 11536, 2423, 5052, 29957, 4724, 14851, 5172, 2655, 13412, 3615, 7435, 6225, 8608, 21292, 1211, 9673, 12984, 6027], "avg_logprob": -0.3105158701775566, "compression_ratio": 1.5393939393939393, "no_speech_prob": 0.0, "words": [{"start": 658.04, "end": 658.38, "word": "إن", "probability": 0.56329345703125}, {"start": 658.38, "end": 658.76, "word": " ال", "probability": 0.673828125}, {"start": 658.76, "end": 659.3, "word": " limits", "probability": 0.9541015625}, {"start": 659.3, "end": 659.68, "word": " تعمل", "probability": 0.7772623697916666}, {"start": 659.68, "end": 660.4, "word": " photographic", "probability": 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"word": " ال", "probability": 0.89794921875}, {"start": 665.06, "end": 665.32, "word": " photo", "probability": 0.90966796875}, {"start": 665.32, "end": 665.68, "word": " conductor", "probability": 0.94091796875}, {"start": 665.68, "end": 665.98, "word": " عندنا", "probability": 0.928955078125}, {"start": 665.98, "end": 666.1, "word": " من", "probability": 0.96484375}, {"start": 666.1, "end": 666.34, "word": " A", "probability": 0.916015625}, {"start": 666.34, "end": 666.6, "word": " ل", "probability": 0.953125}, {"start": 666.6, "end": 667.56, "word": " D،", "probability": 0.594482421875}, {"start": 667.56, "end": 667.92, "word": " بيكون", "probability": 0.888671875}, {"start": 667.92, "end": 668.16, "word": " دايما", "probability": 0.9482421875}, {"start": 668.16, "end": 668.56, "word": " مشحون", "probability": 0.9186197916666666}, {"start": 668.56, "end": 668.64, "word": " ال", "probability": 0.884765625}, {"start": 668.64, "end": 668.84, "word": " photo", "probability": 0.92919921875}, {"start": 668.84, "end": 669.32, "word": " conductor", "probability": 0.94091796875}, {"start": 669.32, "end": 669.9, "word": " بستفت", "probability": 0.60919189453125}, {"start": 669.9, "end": 670.24, "word": " شعج", "probability": 0.79931640625}, {"start": 670.24, "end": 670.36, "word": " ع", "probability": 0.751953125}, {"start": 670.36, "end": 670.64, "word": " سبيل", "probability": 0.4784342447916667}, {"start": 670.64, "end": 671.08, "word": " المثال", "probability": 0.9830729166666666}], "temperature": 1.0}, {"id": 28, "seek": 69111, "start": 672.23, "end": 691.11, "text": "مش اللي بيصير انه لما نحط القماش عشان نعملها copying بيصير combination هاي العملية هنا ما بين ال positive و ال negative charges وبالتالي لما يحطوا الحبر بياخد تسخن ال .. الماد ال .. ال .. النسخة اللي انا بتاخد منها ال copy و الحبر بياخد اللي هي", "tokens": [2304, 8592, 13672, 1829, 4724, 1829, 9381, 13546, 16472, 3224, 5296, 15042, 8717, 5016, 9566, 25062, 2304, 33599, 6225, 8592, 7649, 8717, 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"probability": 0.9755859375}, {"start": 673.53, "end": 673.85, "word": " نحط", "probability": 0.93994140625}, {"start": 673.85, "end": 674.43, "word": " القماش", "probability": 0.94580078125}, {"start": 674.43, "end": 674.77, "word": " عشان", "probability": 0.98486328125}, {"start": 674.77, "end": 675.21, "word": " نعملها", "probability": 0.9837646484375}, {"start": 675.21, "end": 675.71, "word": " copying", "probability": 0.828125}, {"start": 675.71, "end": 676.69, "word": " بيصير", "probability": 0.9139404296875}, {"start": 676.69, "end": 677.37, "word": " combination", "probability": 0.93115234375}, {"start": 677.37, "end": 677.63, "word": " هاي", "probability": 0.5419921875}, {"start": 677.63, "end": 678.05, "word": " العملية", "probability": 0.984375}, {"start": 678.05, "end": 678.31, "word": " هنا", "probability": 0.9658203125}, {"start": 678.31, "end": 678.85, "word": " ما", "probability": 0.57861328125}, {"start": 678.85, "end": 679.13, "word": " بين", "probability": 0.9609375}, {"start": 679.13, "end": 679.29, "word": " ال", "probability": 0.7626953125}, {"start": 679.29, "end": 679.57, "word": " positive", "probability": 0.87255859375}, {"start": 679.57, "end": 679.77, "word": " و", "probability": 0.7724609375}, {"start": 679.77, "end": 679.81, "word": " ال", "probability": 0.58837890625}, {"start": 679.81, "end": 680.05, "word": " negative", "probability": 0.97021484375}, {"start": 680.05, "end": 680.93, "word": " charges", "probability": 0.47509765625}, {"start": 680.93, "end": 682.09, "word": " وبالتالي", "probability": 0.808154296875}, {"start": 682.09, "end": 682.27, "word": " لما", "probability": 0.94140625}, {"start": 682.27, "end": 682.65, "word": " يحطوا", "probability": 0.886962890625}, {"start": 682.65, "end": 683.05, "word": " الحبر", "probability": 0.970703125}, {"start": 683.05, "end": 683.99, "word": " بياخد", "probability": 0.9346923828125}, {"start": 683.99, "end": 684.69, "word": " تسخن", "probability": 0.920166015625}, {"start": 684.69, "end": 684.99, "word": " ال", "probability": 0.486083984375}, {"start": 684.99, "end": 684.99, "word": " ..", "probability": 0.701171875}, {"start": 684.99, "end": 685.53, "word": " الماد", "probability": 0.717529296875}, {"start": 685.53, "end": 685.71, "word": " ال", "probability": 0.408447265625}, {"start": 685.71, "end": 685.85, "word": " ..", "probability": 0.875}, {"start": 685.85, "end": 686.23, "word": " ال", "probability": 0.53271484375}, {"start": 686.23, "end": 686.23, "word": " ..", "probability": 0.896484375}, {"start": 686.23, "end": 687.13, "word": " النسخة", "probability": 0.870849609375}, {"start": 687.13, "end": 687.21, "word": " اللي", "probability": 0.882568359375}, {"start": 687.21, "end": 687.27, "word": " انا", "probability": 0.735595703125}, {"start": 687.27, "end": 687.97, "word": " بتاخد", "probability": 0.69921875}, {"start": 687.97, "end": 688.25, "word": " منها", "probability": 0.928466796875}, {"start": 688.25, "end": 688.43, "word": " ال", "probability": 0.8662109375}, {"start": 688.43, "end": 688.69, "word": " copy", "probability": 0.97216796875}, {"start": 688.69, "end": 689.27, "word": " و", "probability": 0.76025390625}, {"start": 689.27, "end": 689.71, "word": " الحبر", "probability": 0.98828125}, {"start": 689.71, "end": 690.59, "word": " بياخد", "probability": 0.9842529296875}, {"start": 690.59, "end": 690.95, "word": " اللي", "probability": 0.95166015625}, {"start": 690.95, "end": 691.11, "word": " هي", "probability": 0.80908203125}], "temperature": 1.0}, {"id": 29, "seek": 71125, "start": 691.47, "end": 711.25, "text": "الـ form أو يعني بتشكل حسب اللي هي المعلومات اللي موجودة على النسخة الأصلية وبعد هيك بيروح و بيمور عليه الورق الأبيض و بياخد النسخة و بيعمل النسخة إيش اللي طاروا من هذا؟ هذه هي الفكرة إحنا بدنا نقرر أو نحدد we want to determine", "tokens": [6027, 39184, 1254, 34051, 37495, 22653, 39894, 8592, 28820, 11331, 35457, 13672, 1829, 39896, 9673, 30241, 20498, 9307, 13672, 1829, 3714, 29245, 23328, 3660, 15844, 28239, 3794, 9778, 3660, 16247, 9381, 1211, 10632, 46599, 22488, 39896, 4117, 4724, 1829, 32887, 5016, 4032, 4724, 32640, 13063, 47356, 2423, 13063, 4587, 16247, 21292, 11242, 4032, 4724, 1829, 47283, 3215, 28239, 3794, 9778, 3660, 4032, 4724, 1829, 25957, 1211, 28239, 3794, 9778, 3660, 11933, 1829, 8592, 13672, 1829, 23032, 9640, 14407, 9154, 23758, 22807, 29538, 39896, 27188, 4117, 25720, 11933, 5016, 8315, 47525, 8315, 8717, 4587, 2288, 2288, 34051, 8717, 24401, 3215, 321, 528, 281, 6997], "avg_logprob": -0.25090144689266497, "compression_ratio": 1.7522522522522523, "no_speech_prob": 3.9517879486083984e-05, "words": [{"start": 691.47, "end": 692.07, "word": "الـ", "probability": 0.3297119140625}, {"start": 692.07, "end": 692.39, "word": " form", "probability": 0.60205078125}, {"start": 692.39, "end": 692.65, "word": " أو", "probability": 0.347412109375}, {"start": 692.65, "end": 692.81, "word": " يعني", "probability": 0.796875}, {"start": 692.81, "end": 693.35, "word": " بتشكل", "probability": 0.9586588541666666}, {"start": 693.35, "end": 693.81, "word": " حسب", "probability": 0.8232421875}, {"start": 693.81, "end": 694.03, "word": " اللي", "probability": 0.772705078125}, {"start": 694.03, "end": 694.15, "word": " هي", "probability": 0.947265625}, {"start": 694.15, "end": 695.01, "word": " المعلومات", "probability": 0.962646484375}, {"start": 695.01, "end": 695.17, "word": " اللي", "probability": 0.791748046875}, {"start": 695.17, "end": 695.73, "word": " موجودة", "probability": 0.9849853515625}, {"start": 695.73, "end": 696.37, "word": " على", "probability": 0.93115234375}, {"start": 696.37, "end": 697.11, "word": " النسخة", "probability": 0.9010009765625}, {"start": 697.11, "end": 697.69, "word": " الأصلية", "probability": 0.74493408203125}, {"start": 697.69, "end": 698.49, "word": " وبعد", "probability": 0.7705078125}, {"start": 698.49, "end": 698.95, "word": " هيك", "probability": 0.85693359375}, {"start": 698.95, "end": 699.75, "word": " بيروح", "probability": 0.741455078125}, {"start": 699.75, "end": 699.89, "word": " و", "probability": 0.214111328125}, {"start": 699.89, "end": 700.27, "word": " بيمور", "probability": 0.625732421875}, {"start": 700.27, "end": 700.49, "word": " عليه", "probability": 0.93896484375}, {"start": 700.49, "end": 700.77, "word": " الورق", "probability": 0.97021484375}, {"start": 700.77, "end": 701.29, "word": " الأبيض", "probability": 0.9759114583333334}, {"start": 701.29, "end": 701.43, "word": " و", "probability": 0.92724609375}, {"start": 701.43, "end": 701.89, "word": " بياخد", "probability": 0.8795166015625}, {"start": 701.89, "end": 702.53, "word": " النسخة", "probability": 0.95361328125}, {"start": 702.53, "end": 702.89, "word": " و", "probability": 0.299072265625}, {"start": 702.89, "end": 703.15, "word": " بيعمل", "probability": 0.9061279296875}, {"start": 703.15, "end": 703.79, "word": " النسخة", "probability": 0.9808349609375}, {"start": 703.79, "end": 704.53, "word": " إيش", "probability": 0.7132975260416666}, {"start": 704.53, "end": 704.69, "word": " اللي", "probability": 0.9951171875}, {"start": 704.69, "end": 705.01, "word": " طاروا", "probability": 0.7435709635416666}, {"start": 705.01, "end": 705.15, "word": " من", "probability": 0.95361328125}, {"start": 705.15, "end": 705.89, "word": " هذا؟", "probability": 0.3736572265625}, {"start": 705.89, "end": 706.17, "word": " هذه", "probability": 0.273681640625}, {"start": 706.17, "end": 706.31, "word": " هي", "probability": 0.763671875}, {"start": 706.31, "end": 706.75, "word": " الفكرة", "probability": 0.9700520833333334}, {"start": 706.75, "end": 708.79, "word": " إحنا", "probability": 0.7882486979166666}, {"start": 708.79, "end": 709.21, "word": " بدنا", "probability": 0.92724609375}, {"start": 709.21, "end": 709.75, "word": " نقرر", "probability": 0.98876953125}, {"start": 709.75, "end": 709.89, "word": " أو", "probability": 0.908203125}, {"start": 709.89, "end": 710.37, "word": " نحدد", "probability": 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diff --git a/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/UItqMtiDJ-k_postprocess.srt b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/UItqMtiDJ-k_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..e216a7cae73d9c232395f1a6fa99881204ce4f0d
--- /dev/null
+++ b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/UItqMtiDJ-k_postprocess.srt
@@ -0,0 +1,1524 @@
+1
+00:00:20,450 --> 00:00:22,510
+بسم الله الرحمن الرحيم الحمد لله يا رب العالمين
+
+2
+00:00:22,510 --> 00:00:25,150
+والصلاة والسلام على رسول الله اللهم أعلمنا ما
+
+3
+00:00:25,150 --> 00:00:29,450
+ينفعنا وإنفعنا بما أعلمتنا وزدنا الله طب اليوم
+
+4
+00:00:29,450 --> 00:00:33,390
+هنبدأ في chapter 4 هو إيش electrostatic طبعا في
+
+5
+00:00:33,390 --> 00:00:37,770
+بداية ال chapter هنتكلم عن إيش columns law هنش
+
+6
+00:00:37,770 --> 00:00:40,910
+بعرف ليه columns law بحكي لها deals with a force a
+
+7
+00:00:40,910 --> 00:00:43,590
+pointed charge exerts on another pointed charge
+
+8
+00:00:43,590 --> 00:00:48,030
+بتعني بتعامل مع إيش pointed charges طبعا بتعامل مع
+
+9
+00:00:48,030 --> 00:00:52,510
+إيش قوةبتأثر من point of charge على point of
+
+10
+00:00:52,510 --> 00:00:56,170
+charge تاني فاهم بيحكيلي two polarity of charges
+
+11
+00:00:56,170 --> 00:00:59,370
+may be positive or negative فاهم بيحكيلي الشخنات
+
+12
+00:00:59,370 --> 00:01:05,010
+بيكون قطبية اما مشابه او سالق ثم بيحكيلي like
+
+13
+00:01:05,010 --> 00:01:09,810
+charges repel and unlike charges attract فادي ايش
+
+14
+00:01:09,810 --> 00:01:13,450
+معناه ان شخنات متشابهة تتنافع فانا عندي two
+
+15
+00:01:13,450 --> 00:01:16,990
+positive charges بيصير بينهم ايه تنافع او two
+
+16
+00:01:16,990 --> 00:01:20,820
+negative chargesبارضه بيصير بينهم فنافر و بعدين ال
+
+17
+00:01:20,820 --> 00:01:24,360
+liked charges attract يعني الشحنات المختلفة ال
+
+18
+00:01:24,360 --> 00:01:28,480
+مختلفة ايش بيصير بينها تجارب attract فهنا على
+
+19
+00:01:28,480 --> 00:01:31,320
+اليمين في عندى ايش شحنة مجابعة positive في عندى
+
+20
+00:01:31,320 --> 00:01:36,140
+شحنة سالمة negative بيصير بينهم ايش attract تمام و
+
+21
+00:01:36,140 --> 00:01:39,700
+انا بحكيلي charges measured in columns بحكيلي احنا
+
+22
+00:01:39,700 --> 00:01:42,940
+ايش واحدة القياس اللي هي الشحنة عبارة عن ايش
+
+23
+00:01:42,940 --> 00:01:47,160
+column و بحكيلي one column بكافة ستة في عشر او
+
+24
+00:01:47,160 --> 00:01:51,460
+ستمانتاش ايشElectrons طبعا اعتقد ان المفاهيم مرت
+
+25
+00:01:51,460 --> 00:01:55,780
+عليكم اعتقد الفيزيا الفيزيا او الفيزيا بقى طيب هذي
+
+26
+00:01:55,780 --> 00:01:59,160
+بيحكيلي شحنة ال Electron ال E هذي عبارة عن شحنة ال
+
+27
+00:01:59,160 --> 00:02:02,280
+Electron كل واحد point ستة سفر اتنين عشرة أساليب
+
+28
+00:02:02,280 --> 00:02:05,760
+تسعتاش ايه؟ Columns طبعا و بعدين بيحكيلي ال
+
+29
+00:02:05,760 --> 00:02:10,640
+protons has a charge of E و بعدين Electron has a
+
+30
+00:02:10,640 --> 00:02:14,360
+charge of minus E طبعا بنعرف انه زرع بيكون فيها
+
+31
+00:02:14,360 --> 00:02:18,180
+protons و ايه؟ Electrons طبعاو طبعا شحنة ال proton
+
+32
+00:02:18,180 --> 00:02:22,140
+بتكون موجبة و شحنة ال electron ايش بتكون ثالثة
+
+33
+00:02:22,140 --> 00:02:25,060
+فانت بتحكيلي شحنة ال proton هتكون positive E و
+
+34
+00:02:25,060 --> 00:02:28,460
+شحنة ال electron هتكون negative E فهي قيمة ال E
+
+35
+00:02:28,460 --> 00:02:32,780
+ليها N كولوز طبعا و انا بتحكيلي ان atom اللي هي
+
+36
+00:02:32,780 --> 00:02:37,140
+الذرع or group of atoms that has lost one or more
+
+37
+00:02:37,140 --> 00:02:40,840
+electrons gives a net positive charge هتكون عندي
+
+38
+00:02:40,840 --> 00:02:45,800
+ذرع او مجموعة ذرع لما تفقدone or more electrons
+
+39
+00:02:45,800 --> 00:02:48,620
+لما الذرة تفقد electron إيش هيكون عند الشحنة
+
+40
+00:02:48,620 --> 00:02:53,640
+الكلية نت positive charge لإنه لما الذرة تفقد
+
+41
+00:02:53,640 --> 00:02:57,220
+electron هيصير عدد ال protons أكبر من عدد ال
+
+42
+00:02:57,220 --> 00:03:00,820
+electrons وبالتالي بنحكي نت positive charge طبعا
+
+43
+00:03:00,820 --> 00:03:05,720
+العكس؟ العكس صحيح طبعا هل يحكي لي إيه؟ if it
+
+44
+00:03:05,720 --> 00:03:08,520
+gained one or more electrons لو عند ال atom الذرة
+
+45
+00:03:08,520 --> 00:03:11,700
+اكتسبت electron وبالتالي هيصير عدد ال electrons
+
+46
+00:03:11,700 --> 00:03:16,200
+أكتر من عدد ال protonsوبالتالي it gives a net
+
+47
+00:03:16,200 --> 00:03:19,260
+negative charge هيكون عندي إيش negative charge، مش
+
+48
+00:03:19,260 --> 00:03:22,100
+كده احنا بنسميها حيانا positive ion و إيش negative
+
+49
+00:03:22,100 --> 00:03:27,780
+ion طيب
+
+50
+00:03:27,780 --> 00:03:31,760
+هم تكيلي columns law it states that the force F
+
+51
+00:03:31,760 --> 00:03:37,580
+between two point charges Q1 و Q2 قوة عندنا two
+
+52
+00:03:37,580 --> 00:03:42,780
+point charges هيكون بينهم إيش forceحكيلي ال force
+
+53
+00:03:42,780 --> 00:03:45,600
+هي اللي بتكون along the line joining them ايش يعني
+
+54
+00:03:45,600 --> 00:03:48,720
+along the line joining them؟ ال force عبارة عن
+
+55
+00:03:48,720 --> 00:03:53,000
+ايش؟ فكتور متجه يكون اتجاهه على نفس ال line اللي
+
+56
+00:03:53,000 --> 00:03:55,780
+بيجمعته ال points and charges، هاي أول شي نقطة
+
+57
+00:03:55,780 --> 00:03:58,860
+تانية، بيحكيلي directly proportional to the
+
+58
+00:03:58,860 --> 00:04:04,560
+product Q1 Q2 of charges، طبعا؟ بيحكيلي متناسب،
+
+59
+00:04:04,560 --> 00:04:08,900
+طردية، محاصر، دار، شو احنا؟ احنا Q1 و Q2 وبالتالي
+
+60
+00:04:08,900 --> 00:04:12,930
+ال force هذهتتناسب ترضيا مع حاصل ضربه طبعا الكلام
+
+61
+00:04:12,930 --> 00:04:17,070
+هذا هيكون واضح من خلال القانون بعدين بيحكي
+
+62
+00:04:17,070 --> 00:04:20,030
+inversely proportional to the square of the
+
+63
+00:04:20,030 --> 00:04:25,010
+distance R between them وبالتالي بتناسب عكسيا مع
+
+64
+00:04:25,010 --> 00:04:28,310
+مربع المسافة بين ال two points each other طبعا دي
+
+65
+00:04:28,310 --> 00:04:33,050
+طالع القانون هاندي F ايش بيستخدم كي واحد كتنين على
+
+66
+00:04:33,050 --> 00:04:36,430
+R تلوينطب هون K عبارة عن constant و بحكي ال K
+
+67
+00:04:36,430 --> 00:04:40,150
+لحظوا هنا ال K شو بتساوي 1 على أربعة باقي each
+
+68
+00:04:40,150 --> 00:04:43,970
+other فبتلاح يصير عندك قانون ال force هتساوي Q1 و
+
+69
+00:04:43,970 --> 00:04:48,110
+Q2 على أربعة باقي each another R² طب اللحظوا هنا
+
+70
+00:04:48,110 --> 00:04:50,870
+ال force هاد عبارة عن إيش؟ هاد ال magnitude إحنا
+
+71
+00:04:50,870 --> 00:04:53,390
+بنعرف إنه عبارة عن إيش vector ال force في النهاية
+
+72
+00:04:53,390 --> 00:04:56,210
+عبارة عن vector متجه في اتجاه معين ممكن تكون قوة
+
+73
+00:04:56,210 --> 00:04:58,510
+في هذا الاتجاه أو في هذا الاتجاه أو في اتجاه تاني
+
+74
+00:04:58,510 --> 00:05:01,570
+لكن هدا القانون اللي قبل كتبنا عبارة عن إيش ال
+
+75
+00:05:01,570 --> 00:05:06,120
+magnitude لإيش لال forceهذا هنشوف ال force as a
+
+76
+00:05:06,120 --> 00:05:10,420
+vector هنشوف هذا ال K يسمى permittivity of free
+
+77
+00:05:10,420 --> 00:05:15,100
+space و طبعا هذا البرهين constant بيحكي 8.854×10⁻²
+
+78
+00:05:15,100 --> 00:05:20,240
+وهذا تقريبا بالساوية 10⁻9 36 بقى طبعا هذي constant
+
+79
+00:05:20,240 --> 00:05:23,840
+و عروفة و بعد الفيديو دي ال K حكينا دلالة ال Y
+
+80
+00:05:23,840 --> 00:05:31,680
+naught 1⁴Y naught 9×10⁹ تمام متر بفرقة واضح؟
+
+81
+00:05:35,690 --> 00:05:40,510
+طيب هاي في عندي الرسم هان بتوضحلي
+
+82
+00:05:40,510 --> 00:05:44,470
+ان عندي point of charge Q1 point of charge Q2 طب
+
+83
+00:05:44,470 --> 00:05:48,290
+هان عندي ايش ال origins عندي R1 هيكون position
+
+84
+00:05:48,290 --> 00:05:52,050
+vector يعني وين عندي شحنة Q1 located وين موجودة
+
+85
+00:05:52,050 --> 00:05:56,550
+فعندي position vector R وعندي Q2 ورحني فين R؟
+
+86
+00:05:56,550 --> 00:05:59,630
+اتنين position vector يعني ال location لpoint of
+
+87
+00:05:59,630 --> 00:06:03,850
+charge Q2 طب حكينا هيكون بينهم forces هتلاحظوا
+
+88
+00:06:03,850 --> 00:06:11,530
+عندي F1طب ايش المقصود فى F12 ال force على Q2 النجا
+
+89
+00:06:11,530 --> 00:06:16,490
+من point of charge Q1 برغم فى الاندغال F21 هذه
+
+90
+00:06:16,490 --> 00:06:23,490
+معناه ال force on Q1 due to point of charge FQ2
+
+91
+00:06:23,490 --> 00:06:27,830
+واضح طيب بعدين القانون كتبناها مرة تانية فبعدين فى
+
+92
+00:06:27,830 --> 00:06:33,050
+the force F12 طبعا ال F12 حكيها on Q2 due to Q1
+
+93
+00:06:34,780 --> 00:06:39,960
+فهنكتبنا ال force as vector لحظة هون F12 عاملة هنا
+
+94
+00:06:39,960 --> 00:06:43,660
+سهل يعني هذا عبارة عن أيش vector هسو Q1 و Q2 على
+
+95
+00:06:43,660 --> 00:06:49,140
+أربع باقية من ال node R2 في هنشر هنا نسمي unit
+
+96
+00:06:49,140 --> 00:06:56,020
+vector في اتجاه R12 هذا عبارة عن متجه وحدة A R12
+
+97
+00:06:56,020 --> 00:07:03,180
+متجه وحدة في اتجاه R12 طبعا ال R12 هي الرسمماذا
+
+98
+00:07:03,180 --> 00:07:08,960
+يسمى ال vector R12؟ vector على line بين Q1 وQ2
+
+99
+00:07:08,960 --> 00:07:12,180
+وبالتالي هنا متجهة واحدة طبعا المتجهة الوحدة احنا
+
+100
+00:07:12,180 --> 00:07:14,620
+بنعرف كيف بنجيب دايما اي متجهة واحدة لو عندنا اي
+
+101
+00:07:14,620 --> 00:07:19,040
+vector فنجيب unit vector متجهة واحدة ونقسم على ال
+
+102
+00:07:19,040 --> 00:07:25,600
+magnitude تمام؟ وبالتالي هيصير عندي AR عن AR12
+
+103
+00:07:25,600 --> 00:07:32,040
+متجهة واحدة في اتجاه R12 هيسمى المتجهة R12 as a
+
+104
+00:07:32,040 --> 00:07:39,040
+vectorعلى magnitude r12 طبعا و هذا ايش هيساوي
+
+105
+00:07:39,040 --> 00:07:44,160
+لاحظوا r12 ال vector r12 ممكن نديه بالدلالة ال two
+
+106
+00:07:44,160 --> 00:07:49,020
+vectors r1 و r2 هتلاحظوا انه عبارة عن r2 minus r1
+
+107
+00:07:49,020 --> 00:07:55,420
+و إتالة هنعوضها هيصير عندى r2 minus r1 فاكرتها مره
+
+108
+00:07:55,420 --> 00:07:59,340
+أنكم في أول chapter أو تاني chapter او تاني
+
+109
+00:07:59,340 --> 00:08:00,080
+chapter او تاني chapter او تاني chapter او تاني
+
+110
+00:08:00,080 --> 00:08:03,880
+chapter او تاني chapterالمهم الـ magnitude R12
+
+111
+00:08:03,880 --> 00:08:08,660
+خدها في الكتاب و اعملها بالشكل هذا بيعملها Italic
+
+112
+00:08:08,660 --> 00:08:12,800
+ايش هال Italic؟ Magnitude دايما في الكتاب اذا
+
+113
+00:08:12,800 --> 00:08:18,260
+عمللي R Bold هتكون هذا عبارة عن ايش؟ R Bold هذي
+
+114
+00:08:18,260 --> 00:08:22,860
+عبارة عن Vector و بعدين هذي R Italic بالشكل هذا
+
+115
+00:08:22,860 --> 00:08:28,600
+هذي هتكون عبارة عن ايش؟ Magnitude طبعا و أحيانا في
+
+116
+00:08:28,600 --> 00:08:32,340
+بعض الكتب بيعملوا رسالة مع ال vectorبس هبطل مثلا
+
+117
+00:08:32,340 --> 00:08:34,840
+عشان اوضح ان هذا عبارة عن ايش مثلا vector او R12
+
+118
+00:08:34,840 --> 00:08:38,080
+عبارة عن ايش vector طيب و التاني هاي unit vector
+
+119
+00:08:38,080 --> 00:08:45,100
+هيصير R2-R1 على R تمام؟ و ال R هذه عبارة عن
+
+120
+00:08:45,100 --> 00:08:50,220
+magnitude لـ R1 و تالا هيصير عند القانون بس او
+
+121
+00:08:50,220 --> 00:08:56,260
+اضبط ال unit vector هصير Q1 T2 هنلحظ و R2-R1 على
+
+122
+00:08:56,260 --> 00:09:02,370
+R2-R1 تكييب قبل ما هو نجتني التكييبطبعا شوفين هنا
+
+123
+00:09:02,370 --> 00:09:06,930
+R تربيه و في عندي من Linear Vector في عندي برضه
+
+124
+00:09:06,930 --> 00:09:15,170
+ايش هذا برضه magnitude R2-R1 طبعا وبالتالي هندروب
+
+125
+00:09:15,170 --> 00:09:17,950
+في بعض عندي R تربيه و بعدين مضروبة في magnitude R2
+
+126
+00:09:17,950 --> 00:09:23,450
+-R1 فبعندي R2-R1 في ال column تتاعي واضح؟ وبالتالي
+
+127
+00:09:23,450 --> 00:09:25,890
+هو القرون العام لإيش دول ال column دي
+
+128
+00:09:32,800 --> 00:09:36,400
+هكذا كتبنا القانون مرة تانية مرة دلالة unit vector
+
+129
+00:09:36,400 --> 00:09:41,360
+مرة دلالة vectors R2 وR1 ملاحظات بحكي لي the force
+
+130
+00:09:41,360 --> 00:09:45,660
+F21 إحنا طبعا شوفنا ال force F12 إيش القوة؟ طبعا
+
+131
+00:09:45,660 --> 00:09:50,020
+شوفنا إيش القوة على Q2 لنا جامل إيه؟ Q لأنه أحنا
+
+132
+00:09:50,020 --> 00:09:56,720
+بدنا العكس لنشوف إيش القوة على Q1 لجامل من Q2 فهو
+
+133
+00:09:56,720 --> 00:10:00,740
+بيحكي لي the force F2 on Q1 due to Q2 is هو على
+
+134
+00:10:00,740 --> 00:10:08,720
+F21كذلك F12 magnitude A R21 هتلاحظ ان ال forces
+
+135
+00:10:08,720 --> 00:10:12,040
+عبارة متساوية نفس ال magnitude فهذا فكرة F21
+
+136
+00:10:12,040 --> 00:10:17,960
+المagnitude تبعها نفس F12 تمام لما كنت تبقى تتشارج
+
+137
+00:10:17,960 --> 00:10:23,080
+بينهم force تمام هيكون نفس A في ال magnitude هم بس
+
+138
+00:10:23,080 --> 00:10:26,580
+بظل عندي ال direction واضح ان ال direction مختلف
+
+139
+00:10:26,580 --> 00:10:32,340
+فهذا ال direction F21 في اتجاه F21 في هذابالاتجار،
+
+140
+00:10:32,340 --> 00:10:38,040
+تمام؟ و بالتالي هيصير اني Ar2 as unit vector minus
+
+141
+00:10:38,040 --> 00:10:46,120
+Ar12 لأن Ar12 في هذا الاتجار و بالتالي Ar21 هيكون
+
+142
+00:10:46,120 --> 00:10:48,800
+في هذا الاتجار، اتجار مختلف عشان كده حكينا ال
+
+143
+00:10:48,800 --> 00:10:51,860
+forces هيكون لنفس ال magnitude بس الاتجار مختلف
+
+144
+00:10:51,860 --> 00:10:54,540
+واحدة في هذا الاتجار و واحدة في اتجار آخر لكن نفس
+
+145
+00:10:54,540 --> 00:10:59,560
+ايه ال magnitude، تمام؟ هم حكيلي F21 هسوة minus F1
+
+146
+00:10:59,690 --> 00:11:04,550
+بس إنه في اتجاه ال marks واضح؟ طيب و بعدين بيحكيلي
+
+147
+00:11:04,550 --> 00:11:07,090
+the distance R اللي هي المسافة بين ال two pointed
+
+148
+00:11:07,090 --> 00:11:11,690
+charges must be much larger than dimensions of
+
+149
+00:11:11,690 --> 00:11:15,590
+charged bodies Q1 and Q2 طبعا؟ و بعدين بيحكيلي ال
+
+150
+00:11:15,590 --> 00:11:19,550
+مسافة R هتكون أكبر بكتير من ال dimensions لإيش ال
+
+151
+00:11:19,550 --> 00:11:24,790
+charged bodies اللي هي Q1 و Q2 و بعدين بيحكيلي Q1
+
+152
+00:11:24,790 --> 00:11:27,850
+and Q2 must be static addressed
+
+153
+00:11:31,050 --> 00:11:35,910
+الشحنات هذه يجب أن تكون ثابتة تمام؟ و بعدين فكري
+
+154
+00:11:35,910 --> 00:11:40,430
+size of q1 و q2 must be taken into account لماذا
+
+155
+00:11:40,430 --> 00:11:46,530
+اعود هنا في قانون columns لازم انا اخد بالنسبة ليه
+
+156
+00:11:46,530 --> 00:11:49,470
+الإشارة كأن الشحنات بتكون موجبة أو ثالثة وبالتالي
+
+157
+00:11:49,470 --> 00:11:51,350
+باخد هذا الكلام بالنسبة ليه
+
+158
+00:11:55,900 --> 00:11:58,280
+طب نقول لو كان عندي unpointed charges طب و احنا
+
+159
+00:11:58,280 --> 00:12:00,640
+شوفنا لو كان عندنا بس two-pointed charges و لو كان
+
+160
+00:12:00,640 --> 00:12:05,640
+عندي unpointed charges Q1, Q2, Qn located at
+
+161
+00:12:05,640 --> 00:12:09,560
+points with position vectors R1, R2, RN لان عدة
+
+162
+00:12:09,560 --> 00:12:13,360
+pointed charges و هي position vector لكل واحد يعني
+
+163
+00:12:13,360 --> 00:12:16,580
+معروف ال location لكل point تتشارك تحكيلي the
+
+164
+00:12:16,580 --> 00:12:20,920
+resultant force of one charged Q located at point
+
+165
+00:12:21,440 --> 00:12:24,560
+والـ position vector R هو مجرد استخدام مصطلح
+
+166
+00:12:24,560 --> 00:12:29,760
+Superposition ماهو المقصود هنا؟ مقصود
+
+167
+00:12:29,760 --> 00:12:33,900
+Superposition؟ يعني بشكل انه يأخذ قوة بين اتجارات
+
+168
+00:12:33,900 --> 00:12:39,600
+تمام بجمع مع بعض Superposition يعني بيعمل مهمة لو
+
+169
+00:12:39,600 --> 00:12:44,080
+انا عند عدة point اتجارات خليني اوضحها هنا اكتر
+
+170
+00:12:44,080 --> 00:12:54,780
+خليني اقول Q1بعدين Q2 بعدين مثلا Q3 نفترض أن هنا
+
+171
+00:12:54,780 --> 00:12:58,440
+تلاتة point each other إذا كان هنا ال position
+
+172
+00:12:58,440 --> 00:13:01,500
+vector معروف يعني معروف ال location لكل point each
+
+173
+00:13:01,500 --> 00:13:05,960
+other و تلاتة عند ال origin هنا سيكون عندي
+
+174
+00:13:05,960 --> 00:13:11,640
+position vector السمالية R1 بعدين Q2 عندي position
+
+175
+00:13:11,640 --> 00:13:17,620
+vector هنا R2 و Q3 position vector R3أفترض أنها بس
+
+176
+00:13:17,620 --> 00:13:20,600
+لها point charge لكن الكلام هنا أنه unpointed
+
+177
+00:13:20,600 --> 00:13:28,980
+charge طب بيحكي لو كان لدينا شحنة Q طبعا
+
+178
+00:13:28,980 --> 00:13:35,040
+لها position vector R طب بيحكي لي إيش ال force إيش
+
+179
+00:13:35,040 --> 00:13:38,560
+ال total force على Q طب ال total force على Q هيكون
+
+180
+00:13:38,560 --> 00:13:46,520
+friendly force من Q1 على Q طبعاو بعدين هيكون عندى
+
+181
+00:13:46,520 --> 00:13:52,200
+force من ال Q2 على Q و force من ال Q3 على Q عشان
+
+182
+00:13:52,200 --> 00:13:54,700
+كده بنحكى ان ال total force هعمل superposition
+
+183
+00:13:54,700 --> 00:13:57,080
+المقصود في superposition حاجة مع ال force إذا عندى
+
+184
+00:13:57,080 --> 00:13:59,980
+ال force جاء من ال Q1 زاد ال force من ال Q2 زاد ال
+
+185
+00:13:59,980 --> 00:14:02,880
+force من ال Q3 وبالتالي اللى طالع على القلم هال F
+
+186
+00:14:02,880 --> 00:14:06,620
+ده هو المقصود ال F فهو مش 1,2 المقصود ان F total
+
+187
+00:14:06,620 --> 00:14:12,760
+فهنا سميها F total هتساوى QQ1 R minus R1 على 4
+
+188
+00:14:12,760 --> 00:14:16,420
+باقية منهم R minus R1 تكرمفهذه المقصود فيها ال
+
+189
+00:14:16,420 --> 00:14:20,220
+force جاء من Q1 تمام؟ وهي عند ال position vector
+
+190
+00:14:20,220 --> 00:14:25,560
+هى R وهي minus R1 واضح؟ هى ال R position vector
+
+191
+00:14:25,560 --> 00:14:28,320
+لكيو اللى بدى أشوف عندها ال force وR1 position
+
+192
+00:14:28,320 --> 00:14:35,080
+vector لكيو 1 تمام؟ قلتلها R minus R1 فعلاً R
+
+193
+00:14:35,080 --> 00:14:37,840
+minus R1 تديني ال position تديني ال vector هذا
+
+194
+00:14:37,840 --> 00:14:42,780
+اللى هو بين Q1 و Q لما أطرح R minus R1 تديني ال
+
+195
+00:14:42,780 --> 00:14:49,630
+vector هذاهشوف ال force من ال Q2 هتكون Q في Q2 عدد
+
+196
+00:14:49,630 --> 00:14:56,270
+R minus R2 طبعا تاني Q Q2 R minus R2 ع ربع باقية
+
+197
+00:14:56,270 --> 00:15:00,150
+سنة نهر وطبعا من بقية Q تكييب ليه R minus R2 بعدين
+
+198
+00:15:00,150 --> 00:15:04,790
+هضلي أجمل خلاص بصفة ع المزاق لو عندى انا M point
+
+199
+00:15:04,790 --> 00:15:08,770
+of charge سمع هتصير عندى الأخر واحدة QQM R minus
+
+200
+00:15:08,770 --> 00:15:13,230
+RM ع ربع باقية سنة نهر R minus RN يكون ايه التكييب
+
+201
+00:15:13,230 --> 00:15:17,420
+من بقية Qطبعا الكلام اللي ممكن تبقى summation ده
+
+202
+00:15:17,420 --> 00:15:20,620
+بره summation حصير عندي total four ال Q على أربع
+
+203
+00:15:20,620 --> 00:15:23,500
+بقى يابسون نمرة اللي طالع برا مشتركة وضل عندي
+
+204
+00:15:23,500 --> 00:15:27,920
+summation ل QK R minus RK على R minus RK magnitude
+
+205
+00:15:27,920 --> 00:15:32,360
+تكلمة و ال K من واحد لأ نفك ال summation هدا هيتبع
+
+206
+00:15:32,360 --> 00:15:42,180
+عندي المواد اللي لان موجودة طبعا الكلام ده طبعا
+
+207
+00:15:42,180 --> 00:15:47,660
+الأن هنعرفحيث ماقالش Electric Field Intensity طبعا
+
+208
+00:15:47,660 --> 00:15:52,540
+تعريف مهم جدا همور علينا لغاية كرمصية واحد اتنين
+
+209
+00:15:52,540 --> 00:15:56,080
+همضلنا نحكي Electric Field بعدين طيب فهم بيحكيلي
+
+210
+00:15:56,080 --> 00:15:58,500
+Electric Field Intensity or Electric Field
+
+211
+00:15:58,500 --> 00:16:02,760
+Strength E is the force per unit charge when
+
+212
+00:16:02,760 --> 00:16:06,840
+placed in an electric field فماشي المقصود في
+
+213
+00:16:06,840 --> 00:16:09,720
+الكلمة اول شي بيحكيلي ال E Electric Field
+
+214
+00:16:09,720 --> 00:16:16,360
+Intensity مقبرة عن force علىpointed charge رشحنا F
+
+215
+00:16:16,360 --> 00:16:20,640
+على Q هم يسميها Q test طب ايش المقصود في Q test
+
+216
+00:16:20,640 --> 00:16:27,480
+نفترض انا عندي اولش عندي pointed charge هنا طبعا و
+
+217
+00:16:27,480 --> 00:16:31,540
+ليه ال source Q ال pointed charge هذه بيكون ناتج
+
+218
+00:16:31,540 --> 00:16:34,040
+منها حيثما electric field ايش المقصود في electric
+
+219
+00:16:34,040 --> 00:16:38,060
+field مجال كهربي لو انا بتحكي بالمجال كهربي ناتج
+
+220
+00:16:38,060 --> 00:16:40,220
+عن ال source هذه او ال pointed charge هذه النقطة
+
+221
+00:16:40,220 --> 00:16:43,860
+معينة نفترض النقطة هذه هنابتحسب إيش في الـ
+
+222
+00:16:43,860 --> 00:16:46,360
+electric field إيش قيمة المجال الكهربي النقطة
+
+223
+00:16:46,360 --> 00:16:48,480
+مائية لإني لدي point of charge هنا بتحسب المجال
+
+224
+00:16:48,480 --> 00:16:52,060
+الكهربي هنا أو هنا أو عند أي نقطة طبعا فإيش .. إيش
+
+225
+00:16:52,060 --> 00:16:55,380
+بنسوي؟ بيجي بنحط point of charge هان بسميها إيش
+
+226
+00:16:55,380 --> 00:17:00,360
+test اتشارج طبعا بتحسب أنا في electric field هان
+
+227
+00:17:00,360 --> 00:17:04,580
+electric field إيش بيساوي؟ بروح و أحط هنا إيش
+
+228
+00:17:04,580 --> 00:17:08,920
+point of charge طبعا الـ electric field عند النقطة
+
+229
+00:17:08,920 --> 00:17:12,180
+هذه هيساوي ال force مش عارف لما أحط هنا point of
+
+230
+00:17:12,180 --> 00:17:16,810
+chargeهيكون عندى force عليها نتيجة وجود ال source
+
+231
+00:17:16,810 --> 00:17:19,750
+اللى هو Q طبعا فهيكون عند ال electric field هى
+
+232
+00:17:19,750 --> 00:17:25,810
+هيساوة F على Q test هاي ال definition لل electric
+
+233
+00:17:25,810 --> 00:17:29,370
+field هان ال electric field هيساوة F على Q test
+
+234
+00:17:29,370 --> 00:17:33,150
+نجي الآن نعوض ال F ال force ايش ال force اللى جاية
+
+235
+00:17:33,150 --> 00:17:36,610
+على Q test نتيجة وجود ال source Q نحكي اللى F
+
+236
+00:17:36,610 --> 00:17:41,570
+هتساوة Q Q test هتكون point of charge ال Q source
+
+237
+00:17:41,570 --> 00:17:45,520
+و Q testماذا يسمى ال force في هذه الجهة الأعلى؟
+
+238
+00:17:45,520 --> 00:17:51,080
+سيكون حاصل ضغط لـ q test ثم r minus r prime لاحظوا
+
+239
+00:17:51,080 --> 00:17:52,760
+ماذا يسمى الـr و الـr prime؟ موجود في الـposition
+
+240
+00:17:52,760 --> 00:17:56,360
+vector الـr prime موجود في الـposition vector لـ
+
+241
+00:17:56,360 --> 00:18:00,260
+source و الـr موجود في الـposition vector لـ q
+
+242
+00:18:00,260 --> 00:18:05,620
+test ثم الـr minus r prime على أربع أبعاد شرن نوت
+
+243
+00:18:05,620 --> 00:18:09,400
+مجموعة r minus r prime ثالث خطوة، دعونا نطبخها،
+
+244
+00:18:09,400 --> 00:18:13,920
+هذه كولومز نوت لـforce علىQ test لجهيد من Q لان
+
+245
+00:18:13,920 --> 00:18:18,340
+هنحسب ال electric field قاعده النقطة هذه بنتيجة
+
+246
+00:18:18,340 --> 00:18:21,960
+وجود source هذه اللي هو Q فبالتاله هنحسب على Q
+
+247
+00:18:21,960 --> 00:18:25,100
+test فبالتاله هيصير عندى ال electric field F على Q
+
+248
+00:18:25,100 --> 00:18:30,600
+test هصيرش بتساوي Q R minus R prime على 4 minus 9
+
+249
+00:18:30,600 --> 00:18:34,060
+magnitude R minus R prime فبطل عندى في ال electric
+
+250
+00:18:34,060 --> 00:18:37,220
+field هنعنى عندى Q test صار عندى بس ال electric
+
+251
+00:18:37,220 --> 00:18:42,310
+field بس بعتمد على ال source point of chargeطبعا
+
+252
+00:18:42,310 --> 00:18:46,890
+انا بدي احسر ال X الكفير لان النقطة هذه مش
+
+253
+00:18:46,890 --> 00:18:49,930
+function في ال Q دي بس function هيكون في ال A في
+
+254
+00:18:49,930 --> 00:18:53,730
+source في ال Q و لتاني احسر ال R اللي بتكفير ال Q
+
+255
+00:18:53,730 --> 00:18:58,090
+R minus R prime على D اربعة بايو سنون ممكن تشير و
+
+256
+00:18:58,090 --> 00:19:01,710
+تكفر واضح؟ و هذي نفسها ممكن تفترح دلالة A شده
+
+257
+00:19:01,710 --> 00:19:05,450
+نفسها هذي نفسها تصير Q على اربعة بايو سنون و
+
+258
+00:19:05,450 --> 00:19:10,870
+همفردي واحد على R تكبير A R واضح؟هذا عبارة عن
+
+259
+00:19:10,870 --> 00:19:13,990
+قانون الـ electric field و لاحظوش واحدة قياسه
+
+260
+00:19:13,990 --> 00:19:20,210
+نيوتن per كولم تمام؟ نقول إن جانت واحدة القياس هذه
+
+261
+00:19:20,210 --> 00:19:23,030
+نيوتن per كولم طبعا انتوا على ايه؟ من ال
+
+262
+00:19:23,030 --> 00:19:26,670
+definition لل electric field F على Q واحد قياس
+
+263
+00:19:26,670 --> 00:19:32,530
+الفارس نيوتن و Q شحنة كله مفترة نيوتن per كولم
+
+264
+00:19:32,530 --> 00:19:36,170
+طبعا واحدة مستخدمة أكتر هنشوفها بعد ايه؟ اللي هي
+
+265
+00:19:36,170 --> 00:19:45,060
+عبارة عن ايه؟ volt per meterطبعا فهي هنشوفها بعد
+
+266
+00:19:45,060 --> 00:19:51,220
+هترين دي volt ساوة كام من E dot دقيقة طبعا بس عشان
+
+267
+00:19:51,220 --> 00:19:54,220
+نعرف وحدة القياسة التانية من وين جاية فهتحك واحدة
+
+268
+00:19:54,220 --> 00:19:57,360
+ال electric field هيكون عبارة عن إيش voltage K P
+
+269
+00:19:57,360 --> 00:20:05,060
+هشوفها دي بعد طبعا هتحكي
+
+270
+00:20:05,060 --> 00:20:09,700
+electric field intensity at point Rdue to a point
+
+271
+00:20:09,700 --> 00:20:15,100
+in charge Q هذي عبارة عن إيش انتقال كتير وعندي
+
+272
+00:20:15,100 --> 00:20:20,140
+ملاحظة، if we increase a Q test force F increases
+
+273
+00:20:20,140 --> 00:20:25,520
+by the same factor احنا لو زوزنا ال Q test ها، ال
+
+274
+00:20:25,520 --> 00:20:29,380
+F مالها، هزيد، لما عندي ال F عبارة عن ال Q في Q
+
+275
+00:20:29,380 --> 00:20:33,570
+test، لما زوز أنا ال Q، ال F مالها، هزيدوهذا بيحكي
+
+276
+00:20:33,570 --> 00:20:37,010
+أن hence E بيساوي F ع Q is the same at the
+
+277
+00:20:37,010 --> 00:20:41,190
+location where A where E is to B فهو هل إيش معناه
+
+278
+00:20:41,190 --> 00:20:45,910
+أنه بغض النظر عن قيمة ال Q test ال electric field
+
+279
+00:20:45,910 --> 00:20:50,650
+هنا هيكون إيش ثالث طالما ال Q source خلاص قيمة
+
+280
+00:20:50,650 --> 00:20:54,150
+ثالثة ال electric field النقطة هذه هيكون ثالث بغض
+
+281
+00:20:54,150 --> 00:20:56,250
+النظر عن إيش ال Q test
+
+282
+00:21:02,990 --> 00:21:05,630
+طب احنا تو شفنا ايش ال electric field لو كان عندي
+
+283
+00:21:05,630 --> 00:21:08,690
+one pointed charge لو كان عندي unpointed charges
+
+284
+00:21:08,690 --> 00:21:12,510
+برضه هنعمل a superposition يعني هنشوف ال electric
+
+285
+00:21:12,510 --> 00:21:17,270
+field الجا من ال Q الأولى زائد ال electric field
+
+286
+00:21:17,270 --> 00:21:20,330
+من التالى و سواء لغاية ليه ال pointed charge قبل
+
+287
+00:21:20,330 --> 00:21:27,090
+فهذا تحكي
+
+288
+00:21:27,090 --> 00:21:31,490
+لي if there are unpointed charges Q1 Q2 لغاية QN
+
+289
+00:21:32,250 --> 00:21:36,290
+located at مدينة الـ position vector R1 R2 Rn الـ
+
+290
+00:21:36,290 --> 00:21:41,230
+electric field intensity and point R is ليه بتساوي
+
+291
+00:21:41,230 --> 00:21:47,690
+Q1 R-R1 على أربع وضعين سنة منه مدينة R-R1 لكل
+
+292
+00:21:47,690 --> 00:21:52,930
+تكييب طب هذا عبارة عن إيش ال electric field due to
+
+293
+00:21:52,930 --> 00:21:59,230
+point of charge Q1 طبعا شو هي نفس الرسمة لها بفترض
+
+294
+00:21:59,230 --> 00:22:01,130
+أنك تحسر ال electric field هنا
+
+295
+00:22:03,730 --> 00:22:06,810
+بتحسب ال electric field عند النقطة هذه هيش بيساوي
+
+296
+00:22:06,810 --> 00:22:09,950
+هشوف ال electric field اللي جال من Q1 هدفه طبعا
+
+297
+00:22:09,950 --> 00:22:12,950
+soft طبعا في ندي point تشارج زي ما بيكون حوالها في
+
+298
+00:22:12,950 --> 00:22:15,890
+ال electric field فبتعرف ال electric field عند
+
+299
+00:22:15,890 --> 00:22:19,990
+النقطة هذه اللي هي ال position vector هيش R
+
+300
+00:22:19,990 --> 00:22:27,590
+ولبتالي هش هيساوي Q1R-R1 بعدين هلايهيش 4πH0 من
+
+301
+00:22:27,590 --> 00:22:33,090
+نيتيوتر 4R-R1 بعدين هشوفالـ Electric field من
+
+302
+00:22:33,090 --> 00:22:37,790
+التانية و سواء تغيرت أخر واضح؟ أول ممكن نقطة
+
+303
+00:22:37,790 --> 00:22:39,570
+القانون اللي بدأت ال summation يعني أحد أربعة بيض
+
+304
+00:22:39,570 --> 00:22:43,630
+من نوع تحيه اندي summation سارة اندي QK R-RK ممكن
+
+305
+00:22:43,630 --> 00:22:50,350
+تسيب تكعيب R-RK واضح؟ طبعا لاحظوا نفس القانون ال
+
+306
+00:22:50,350 --> 00:22:54,370
+electric field و ال force بس إيش الاختلاف؟ هناك
+
+307
+00:22:54,370 --> 00:22:57,870
+اندي Q1 و Q2 في ال force هنا في ال electric field
+
+308
+00:22:57,870 --> 00:23:01,470
+بس مش ريندي إلا Q1 تمام؟ ال Q1 ليه ال source لل
+
+309
+00:23:01,470 --> 00:23:02,190
+electric field؟
+
+310
+00:23:09,410 --> 00:23:12,170
+واضح؟ طب هاي الكلام اللي حكيناه لو عندنا ثلاث
+
+311
+00:23:12,170 --> 00:23:19,810
+شحنات مثلا Q1, Q2, Q3 و هنحن دي test charge Qt
+
+312
+00:23:19,810 --> 00:23:24,470
+هيكون عليها force F force F يعني هنجمها
+
+313
+00:23:24,470 --> 00:23:30,350
+superposition force من Q1 من 2 و من 3وهنا في B
+
+314
+00:23:30,350 --> 00:23:32,870
+رسمة B برضه نفس الشيء هنا تلاتة pointy charges
+
+315
+00:23:32,870 --> 00:23:36,930
+فانا بدي أحسب ال electric field من النقطة هذه وهنا
+
+316
+00:23:36,930 --> 00:23:41,150
+بيحكيلي هتساوي F اللي هي ال total force هانا و
+
+317
+00:23:41,150 --> 00:23:45,990
+كاريندي تست شار على ايش Q تست شار واضح؟ بس هذا
+
+318
+00:23:45,990 --> 00:23:53,010
+ملخص لكلام الحكيم طب ناخد مثال بيحكي لنا pointy
+
+319
+00:23:53,010 --> 00:23:56,710
+charges one milli column and minus اتنين milli
+
+320
+00:23:56,710 --> 00:24:01,000
+coin are locatedتلاتة اتنين مانس واحد and مانس
+
+321
+00:24:01,000 --> 00:24:05,120
+واحد مانس واحد اربع مديني two pointed charges Q
+
+322
+00:24:05,120 --> 00:24:19,740
+واحد و Q اتنين خلينا نسميها انا Q واحد نفترض
+
+323
+00:24:19,740 --> 00:24:23,560
+Q واحد ايش متساوي واحد
+
+324
+00:24:31,390 --> 00:24:40,730
+ممكن نرسل برضه للتوضيح بس انا عندي x, y, z ال
+
+325
+00:24:40,730 --> 00:24:43,810
+point charge يقول كيوة قرن تلاتة بس تقريب للرسم
+
+326
+00:24:43,810 --> 00:24:48,370
+تلاتة اتنين ماناس واحد خلينا نحكي هنا موجودة على
+
+327
+00:24:48,370 --> 00:24:51,950
+سبيل المثال هي كيوة واحد دي ال position إليها
+
+328
+00:24:51,950 --> 00:24:55,330
+تلاتة اتنين ماناس واحد
+
+329
+00:24:58,390 --> 00:25:02,950
+بعدين فينا point of charge تانية سالب واحد سالب
+
+330
+00:25:02,950 --> 00:25:10,390
+واحد ال X minus وال Y minus وزي اربع ثاني مثلا هي
+
+331
+00:25:10,390 --> 00:25:16,310
+Q2 موجودة من هنا minus اتنين ملي كولوم وهي
+
+332
+00:25:16,310 --> 00:25:21,290
+location كلها minus واحد minus واحد واش اربع طبعا
+
+333
+00:25:21,290 --> 00:25:26,660
+فالان احنا باش نحسب طلب من ال calculateElectric
+
+334
+00:25:26,660 --> 00:25:32,320
+force on 10 nano column of charge located 0 3 1
+
+335
+00:25:32,320 --> 00:25:37,520
+وبالتالي في عندنا point of charge 10 nano column
+
+336
+00:25:37,520 --> 00:25:45,360
+location X0 Y3 Z1 وبالتالي هي point of charge هنا
+
+337
+00:25:45,360 --> 00:25:50,840
+Q 10 nano column تبدأ حسين ال force عليها وبالتالي
+
+338
+00:25:50,840 --> 00:25:53,980
+ال force عليها هيكون في عندى force جاية من Q1
+
+339
+00:25:57,930 --> 00:26:06,230
+الـ electric field عند النقطة هذه واضح؟ فهنا هيكون
+
+340
+00:26:06,230 --> 00:26:09,450
+عندى position vector حنا ده ماشي بنسميه عند النقطة
+
+341
+00:26:09,450 --> 00:26:11,410
+اللى بتحصل عندها ال force او ال electric field
+
+342
+00:26:11,410 --> 00:26:16,330
+ماشي بنسميه position vector R اه بعدين هنا اذا هاد
+
+343
+00:26:16,330 --> 00:26:20,610
+Q واحد فهو position vector فهيعمل vector بين
+
+344
+00:26:20,610 --> 00:26:24,510
+النقطة و بين ال origin فبالتالي هاد ايش هيكون سميه
+
+345
+00:26:24,510 --> 00:26:32,650
+R واحدفار اتنين واضح؟ فبالتالي هيصير عندي ال force
+
+346
+00:26:32,650 --> 00:26:38,570
+ال force حمق كتاب من المفهوم الأول طبعا و هي q و
+
+347
+00:26:38,570 --> 00:26:41,170
+هي q واحد و q اتنين و هي ال position vector الأول
+
+348
+00:26:41,170 --> 00:26:44,630
+هو هسينا ال total force q على نهر واحد يبسن من نهر
+
+349
+00:26:44,630 --> 00:26:49,090
+بعدين عندي عشر أساليب تلاتة ليش متمثل؟ الأولة
+
+350
+00:26:49,090 --> 00:26:53,650
+المهم كيو كيو كتير هذه متمثلة كيو واحد بعدين صفر
+
+351
+00:26:53,650 --> 00:27:01,030
+تلاتة واحد R ناقص R واحدR-R1 وهذا يمثل لي position
+
+352
+00:27:01,030 --> 00:27:07,930
+vector 0 3 1 3 2-1 R-R1 على ال magnitude بعدين
+
+353
+00:27:07,930 --> 00:27:12,310
+minus ليش هنا minus؟ عشان الشحن أصلا، عشان الشحن
+
+354
+00:27:12,310 --> 00:27:20,090
+التاني بالساقر، وبالتالي هذي يبقى Q2R-R2 على ال
+
+355
+00:27:20,090 --> 00:27:24,640
+magnitude الكلواضح؟ لان صراحة انا بستعود كتبنا
+
+356
+00:27:24,640 --> 00:27:33,100
+القانون و هاي ال total force بس عوضناها هسي
+
+357
+00:27:33,100 --> 00:27:36,840
+لاندي هاي ال total force بالساعة و كلمة أربعة و
+
+358
+00:27:36,840 --> 00:27:40,900
+مات هاي عبارة عن إبسلون نار و هنطلحنا ال vectors R
+
+359
+00:27:40,900 --> 00:27:44,440
+minus R واحد و R minus R اتنين و هم يجيبنى تلاتة ع
+
+360
+00:27:44,440 --> 00:27:48,220
+اتنين نرجحها
+
+361
+00:27:52,400 --> 00:27:56,460
+هو ايش حصل طرح اللي هو 2 vector هدوء؟ ايش بطلع
+
+362
+00:27:56,460 --> 00:28:08,520
+عندك؟ سارب ثلاثة واحد و اتنين طبعا ال magnitude ال
+
+363
+00:28:08,520 --> 00:28:11,480
+magnitude هذا الكلام عبارة عن vector هيصير جزر
+
+364
+00:28:11,480 --> 00:28:17,080
+الترميعي بتسعة زائد واحد زائد اربع اربعة
+
+365
+00:28:21,000 --> 00:28:26,480
+و طب هدى كلها مفروض أُس إيه؟ تلاتة هدى كلها أُس
+
+366
+00:28:26,480 --> 00:28:33,640
+تلاتة عشان كده هتصبح أربع طاعش أس إيه؟ تلاتة على
+
+367
+00:28:33,640 --> 00:28:39,960
+تلاتة واضح؟ و هو نفس الشيء بالنسبة ل R minus R
+
+368
+00:28:39,960 --> 00:28:44,300
+إتنين من Q سكريت هنضغط و هنشرب ال force بتساوي
+
+369
+00:28:44,300 --> 00:28:47,480
+الكلام هو حكى ال force عبارة عن vector مُتشَك و هو
+
+370
+00:28:47,480 --> 00:28:52,800
+واضح إن هو مُتشَك بجه X بجه Y بجهزب و هن متني نيوت
+
+371
+00:28:52,800 --> 00:28:58,000
+هاي ال force لو نحسب ال electric field حسبنا ال F
+
+372
+00:28:58,000 --> 00:29:01,460
+عند النقطة هنحسب ال electric field هنا حسبنا ال F
+
+373
+00:29:01,460 --> 00:29:04,020
+هنحسب ال electric field هنقسم على .. اذا انا عارف
+
+374
+00:29:04,020 --> 00:29:07,780
+ال force هان لجانب ال Q1 و Q2 كده هس ال electric
+
+375
+00:29:07,780 --> 00:29:11,700
+field هقسم على PQ وبالتالي الدلت point اللي هي
+
+376
+00:29:11,700 --> 00:29:16,540
+point Q هنحسب ال field F على Q طبعا هو عشر أساعد
+
+377
+00:29:16,540 --> 00:29:23,800
+ثلاثةهنا عندي ملي ميمتر فيه هال F على Q ليه عشرة
+
+378
+00:29:23,800 --> 00:29:27,620
+نانو عشرة عندي هالقيمة ال electric field عندي ال
+
+379
+00:29:27,620 --> 00:29:32,240
+bonded charge واضح؟ خلاص احنا طبعا مكتفن اليوم و
+
+380
+00:29:32,240 --> 00:29:35,700
+منكمل مرة جاية بتدعم المثال H اربعة اتنان خلاص
+
+381
+00:29:35,700 --> 00:29:36,360
+تبقى العامة
+
diff --git a/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/UItqMtiDJ-k_raw.srt b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/UItqMtiDJ-k_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..e216a7cae73d9c232395f1a6fa99881204ce4f0d
--- /dev/null
+++ b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/UItqMtiDJ-k_raw.srt
@@ -0,0 +1,1524 @@
+1
+00:00:20,450 --> 00:00:22,510
+بسم الله الرحمن الرحيم الحمد لله يا رب العالمين
+
+2
+00:00:22,510 --> 00:00:25,150
+والصلاة والسلام على رسول الله اللهم أعلمنا ما
+
+3
+00:00:25,150 --> 00:00:29,450
+ينفعنا وإنفعنا بما أعلمتنا وزدنا الله طب اليوم
+
+4
+00:00:29,450 --> 00:00:33,390
+هنبدأ في chapter 4 هو إيش electrostatic طبعا في
+
+5
+00:00:33,390 --> 00:00:37,770
+بداية ال chapter هنتكلم عن إيش columns law هنش
+
+6
+00:00:37,770 --> 00:00:40,910
+بعرف ليه columns law بحكي لها deals with a force a
+
+7
+00:00:40,910 --> 00:00:43,590
+pointed charge exerts on another pointed charge
+
+8
+00:00:43,590 --> 00:00:48,030
+بتعني بتعامل مع إيش pointed charges طبعا بتعامل مع
+
+9
+00:00:48,030 --> 00:00:52,510
+إيش قوةبتأثر من point of charge على point of
+
+10
+00:00:52,510 --> 00:00:56,170
+charge تاني فاهم بيحكيلي two polarity of charges
+
+11
+00:00:56,170 --> 00:00:59,370
+may be positive or negative فاهم بيحكيلي الشخنات
+
+12
+00:00:59,370 --> 00:01:05,010
+بيكون قطبية اما مشابه او سالق ثم بيحكيلي like
+
+13
+00:01:05,010 --> 00:01:09,810
+charges repel and unlike charges attract فادي ايش
+
+14
+00:01:09,810 --> 00:01:13,450
+معناه ان شخنات متشابهة تتنافع فانا عندي two
+
+15
+00:01:13,450 --> 00:01:16,990
+positive charges بيصير بينهم ايه تنافع او two
+
+16
+00:01:16,990 --> 00:01:20,820
+negative chargesبارضه بيصير بينهم فنافر و بعدين ال
+
+17
+00:01:20,820 --> 00:01:24,360
+liked charges attract يعني الشحنات المختلفة ال
+
+18
+00:01:24,360 --> 00:01:28,480
+مختلفة ايش بيصير بينها تجارب attract فهنا على
+
+19
+00:01:28,480 --> 00:01:31,320
+اليمين في عندى ايش شحنة مجابعة positive في عندى
+
+20
+00:01:31,320 --> 00:01:36,140
+شحنة سالمة negative بيصير بينهم ايش attract تمام و
+
+21
+00:01:36,140 --> 00:01:39,700
+انا بحكيلي charges measured in columns بحكيلي احنا
+
+22
+00:01:39,700 --> 00:01:42,940
+ايش واحدة القياس اللي هي الشحنة عبارة عن ايش
+
+23
+00:01:42,940 --> 00:01:47,160
+column و بحكيلي one column بكافة ستة في عشر او
+
+24
+00:01:47,160 --> 00:01:51,460
+ستمانتاش ايشElectrons طبعا اعتقد ان المفاهيم مرت
+
+25
+00:01:51,460 --> 00:01:55,780
+عليكم اعتقد الفيزيا الفيزيا او الفيزيا بقى طيب هذي
+
+26
+00:01:55,780 --> 00:01:59,160
+بيحكيلي شحنة ال Electron ال E هذي عبارة عن شحنة ال
+
+27
+00:01:59,160 --> 00:02:02,280
+Electron كل واحد point ستة سفر اتنين عشرة أساليب
+
+28
+00:02:02,280 --> 00:02:05,760
+تسعتاش ايه؟ Columns طبعا و بعدين بيحكيلي ال
+
+29
+00:02:05,760 --> 00:02:10,640
+protons has a charge of E و بعدين Electron has a
+
+30
+00:02:10,640 --> 00:02:14,360
+charge of minus E طبعا بنعرف انه زرع بيكون فيها
+
+31
+00:02:14,360 --> 00:02:18,180
+protons و ايه؟ Electrons طبعاو طبعا شحنة ال proton
+
+32
+00:02:18,180 --> 00:02:22,140
+بتكون موجبة و شحنة ال electron ايش بتكون ثالثة
+
+33
+00:02:22,140 --> 00:02:25,060
+فانت بتحكيلي شحنة ال proton هتكون positive E و
+
+34
+00:02:25,060 --> 00:02:28,460
+شحنة ال electron هتكون negative E فهي قيمة ال E
+
+35
+00:02:28,460 --> 00:02:32,780
+ليها N كولوز طبعا و انا بتحكيلي ان atom اللي هي
+
+36
+00:02:32,780 --> 00:02:37,140
+الذرع or group of atoms that has lost one or more
+
+37
+00:02:37,140 --> 00:02:40,840
+electrons gives a net positive charge هتكون عندي
+
+38
+00:02:40,840 --> 00:02:45,800
+ذرع او مجموعة ذرع لما تفقدone or more electrons
+
+39
+00:02:45,800 --> 00:02:48,620
+لما الذرة تفقد electron إيش هيكون عند الشحنة
+
+40
+00:02:48,620 --> 00:02:53,640
+الكلية نت positive charge لإنه لما الذرة تفقد
+
+41
+00:02:53,640 --> 00:02:57,220
+electron هيصير عدد ال protons أكبر من عدد ال
+
+42
+00:02:57,220 --> 00:03:00,820
+electrons وبالتالي بنحكي نت positive charge طبعا
+
+43
+00:03:00,820 --> 00:03:05,720
+العكس؟ العكس صحيح طبعا هل يحكي لي إيه؟ if it
+
+44
+00:03:05,720 --> 00:03:08,520
+gained one or more electrons لو عند ال atom الذرة
+
+45
+00:03:08,520 --> 00:03:11,700
+اكتسبت electron وبالتالي هيصير عدد ال electrons
+
+46
+00:03:11,700 --> 00:03:16,200
+أكتر من عدد ال protonsوبالتالي it gives a net
+
+47
+00:03:16,200 --> 00:03:19,260
+negative charge هيكون عندي إيش negative charge، مش
+
+48
+00:03:19,260 --> 00:03:22,100
+كده احنا بنسميها حيانا positive ion و إيش negative
+
+49
+00:03:22,100 --> 00:03:27,780
+ion طيب
+
+50
+00:03:27,780 --> 00:03:31,760
+هم تكيلي columns law it states that the force F
+
+51
+00:03:31,760 --> 00:03:37,580
+between two point charges Q1 و Q2 قوة عندنا two
+
+52
+00:03:37,580 --> 00:03:42,780
+point charges هيكون بينهم إيش forceحكيلي ال force
+
+53
+00:03:42,780 --> 00:03:45,600
+هي اللي بتكون along the line joining them ايش يعني
+
+54
+00:03:45,600 --> 00:03:48,720
+along the line joining them؟ ال force عبارة عن
+
+55
+00:03:48,720 --> 00:03:53,000
+ايش؟ فكتور متجه يكون اتجاهه على نفس ال line اللي
+
+56
+00:03:53,000 --> 00:03:55,780
+بيجمعته ال points and charges، هاي أول شي نقطة
+
+57
+00:03:55,780 --> 00:03:58,860
+تانية، بيحكيلي directly proportional to the
+
+58
+00:03:58,860 --> 00:04:04,560
+product Q1 Q2 of charges، طبعا؟ بيحكيلي متناسب،
+
+59
+00:04:04,560 --> 00:04:08,900
+طردية، محاصر، دار، شو احنا؟ احنا Q1 و Q2 وبالتالي
+
+60
+00:04:08,900 --> 00:04:12,930
+ال force هذهتتناسب ترضيا مع حاصل ضربه طبعا الكلام
+
+61
+00:04:12,930 --> 00:04:17,070
+هذا هيكون واضح من خلال القانون بعدين بيحكي
+
+62
+00:04:17,070 --> 00:04:20,030
+inversely proportional to the square of the
+
+63
+00:04:20,030 --> 00:04:25,010
+distance R between them وبالتالي بتناسب عكسيا مع
+
+64
+00:04:25,010 --> 00:04:28,310
+مربع المسافة بين ال two points each other طبعا دي
+
+65
+00:04:28,310 --> 00:04:33,050
+طالع القانون هاندي F ايش بيستخدم كي واحد كتنين على
+
+66
+00:04:33,050 --> 00:04:36,430
+R تلوينطب هون K عبارة عن constant و بحكي ال K
+
+67
+00:04:36,430 --> 00:04:40,150
+لحظوا هنا ال K شو بتساوي 1 على أربعة باقي each
+
+68
+00:04:40,150 --> 00:04:43,970
+other فبتلاح يصير عندك قانون ال force هتساوي Q1 و
+
+69
+00:04:43,970 --> 00:04:48,110
+Q2 على أربعة باقي each another R² طب اللحظوا هنا
+
+70
+00:04:48,110 --> 00:04:50,870
+ال force هاد عبارة عن إيش؟ هاد ال magnitude إحنا
+
+71
+00:04:50,870 --> 00:04:53,390
+بنعرف إنه عبارة عن إيش vector ال force في النهاية
+
+72
+00:04:53,390 --> 00:04:56,210
+عبارة عن vector متجه في اتجاه معين ممكن تكون قوة
+
+73
+00:04:56,210 --> 00:04:58,510
+في هذا الاتجاه أو في هذا الاتجاه أو في اتجاه تاني
+
+74
+00:04:58,510 --> 00:05:01,570
+لكن هدا القانون اللي قبل كتبنا عبارة عن إيش ال
+
+75
+00:05:01,570 --> 00:05:06,120
+magnitude لإيش لال forceهذا هنشوف ال force as a
+
+76
+00:05:06,120 --> 00:05:10,420
+vector هنشوف هذا ال K يسمى permittivity of free
+
+77
+00:05:10,420 --> 00:05:15,100
+space و طبعا هذا البرهين constant بيحكي 8.854×10⁻²
+
+78
+00:05:15,100 --> 00:05:20,240
+وهذا تقريبا بالساوية 10⁻9 36 بقى طبعا هذي constant
+
+79
+00:05:20,240 --> 00:05:23,840
+و عروفة و بعد الفيديو دي ال K حكينا دلالة ال Y
+
+80
+00:05:23,840 --> 00:05:31,680
+naught 1⁴Y naught 9×10⁹ تمام متر بفرقة واضح؟
+
+81
+00:05:35,690 --> 00:05:40,510
+طيب هاي في عندي الرسم هان بتوضحلي
+
+82
+00:05:40,510 --> 00:05:44,470
+ان عندي point of charge Q1 point of charge Q2 طب
+
+83
+00:05:44,470 --> 00:05:48,290
+هان عندي ايش ال origins عندي R1 هيكون position
+
+84
+00:05:48,290 --> 00:05:52,050
+vector يعني وين عندي شحنة Q1 located وين موجودة
+
+85
+00:05:52,050 --> 00:05:56,550
+فعندي position vector R وعندي Q2 ورحني فين R؟
+
+86
+00:05:56,550 --> 00:05:59,630
+اتنين position vector يعني ال location لpoint of
+
+87
+00:05:59,630 --> 00:06:03,850
+charge Q2 طب حكينا هيكون بينهم forces هتلاحظوا
+
+88
+00:06:03,850 --> 00:06:11,530
+عندي F1طب ايش المقصود فى F12 ال force على Q2 النجا
+
+89
+00:06:11,530 --> 00:06:16,490
+من point of charge Q1 برغم فى الاندغال F21 هذه
+
+90
+00:06:16,490 --> 00:06:23,490
+معناه ال force on Q1 due to point of charge FQ2
+
+91
+00:06:23,490 --> 00:06:27,830
+واضح طيب بعدين القانون كتبناها مرة تانية فبعدين فى
+
+92
+00:06:27,830 --> 00:06:33,050
+the force F12 طبعا ال F12 حكيها on Q2 due to Q1
+
+93
+00:06:34,780 --> 00:06:39,960
+فهنكتبنا ال force as vector لحظة هون F12 عاملة هنا
+
+94
+00:06:39,960 --> 00:06:43,660
+سهل يعني هذا عبارة عن أيش vector هسو Q1 و Q2 على
+
+95
+00:06:43,660 --> 00:06:49,140
+أربع باقية من ال node R2 في هنشر هنا نسمي unit
+
+96
+00:06:49,140 --> 00:06:56,020
+vector في اتجاه R12 هذا عبارة عن متجه وحدة A R12
+
+97
+00:06:56,020 --> 00:07:03,180
+متجه وحدة في اتجاه R12 طبعا ال R12 هي الرسمماذا
+
+98
+00:07:03,180 --> 00:07:08,960
+يسمى ال vector R12؟ vector على line بين Q1 وQ2
+
+99
+00:07:08,960 --> 00:07:12,180
+وبالتالي هنا متجهة واحدة طبعا المتجهة الوحدة احنا
+
+100
+00:07:12,180 --> 00:07:14,620
+بنعرف كيف بنجيب دايما اي متجهة واحدة لو عندنا اي
+
+101
+00:07:14,620 --> 00:07:19,040
+vector فنجيب unit vector متجهة واحدة ونقسم على ال
+
+102
+00:07:19,040 --> 00:07:25,600
+magnitude تمام؟ وبالتالي هيصير عندي AR عن AR12
+
+103
+00:07:25,600 --> 00:07:32,040
+متجهة واحدة في اتجاه R12 هيسمى المتجهة R12 as a
+
+104
+00:07:32,040 --> 00:07:39,040
+vectorعلى magnitude r12 طبعا و هذا ايش هيساوي
+
+105
+00:07:39,040 --> 00:07:44,160
+لاحظوا r12 ال vector r12 ممكن نديه بالدلالة ال two
+
+106
+00:07:44,160 --> 00:07:49,020
+vectors r1 و r2 هتلاحظوا انه عبارة عن r2 minus r1
+
+107
+00:07:49,020 --> 00:07:55,420
+و إتالة هنعوضها هيصير عندى r2 minus r1 فاكرتها مره
+
+108
+00:07:55,420 --> 00:07:59,340
+أنكم في أول chapter أو تاني chapter او تاني
+
+109
+00:07:59,340 --> 00:08:00,080
+chapter او تاني chapter او تاني chapter او تاني
+
+110
+00:08:00,080 --> 00:08:03,880
+chapter او تاني chapterالمهم الـ magnitude R12
+
+111
+00:08:03,880 --> 00:08:08,660
+خدها في الكتاب و اعملها بالشكل هذا بيعملها Italic
+
+112
+00:08:08,660 --> 00:08:12,800
+ايش هال Italic؟ Magnitude دايما في الكتاب اذا
+
+113
+00:08:12,800 --> 00:08:18,260
+عمللي R Bold هتكون هذا عبارة عن ايش؟ R Bold هذي
+
+114
+00:08:18,260 --> 00:08:22,860
+عبارة عن Vector و بعدين هذي R Italic بالشكل هذا
+
+115
+00:08:22,860 --> 00:08:28,600
+هذي هتكون عبارة عن ايش؟ Magnitude طبعا و أحيانا في
+
+116
+00:08:28,600 --> 00:08:32,340
+بعض الكتب بيعملوا رسالة مع ال vectorبس هبطل مثلا
+
+117
+00:08:32,340 --> 00:08:34,840
+عشان اوضح ان هذا عبارة عن ايش مثلا vector او R12
+
+118
+00:08:34,840 --> 00:08:38,080
+عبارة عن ايش vector طيب و التاني هاي unit vector
+
+119
+00:08:38,080 --> 00:08:45,100
+هيصير R2-R1 على R تمام؟ و ال R هذه عبارة عن
+
+120
+00:08:45,100 --> 00:08:50,220
+magnitude لـ R1 و تالا هيصير عند القانون بس او
+
+121
+00:08:50,220 --> 00:08:56,260
+اضبط ال unit vector هصير Q1 T2 هنلحظ و R2-R1 على
+
+122
+00:08:56,260 --> 00:09:02,370
+R2-R1 تكييب قبل ما هو نجتني التكييبطبعا شوفين هنا
+
+123
+00:09:02,370 --> 00:09:06,930
+R تربيه و في عندي من Linear Vector في عندي برضه
+
+124
+00:09:06,930 --> 00:09:15,170
+ايش هذا برضه magnitude R2-R1 طبعا وبالتالي هندروب
+
+125
+00:09:15,170 --> 00:09:17,950
+في بعض عندي R تربيه و بعدين مضروبة في magnitude R2
+
+126
+00:09:17,950 --> 00:09:23,450
+-R1 فبعندي R2-R1 في ال column تتاعي واضح؟ وبالتالي
+
+127
+00:09:23,450 --> 00:09:25,890
+هو القرون العام لإيش دول ال column دي
+
+128
+00:09:32,800 --> 00:09:36,400
+هكذا كتبنا القانون مرة تانية مرة دلالة unit vector
+
+129
+00:09:36,400 --> 00:09:41,360
+مرة دلالة vectors R2 وR1 ملاحظات بحكي لي the force
+
+130
+00:09:41,360 --> 00:09:45,660
+F21 إحنا طبعا شوفنا ال force F12 إيش القوة؟ طبعا
+
+131
+00:09:45,660 --> 00:09:50,020
+شوفنا إيش القوة على Q2 لنا جامل إيه؟ Q لأنه أحنا
+
+132
+00:09:50,020 --> 00:09:56,720
+بدنا العكس لنشوف إيش القوة على Q1 لجامل من Q2 فهو
+
+133
+00:09:56,720 --> 00:10:00,740
+بيحكي لي the force F2 on Q1 due to Q2 is هو على
+
+134
+00:10:00,740 --> 00:10:08,720
+F21كذلك F12 magnitude A R21 هتلاحظ ان ال forces
+
+135
+00:10:08,720 --> 00:10:12,040
+عبارة متساوية نفس ال magnitude فهذا فكرة F21
+
+136
+00:10:12,040 --> 00:10:17,960
+المagnitude تبعها نفس F12 تمام لما كنت تبقى تتشارج
+
+137
+00:10:17,960 --> 00:10:23,080
+بينهم force تمام هيكون نفس A في ال magnitude هم بس
+
+138
+00:10:23,080 --> 00:10:26,580
+بظل عندي ال direction واضح ان ال direction مختلف
+
+139
+00:10:26,580 --> 00:10:32,340
+فهذا ال direction F21 في اتجاه F21 في هذابالاتجار،
+
+140
+00:10:32,340 --> 00:10:38,040
+تمام؟ و بالتالي هيصير اني Ar2 as unit vector minus
+
+141
+00:10:38,040 --> 00:10:46,120
+Ar12 لأن Ar12 في هذا الاتجار و بالتالي Ar21 هيكون
+
+142
+00:10:46,120 --> 00:10:48,800
+في هذا الاتجار، اتجار مختلف عشان كده حكينا ال
+
+143
+00:10:48,800 --> 00:10:51,860
+forces هيكون لنفس ال magnitude بس الاتجار مختلف
+
+144
+00:10:51,860 --> 00:10:54,540
+واحدة في هذا الاتجار و واحدة في اتجار آخر لكن نفس
+
+145
+00:10:54,540 --> 00:10:59,560
+ايه ال magnitude، تمام؟ هم حكيلي F21 هسوة minus F1
+
+146
+00:10:59,690 --> 00:11:04,550
+بس إنه في اتجاه ال marks واضح؟ طيب و بعدين بيحكيلي
+
+147
+00:11:04,550 --> 00:11:07,090
+the distance R اللي هي المسافة بين ال two pointed
+
+148
+00:11:07,090 --> 00:11:11,690
+charges must be much larger than dimensions of
+
+149
+00:11:11,690 --> 00:11:15,590
+charged bodies Q1 and Q2 طبعا؟ و بعدين بيحكيلي ال
+
+150
+00:11:15,590 --> 00:11:19,550
+مسافة R هتكون أكبر بكتير من ال dimensions لإيش ال
+
+151
+00:11:19,550 --> 00:11:24,790
+charged bodies اللي هي Q1 و Q2 و بعدين بيحكيلي Q1
+
+152
+00:11:24,790 --> 00:11:27,850
+and Q2 must be static addressed
+
+153
+00:11:31,050 --> 00:11:35,910
+الشحنات هذه يجب أن تكون ثابتة تمام؟ و بعدين فكري
+
+154
+00:11:35,910 --> 00:11:40,430
+size of q1 و q2 must be taken into account لماذا
+
+155
+00:11:40,430 --> 00:11:46,530
+اعود هنا في قانون columns لازم انا اخد بالنسبة ليه
+
+156
+00:11:46,530 --> 00:11:49,470
+الإشارة كأن الشحنات بتكون موجبة أو ثالثة وبالتالي
+
+157
+00:11:49,470 --> 00:11:51,350
+باخد هذا الكلام بالنسبة ليه
+
+158
+00:11:55,900 --> 00:11:58,280
+طب نقول لو كان عندي unpointed charges طب و احنا
+
+159
+00:11:58,280 --> 00:12:00,640
+شوفنا لو كان عندنا بس two-pointed charges و لو كان
+
+160
+00:12:00,640 --> 00:12:05,640
+عندي unpointed charges Q1, Q2, Qn located at
+
+161
+00:12:05,640 --> 00:12:09,560
+points with position vectors R1, R2, RN لان عدة
+
+162
+00:12:09,560 --> 00:12:13,360
+pointed charges و هي position vector لكل واحد يعني
+
+163
+00:12:13,360 --> 00:12:16,580
+معروف ال location لكل point تتشارك تحكيلي the
+
+164
+00:12:16,580 --> 00:12:20,920
+resultant force of one charged Q located at point
+
+165
+00:12:21,440 --> 00:12:24,560
+والـ position vector R هو مجرد استخدام مصطلح
+
+166
+00:12:24,560 --> 00:12:29,760
+Superposition ماهو المقصود هنا؟ مقصود
+
+167
+00:12:29,760 --> 00:12:33,900
+Superposition؟ يعني بشكل انه يأخذ قوة بين اتجارات
+
+168
+00:12:33,900 --> 00:12:39,600
+تمام بجمع مع بعض Superposition يعني بيعمل مهمة لو
+
+169
+00:12:39,600 --> 00:12:44,080
+انا عند عدة point اتجارات خليني اوضحها هنا اكتر
+
+170
+00:12:44,080 --> 00:12:54,780
+خليني اقول Q1بعدين Q2 بعدين مثلا Q3 نفترض أن هنا
+
+171
+00:12:54,780 --> 00:12:58,440
+تلاتة point each other إذا كان هنا ال position
+
+172
+00:12:58,440 --> 00:13:01,500
+vector معروف يعني معروف ال location لكل point each
+
+173
+00:13:01,500 --> 00:13:05,960
+other و تلاتة عند ال origin هنا سيكون عندي
+
+174
+00:13:05,960 --> 00:13:11,640
+position vector السمالية R1 بعدين Q2 عندي position
+
+175
+00:13:11,640 --> 00:13:17,620
+vector هنا R2 و Q3 position vector R3أفترض أنها بس
+
+176
+00:13:17,620 --> 00:13:20,600
+لها point charge لكن الكلام هنا أنه unpointed
+
+177
+00:13:20,600 --> 00:13:28,980
+charge طب بيحكي لو كان لدينا شحنة Q طبعا
+
+178
+00:13:28,980 --> 00:13:35,040
+لها position vector R طب بيحكي لي إيش ال force إيش
+
+179
+00:13:35,040 --> 00:13:38,560
+ال total force على Q طب ال total force على Q هيكون
+
+180
+00:13:38,560 --> 00:13:46,520
+friendly force من Q1 على Q طبعاو بعدين هيكون عندى
+
+181
+00:13:46,520 --> 00:13:52,200
+force من ال Q2 على Q و force من ال Q3 على Q عشان
+
+182
+00:13:52,200 --> 00:13:54,700
+كده بنحكى ان ال total force هعمل superposition
+
+183
+00:13:54,700 --> 00:13:57,080
+المقصود في superposition حاجة مع ال force إذا عندى
+
+184
+00:13:57,080 --> 00:13:59,980
+ال force جاء من ال Q1 زاد ال force من ال Q2 زاد ال
+
+185
+00:13:59,980 --> 00:14:02,880
+force من ال Q3 وبالتالي اللى طالع على القلم هال F
+
+186
+00:14:02,880 --> 00:14:06,620
+ده هو المقصود ال F فهو مش 1,2 المقصود ان F total
+
+187
+00:14:06,620 --> 00:14:12,760
+فهنا سميها F total هتساوى QQ1 R minus R1 على 4
+
+188
+00:14:12,760 --> 00:14:16,420
+باقية منهم R minus R1 تكرمفهذه المقصود فيها ال
+
+189
+00:14:16,420 --> 00:14:20,220
+force جاء من Q1 تمام؟ وهي عند ال position vector
+
+190
+00:14:20,220 --> 00:14:25,560
+هى R وهي minus R1 واضح؟ هى ال R position vector
+
+191
+00:14:25,560 --> 00:14:28,320
+لكيو اللى بدى أشوف عندها ال force وR1 position
+
+192
+00:14:28,320 --> 00:14:35,080
+vector لكيو 1 تمام؟ قلتلها R minus R1 فعلاً R
+
+193
+00:14:35,080 --> 00:14:37,840
+minus R1 تديني ال position تديني ال vector هذا
+
+194
+00:14:37,840 --> 00:14:42,780
+اللى هو بين Q1 و Q لما أطرح R minus R1 تديني ال
+
+195
+00:14:42,780 --> 00:14:49,630
+vector هذاهشوف ال force من ال Q2 هتكون Q في Q2 عدد
+
+196
+00:14:49,630 --> 00:14:56,270
+R minus R2 طبعا تاني Q Q2 R minus R2 ع ربع باقية
+
+197
+00:14:56,270 --> 00:15:00,150
+سنة نهر وطبعا من بقية Q تكييب ليه R minus R2 بعدين
+
+198
+00:15:00,150 --> 00:15:04,790
+هضلي أجمل خلاص بصفة ع المزاق لو عندى انا M point
+
+199
+00:15:04,790 --> 00:15:08,770
+of charge سمع هتصير عندى الأخر واحدة QQM R minus
+
+200
+00:15:08,770 --> 00:15:13,230
+RM ع ربع باقية سنة نهر R minus RN يكون ايه التكييب
+
+201
+00:15:13,230 --> 00:15:17,420
+من بقية Qطبعا الكلام اللي ممكن تبقى summation ده
+
+202
+00:15:17,420 --> 00:15:20,620
+بره summation حصير عندي total four ال Q على أربع
+
+203
+00:15:20,620 --> 00:15:23,500
+بقى يابسون نمرة اللي طالع برا مشتركة وضل عندي
+
+204
+00:15:23,500 --> 00:15:27,920
+summation ل QK R minus RK على R minus RK magnitude
+
+205
+00:15:27,920 --> 00:15:32,360
+تكلمة و ال K من واحد لأ نفك ال summation هدا هيتبع
+
+206
+00:15:32,360 --> 00:15:42,180
+عندي المواد اللي لان موجودة طبعا الكلام ده طبعا
+
+207
+00:15:42,180 --> 00:15:47,660
+الأن هنعرفحيث ماقالش Electric Field Intensity طبعا
+
+208
+00:15:47,660 --> 00:15:52,540
+تعريف مهم جدا همور علينا لغاية كرمصية واحد اتنين
+
+209
+00:15:52,540 --> 00:15:56,080
+همضلنا نحكي Electric Field بعدين طيب فهم بيحكيلي
+
+210
+00:15:56,080 --> 00:15:58,500
+Electric Field Intensity or Electric Field
+
+211
+00:15:58,500 --> 00:16:02,760
+Strength E is the force per unit charge when
+
+212
+00:16:02,760 --> 00:16:06,840
+placed in an electric field فماشي المقصود في
+
+213
+00:16:06,840 --> 00:16:09,720
+الكلمة اول شي بيحكيلي ال E Electric Field
+
+214
+00:16:09,720 --> 00:16:16,360
+Intensity مقبرة عن force علىpointed charge رشحنا F
+
+215
+00:16:16,360 --> 00:16:20,640
+على Q هم يسميها Q test طب ايش المقصود في Q test
+
+216
+00:16:20,640 --> 00:16:27,480
+نفترض انا عندي اولش عندي pointed charge هنا طبعا و
+
+217
+00:16:27,480 --> 00:16:31,540
+ليه ال source Q ال pointed charge هذه بيكون ناتج
+
+218
+00:16:31,540 --> 00:16:34,040
+منها حيثما electric field ايش المقصود في electric
+
+219
+00:16:34,040 --> 00:16:38,060
+field مجال كهربي لو انا بتحكي بالمجال كهربي ناتج
+
+220
+00:16:38,060 --> 00:16:40,220
+عن ال source هذه او ال pointed charge هذه النقطة
+
+221
+00:16:40,220 --> 00:16:43,860
+معينة نفترض النقطة هذه هنابتحسب إيش في الـ
+
+222
+00:16:43,860 --> 00:16:46,360
+electric field إيش قيمة المجال الكهربي النقطة
+
+223
+00:16:46,360 --> 00:16:48,480
+مائية لإني لدي point of charge هنا بتحسب المجال
+
+224
+00:16:48,480 --> 00:16:52,060
+الكهربي هنا أو هنا أو عند أي نقطة طبعا فإيش .. إيش
+
+225
+00:16:52,060 --> 00:16:55,380
+بنسوي؟ بيجي بنحط point of charge هان بسميها إيش
+
+226
+00:16:55,380 --> 00:17:00,360
+test اتشارج طبعا بتحسب أنا في electric field هان
+
+227
+00:17:00,360 --> 00:17:04,580
+electric field إيش بيساوي؟ بروح و أحط هنا إيش
+
+228
+00:17:04,580 --> 00:17:08,920
+point of charge طبعا الـ electric field عند النقطة
+
+229
+00:17:08,920 --> 00:17:12,180
+هذه هيساوي ال force مش عارف لما أحط هنا point of
+
+230
+00:17:12,180 --> 00:17:16,810
+chargeهيكون عندى force عليها نتيجة وجود ال source
+
+231
+00:17:16,810 --> 00:17:19,750
+اللى هو Q طبعا فهيكون عند ال electric field هى
+
+232
+00:17:19,750 --> 00:17:25,810
+هيساوة F على Q test هاي ال definition لل electric
+
+233
+00:17:25,810 --> 00:17:29,370
+field هان ال electric field هيساوة F على Q test
+
+234
+00:17:29,370 --> 00:17:33,150
+نجي الآن نعوض ال F ال force ايش ال force اللى جاية
+
+235
+00:17:33,150 --> 00:17:36,610
+على Q test نتيجة وجود ال source Q نحكي اللى F
+
+236
+00:17:36,610 --> 00:17:41,570
+هتساوة Q Q test هتكون point of charge ال Q source
+
+237
+00:17:41,570 --> 00:17:45,520
+و Q testماذا يسمى ال force في هذه الجهة الأعلى؟
+
+238
+00:17:45,520 --> 00:17:51,080
+سيكون حاصل ضغط لـ q test ثم r minus r prime لاحظوا
+
+239
+00:17:51,080 --> 00:17:52,760
+ماذا يسمى الـr و الـr prime؟ موجود في الـposition
+
+240
+00:17:52,760 --> 00:17:56,360
+vector الـr prime موجود في الـposition vector لـ
+
+241
+00:17:56,360 --> 00:18:00,260
+source و الـr موجود في الـposition vector لـ q
+
+242
+00:18:00,260 --> 00:18:05,620
+test ثم الـr minus r prime على أربع أبعاد شرن نوت
+
+243
+00:18:05,620 --> 00:18:09,400
+مجموعة r minus r prime ثالث خطوة، دعونا نطبخها،
+
+244
+00:18:09,400 --> 00:18:13,920
+هذه كولومز نوت لـforce علىQ test لجهيد من Q لان
+
+245
+00:18:13,920 --> 00:18:18,340
+هنحسب ال electric field قاعده النقطة هذه بنتيجة
+
+246
+00:18:18,340 --> 00:18:21,960
+وجود source هذه اللي هو Q فبالتاله هنحسب على Q
+
+247
+00:18:21,960 --> 00:18:25,100
+test فبالتاله هيصير عندى ال electric field F على Q
+
+248
+00:18:25,100 --> 00:18:30,600
+test هصيرش بتساوي Q R minus R prime على 4 minus 9
+
+249
+00:18:30,600 --> 00:18:34,060
+magnitude R minus R prime فبطل عندى في ال electric
+
+250
+00:18:34,060 --> 00:18:37,220
+field هنعنى عندى Q test صار عندى بس ال electric
+
+251
+00:18:37,220 --> 00:18:42,310
+field بس بعتمد على ال source point of chargeطبعا
+
+252
+00:18:42,310 --> 00:18:46,890
+انا بدي احسر ال X الكفير لان النقطة هذه مش
+
+253
+00:18:46,890 --> 00:18:49,930
+function في ال Q دي بس function هيكون في ال A في
+
+254
+00:18:49,930 --> 00:18:53,730
+source في ال Q و لتاني احسر ال R اللي بتكفير ال Q
+
+255
+00:18:53,730 --> 00:18:58,090
+R minus R prime على D اربعة بايو سنون ممكن تشير و
+
+256
+00:18:58,090 --> 00:19:01,710
+تكفر واضح؟ و هذي نفسها ممكن تفترح دلالة A شده
+
+257
+00:19:01,710 --> 00:19:05,450
+نفسها هذي نفسها تصير Q على اربعة بايو سنون و
+
+258
+00:19:05,450 --> 00:19:10,870
+همفردي واحد على R تكبير A R واضح؟هذا عبارة عن
+
+259
+00:19:10,870 --> 00:19:13,990
+قانون الـ electric field و لاحظوش واحدة قياسه
+
+260
+00:19:13,990 --> 00:19:20,210
+نيوتن per كولم تمام؟ نقول إن جانت واحدة القياس هذه
+
+261
+00:19:20,210 --> 00:19:23,030
+نيوتن per كولم طبعا انتوا على ايه؟ من ال
+
+262
+00:19:23,030 --> 00:19:26,670
+definition لل electric field F على Q واحد قياس
+
+263
+00:19:26,670 --> 00:19:32,530
+الفارس نيوتن و Q شحنة كله مفترة نيوتن per كولم
+
+264
+00:19:32,530 --> 00:19:36,170
+طبعا واحدة مستخدمة أكتر هنشوفها بعد ايه؟ اللي هي
+
+265
+00:19:36,170 --> 00:19:45,060
+عبارة عن ايه؟ volt per meterطبعا فهي هنشوفها بعد
+
+266
+00:19:45,060 --> 00:19:51,220
+هترين دي volt ساوة كام من E dot دقيقة طبعا بس عشان
+
+267
+00:19:51,220 --> 00:19:54,220
+نعرف وحدة القياسة التانية من وين جاية فهتحك واحدة
+
+268
+00:19:54,220 --> 00:19:57,360
+ال electric field هيكون عبارة عن إيش voltage K P
+
+269
+00:19:57,360 --> 00:20:05,060
+هشوفها دي بعد طبعا هتحكي
+
+270
+00:20:05,060 --> 00:20:09,700
+electric field intensity at point Rdue to a point
+
+271
+00:20:09,700 --> 00:20:15,100
+in charge Q هذي عبارة عن إيش انتقال كتير وعندي
+
+272
+00:20:15,100 --> 00:20:20,140
+ملاحظة، if we increase a Q test force F increases
+
+273
+00:20:20,140 --> 00:20:25,520
+by the same factor احنا لو زوزنا ال Q test ها، ال
+
+274
+00:20:25,520 --> 00:20:29,380
+F مالها، هزيد، لما عندي ال F عبارة عن ال Q في Q
+
+275
+00:20:29,380 --> 00:20:33,570
+test، لما زوز أنا ال Q، ال F مالها، هزيدوهذا بيحكي
+
+276
+00:20:33,570 --> 00:20:37,010
+أن hence E بيساوي F ع Q is the same at the
+
+277
+00:20:37,010 --> 00:20:41,190
+location where A where E is to B فهو هل إيش معناه
+
+278
+00:20:41,190 --> 00:20:45,910
+أنه بغض النظر عن قيمة ال Q test ال electric field
+
+279
+00:20:45,910 --> 00:20:50,650
+هنا هيكون إيش ثالث طالما ال Q source خلاص قيمة
+
+280
+00:20:50,650 --> 00:20:54,150
+ثالثة ال electric field النقطة هذه هيكون ثالث بغض
+
+281
+00:20:54,150 --> 00:20:56,250
+النظر عن إيش ال Q test
+
+282
+00:21:02,990 --> 00:21:05,630
+طب احنا تو شفنا ايش ال electric field لو كان عندي
+
+283
+00:21:05,630 --> 00:21:08,690
+one pointed charge لو كان عندي unpointed charges
+
+284
+00:21:08,690 --> 00:21:12,510
+برضه هنعمل a superposition يعني هنشوف ال electric
+
+285
+00:21:12,510 --> 00:21:17,270
+field الجا من ال Q الأولى زائد ال electric field
+
+286
+00:21:17,270 --> 00:21:20,330
+من التالى و سواء لغاية ليه ال pointed charge قبل
+
+287
+00:21:20,330 --> 00:21:27,090
+فهذا تحكي
+
+288
+00:21:27,090 --> 00:21:31,490
+لي if there are unpointed charges Q1 Q2 لغاية QN
+
+289
+00:21:32,250 --> 00:21:36,290
+located at مدينة الـ position vector R1 R2 Rn الـ
+
+290
+00:21:36,290 --> 00:21:41,230
+electric field intensity and point R is ليه بتساوي
+
+291
+00:21:41,230 --> 00:21:47,690
+Q1 R-R1 على أربع وضعين سنة منه مدينة R-R1 لكل
+
+292
+00:21:47,690 --> 00:21:52,930
+تكييب طب هذا عبارة عن إيش ال electric field due to
+
+293
+00:21:52,930 --> 00:21:59,230
+point of charge Q1 طبعا شو هي نفس الرسمة لها بفترض
+
+294
+00:21:59,230 --> 00:22:01,130
+أنك تحسر ال electric field هنا
+
+295
+00:22:03,730 --> 00:22:06,810
+بتحسب ال electric field عند النقطة هذه هيش بيساوي
+
+296
+00:22:06,810 --> 00:22:09,950
+هشوف ال electric field اللي جال من Q1 هدفه طبعا
+
+297
+00:22:09,950 --> 00:22:12,950
+soft طبعا في ندي point تشارج زي ما بيكون حوالها في
+
+298
+00:22:12,950 --> 00:22:15,890
+ال electric field فبتعرف ال electric field عند
+
+299
+00:22:15,890 --> 00:22:19,990
+النقطة هذه اللي هي ال position vector هيش R
+
+300
+00:22:19,990 --> 00:22:27,590
+ولبتالي هش هيساوي Q1R-R1 بعدين هلايهيش 4πH0 من
+
+301
+00:22:27,590 --> 00:22:33,090
+نيتيوتر 4R-R1 بعدين هشوفالـ Electric field من
+
+302
+00:22:33,090 --> 00:22:37,790
+التانية و سواء تغيرت أخر واضح؟ أول ممكن نقطة
+
+303
+00:22:37,790 --> 00:22:39,570
+القانون اللي بدأت ال summation يعني أحد أربعة بيض
+
+304
+00:22:39,570 --> 00:22:43,630
+من نوع تحيه اندي summation سارة اندي QK R-RK ممكن
+
+305
+00:22:43,630 --> 00:22:50,350
+تسيب تكعيب R-RK واضح؟ طبعا لاحظوا نفس القانون ال
+
+306
+00:22:50,350 --> 00:22:54,370
+electric field و ال force بس إيش الاختلاف؟ هناك
+
+307
+00:22:54,370 --> 00:22:57,870
+اندي Q1 و Q2 في ال force هنا في ال electric field
+
+308
+00:22:57,870 --> 00:23:01,470
+بس مش ريندي إلا Q1 تمام؟ ال Q1 ليه ال source لل
+
+309
+00:23:01,470 --> 00:23:02,190
+electric field؟
+
+310
+00:23:09,410 --> 00:23:12,170
+واضح؟ طب هاي الكلام اللي حكيناه لو عندنا ثلاث
+
+311
+00:23:12,170 --> 00:23:19,810
+شحنات مثلا Q1, Q2, Q3 و هنحن دي test charge Qt
+
+312
+00:23:19,810 --> 00:23:24,470
+هيكون عليها force F force F يعني هنجمها
+
+313
+00:23:24,470 --> 00:23:30,350
+superposition force من Q1 من 2 و من 3وهنا في B
+
+314
+00:23:30,350 --> 00:23:32,870
+رسمة B برضه نفس الشيء هنا تلاتة pointy charges
+
+315
+00:23:32,870 --> 00:23:36,930
+فانا بدي أحسب ال electric field من النقطة هذه وهنا
+
+316
+00:23:36,930 --> 00:23:41,150
+بيحكيلي هتساوي F اللي هي ال total force هانا و
+
+317
+00:23:41,150 --> 00:23:45,990
+كاريندي تست شار على ايش Q تست شار واضح؟ بس هذا
+
+318
+00:23:45,990 --> 00:23:53,010
+ملخص لكلام الحكيم طب ناخد مثال بيحكي لنا pointy
+
+319
+00:23:53,010 --> 00:23:56,710
+charges one milli column and minus اتنين milli
+
+320
+00:23:56,710 --> 00:24:01,000
+coin are locatedتلاتة اتنين مانس واحد and مانس
+
+321
+00:24:01,000 --> 00:24:05,120
+واحد مانس واحد اربع مديني two pointed charges Q
+
+322
+00:24:05,120 --> 00:24:19,740
+واحد و Q اتنين خلينا نسميها انا Q واحد نفترض
+
+323
+00:24:19,740 --> 00:24:23,560
+Q واحد ايش متساوي واحد
+
+324
+00:24:31,390 --> 00:24:40,730
+ممكن نرسل برضه للتوضيح بس انا عندي x, y, z ال
+
+325
+00:24:40,730 --> 00:24:43,810
+point charge يقول كيوة قرن تلاتة بس تقريب للرسم
+
+326
+00:24:43,810 --> 00:24:48,370
+تلاتة اتنين ماناس واحد خلينا نحكي هنا موجودة على
+
+327
+00:24:48,370 --> 00:24:51,950
+سبيل المثال هي كيوة واحد دي ال position إليها
+
+328
+00:24:51,950 --> 00:24:55,330
+تلاتة اتنين ماناس واحد
+
+329
+00:24:58,390 --> 00:25:02,950
+بعدين فينا point of charge تانية سالب واحد سالب
+
+330
+00:25:02,950 --> 00:25:10,390
+واحد ال X minus وال Y minus وزي اربع ثاني مثلا هي
+
+331
+00:25:10,390 --> 00:25:16,310
+Q2 موجودة من هنا minus اتنين ملي كولوم وهي
+
+332
+00:25:16,310 --> 00:25:21,290
+location كلها minus واحد minus واحد واش اربع طبعا
+
+333
+00:25:21,290 --> 00:25:26,660
+فالان احنا باش نحسب طلب من ال calculateElectric
+
+334
+00:25:26,660 --> 00:25:32,320
+force on 10 nano column of charge located 0 3 1
+
+335
+00:25:32,320 --> 00:25:37,520
+وبالتالي في عندنا point of charge 10 nano column
+
+336
+00:25:37,520 --> 00:25:45,360
+location X0 Y3 Z1 وبالتالي هي point of charge هنا
+
+337
+00:25:45,360 --> 00:25:50,840
+Q 10 nano column تبدأ حسين ال force عليها وبالتالي
+
+338
+00:25:50,840 --> 00:25:53,980
+ال force عليها هيكون في عندى force جاية من Q1
+
+339
+00:25:57,930 --> 00:26:06,230
+الـ electric field عند النقطة هذه واضح؟ فهنا هيكون
+
+340
+00:26:06,230 --> 00:26:09,450
+عندى position vector حنا ده ماشي بنسميه عند النقطة
+
+341
+00:26:09,450 --> 00:26:11,410
+اللى بتحصل عندها ال force او ال electric field
+
+342
+00:26:11,410 --> 00:26:16,330
+ماشي بنسميه position vector R اه بعدين هنا اذا هاد
+
+343
+00:26:16,330 --> 00:26:20,610
+Q واحد فهو position vector فهيعمل vector بين
+
+344
+00:26:20,610 --> 00:26:24,510
+النقطة و بين ال origin فبالتالي هاد ايش هيكون سميه
+
+345
+00:26:24,510 --> 00:26:32,650
+R واحدفار اتنين واضح؟ فبالتالي هيصير عندي ال force
+
+346
+00:26:32,650 --> 00:26:38,570
+ال force حمق كتاب من المفهوم الأول طبعا و هي q و
+
+347
+00:26:38,570 --> 00:26:41,170
+هي q واحد و q اتنين و هي ال position vector الأول
+
+348
+00:26:41,170 --> 00:26:44,630
+هو هسينا ال total force q على نهر واحد يبسن من نهر
+
+349
+00:26:44,630 --> 00:26:49,090
+بعدين عندي عشر أساليب تلاتة ليش متمثل؟ الأولة
+
+350
+00:26:49,090 --> 00:26:53,650
+المهم كيو كيو كتير هذه متمثلة كيو واحد بعدين صفر
+
+351
+00:26:53,650 --> 00:27:01,030
+تلاتة واحد R ناقص R واحدR-R1 وهذا يمثل لي position
+
+352
+00:27:01,030 --> 00:27:07,930
+vector 0 3 1 3 2-1 R-R1 على ال magnitude بعدين
+
+353
+00:27:07,930 --> 00:27:12,310
+minus ليش هنا minus؟ عشان الشحن أصلا، عشان الشحن
+
+354
+00:27:12,310 --> 00:27:20,090
+التاني بالساقر، وبالتالي هذي يبقى Q2R-R2 على ال
+
+355
+00:27:20,090 --> 00:27:24,640
+magnitude الكلواضح؟ لان صراحة انا بستعود كتبنا
+
+356
+00:27:24,640 --> 00:27:33,100
+القانون و هاي ال total force بس عوضناها هسي
+
+357
+00:27:33,100 --> 00:27:36,840
+لاندي هاي ال total force بالساعة و كلمة أربعة و
+
+358
+00:27:36,840 --> 00:27:40,900
+مات هاي عبارة عن إبسلون نار و هنطلحنا ال vectors R
+
+359
+00:27:40,900 --> 00:27:44,440
+minus R واحد و R minus R اتنين و هم يجيبنى تلاتة ع
+
+360
+00:27:44,440 --> 00:27:48,220
+اتنين نرجحها
+
+361
+00:27:52,400 --> 00:27:56,460
+هو ايش حصل طرح اللي هو 2 vector هدوء؟ ايش بطلع
+
+362
+00:27:56,460 --> 00:28:08,520
+عندك؟ سارب ثلاثة واحد و اتنين طبعا ال magnitude ال
+
+363
+00:28:08,520 --> 00:28:11,480
+magnitude هذا الكلام عبارة عن vector هيصير جزر
+
+364
+00:28:11,480 --> 00:28:17,080
+الترميعي بتسعة زائد واحد زائد اربع اربعة
+
+365
+00:28:21,000 --> 00:28:26,480
+و طب هدى كلها مفروض أُس إيه؟ تلاتة هدى كلها أُس
+
+366
+00:28:26,480 --> 00:28:33,640
+تلاتة عشان كده هتصبح أربع طاعش أس إيه؟ تلاتة على
+
+367
+00:28:33,640 --> 00:28:39,960
+تلاتة واضح؟ و هو نفس الشيء بالنسبة ل R minus R
+
+368
+00:28:39,960 --> 00:28:44,300
+إتنين من Q سكريت هنضغط و هنشرب ال force بتساوي
+
+369
+00:28:44,300 --> 00:28:47,480
+الكلام هو حكى ال force عبارة عن vector مُتشَك و هو
+
+370
+00:28:47,480 --> 00:28:52,800
+واضح إن هو مُتشَك بجه X بجه Y بجهزب و هن متني نيوت
+
+371
+00:28:52,800 --> 00:28:58,000
+هاي ال force لو نحسب ال electric field حسبنا ال F
+
+372
+00:28:58,000 --> 00:29:01,460
+عند النقطة هنحسب ال electric field هنا حسبنا ال F
+
+373
+00:29:01,460 --> 00:29:04,020
+هنحسب ال electric field هنقسم على .. اذا انا عارف
+
+374
+00:29:04,020 --> 00:29:07,780
+ال force هان لجانب ال Q1 و Q2 كده هس ال electric
+
+375
+00:29:07,780 --> 00:29:11,700
+field هقسم على PQ وبالتالي الدلت point اللي هي
+
+376
+00:29:11,700 --> 00:29:16,540
+point Q هنحسب ال field F على Q طبعا هو عشر أساعد
+
+377
+00:29:16,540 --> 00:29:23,800
+ثلاثةهنا عندي ملي ميمتر فيه هال F على Q ليه عشرة
+
+378
+00:29:23,800 --> 00:29:27,620
+نانو عشرة عندي هالقيمة ال electric field عندي ال
+
+379
+00:29:27,620 --> 00:29:32,240
+bonded charge واضح؟ خلاص احنا طبعا مكتفن اليوم و
+
+380
+00:29:32,240 --> 00:29:35,700
+منكمل مرة جاية بتدعم المثال H اربعة اتنان خلاص
+
+381
+00:29:35,700 --> 00:29:36,360
+تبقى العامة
+
diff --git a/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/XWXuB9Lj7KU_raw.srt b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/XWXuB9Lj7KU_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..b4716728fb03a90f57e57acf3694b94b3847c79b
--- /dev/null
+++ b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/XWXuB9Lj7KU_raw.srt
@@ -0,0 +1,2384 @@
+1
+00:00:20,270 --> 00:00:23,110
+بسم الله الرحمن الرحيم السلام عليكم ورحمة الله
+
+2
+00:00:23,110 --> 00:00:25,950
+وبركاته احنا اليوم ان شاء الله هنكمل في ال vector
+
+3
+00:00:25,950 --> 00:00:28,790
+calculus و هناخد اللي هو divergence في الحدث
+
+4
+00:00:28,790 --> 00:00:32,030
+الماضي احنا شفنا ال gradient انه بإيس ال magnitude
+
+5
+00:00:32,030 --> 00:00:37,770
+والاتجاه ل ال maximum change لأي scalar field ال
+
+6
+00:00:37,770 --> 00:00:42,600
+divergence بكونش اللي مع vectorDiverge a vector
+
+7
+00:00:42,600 --> 00:00:47,560
+يعني دل دُت a vector field يعني في هذه الحالة أن
+
+8
+00:00:47,560 --> 00:00:52,180
+ال a بتمثل vector field اذا ان dive a هو عبارة عن
+
+9
+00:00:52,180 --> 00:00:58,610
+دل a او diverge a يعني الدلة اللي هي ال operator.a
+
+10
+00:00:58,610 --> 00:01:02,790
+is a divergence of a at a given point is a outward
+
+11
+00:01:02,790 --> 00:01:06,670
+flux per unit volume as volume shrinks above b
+
+12
+00:01:06,670 --> 00:01:10,850
+يعني بتمثل اللي ال divergence a هو ال output flux
+
+13
+00:01:10,850 --> 00:01:16,070
+يعني لو كان عندي field اما لو باخد surface عداش
+
+14
+00:01:16,070 --> 00:01:20,590
+بطلع عندي flux عداش بطلع عندي field هو بنسميه flux
+
+15
+00:01:20,590 --> 00:01:25,250
+عداش بطلع من هذا ال field per unit volume في أثناء
+
+16
+00:01:25,250 --> 00:01:30,770
+ان هذا ال volume بروح ل0حيث ان دلتا V هو ال volume
+
+17
+00:01:30,770 --> 00:01:33,650
+اللى بيسكروه اسف لان ال surface بيكون محيط ال
+
+18
+00:01:33,650 --> 00:01:38,950
+volume فإذا عندي volume عمال عندى فيه field بيمر ف
+
+19
+00:01:38,950 --> 00:01:42,870
+ال diverse هذا ال field بتمثل لقداش من هذا ال
+
+20
+00:01:42,870 --> 00:01:49,410
+field بيطلع من خلال هذا ال volume احنا
+
+21
+00:01:49,410 --> 00:01:51,530
+لو طلعنا طبعا ال diverse في حاجة مهمة في ال
+
+22
+00:01:51,530 --> 00:01:54,510
+diverse ال diverse دائما بيقوللي ان فيه source ال
+
+23
+00:01:54,510 --> 00:01:57,710
+diverse بقوللي دائما ان فيه source ايش معناه؟إنه
+
+24
+00:01:57,710 --> 00:02:01,530
+بده يكون عندى حاجة يا بطلع منها ال field يا بدخل
+
+25
+00:02:01,530 --> 00:02:05,030
+منها ال field عشان يصير اصلا عندى field يخترق ال
+
+26
+00:02:05,030 --> 00:02:08,810
+surface لازم يكون عندى source لهذا ال field فال
+
+27
+00:02:08,810 --> 00:02:12,810
+diverge دايما تعني ليه انه في مكان بطلع منه ال
+
+28
+00:02:12,810 --> 00:02:18,730
+field يعني مثلا هذا النقطة بتمثل زى source و عمال
+
+29
+00:02:18,730 --> 00:02:21,510
+بطلع منها ال field يعني انت تتذكروا ال charge بصي
+
+30
+00:02:21,510 --> 00:02:24,270
+في ال charge مش بصي في ال charge بطلع منها ال
+
+31
+00:02:24,270 --> 00:02:29,150
+field ال electric fieldهذا ما نسميه ان عماله ال
+
+32
+00:02:29,150 --> 00:02:34,650
+field بيطلع من ال point هنا ما نلاقي ان ال field
+
+33
+00:02:34,650 --> 00:02:38,670
+عماله بدخل ل ال point فهنا ما نسميه sink يعني هنا
+
+34
+00:02:38,670 --> 00:02:42,290
+بدخل و هنا ماله diverge يعني انه بيطلع من النقطة
+
+35
+00:02:42,290 --> 00:02:46,490
+او هنا ممكن يدخل على النقطة اذا هذا ما نسميه
+
+36
+00:02:46,490 --> 00:02:49,330
+positive divergence وهذا ما نسميه negative
+
+37
+00:02:49,330 --> 00:02:53,530
+divergence بينما هنا مايوجد source يدخل من ال
+
+38
+00:02:53,530 --> 00:02:57,260
+fieldفهذه zero كلمة مرة divergence معناه ان في
+
+39
+00:02:57,260 --> 00:03:01,780
+عندى source بالتمام زى انتوا تخيلوا المغصلة وفي
+
+40
+00:03:01,780 --> 00:03:03,920
+عندى اللى هي البلوة تحت المياشي بس اللى المياه
+
+41
+00:03:03,920 --> 00:03:07,360
+بتنزل يعني في عندى divergence بسمعه negative
+
+42
+00:03:07,360 --> 00:03:10,840
+divergence لازم يكون فيه source يعني تخيلوا اللى
+
+43
+00:03:10,840 --> 00:03:12,860
+هي النقطة اللى بدخل منها المياه كأنه هي ال source
+
+44
+00:03:12,860 --> 00:03:16,680
+لو عكسنا الاتجاه هيكون positive divergence مافيش
+
+45
+00:03:16,680 --> 00:03:19,600
+عندى source بتطلع منه او بدخل زى الحالة هذه اللى
+
+46
+00:03:19,600 --> 00:03:25,260
+هي البيتالخطوط المتوازية هنا لا توجد divergence لا
+
+47
+00:03:25,260 --> 00:03:27,560
+توجد عملية حرف تدخل أو تدخل أو تطور لا توجد
+
+48
+00:03:27,560 --> 00:03:30,900
+divergence فهنا تكون divergence بالساوة 0 اذا كم
+
+49
+00:03:30,900 --> 00:03:33,720
+انا راح اتحكم positive divergence او negative
+
+50
+00:03:33,720 --> 00:03:37,240
+divergence او هنا لا يوجد positive ولا negative
+
+51
+00:03:37,240 --> 00:03:39,260
+divergence هنا zero divergence
+
+52
+00:03:42,660 --> 00:03:46,100
+لازم ال divergence لازم اعرفه في ال three spaces
+
+53
+00:03:46,100 --> 00:03:49,040
+زي ما شوفنا احنا في ال gradient برضه divergence
+
+54
+00:03:49,040 --> 00:03:52,420
+طبعا ال divergence البساطة هو اقارة عن الدل اللي
+
+55
+00:03:52,420 --> 00:03:56,220
+بخدناه ب Cartesian اش حتة معناه الدل احنا قمنا بقع
+
+56
+00:03:56,220 --> 00:04:03,840
+دي بي بي اكس اكسها ذات دي بي بي وي ويها ذات دي بي
+
+57
+00:04:03,840 --> 00:04:05,340
+بي دي زد زدها
+
+58
+00:04:12,060 --> 00:04:17,060
+زي الـ aY Y hat زي الـ aZ Z hat احنا الـ dot
+
+59
+00:04:17,060 --> 00:04:21,560
+البرودكت نعرف ان ال X Dot X هي الواحد X hat Dot X
+
+60
+00:04:21,560 --> 00:04:25,320
+هي الواحد ال Y hat Dot Y hat هي الواحد زي ال dot Y
+
+61
+00:04:25,320 --> 00:04:27,080
+hat Dot Y hat Dot Z hat Dot Y hat Dot Y hat Dot Z
+
+62
+00:04:27,080 --> 00:04:29,600
+hat Dot Y hat Dot Y hat Dot Z hat Dot Y hat Dot Z
+
+63
+00:04:29,600 --> 00:04:31,960
+hat Dot Y hat Dot Y hat Dot Y hat Dot Y hat Dot Y
+
+64
+00:04:31,960 --> 00:04:32,040
+hat Dot Y hat Dot Y hat Dot Y hat Dot Y hat Dot Y
+
+65
+00:04:32,040 --> 00:04:32,060
+hat Dot Y hat Dot Y hat Dot Y hat Dot Y hat Dot Y
+
+66
+00:04:32,060 --> 00:04:32,060
+hat Dot Y hat Dot Y hat Dot Y hat Dot Y hat Dot Y
+
+67
+00:04:32,060 --> 00:04:32,060
+hat Dot Y hat Dot Y hat Dot Y hat Dot Y hat Dot Y
+
+68
+00:04:32,060 --> 00:04:32,060
+hat Dot Y hat Dot Y hat Dot Y hat Dot Y hat Dot Y
+
+69
+00:04:32,060 --> 00:04:32,060
+hat Dot Y hat Dot Y hat Dot Y hat Dot Y hat Dot Y
+
+70
+00:04:32,060 --> 00:04:32,060
+hat Dot Y hat Dot Y hat Dot Y hat Dot Y hat Dot Y
+
+71
+00:04:32,060 --> 00:04:36,170
+hat Dot Y hat Dot Y hat Dot Y hat Dot Yده مانيش
+
+72
+00:04:36,170 --> 00:04:39,530
+يعمل ال-doting عن هاي مش بس انه اللي بقى بتطلع ال
+
+73
+00:04:39,530 --> 00:04:41,730
+X hat و X hat واحد كمان لإن هنا فيه
+
+74
+00:04:41,730 --> 00:04:47,910
+differentiation E X by E X التانية لإن ال operator
+
+75
+00:04:47,910 --> 00:04:55,950
+عمله بأسرع ال field هيكون P A Y I P Y ذات P A Z Y
+
+76
+00:04:55,950 --> 00:04:59,050
+P Z عن هاي تعملين ال component X هاي component R
+
+77
+00:04:59,050 --> 00:05:01,010
+ممكن تكون كلهم function في X و Y و Z
+
+78
+00:05:05,890 --> 00:05:08,330
+ممكن تكون function بس في X، ممكن تكون function بس
+
+79
+00:05:08,330 --> 00:05:12,070
+في Y، وهذا بحدد مين ال surviving differentiation،
+
+80
+00:05:12,070 --> 00:05:16,030
+ماضي؟ إذا نهجوا و عماروا عن ال divergence تبع ال
+
+81
+00:05:16,030 --> 00:05:20,670
+field، تعرفت معناه أنه يا sinking يابتخلق او تخلق
+
+82
+00:05:20,670 --> 00:05:24,370
+او تخلق او تخلق او تخلق او تخلق او تخلق او تخلق او
+
+83
+00:05:24,370 --> 00:05:32,910
+تخلق او تخلق او تخلق او تخلق او تخلق او تخلق او
+
+84
+00:05:32,910 --> 00:05:32,990
+تخلق او تخلق او تخلق او تخلق او تخلق او تخلق او
+
+85
+00:05:32,990 --> 00:05:33,030
+تخلق او تخلق او تخلق او تخلق او تخلق او تخلق او
+
+86
+00:05:33,030 --> 00:05:34,990
+تخلق او تخلق او تخلق او تخلق او تخلق او تخلق او
+
+87
+00:05:34,990 --> 00:05:46,530
+تخلق او تخلق او تخلق او تخلق او تخلق او
+
+88
+00:05:46,530 --> 00:05:48,880
+تبينما بالـ spherical coordinate هيكون ال
+
+89
+00:05:48,880 --> 00:05:54,520
+divergence 1 على r تربيع d by dr r تربيع ar زائد 1
+
+90
+00:05:54,520 --> 00:05:57,960
+على r sin theta d by d theta a theta sin theta
+
+91
+00:05:57,960 --> 00:06:03,560
+زائد 1 على r sin theta d a pi by d piفي أسف صلحت
+
+92
+00:06:03,560 --> 00:06:06,560
+هنا اذا كل اللي عرفناه اليوم هو ال divergence
+
+93
+00:06:06,560 --> 00:06:10,540
+قولنا divergence هو ببساطة الدل dot مع ال vector و
+
+94
+00:06:10,540 --> 00:06:12,680
+احنا عارفين الدل سيبناه من المحاضرة الماضية في
+
+95
+00:06:12,680 --> 00:06:15,480
+الcartesian و في الcyclical و الcyclical ماعليه
+
+96
+00:06:15,480 --> 00:06:20,120
+اللي عاملها dot مع ال vector تبعنا حلوة أحسن
+
+97
+00:06:20,120 --> 00:06:24,940
+التالي في خصائص ال divergence it produces a scalar
+
+98
+00:06:24,940 --> 00:06:28,540
+field احنا اتفقنا ان الفتبر ده بتاعة النتج معله
+
+99
+00:06:28,540 --> 00:06:35,280
+scalar اي نتجمافيش فيه اي vector اي dot ل two
+
+100
+00:06:35,280 --> 00:06:39,080
+vectors بكون scalar فبالنسبة لأ ال divergence
+
+101
+00:06:39,080 --> 00:06:42,360
+هيكون scalar فال gradient الذاكرين كان vector كان
+
+102
+00:06:42,360 --> 00:06:45,720
+له magnitude و اتجاه بعبّرله عن magnitude و اتجاه
+
+103
+00:06:45,720 --> 00:06:49,200
+لأ it's a maximum change في ال field ال scalar
+
+104
+00:06:49,200 --> 00:06:53,020
+field لكن في ال divergence انها تجمع له scalar اي
+
+105
+00:06:53,020 --> 00:06:56,820
+اول نقطة نقطة تانية ال divergence of a scalar
+
+106
+00:06:56,820 --> 00:07:02,190
+field اللي هو del V makes no senseلأن لو انا عندي
+
+107
+00:07:02,190 --> 00:07:06,330
+scalar field بدي اجيب ال dot مع scalar field اللي
+
+108
+00:07:06,330 --> 00:07:11,570
+معناه ال divergence between two vector fields لما
+
+109
+00:07:11,570 --> 00:07:15,210
+اقول بدي ايش ال divergence بتاع scalar field ولا
+
+110
+00:07:15,210 --> 00:07:18,610
+اشي مالهوش معناه has no sense ماهوش اي معنى نقول
+
+111
+00:07:18,610 --> 00:07:22,170
+في divergence of scalar field has no meaning has
+
+112
+00:07:22,170 --> 00:07:25,230
+no sense يعني فقط divergence ل vector field انا
+
+113
+00:07:25,230 --> 00:07:28,450
+قلت product بيه vector field زي ال electric field
+
+114
+00:07:28,450 --> 00:07:32,080
+مثلازي الـ negative field باخد ال divergence لكن
+
+115
+00:07:32,080 --> 00:07:34,720
+scalar field زي الـ pi اللى هنشوفها في المحاورات
+
+116
+00:07:34,720 --> 00:07:37,920
+القاعدة هيكون مفيش ايضا معناه اقول في divergence
+
+117
+00:07:37,920 --> 00:07:42,820
+افضل في ال gradient افضل في ال gradient افضل في ال
+
+118
+00:07:42,820 --> 00:07:48,220
+gradient ال scalar هو دي vector كله كمان؟ كمان في
+
+119
+00:07:48,220 --> 00:07:52,560
+توزيعية distributed يعني diverge A زي B يعني لو
+
+120
+00:07:52,560 --> 00:07:56,580
+انا اول جمعت ال fields A مع Bبعدين جبتهم ال
+
+121
+00:07:56,580 --> 00:07:59,620
+divergence نفس الشيء لو جبت ال divergence تبع ال A
+
+122
+00:07:59,620 --> 00:08:03,740
+جمعته بال divergence تبع ال B واضح؟ اذا انا
+
+123
+00:08:03,740 --> 00:08:11,960
+بالنسبة لدى divergence اذا
+
+124
+00:08:11,960 --> 00:08:16,700
+انا عندى two vectors A وB او two fields A وB وجمعت
+
+125
+00:08:16,700 --> 00:08:19,940
+هدولة ال two fields مع بعض اول وجبت ال divergence
+
+126
+00:08:19,940 --> 00:08:23,900
+لازم بتاعه يساوي لو جبت اول ال divergence تبع A و
+
+127
+00:08:23,900 --> 00:08:28,750
+بعدين divergenceالاخر حاجة ال divergence ل scalar
+
+128
+00:08:28,750 --> 00:08:34,590
+مع vector هذا scalar وهذا vector هيصير high
+
+129
+00:08:34,590 --> 00:08:38,770
+identity تقول إنه هتكون سوى V تطلع برا divergence
+
+130
+00:08:38,770 --> 00:08:44,710
+لأنها scalar diverse A زائد A dot grade V يعني ال
+
+131
+00:08:44,710 --> 00:08:49,390
+dot grade V هيظلوا دائما معين مع ال vectorsهي تشبه
+
+132
+00:08:49,390 --> 00:08:52,390
+لي تفاضل ال two quantities يعني الأول تتفاضل
+
+133
+00:08:52,390 --> 00:08:56,430
+التاني زي التاني تتفاضل الأول بس هنا بمانعت بيه ال
+
+134
+00:08:56,430 --> 00:09:03,110
+dot و المنفعة يعني عندي الدل V A V هو اللي بطلعها
+
+135
+00:09:03,110 --> 00:09:07,630
+هو الفاضل كأنه التاني اللي هو diverge ال A يعني هي
+
+136
+00:09:07,630 --> 00:09:13,150
+dA by dx زي dA by dy ال term التاني أنا بطلع أن هو
+
+137
+00:09:13,150 --> 00:09:16,530
+ال Aلكن لما بقدرش فاش حاجة عندي اسمها اللي هي
+
+138
+00:09:16,530 --> 00:09:21,910
+divergence دي، لكن عندي a dot gradient دي، مش
+
+139
+00:09:21,910 --> 00:09:24,370
+مطلوب من نسمتهم، بس هو احنا ممكن نسمتهم هدولة و
+
+140
+00:09:24,370 --> 00:09:27,730
+قاعدين بس، بس بدي اذاكر .. يعني انا بس بس اذاكركم
+
+141
+00:09:27,730 --> 00:09:30,510
+فيه، يعني بطريقة انا اذاكرهم، انه divergence two
+
+142
+00:09:30,510 --> 00:09:33,610
+quantities واحد scalar واحد vector هيكون ال scalar
+
+143
+00:09:33,610 --> 00:09:37,550
+مضروف في divergence ال vector زائد ال vector
+
+144
+00:09:37,550 --> 00:09:39,910
+dotted مع gradient ال scalar
+
+145
+00:09:43,320 --> 00:09:46,940
+فهي حاجة مهمة كتير احنا هتعلمها وهي كتير اللي هدور
+
+146
+00:09:46,940 --> 00:09:50,660
+في ال electromagnetic و هنشوفها برضه لما ناخد عن
+
+147
+00:09:50,660 --> 00:09:53,700
+ال fields اللي اسمها ال divergence theorem ال
+
+148
+00:09:53,700 --> 00:09:57,440
+divergence theorem يتطبق لعلاقة بين surface field
+
+149
+00:09:57,440 --> 00:10:01,940
+integral مع volume integral ال divergence theorem
+
+150
+00:10:01,940 --> 00:10:04,940
+أكيد هيكون فيها divergence من اسمها فال divergence
+
+151
+00:10:04,940 --> 00:10:08,200
+اش قلنا دل ال vector لما أحكي عن ال divergence
+
+152
+00:10:08,200 --> 00:10:11,020
+theorem أكيد هيكون و أكيد هيكون دل ال divergence
+
+153
+00:10:11,920 --> 00:10:15,460
+ماذا يعني بيبرجشون؟ لو أنا اللي بتعمل over closed
+
+154
+00:10:15,460 --> 00:10:19,880
+surface يعني عندي volume و اعطيه خاول الاحياء ده
+
+155
+00:10:19,880 --> 00:10:24,860
+هذا ال volume حوالي ال surface سياس هون ال volume
+
+156
+00:10:24,860 --> 00:10:28,800
+هيكون with closed integral على ال surface على
+
+157
+00:10:28,800 --> 00:10:32,740
+الشلب تبع ال surface with closed integral يعني ايش
+
+158
+00:10:32,740 --> 00:10:38,360
+معناه؟ هيكون فاي هو من zero ل Y و ثتا من zero ل Y
+
+159
+00:10:38,360 --> 00:10:45,000
+و R من zero ل infinityعلى كل ال surface لما
+
+160
+00:10:45,000 --> 00:10:49,640
+أفضل أكمل closed surface integral لأي vector doted
+
+161
+00:10:49,640 --> 00:10:52,820
+مع ال surface واحنا اتفقنا اي surface اي surface
+
+162
+00:10:52,820 --> 00:10:58,920
+ايش ان الاتجاه تبعه هو ال norm اللي عمودي على ال
+
+163
+00:10:58,920 --> 00:11:02,400
+surface و الطالع من ال volume يعني هيكون هي اتجاه
+
+164
+00:11:02,400 --> 00:11:05,660
+مثلا لو احنا قيلنا هذه الاسفير هيكون اتجاه main
+
+165
+00:11:05,660 --> 00:11:06,840
+earth هذا ال norm
+
+166
+00:11:15,570 --> 00:11:23,070
+الحلقة التالية ستتخص في DS إذا
+
+167
+00:11:23,070 --> 00:11:24,570
+نختار surface integral
+
+168
+00:11:28,680 --> 00:11:32,480
+انها ال vector a تبعنا و دي أصل هو ال element تبع
+
+169
+00:11:32,480 --> 00:11:34,580
+ال surface و احنا أخدنا ال element تبع ال surface
+
+170
+00:11:34,580 --> 00:11:36,880
+في ال Cartesian وفي ال Cylinder Calcificrical
+
+171
+00:11:36,880 --> 00:11:40,820
+وعرفنا ان هو vector واتجاهه هو تمام عمودي على
+
+172
+00:11:40,820 --> 00:11:45,620
+اتجاه ال surface هذا ال clause integral يساوي تمام
+
+173
+00:11:45,620 --> 00:11:49,860
+integral over volume ل diverge air
+
+174
+00:11:57,980 --> 00:12:01,580
+هذه هي ال divergence يعني كتير نحتاجها احنا عشان
+
+175
+00:12:01,580 --> 00:12:05,840
+نوصل لبعض الحلول للتبسيط على ال integrals و احنا
+
+176
+00:12:05,840 --> 00:12:08,440
+في الرياضيات كمان نستخدمها لما يكون أسهل عليا
+
+177
+00:12:08,440 --> 00:12:12,240
+أكامل ال volume أو ال surface أنتقل من هذا لهذا ال
+
+178
+00:12:12,240 --> 00:12:16,320
+surface ممكن فيها divergenceاللي فى ال calculus
+
+179
+00:12:16,320 --> 00:12:20,300
+يمكن تـC أخدتوا vector انتوا و انا أخدناها فى ال
+
+180
+00:12:20,300 --> 00:12:22,840
+calculus نفس العظيم بس ماكناش ناخدها انها fields
+
+181
+00:12:22,840 --> 00:12:27,200
+فانا هدوسل شرّد وسيلة انه ان انت تساعدني على الحل
+
+182
+00:12:27,200 --> 00:12:30,620
+ان هو أسرع ان أحل على ال surface ولا على ال volume
+
+183
+00:12:30,620 --> 00:12:35,660
+اذا ايش بتقولنا ال divergence يعني ان كل flux ها
+
+184
+00:12:35,660 --> 00:12:41,000
+دى بتمثلى ده فلكس تتذكرها ده يعني closed surface
+
+185
+00:12:41,000 --> 00:12:47,040
+integral لأى fieldهو الـ total flux عشان الـ
+
+186
+00:12:47,040 --> 00:12:50,020
+closed integral يعني بيقول قداش كل flux اللي
+
+187
+00:12:50,020 --> 00:12:54,920
+بيطالع من ال surface ال divergence هو كل ال total
+
+188
+00:12:54,920 --> 00:12:58,660
+outward flux of a vector A through closed surface
+
+189
+00:12:58,660 --> 00:13:02,520
+S is the same as ال volume integral ال divergence
+
+190
+00:13:02,520 --> 00:13:08,080
+لهذا الهيلد، واضح؟
+
+191
+00:13:08,080 --> 00:13:11,560
+لأ، اسبعتها
+
+192
+00:13:14,640 --> 00:13:17,340
+أذا انا انهدى كمان مرة مثلا لو كان سليندر الـ
+
+193
+00:13:17,340 --> 00:13:20,000
+closed surface ايش هيكون؟ اللي هو الـ shell تبع
+
+194
+00:13:20,000 --> 00:13:24,100
+السليندر لكن ال volume اللي في قلبها اللي محتوى في
+
+195
+00:13:24,100 --> 00:13:31,740
+قلب السليندر نشوف مثال، بدنا لو نشوف ال divergence
+
+196
+00:13:31,740 --> 00:13:38,080
+لهدولة ال vectors ناخد مثال واحد من هون ناخد ال
+
+197
+00:13:38,080 --> 00:13:40,540
+cylindrical و ال spherical اللي هي لل Cartesian
+
+198
+00:13:40,540 --> 00:13:45,770
+أصل إشي تبدو Cartesian كل فضولةالواحد من اتين
+
+199
+00:13:45,770 --> 00:13:54,230
+هدوله طب يالا تصلي على ميز؟ يالا تعال كيف لقاليه؟
+
+200
+00:13:54,230 --> 00:13:56,550
+عشان ماحللتوش المراعي دي، المراعي دي كل اللي حللوه
+
+201
+00:13:56,550 --> 00:14:01,030
+ما سنة تالتة و
+
+202
+00:14:01,030 --> 00:14:08,090
+لما دايما تطبع لسه
+
+203
+00:14:08,090 --> 00:14:09,870
+الجميع قالت انا بدي ..
+
+204
+00:14:21,540 --> 00:14:26,600
+الطبيعة QQ هو vector من الـ cylindrical coordinate
+
+205
+00:14:26,600 --> 00:14:31,120
+اذا
+
+206
+00:14:31,120 --> 00:14:35,640
+حفظها لنا هي بتكتبها على اللوح او انه عشان نتاكد
+
+207
+00:14:35,640 --> 00:14:43,000
+ان هي واحد على رو دي by ديPlus 1 على رو دي اي فاي
+
+208
+00:14:43,000 --> 00:14:54,860
+فاي دي فاي ثائق دي اي زي فاي دي سبعون تاسع رو،
+
+209
+00:14:54,860 --> 00:14:58,480
+ايش ال raw component ل ال Q؟ طبعا هنا خلينا بس
+
+210
+00:14:58,480 --> 00:15:03,380
+عشان نقول انهم ل Q حاطة، زبطيهم ل Q رو Q فاي Q زي
+
+211
+00:15:05,090 --> 00:15:07,570
+عشان مايكونش في هذه الطرف انت Q و هذه الطرف
+
+212
+00:15:07,570 --> 00:15:13,370
+التانية اذا
+
+213
+00:15:13,370 --> 00:15:18,270
+عندي اللي هي رو ساين الفاي هي ال رو component لل Q
+
+214
+00:15:18,270 --> 00:15:25,530
+و الفاي component اللي هي رو تربيه زت و ال زتو
+
+215
+00:15:25,530 --> 00:15:33,730
+component اللي هي رو تربيه زت و فاي
+
+216
+00:15:33,730 --> 00:15:39,630
+زتووانا هتفضل رو تربيه ومنه هتكون اتنين رو بصينت
+
+217
+00:15:39,630 --> 00:15:44,710
+باي ومافيش اي five هتطلع zero واخر term هيكون
+
+218
+00:15:44,710 --> 00:15:49,730
+cosine of five لنبسطها
+
+219
+00:15:49,730 --> 00:15:53,030
+رو بصينت باي لأ مفيشه بس cancel ال cancel يخليه
+
+220
+00:15:53,030 --> 00:15:55,430
+يتوفر answer ايه ايه ايه ايه ايه ايه ايه ايه ايه
+
+221
+00:15:55,430 --> 00:15:57,630
+ايه ايه ايه ايه ايه ايه ايه ايه
+
+222
+00:16:02,870 --> 00:16:06,250
+بساطة هو بسبقى بجيب الدل بـsymmetrical coordinate
+
+223
+00:16:06,250 --> 00:16:11,730
+وبعوض على ال components بتاعة Q و بفاضر و بحسب على
+
+224
+00:16:11,730 --> 00:16:15,950
+N شكرا
+
+225
+00:16:15,950 --> 00:16:20,570
+يا رمضان
+
+226
+00:16:20,570 --> 00:16:26,710
+شوف كده
+
+227
+00:16:26,710 --> 00:16:31,070
+مثال هي أن جيب أربع ساعة مستحيلة تانية صغيرة
+
+228
+00:16:45,280 --> 00:16:49,200
+مش طالب مني بده نجيب ال flux عندي أنا vector field
+
+229
+00:16:49,200 --> 00:16:55,040
+G of R اللي قيمته 10E to the minus 2Z روره هات زاد
+
+230
+00:16:55,040 --> 00:16:59,960
+زد هات و بدي مني اجيب ال flux G out of the entire
+
+231
+00:16:59,960 --> 00:17:04,420
+surface of a cylinder رو قيمتها واحد و Z بتروح من
+
+232
+00:17:04,420 --> 00:17:07,860
+Zero لواحد confirm the results using divergence
+
+233
+00:17:07,860 --> 00:17:10,740
+theorems يعني ايه شو طالب مني اول طالب مني اول
+
+234
+00:17:10,740 --> 00:17:14,410
+اجيبالـ total flux باستخدام ما هو الـ closed
+
+235
+00:17:14,410 --> 00:17:19,310
+surface integral الـ closed surface integral لـ g
+
+236
+00:17:19,310 --> 00:17:24,570
+dot ds فهي المطوبة أول جزء من الأجيب الجزء اللي هو
+
+237
+00:17:24,570 --> 00:17:29,130
+ال flux و اتفقنا أن الـ total flux تنبغي جزء من ال
+
+238
+00:17:29,130 --> 00:17:35,210
+flux بهذا الشكل بساوي ال closed integral ل g dot
+
+239
+00:17:35,210 --> 00:17:39,270
+ds أو خلينا نكتب بس ال flux
+
+240
+00:17:49,930 --> 00:17:54,590
+هي أول جزء، الجزء التاني طالب مني أن أثبت أن جوايا
+
+241
+00:17:54,590 --> 00:17:59,030
+نفس الحاجة لو أنا أخدت Volume Integra لدعي الدرج
+
+242
+00:17:59,030 --> 00:18:05,160
+G، اللي هو ال divergence sphericalعشان أول حاجة
+
+243
+00:18:05,160 --> 00:18:08,760
+بدي أحل بالاستعانة بتعريف ال flux اللي هو ال raw
+
+244
+00:18:08,760 --> 00:18:12,560
+surface integral د جيجو دي اسك و أثبت إن النتيجة
+
+245
+00:18:12,560 --> 00:18:16,780
+لا تختلف لو أخدت انا ال integral على الوضع نبدأ
+
+246
+00:18:16,780 --> 00:18:21,060
+بالجزء الأول لكي نشوف الرسمة طبعا هو جزء من ال
+
+247
+00:18:21,060 --> 00:18:23,780
+surface أو ال surface اللي ماتينا إياه هو raw
+
+248
+00:18:23,780 --> 00:18:29,460
+بتسوا واحد وزد قيمتها من zero لواحد وطالب منها
+
+249
+00:18:29,460 --> 00:18:34,220
+اللي هو ال total flux اللي هو إبسايدT Psi S Psi P
+
+250
+00:18:34,220 --> 00:18:42,780
+Psi Top Psi Bottom Psi S Psi
+
+251
+00:18:42,780 --> 00:18:52,860
+Psi
+
+252
+00:18:52,860 --> 00:18:57,440
+Psi Top Psi Bottom Psi S Psi Psi Psi Psi Psi Psi
+
+253
+00:18:57,440 --> 00:18:57,440
+Psi Psi Psi Psi Psi Psi Psi Psi Psi Psi Psi Psi
+
+254
+00:18:57,440 --> 00:18:57,480
+Psi Psi Psi Psi Psi Psi Psi Psi Psi Psi Psi Psi
+
+255
+00:18:57,480 --> 00:18:57,480
+Psi Psi Psi Psi Psi Psi Psi Psi Psi Psi Psi Psi
+
+256
+00:18:57,480 --> 00:18:57,560
+Psi Psi Psi Psi Psi Psi Psi Psi Psi Psi Psi Psi
+
+257
+00:18:57,560 --> 00:18:57,600
+Psi Psi Psi Psi Psi Psi Psi Psi Psi Psi Psi Psi
+
+258
+00:18:57,600 --> 00:18:57,620
+Psi Psi Psi Psi Psi Psi Psi Psi Psi Psi Psi Psi
+
+259
+00:18:57,620 --> 00:18:57,620
+Psi Psi Psi Psi Psi Psi Psi Psi Psi Psi Psi Psi
+
+260
+00:18:57,620 --> 00:19:00,000
+Psi Psi Psi Psi Psi Psi Psi Pطبعا الـ Psi لكل
+
+261
+00:19:00,000 --> 00:19:02,900
+واحدة ليست closed integral هي Psi على ال surface
+
+262
+00:19:02,900 --> 00:19:05,820
+المعين تبعها المجموعة الموجودة بال closed integral
+
+263
+00:19:05,820 --> 00:19:13,180
+نبدأ بالواقع التوب Psi توب احنا قلنا طول ال Z بروح
+
+264
+00:19:13,180 --> 00:19:17,640
+من Zero لواحد روه بتسوا واحد هذا ال surface
+
+265
+00:19:17,640 --> 00:19:21,660
+الفغاني قشط بتغير قيمة زكريم هو عبارة عن رو دي رو
+
+266
+00:19:21,660 --> 00:19:25,920
+دي فاي رو دي رو دي فاي Z ثابتة Z قيمتها واحد
+
+267
+00:19:27,540 --> 00:19:30,760
+واتجاهها ال surface ال normal عليها و اللي ماله
+
+268
+00:19:30,760 --> 00:19:34,920
+outward ال volume اتفقنا دائما ال mod تبع ال
+
+269
+00:19:34,920 --> 00:19:42,980
+surface and the top هو يكون هذه الدائرة هيكون عمود
+
+270
+00:19:42,980 --> 00:19:45,700
+عليها و برا ال volume ليه هتكون في هذه الحالة ال
+
+271
+00:19:45,700 --> 00:19:51,940
+plus زدها اذا دي ال aspect of هتكون اللي هو ال
+
+272
+00:19:51,940 --> 00:19:56,180
+element من هذه الدائرة اللي هو بيساوي
+
+273
+00:20:16,640 --> 00:20:23,220
+الكامل الجزء الأولاني اللي هو ال integral ل G dot
+
+274
+00:20:23,220 --> 00:20:27,840
+DSاللي هي على ال top surface رو اللي بتروح من وين
+
+275
+00:20:27,840 --> 00:20:30,880
+من zero ل واحد اقصى قيمة لرو ايه لنا واحد السلين
+
+276
+00:20:30,880 --> 00:20:36,080
+ده ال radius تبعها واحد ويه الفاي هتروح من zero ل
+
+277
+00:20:36,080 --> 00:20:38,920
+two pi عشان تطيير الدائرة هاخد ال dot product
+
+278
+00:20:38,920 --> 00:20:43,500
+بالجي و ال DS و الاتجارها في ال z hat اذا انفقدت
+
+279
+00:20:43,500 --> 00:20:46,100
+هيتبقى عندنا ال z hat component انا عندى two
+
+280
+00:20:46,100 --> 00:20:49,740
+components واحد اتجار ال رو هات واحد اتجار ال دس
+
+281
+00:20:49,740 --> 00:20:55,130
+هات بس احنا عاملنا نوع ال dot product g dot dsفهذا
+
+282
+00:20:55,130 --> 00:20:58,910
+ال term هيكون zero و هتوقع عندي إيه هو z هذا هيدلع
+
+283
+00:20:58,910 --> 00:21:06,130
+اندي عشرة e to the minus اتنين z هي اللي هو d z ال
+
+284
+00:21:06,130 --> 00:21:11,290
+zهات سوات مع ال z هات واحد رو زي رو بي خاطر و طبعا
+
+285
+00:21:11,290 --> 00:21:15,850
+عرضنا هو عن اللي هي ال z قيمتها واحد لإن عند هذا
+
+286
+00:21:15,850 --> 00:21:21,510
+ال surface ال surface z تساوي واحد
+
+287
+00:21:31,110 --> 00:21:34,950
+بعد ذلك التكامل عادي العشرة تطلع برا ال Integral
+
+288
+00:21:34,950 --> 00:21:38,830
+ال raw تكملها رو تر بطبعه و ال H ثمانه ثامه تطلع
+
+289
+00:21:38,830 --> 00:21:42,150
+برا ال Integral ال constants دولة رو دي روه بتصير
+
+290
+00:21:42,150 --> 00:21:46,690
+رو تر بي على اتنين من Zero لواحد و دي five بتصير
+
+291
+00:21:46,690 --> 00:21:48,270
+five من Zero ل two pi
+
+292
+00:21:52,780 --> 00:21:59,060
+10E⁻² بروفر B على 2 من 0 و 1 و دي فايفة تقيمة فايف
+
+293
+00:21:59,060 --> 00:22:06,180
+من 0 تقيمة فايف A هتزاوى 10 ع 2 او 10 ع 2 مانصر 2
+
+294
+00:22:06,180 --> 00:22:14,280
+P هو 2 Pi على 8 فايف 1 نص و فايفة تقيمة فايف 2 ع 2
+
+295
+00:22:14,280 --> 00:22:20,470
+هتقيم ع 10 بروفر B على 2 من 0 و 1الـ Flux أو الـ
+
+296
+00:22:20,470 --> 00:22:29,870
+Flux اللى طالع من ال top surface واضح
+
+297
+00:22:29,870 --> 00:22:35,570
+فيها ايه السؤال اللى حديناه نجي ل ال bottom
+
+298
+00:22:35,570 --> 00:22:43,270
+surface عند ال bottom surface عند
+
+299
+00:22:43,270 --> 00:22:47,370
+ال bottom surface عند هذه الدائرة
+
+300
+00:23:05,370 --> 00:23:10,090
+بتجاه اين بيكون نام اللى على ال surface و برا ال
+
+301
+00:23:10,090 --> 00:23:14,950
+volume طالع برا ال volume
+
+302
+00:23:17,670 --> 00:23:24,250
+ن تاب بي تساوي ماينص تاب واقل كمراه ده ناخد النقم
+
+303
+00:23:24,250 --> 00:23:27,270
+على ال surface اللي عمودي عليه و برا ال volume
+
+304
+00:23:27,270 --> 00:23:32,470
+فإذا عندي slender زي هذا القلم مثلا وهي انا عندي
+
+305
+00:23:33,900 --> 00:23:37,980
+العمودي عليه باخدش اللى جوا تجهه طالع برا حقيقة
+
+306
+00:23:37,980 --> 00:23:41,180
+محتوى السلندر بيكون طالع لبرا ال volume مش داخل
+
+307
+00:23:41,180 --> 00:23:45,340
+فقلب ال volume هذا ال top هيكون برا طالع ال norm
+
+308
+00:23:45,340 --> 00:23:48,660
+عمودي عليه و خارج ال volume مش داخل ال volume
+
+309
+00:23:48,660 --> 00:23:53,780
+تمام؟ إذا عندي ال bottom هيكون ما نزلها و ال
+
+310
+00:23:53,780 --> 00:23:57,840
+integral بتاع مش بهذا ال integral لأنه هيكون دي
+
+311
+00:23:57,840 --> 00:24:03,700
+أسر فرقية بدل زدها ما نزلهاإذا بس هيظل عندي إزدها
+
+312
+00:24:03,700 --> 00:24:08,320
+component بس الفرقية إنه قدامها في minus فكوفة
+
+313
+00:24:08,320 --> 00:24:11,880
+عامة هيكون في أي تغيرات هيكون نفس الجواب بس قدامه
+
+314
+00:24:11,880 --> 00:24:15,820
+minus يعني
+
+315
+00:24:15,820 --> 00:24:23,140
+هذا بالنسبة للبطم z
+
+316
+00:24:23,140 --> 00:24:26,880
+قبلتها zero فهنا بس فينا z هنا if I apply E to the
+
+317
+00:24:26,880 --> 00:24:31,760
+2z أنت قولتلي بقى هناان جي قولنا فيها a to the
+
+318
+00:24:31,760 --> 00:24:35,520
+minus 2z هنا بتفرق بس هذا ال term اللي هو a to the
+
+319
+00:24:35,520 --> 00:24:39,540
+minus 2 بيصير a to the zero لإن زت zero فبصير عشر
+
+320
+00:24:39,540 --> 00:24:44,180
+أبعاد و بالسالق في إشارة سالق بس ال Integra اللي
+
+321
+00:24:44,180 --> 00:24:47,320
+هو محتوى للقلب ال Integra مش هيخلق لكن هيخلق فيه
+
+322
+00:24:47,320 --> 00:24:51,300
+ال exponential و السالق إذا الناتج هو عشر أبعاد
+
+323
+00:24:51,300 --> 00:24:56,400
+إذا نصرنا عارفين قيمة ال flux على ال top surface و
+
+324
+00:24:56,400 --> 00:24:58,900
+ال flux على ال bottom surface بطل عليها ال flux
+
+325
+00:24:58,900 --> 00:25:04,020
+اللي علىالمحيط تبع السليندر المساحة الجانبية
+
+326
+00:25:04,020 --> 00:25:09,360
+لسليندر كأن ورّا المساحة الجانبية لسليندر قلنا هذا
+
+327
+00:25:09,360 --> 00:25:12,020
+ال surface اللي هو زي هذا ال surface تبع القلم
+
+328
+00:25:12,020 --> 00:25:16,220
+انهم اشماله هيكون برا ال volume يعني هيكون اتجاه و
+
+329
+00:25:16,220 --> 00:25:20,160
+اتجاه مي رو هات هذا الاتجاه هيكون اتجاه رو هات
+
+330
+00:25:23,320 --> 00:25:26,560
+هنا ال surface ايش اللي بتغير؟ ال z بتغير من zero
+
+331
+00:25:26,560 --> 00:25:29,660
+ل واحد من اللي ثابت رو رو ده يعني عنده قيمة واحد
+
+332
+00:25:29,660 --> 00:25:32,620
+على هذا ال surface على هذا ال surface المحيط
+
+333
+00:25:32,620 --> 00:25:38,500
+الخارجي ثابت ال رو واحد بتغيرش و هيكون التغير ال z
+
+334
+00:25:38,500 --> 00:25:42,280
+من zero ل واحد و في اللي بتروح من zero ل two في
+
+335
+00:25:42,280 --> 00:25:48,840
+اذا دي اسفة الحالة هي عبارة عن دي z في اللي هو رو
+
+336
+00:25:48,840 --> 00:25:53,720
+دي فيعند فاى هتروح او اللى هيكون في عند ال element
+
+337
+00:25:53,720 --> 00:25:59,400
+بهذا الشكل DZ و هذا القاص DZ و القاص اللى هيكون رو
+
+338
+00:25:59,400 --> 00:26:03,060
+D فاى صحيح بتذكرينه هذا اللى حكى لو أخدت شقه من
+
+339
+00:26:03,060 --> 00:26:07,200
+هنا هيكون DZ و هذا اللى هو اقفال الزاوية D5 هيكون
+
+340
+00:26:07,200 --> 00:26:13,740
+رو D5 رو قنقتها واحد و Z بتتغير من zero لواحد و
+
+341
+00:26:13,740 --> 00:26:19,900
+فاى من zero ل two piواتجاهه قلنا مين؟ روهات فنرجع
+
+342
+00:26:19,900 --> 00:26:23,160
+لها ال G ونشوف ان هو ال term اللي بدي ضم عندي
+
+343
+00:26:23,160 --> 00:26:25,460
+اتجاه ال روهات هذا ال term اللي هيضم وهذا هيكون
+
+344
+00:26:25,460 --> 00:26:29,540
+Zero لازم هيضم ال term الأولاني اللي هو عشرة روه
+
+345
+00:26:29,540 --> 00:26:30,740
+يتوزن مع ناس اتنين زي
+
+346
+00:26:34,850 --> 00:26:38,470
+عند رو ستة واحد و دي اس اللي هي رو دي زد دي فاي
+
+347
+00:26:38,470 --> 00:26:43,290
+فرو هات فهاخد التبردر تقولنا هتظل ال term الأولاني
+
+348
+00:26:43,290 --> 00:26:45,930
+اللي هو عشرة رو eight ومانس من زد و فيهم دي رو
+
+349
+00:26:45,930 --> 00:26:49,930
+فبتصير رو تربية من ال DS فدي زد دي فاي و ال z
+
+350
+00:26:49,930 --> 00:26:54,790
+بتروح من zero لواحد و five من zero ل two five اذا
+
+351
+00:26:54,790 --> 00:26:58,430
+عند مين ال constant اللي هو ال raw into واحد بعوض
+
+352
+00:26:58,430 --> 00:26:59,150
+عنه واحد
+
+353
+00:27:01,780 --> 00:27:04,680
+هيطلع العشرة برا الانتيجرا بيصير ان الانتيجرا الا
+
+354
+00:27:04,680 --> 00:27:09,580
+E زو ماينوس اثنين زد Zero ل واحد و دي فاية من Zero
+
+355
+00:27:09,580 --> 00:27:12,840
+to Pi فاية اكملها حتين اتنين Pi و الا E زو ماينوس
+
+356
+00:27:12,840 --> 00:27:15,440
+اثنين زد مش هتكون E زو ماينوس اثنين زد على ماينوس
+
+357
+00:27:15,440 --> 00:27:19,400
+اثنين Zero ل واحد تابعين اللي هنتقلها ان احنا
+
+358
+00:27:19,400 --> 00:27:24,820
+بتفسر هذا ال rotor B هيطلع
+
+359
+00:27:24,820 --> 00:27:30,050
+عند العشرةويقلع الفوضى على برا ويتكامل على Z من 0
+
+360
+00:27:30,050 --> 00:27:37,110
+ل 1 E to the minus 2Z EZ ويتكامل من 0 ل 2π E5 هي
+
+361
+00:27:37,110 --> 00:27:41,410
+تقيمة 2π فهي تكملها ل E to the minus 2Z على minus
+
+362
+00:27:41,410 --> 00:27:46,590
+2 وفدي أكملها .. ففدي أخد التقيم من 1 ل 0 عند ال 1
+
+363
+00:27:46,590 --> 00:27:51,590
+إيش هتعطيني E to the minus 2 وعند ال 0 هتعطيني 1
+
+364
+00:27:51,590 --> 00:27:59,510
+يعني هتكون 10 E to the πفى E طبعا على ماينوس سنين
+
+365
+00:27:59,510 --> 00:28:05,310
+E دوز ماينوس سنين ماينوس واحد هزد واحد هحيطني E
+
+366
+00:28:05,310 --> 00:28:09,130
+دوز ماينوس سنين وعندي ال zero كافية واحد اثنين مع
+
+367
+00:28:09,130 --> 00:28:16,230
+اثنين هتصير عشرة by فى E دوز ماينوس سنين ناقص
+
+368
+00:28:24,930 --> 00:28:29,010
+أذا إحنا جيبنا ال surface اللي على ال top كما قلته
+
+369
+00:28:29,010 --> 00:28:35,350
+هو أضارة أصلا عشرة into minus 2pi و ال surface و
+
+370
+00:28:35,350 --> 00:28:41,150
+ال flux على ال photon هو minus 10pi و ال flux على
+
+371
+00:28:41,150 --> 00:28:49,070
+سوا ال surface هو minus 10pi into minus 2 minus 1
+
+372
+00:28:49,070 --> 00:28:52,930
+لو أنا جيبتهم كلهم جمعتهم مع بعض عشان أجيبوا طفل
+
+373
+00:28:52,930 --> 00:28:59,230
+ال fluxماذا نفعن عنه؟ ال total of blocks يمكن أن
+
+374
+00:28:59,230 --> 00:29:03,010
+يكون plus 10x أو minus 2pi أو minus 10pi أو minus
+
+375
+00:29:03,010 --> 00:29:07,150
+2 بيروحوا مع بعض عند minus 10pi أو plus 10pi يكون
+
+376
+00:29:07,150 --> 00:29:10,210
+ال total of blocks بيساوي 0
+
+377
+00:29:15,140 --> 00:29:19,180
+مفروض ان اذا استخدمت ال divergence سورين احنا قلنا
+
+378
+00:29:19,180 --> 00:29:23,280
+ال clause service-integra ل G.DS لازم يساوي ال
+
+379
+00:29:23,280 --> 00:29:27,020
+volume-integra ال divergence GDV فلو استخدمت ال
+
+380
+00:29:27,020 --> 00:29:30,500
+divergence سورين المفروض يعطي نفس الجواب انشوف ايش
+
+381
+00:29:30,500 --> 00:29:33,740
+هو ال divergence احنا عندنا ال vector بيسم ذلك ال
+
+382
+00:29:33,740 --> 00:29:34,100
+coordinate
+
+383
+00:29:36,850 --> 00:29:40,270
+الـ vector كانت سيلينريكال كواردينات فبعمل الدل
+
+384
+00:29:40,270 --> 00:29:43,970
+بسيلينريكال كواردينات يعني واحد على رو D رو D by D
+
+385
+00:29:43,970 --> 00:29:48,710
+رو رو في جيه رو زي واحد على رو D by D فاي جيه فاي
+
+386
+00:29:48,710 --> 00:29:53,190
+زي D by D زي جيه زيك بس قدرت قليل لما سمعت منيا
+
+387
+00:29:53,190 --> 00:29:57,470
+بسمع عليه بعوض على ال components احنا مفيش يمنا
+
+388
+00:29:57,470 --> 00:30:01,090
+جيه فاي في جينه احنا بسمنا رو component وفاي
+
+389
+00:30:01,090 --> 00:30:08,380
+component فبعوض عنه جيه رو بيبعدرو تر بيه فيه طبعا
+
+390
+00:30:08,380 --> 00:30:10,860
+من الرو رو في الرو رو تر بيه في عشرة E to the
+
+391
+00:30:10,860 --> 00:30:16,040
+minus اتنين زد ويه
+
+392
+00:30:16,040 --> 00:30:22,880
+ال five with z component اللي يبقى E by BZ الجزد
+
+393
+00:30:22,880 --> 00:30:27,320
+هي E to the minus عشرة E to the minus اتنين زد على
+
+394
+00:30:27,320 --> 00:30:32,640
+طول هنا الفضلها هي عشرة E to the minus اتنين زد
+
+395
+00:30:37,310 --> 00:30:45,710
+عشرة و ال j زد زد بيه عشرة مفزوقة نصفين زد زد ثلاث
+
+396
+00:30:45,710 --> 00:30:56,510
+و ال j رو عبارة عن عشرة مفزوقة نصفين زد رو أحد
+
+397
+00:31:13,750 --> 00:31:18,250
+الجهة Z هي جهة Z component فيها اندعش رقيته بمعنى
+
+398
+00:31:18,250 --> 00:31:20,190
+Z رو
+
+399
+00:31:38,100 --> 00:31:42,080
+هنا في روح الـ z و لا في روح الـ z أسفل هاي ال z
+
+400
+00:31:42,080 --> 00:31:50,160
+component فضلوا تقولوا اللي بتطلع على التحت إذا
+
+401
+00:31:50,160 --> 00:31:55,160
+ال z component ببساطة d by dz طب فاضل بالنسبة ل z
+
+402
+00:31:55,160 --> 00:31:59,080
+إيش هتعطيلي minus 2z هتبتسي minus 2x minus 2z هذا
+
+403
+00:31:59,080 --> 00:32:02,680
+هو الرفع الينيجي اقول فضلنا ال z component فminus
+
+404
+00:32:02,680 --> 00:32:09,500
+2x minus 2z بالنسبة لل rhoRaw تصبح روه تربيه عشرة
+
+405
+00:32:09,500 --> 00:32:14,600
+ايته ضمه على اثنين زيت فاكتر قبلها ال ايته ضمه على
+
+406
+00:32:14,600 --> 00:32:17,140
+اثنين زيت كونستان بالنسبالي روه والعشرة كونستان
+
+407
+00:32:17,140 --> 00:32:20,800
+بتطلع وفضلي واحد على روه دي روه تربيه بالنسبالي
+
+408
+00:32:20,800 --> 00:32:26,280
+روه دي هتكون اتنين روه فالراوه بتروح مع الراوه
+
+409
+00:32:26,280 --> 00:32:29,940
+يعني اكتر منها او احلى اصلا كونستان انا مش مستغلة
+
+410
+00:32:29,940 --> 00:32:35,450
+يعني واحد على روههي عشرة اكتر من اكتر من اكتر من
+
+411
+00:32:35,450 --> 00:32:36,310
+اكتر من اكتر من اكتر من اكتر من اكتر من اكتر من
+
+412
+00:32:36,310 --> 00:32:40,730
+اكتر من اكتر من اكتر من اكتر من اكتر من اكتر من
+
+413
+00:32:40,730 --> 00:32:46,830
+اكتر من اكتر من اكتر من اكتر من اكتر من اكتر من
+
+414
+00:32:46,830 --> 00:32:46,850
+اكتر من اكتر من اكتر من اكتر من اكتر من اكتر من
+
+415
+00:32:46,850 --> 00:32:46,850
+اكتر من اكتر من اكتر من اكتر من اكتر من اكتر من
+
+416
+00:32:46,850 --> 00:32:47,590
+اكتر من اكتر من اكتر من اكتر من اكتر من اكتر من
+
+417
+00:32:47,590 --> 00:32:49,930
+اكتر من اكتر من اكتر من اكتر من اكتر
+
+418
+00:32:54,320 --> 00:32:57,840
+الخطوة واحدة يعني ان الواحد بلاقى انه أسهل بكتير
+
+419
+00:32:57,840 --> 00:33:00,440
+في ال divergence من اللى هى ال volume integral من
+
+420
+00:33:00,440 --> 00:33:02,900
+ال surface لإن ال surface بتاخد اللى فوق و اللى
+
+421
+00:33:02,900 --> 00:33:06,760
+تحت و اللى حوالها لما أخدت ال divergence و بس عملت
+
+422
+00:33:06,760 --> 00:33:10,340
+عملت ال divergence و حتى لسه قبل ما أعمل ال volume
+
+423
+00:33:10,340 --> 00:33:12,740
+integral و حصل اللى ال divergence هو اللى زى
+
+424
+00:33:17,210 --> 00:33:20,550
+انتوا متذكرين ايش حكينا؟ احنا قولنا ال divergence
+
+425
+00:33:20,550 --> 00:33:23,610
+يا داخل يا طالع اذا طلعنا احنا على ال field اللي
+
+426
+00:33:23,610 --> 00:33:28,710
+قدامنا فيه عمدي اللي هو field طالع من ال raw اتجاه
+
+427
+00:33:28,710 --> 00:33:32,270
+ال raw و واحد اتجاه ال z الشكل تبعه هذا هو هاي ال
+
+428
+00:33:32,270 --> 00:33:35,650
+components تاومة واحدة اتجاه ال raw واحدة اتجاه ال
+
+429
+00:33:35,650 --> 00:33:39,330
+z احنا قولنا ال divergence اشماله يا داخل على نقطة
+
+430
+00:33:39,330 --> 00:33:43,550
+يا طالع من النقطة فهنا اكيد ال divergence zero
+
+431
+00:33:48,420 --> 00:33:51,440
+أذن احنا أثبتنا أنه سواء استخدام ال volume
+
+432
+00:33:51,440 --> 00:33:53,940
+integral اللي هو ال integral of volume divergence
+
+433
+00:33:53,940 --> 00:33:57,700
+EDV أو ال surface integral closed closed معناه بدي
+
+434
+00:33:57,700 --> 00:34:00,200
+أغطي كل ال surface يعني أطلع لو أنا سفيرة على كل
+
+435
+00:34:00,200 --> 00:34:04,880
+الأجزات على السفير سلندر وحتى لو مكعب بدي أطلع على
+
+436
+00:34:04,880 --> 00:34:06,880
+كل ال surface عشان هاي ال closed surface
+
+437
+00:34:11,270 --> 00:34:14,470
+التانية اللى هى Stokes serum برضه من أهم النظريات
+
+438
+00:34:14,470 --> 00:34:18,210
+اللى هستخدمها هى ال electromagnetic و Stokes serum
+
+439
+00:34:18,210 --> 00:34:22,570
+بتقول ليه أول خليني أحكي ع ال curl و بعدين برجع ل
+
+440
+00:34:22,570 --> 00:34:26,730
+Stokes serum نجعل ال curl ايش معناه ال curl برضه
+
+441
+00:34:26,730 --> 00:34:31,210
+ال curl هو vector vector constant
+
+442
+00:34:33,920 --> 00:34:37,740
+هو هو carol بس هو del across a بس ماحدش بقول del
+
+443
+00:34:37,740 --> 00:34:41,120
+across a مش بقول بروح ال carol a ال carol a معناه
+
+444
+00:34:41,120 --> 00:34:43,380
+انه ال del across معاك تتقبل
+
+445
+00:34:46,370 --> 00:34:49,770
+هو is an axial or rotational يعني بعبّرلى عن حاجة
+
+446
+00:34:49,770 --> 00:34:52,510
+rotation يعني احنا ال divergence قلنا يا حاجة
+
+447
+00:34:52,510 --> 00:34:55,990
+بتدخل يا بتطلع sinking or outward يعني زي قلنا لو
+
+448
+00:34:55,990 --> 00:34:59,210
+في عندى charge هذا يتمثللى مصدر يعني ده ال
+
+449
+00:34:59,210 --> 00:35:02,730
+divergence انك تكون عندى مصدر مصدر زى ال charge
+
+450
+00:35:02,730 --> 00:35:06,470
+إيش بتسوي لك electric field طالع لو كانت موجبة أو
+
+451
+00:35:06,470 --> 00:35:11,410
+داخل لو كانت سالبة تمام هذا مين ال divergence ال
+
+452
+00:35:11,410 --> 00:35:15,370
+curve تمثللى rotation يعني حاجة بتلوف حوالين حاجة
+
+453
+00:35:16,020 --> 00:35:21,080
+مش محتاجة ال source، ماشي bluff، rotation whose
+
+454
+00:35:21,080 --> 00:35:24,600
+magnitude is the maximum circulation of every unit
+
+455
+00:35:24,600 --> 00:35:28,300
+area as the area tends to zero and whose direction
+
+456
+00:35:28,300 --> 00:35:33,140
+is the normal direction of the area when the area
+
+457
+00:35:33,140 --> 00:35:36,280
+is oriented so as to make the circulation maximum
+
+458
+00:35:36,730 --> 00:35:40,730
+يعني اتجاهه اتجاه اللي هو ال maximum direction ل
+
+459
+00:35:40,730 --> 00:35:45,290
+اللي هو ال area بساطة هذا هو التعبير الرياضي لل
+
+460
+00:35:45,290 --> 00:35:48,710
+curve اللي هو line integral ل a dot dl اللي هو
+
+461
+00:35:48,710 --> 00:35:50,710
+اللي حكيته هنا ال circulation اللي هو ال
+
+462
+00:35:50,710 --> 00:35:53,950
+integration على اللي هو ال surface per unit area
+
+463
+00:35:53,950 --> 00:35:57,890
+as ال area بتروح ل zero واتجاهه اللي هو ال maximum
+
+464
+00:35:57,890 --> 00:36:02,010
+اتجاه اللي بيعطينا ال maximum circulation فذا ال
+
+465
+00:36:02,010 --> 00:36:04,930
+curve A هو بساطة الدل cross A
+
+466
+00:36:07,610 --> 00:36:09,690
+الكئر في الـ Cartesian coordinate أو في الـ
+
+467
+00:36:09,690 --> 00:36:11,770
+cylindrical أو في الـ spherical هو determinant
+
+468
+00:36:11,770 --> 00:36:17,370
+يعني ممكن أنا أحله manually أقول الكتر الدم مثلا
+
+469
+00:36:17,370 --> 00:36:22,810
+في الـ Cartesian الدم بسوء dy dx وهذا الحق كل
+
+470
+00:36:22,810 --> 00:36:30,490
+الكئر ذئب الـ dy درجه ويها ذئب الـ dy بزدها والكتر
+
+471
+00:36:30,490 --> 00:36:39,190
+تبعين بسوء Ax أسها ذئب Ay بيهازائد a z زرها احنا
+
+472
+00:36:39,190 --> 00:36:45,370
+اخدنا اللي هو a cross b صح اخدنا ال a cross b
+
+473
+00:36:45,370 --> 00:36:48,350
+وقلنا برضه التامة بس كله ده مقدر اقضى بحلو فى
+
+474
+00:36:48,350 --> 00:36:52,270
+الحال يعنى اول اخد cross مع cross هذا zero هذا مع
+
+475
+00:36:52,270 --> 00:36:56,290
+هذا minus component هذا مع هذا minus y هذا مع هذا
+
+476
+00:36:56,290 --> 00:37:04,600
+يعطينا y x minus zY X Y Zero و Y X Xها و هكذا لكن
+
+477
+00:37:04,600 --> 00:37:09,360
+هذه ممكن أضيع فيها إشارات و أضيع فيها دمية فكله
+
+478
+00:37:09,360 --> 00:37:13,380
+اختصارا هنا ال curl انه بعمل ال determinant الصفر
+
+479
+00:37:13,380 --> 00:37:18,400
+الأول اللي هو unit vectors Xها و Yها و ال vector
+
+480
+00:37:18,400 --> 00:37:21,760
+الأولاني يكون الصفر الأول التاني و ال unit vector
+
+481
+00:37:21,760 --> 00:37:26,560
+التالك التاني يكون Y صفر التالك فانا بس افرغ ال A
+
+482
+00:37:26,560 --> 00:37:35,910
+X B صار تل cross Aالصف التانى لادل
+
+483
+00:37:35,910 --> 00:37:40,430
+والصف التالف لادل كارتيزن
+
+484
+00:37:40,430 --> 00:37:57,650
+XYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
+
+485
+00:37:58,170 --> 00:38:02,510
+D by D rho, D by D pi, D by D z, A rho, rho, A pi,
+
+486
+00:38:02,610 --> 00:38:09,310
+A z وفي الـcylindrical coordinate, curl الـA هيكون
+
+487
+00:38:09,310 --> 00:38:13,070
+واحدة لارتر بيها الـsin θ ال determinant لارها
+
+488
+00:38:13,070 --> 00:38:15,210
+ارتر بيها الارتر بيها الارتر بيها الارتر بيها
+
+489
+00:38:15,210 --> 00:38:16,190
+الارتر بيها الارتر بيها الارتر بيها الارتر بيها
+
+490
+00:38:16,190 --> 00:38:17,110
+الارتر بيها الارتر بيها الارتر بيها الارتر بيها
+
+491
+00:38:17,110 --> 00:38:18,650
+الارتر بيها الارتر بيها الارتر بيها الارتر بيها
+
+492
+00:38:18,650 --> 00:38:19,150
+الارتر بيها الارتر بيها الارتر بيها الارتر بيها
+
+493
+00:38:19,150 --> 00:38:22,210
+الارتر بيها الارتر بيها الارتر بيها الارتر
+
+494
+00:38:22,310 --> 00:38:25,670
+الكمبونات تانية R في A ثتا R مضروبة في الكمبونات
+
+495
+00:38:25,670 --> 00:38:30,590
+في A ثتا R ثانية ثتا مضروبة في A فعلا تانية تانية
+
+496
+00:38:30,590 --> 00:38:33,510
+تانية تانية تانية تانية تانية تانية تانية تانية
+
+497
+00:38:33,510 --> 00:38:33,970
+تانية تانية تانية تانية تانية تانية تانية تانية
+
+498
+00:38:33,970 --> 00:38:37,670
+تانية تانية تانية تانية تانية تانية تانية تانية
+
+499
+00:38:37,670 --> 00:38:37,870
+تانية تانية تانية تانية تانية تانية تانية تانية
+
+500
+00:38:37,870 --> 00:38:38,390
+تانية تانية تانية تانية تانية تانية تانية تانية
+
+501
+00:38:38,390 --> 00:38:38,410
+تانية تانية تانية تانية تانية تانية تانية تانية
+
+502
+00:38:38,410 --> 00:38:48,110
+تانية تانية تانية تانية تانية تانية تانية تانية
+
+503
+00:38:48,110 --> 00:38:50,130
+تان
+
+504
+00:38:51,680 --> 00:38:56,380
+cross product دايما بيعطيني vector quantity curl
+
+505
+00:38:56,380 --> 00:38:59,640
+scalar زي divergence ل scalar يعني ماقدر أقول curl
+
+506
+00:38:59,640 --> 00:39:05,880
+scalar عجب scalar لأ دي مالهاش أي معنى ال cross
+
+507
+00:39:05,880 --> 00:39:09,820
+product بين two vectors فإذا بقول a cross scalar
+
+508
+00:39:09,820 --> 00:39:12,980
+مالهاش معنى برضه دل a cross scalar مالهاش معنى
+
+509
+00:39:15,730 --> 00:39:19,490
+كيرل A زي B يعني لو انا جمعت ال two fields ال
+
+510
+00:39:19,490 --> 00:39:22,810
+field الأول مع التاني و جبت لهم الكيرل نفس الشيء
+
+511
+00:39:22,810 --> 00:39:26,010
+لو جبت الكيرل الأول و الكيرل التاني و جمعتهم مع
+
+512
+00:39:26,010 --> 00:39:31,670
+بعض كيرل A cross B ليس بسيطا لإنه يوجد هناك
+
+513
+00:39:31,670 --> 00:39:35,290
+differentiation الدل هي ده فقط تفاضل ببعبر عنها
+
+514
+00:39:35,290 --> 00:39:37,830
+بال identity high و high مهمة كتير في ال
+
+515
+00:39:37,830 --> 00:39:42,630
+electromagnetic high كيرل A cross B هي عبارة عن
+
+516
+00:39:54,670 --> 00:39:57,330
+الـDEL بتأثر أولا على الـB و بعدين ناخده ضد ال
+
+517
+00:39:57,330 --> 00:40:01,470
+product واضح؟ يعني هاي تفاضل الـDEL تفاضل بيها في
+
+518
+00:40:01,470 --> 00:40:05,270
+A cross DEL across ال A cross B تعبر عنها في هاي
+
+519
+00:40:05,270 --> 00:40:11,560
+الآيةScalar مع vector بتعمل لإنه مثلًا احنا بتشبه
+
+520
+00:40:11,560 --> 00:40:17,120
+ده تفاضل two terms بس هنا Divergence كنا بس محددت
+
+521
+00:40:17,120 --> 00:40:23,360
+هنا بس scale يعني عندي v k لل a زائد gradient ال v
+
+522
+00:40:23,360 --> 00:40:27,800
+cross a يعني دل هيعمل application على ال scalar
+
+523
+00:40:27,800 --> 00:40:31,000
+وعلى ال vector يعني هيفضل ال scalar و ال vector بس
+
+524
+00:40:31,000 --> 00:40:34,020
+لما ييجي على ال vector هيكون cross product وعلى ال
+
+525
+00:40:34,020 --> 00:40:36,340
+scalar هيكون ال gradient تبع ال scalar
+
+526
+00:40:39,450 --> 00:40:43,310
+الـ divergence of a curl هيكون دايماً zero ال
+
+527
+00:40:43,310 --> 00:40:46,230
+divergence of a curl of a vector فانش يعني ال
+
+528
+00:40:46,230 --> 00:40:49,750
+divergence of curl A بتسوء zero ال divergence
+
+529
+00:40:49,750 --> 00:40:56,650
+لcurl A بيسوء zero كمان ال cross أو ال curl لدل أو
+
+530
+00:40:56,650 --> 00:40:59,970
+لل gradient بيسوء zero هدولة التمثيل مهمين كتير
+
+531
+00:40:59,970 --> 00:41:03,050
+برضه اللي هي الفيه تسيوري أو أسبوطات الفيه تسيوري
+
+532
+00:41:03,050 --> 00:41:07,230
+لما تبقوا علينا أي divergence للcurl
+
+533
+00:41:25,110 --> 00:41:29,470
+بس احنا عاملة كامل ايه؟ ايش مابمثلين؟ Circulation
+
+534
+00:41:29,470 --> 00:41:34,710
+مابمثلينش divergenceكيرل الـ A بس دي circulation
+
+535
+00:41:34,710 --> 00:41:37,350
+بحيث ال divergence عشان مايكونش بساوة صفر لازم
+
+536
+00:41:37,350 --> 00:41:40,370
+يكون عند ال source يا طالع يا داخل ف divergence
+
+537
+00:41:40,370 --> 00:41:43,950
+الكيرل أكيد zero نفس الشيء لل gradient مثلنيشي
+
+538
+00:41:43,950 --> 00:41:47,130
+حاجة سواء طالع أو داخل لو تقصتيشي ناتج أنه في
+
+539
+00:41:47,130 --> 00:41:53,950
+source داخل أو طالع فكرل ال gradient بساوة zero لو
+
+540
+00:41:53,950 --> 00:41:56,510
+طلعته أكتر في علم أكتر من هيكي موجودين في ال
+
+541
+00:41:56,510 --> 00:42:00,330
+appendix A في الكتاب عن حصائص ان هو الكيرل
+
+542
+00:42:05,360 --> 00:42:08,860
+هذا هو شكل ال curling هي اللي انا بحكيه انه ال
+
+543
+00:42:08,860 --> 00:42:12,720
+curling حاجة بتلف يعني بمثل ال curl دوران
+
+544
+00:42:12,720 --> 00:42:17,460
+circulation هذا المثال اللي في a بيعمللي ان ال
+
+545
+00:42:17,460 --> 00:42:21,500
+curl ال vector هيكون لا يساوي zero بينما في المثال
+
+546
+00:42:21,500 --> 00:42:25,660
+هذا ال curve بيساوي zero يعني لو انا قلتلك ان ال
+
+547
+00:42:25,660 --> 00:42:31,240
+field تبع a بيساوي خمسة z hat خمسة z ولا خمسة rho
+
+548
+00:42:31,240 --> 00:42:33,380
+z hat اتجاه و اتجاه z hat
+
+549
+00:42:36,110 --> 00:42:39,390
+لأ انا مش شايفش انه circulation لكن لو قلت انه
+
+550
+00:42:39,390 --> 00:42:44,430
+اتجاهه مثلا ال raw hat الفاي هات الفاي هات اتجاه
+
+551
+00:42:44,430 --> 00:42:50,390
+ال circulation فبكون الوكبير هاي
+
+552
+00:42:50,390 --> 00:42:52,390
+stock serum، stock serum برضه زي ال diversion
+
+553
+00:42:52,390 --> 00:42:56,530
+serum من اللي هم نظريات مهمة جدا في الدراسة
+
+554
+00:42:56,530 --> 00:43:01,100
+النفسية و ال stock serum مش كلهالـ closed line
+
+555
+00:43:01,100 --> 00:43:04,120
+integral هد أخدناها شهودها الـ circulation
+
+556
+00:43:04,120 --> 00:43:07,240
+بتذكرين؟ ال circulation قلنا ال closed path
+
+557
+00:43:07,240 --> 00:43:10,020
+integral لA وDL وحلينا أمثل عليه في الحضرة الماضية
+
+558
+00:43:10,020 --> 00:43:13,100
+سميناها ال circulation ال circulation قلنا ال
+
+559
+00:43:13,100 --> 00:43:18,260
+closed line integral لA وDL هد ال circulation
+
+560
+00:43:18,260 --> 00:43:24,480
+بناسرني أو بقتلان بساوي ال surface integral لكر
+
+561
+00:43:24,480 --> 00:43:29,200
+للA وDL اذا ال circulation اللي هو ال closed path
+
+562
+00:43:30,460 --> 00:43:35,720
+للـ vector.dl بساوي ال surface integral ل curl A
+
+563
+00:43:35,720 --> 00:43:42,680
+dot DS المثل اللى قدامنا احنا فيه باص اسمه
+
+564
+00:43:42,680 --> 00:43:46,160
+L محيط في ال surface الأزرق هو ال surface يعني مثل
+
+565
+00:43:46,160 --> 00:43:52,900
+الطاولة وهي محيط الطاولة لو انا اخدت ال line
+
+566
+00:43:52,900 --> 00:43:58,480
+integral لل vector A حول ال line لازم يساوي ال
+
+567
+00:43:58,480 --> 00:44:02,140
+surface integralلمن؟ لـ cross product تبع ال
+
+568
+00:44:02,140 --> 00:44:06,780
+vector plotted مع ال DS طبعا
+
+569
+00:44:06,780 --> 00:44:10,860
+لو احنا قسمنا هذه ال circulation يعني قسمنا ال
+
+570
+00:44:10,860 --> 00:44:13,140
+surface لأزاقة صغيرة كتير كتير واخدت ال
+
+571
+00:44:13,140 --> 00:44:16,580
+circulation مثلا لهذا ال surface و بعدين اخدت ال
+
+572
+00:44:16,580 --> 00:44:19,360
+circulation لهذا ال surface ايش بلاحظ؟ بلاحظ عند
+
+573
+00:44:19,360 --> 00:44:23,060
+ال boundaries دايما في حاجة بتعصي البعض مثلا هذا
+
+574
+00:44:23,060 --> 00:44:24,460
+اللي قسمت ال surfaces
+
+575
+00:44:30,640 --> 00:44:36,580
+أجروا هذا ال surface هاي ال circulation دلوقت
+
+576
+00:44:36,580 --> 00:44:41,500
+الدورة التانية هيت cancel معاها يعني جوا ال
+
+577
+00:44:41,500 --> 00:44:45,400
+circulation عشان نفسر ليش أنه ال surface انتجرة
+
+578
+00:44:45,400 --> 00:44:50,240
+بالآخر بستور الله انتجرة احنا قلنا ال curve هو ال
+
+579
+00:44:50,240 --> 00:44:53,020
+circulation و لو أنا أقسمت ال surface لمجموعة
+
+580
+00:44:53,020 --> 00:44:56,740
+surfaces بحط هاي كمان هنا مثلا هاي ال surface هذا
+
+581
+00:44:56,740 --> 00:45:02,670
+هاي ال circulationفهذا برضه سيظهر من هذا فبالنهاية
+
+582
+00:45:02,670 --> 00:45:06,430
+هلاحظ ان هو جزء الكيرل بالتمام بيساوي ال line
+
+583
+00:45:06,430 --> 00:45:12,470
+integral كيرل A ضد S او انا عملته على أزاق ملاحظ
+
+584
+00:45:12,470 --> 00:45:16,210
+ان ال boundaries كله جواها تتقنصلوا بعض كله
+
+585
+00:45:16,210 --> 00:45:20,190
+هيتقنصل هذا بس هيدوم عندي البرامج فهذا بتدرّبنا
+
+586
+00:45:20,190 --> 00:45:25,010
+ليش ان ال surface integral لكرل A ضد S بيساوي
+
+587
+00:45:25,010 --> 00:45:27,570
+بالتمام ال circulation اللي هو ال line integral
+
+588
+00:45:31,740 --> 00:45:37,620
+هذه تمثيلة لـ Stock Theorem لالـ vector.dl أنا
+
+589
+00:45:37,620 --> 00:45:41,920
+في اللقاء القادم هنشوف الأمثلة نفس الفكرة احنا
+
+590
+00:45:41,920 --> 00:45:45,020
+هنشوف أول حاجة انجيب الkeyword بتاع ال vector و
+
+591
+00:45:45,020 --> 00:45:48,280
+بعدين هناخد مثال ان تشوف فيه اللي هو stock theorem
+
+592
+00:45:48,280 --> 00:45:51,680
+اللي هتتحقق ولا لا زي هذا المثال اللي هو ان
+
+593
+00:45:54,790 --> 00:45:58,350
+اللي هو في البيت، هذا من الساعة تلاتة point تسعة و
+
+594
+00:45:58,350 --> 00:46:02,490
+هو هذا من الساعة تلاتة point ستة، دربوا عليهم في
+
+595
+00:46:02,490 --> 00:46:04,690
+البيت، شكرا لكوا العارفة و ان شاء الله نشوفكوا
+
+596
+00:46:04,690 --> 00:46:05,470
+القيادة الحاضرة
+
diff --git a/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/c40WAEfGwMA.srt b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/c40WAEfGwMA.srt
new file mode 100644
index 0000000000000000000000000000000000000000..3a8482cf3b85279d4b9cfeee09b336cac2a49722
--- /dev/null
+++ b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/c40WAEfGwMA.srt
@@ -0,0 +1,2058 @@
+1
+00:00:20,790 --> 00:00:23,110
+بسم الله الرحمن الرحيم السلام عليكم و رحمة الله و 
+
+2
+00:00:23,110 --> 00:00:25,950
+بركاته، إحنا اليوم إن شاء الله هنتابع موضوعنا، في 
+
+3
+00:00:25,950 --> 00:00:28,310
+المحاضرة الماضية وقفنا عند اللي هو ال electric
+
+4
+00:00:28,310 --> 00:00:31,210
+dipole و ال flux lines، حكينا إيش هو ال electric
+
+5
+00:00:31,210 --> 00:00:34,670
+dipole، قلنا هو عبارة عن two charges، كل واحدة لها 
+
+6
+00:00:34,670 --> 00:00:38,450
+شحنة من  خلفها للتانية وبينهم مسافة صغيرة، بالنسبة
+
+7
+00:00:38,450 --> 00:00:43,130
+لمين؟ للمسافة اللي بتؤثر عندها ال electric field أو 
+
+8
+00:00:43,130 --> 00:00:45,050
+ال electric potential وإحنا شفنا من المحاضرة 
+
+9
+00:00:45,050 --> 00:00:47,550
+الماضية إن كيف أحسب ال potential عند أي نقطة في ال
+
+10
+00:00:47,550 --> 00:00:51,770
+space فأنا إذا عندي أنا two charges زي في هذا
+
+11
+00:00:51,770 --> 00:00:57,110
+الصورة Q minus Q المسافة بينهم D وبدي أشوف ال
+
+12
+00:00:57,110 --> 00:00:59,330
+potential ناتج عن هذا ال dipole قولنا على طول
+
+13
+00:00:59,330 --> 00:01:03,130
+بسميه Q minus Q المسافة بينهم D اللي هي أقل بكثير 
+
+14
+00:01:03,130 --> 00:01:07,990
+من R نسميه electric dipole قولنا إيه بقدر أحسب ال
+
+15
+00:01:07,990 --> 00:01:11,110
+potential عند أي نقطة في ال space Q
+
+16
+00:01:19,820 --> 00:01:23,580
+الشحنة الأولى زاد ال potential الناتج من الشحنة 
+
+17
+00:01:23,580 --> 00:01:29,700
+التانية السالب جاء من ال Q إنها سالبة طبعا
+
+18
+00:01:29,700 --> 00:01:32,420
+لو في هنلاقي constant of integration هي ناقصها تروح 
+
+19
+00:01:32,420 --> 00:01:35,120
+يعني مجموعها بقى هنضفه على ال constant of
+
+20
+00:01:35,120 --> 00:01:40,410
+integration إذا عندي ال total potential إيش هيساوي؟ Q
+
+21
+00:01:40,410 --> 00:01:45,430
+على 4 باي epsilon note R2 minus R1 على R1 في R2
+
+22
+00:01:45,430 --> 00:01:49,350
+قولنا من وين هي بنجيبها من توحيد المقامات R2 minus
+
+23
+00:01:49,350 --> 00:01:53,410
+R1 حسبناها المحاضرة الماضية قولنا R2 ناقص R1 لو
+
+24
+00:01:53,410 --> 00:01:58,750
+أنا أسقطت عمود من الطفل Q على R2 هلاقي هذه R2 ناقص 
+
+25
+00:01:58,750 --> 00:02:02,870
+R1 هذه المسافة لو سمينا θتا اللي هي الزاوية بين
+
+26
+00:02:02,870 --> 00:02:06,350
+اتجاه ال dipole اللي هي المسافة اللي واصلة بين ال
+
+27
+00:02:06,350 --> 00:02:11,550
+two charges و ال line اللي بيوصل ما بين ال center
+
+28
+00:02:11,550 --> 00:02:14,490
+تبع ال dipole و النقطة اللي عندها اللي بتنشر
+
+29
+00:02:14,490 --> 00:02:17,730
+هذه سميناها ال θتا هي برضه هتكون θتا لأنها علاقة 
+
+30
+00:02:17,730 --> 00:02:23,290
+بالتناظر لذا هذه المسافة هتكون d cos θتا لو عوضنا 
+
+31
+00:02:23,290 --> 00:02:29,850
+عنهم في المعادلة R2-R1 Dcosθ وتقريبا إن R1
+
+32
+00:02:29,850 --> 00:02:33,270
+بتساوي R2 بتساوي R دي تقريبا  لأن هذه مسافة 
+
+33
+00:02:33,270 --> 00:02:36,150
+بعيدة كثير يعني هلاقيهم كأنهم صاروا على التوازن
+
+34
+00:02:36,150 --> 00:02:39,770
+وهذه المسافة صغيرة كثير فبقدر أقول إن R1 في R2
+
+35
+00:02:39,770 --> 00:02:47,990
+بتساوي R تربيع يعني البوتنشن ناتج عن دايول هو QD cos θ 
+
+36
+00:02:47,990 --> 00:02:51,350
+على 4 π إبسلون R تربيع طب قولنا D cos θ إيش أنا 
+
+37
+00:02:51,350 --> 00:02:54,710
+بقدر أعبر عنها إذا بتذكروا في ال vector لما درسنا
+
+38
+00:02:54,710 --> 00:02:57,410
+ال vector قولنا أي حاجة D cos θ هي ال projection
+
+39
+00:02:57,410 --> 00:03:03,640
+تبع vector component على اتجاه معين فمين هي الاتجاه
+
+40
+00:03:03,640 --> 00:03:08,480
+في حالتنا اللي هو اتجاه ال R لأن ال θ دي كوساين ثتا
+
+41
+00:03:08,480 --> 00:03:13,820
+هيكون في اتجاه مين؟ ال R hat هتكون دي ضد R hat دي 
+
+42
+00:03:13,820 --> 00:03:17,720
+ضد R hat هتلاقوها دي كوساين ثتا حيث دي مين؟ هي دي
+
+43
+00:03:17,720 --> 00:03:21,240
+المسافة اللي بين ال two dipoles فهي في الحالة إيش 
+
+44
+00:03:21,240 --> 00:03:25,180
+اتجاهها Z hat ليش أخدناها Z hat؟ لأن أنا دائما باخد 
+
+45
+00:03:25,180 --> 00:03:29,870
+اتجاه ال dipole من السالب للموجب اتجاههم يسموه جبه، 
+
+46
+00:03:29,870 --> 00:03:33,230
+وكمان في حاجة نبهتكم عليها المحاضرة الماضية إن هذا
+
+47
+00:03:33,230 --> 00:03:37,210
+ال dipole ماله؟ ال center تبعه قاعد على ال origin مش
+
+48
+00:03:37,210 --> 00:03:39,650
+دائما ال dipole بيكون عندي قاعد على ال origin ممكن
+
+49
+00:03:39,650 --> 00:03:42,670
+يكون برضه قاعد في أي مكان في ال space بس إنت بتحسب
+
+50
+00:03:42,670 --> 00:03:48,900
+ال center قد إيش بيبعد عن ال origin حسابنا D cosθ
+
+51
+00:03:48,900 --> 00:03:52,560
+عبرنا عنها D دول D R ونحطها في معادلة مين؟ اللي هو 
+
+52
+00:03:52,560 --> 00:03:55,180
+ال potential طبعا إذا إحنا حكينا بدنا نعرف ال new
+
+53
+00:03:55,180 --> 00:03:58,140
+quantity اللي هي ال dipole moment P وP hat هي
+
+54
+00:03:58,140 --> 00:04:01,500
+عبارة عن Q في D ميني Q اللي هي ال charge بتاعة ال
+
+55
+00:04:01,500 --> 00:04:05,120
+dipole واحدة من ال charges قيمة ال charge وD اللي 
+
+56
+00:04:05,120 --> 00:04:10,780
+عرفناها ال vector اللي عبارة عن D dot R hat D 
+
+57
+00:04:10,780 --> 00:04:13,520
+متأسفة المسافة بين ال two dipoles اللي بنعرفها من
+
+58
+00:04:13,520 --> 00:04:17,220
+السالب ال quantity لبساطة يعني في هالحالة HD
+
+59
+00:04:17,220 --> 00:04:20,060
+اتجاهها D زدها لأنها جايه من ال minus لل plus
+
+60
+00:04:20,060 --> 00:04:25,600
+فهيكون Z hat فإذا بيبقى يساوي Q في D اللي هي vector
+
+61
+00:04:25,600 --> 00:04:29,420
+quantity vector quantity Q scalar لكن دي مالها
+
+62
+00:04:29,420 --> 00:04:32,400
+vector إذا إنت عاجبك ال moment ماله؟ vector
+
+63
+00:04:32,400 --> 00:04:35,980
+quantity نرجع للـ Potential الـ Potential إيش 
+
+64
+00:04:35,980 --> 00:04:40,880
+هيساوي؟ Q في D Cos θ على 4π أبسلون نقطة R تربيع نكتبه
+
+65
+00:04:40,880 --> 00:04:44,840
+على شكل Vector D Cos θ وأنا إيش مكتوبها؟ D Dot R
+
+66
+00:04:44,840 --> 00:04:50,660
+Hat Q دي Vector إيش بدها تكون؟ P بتكون V بتساوي P
+
+67
+00:04:50,660 --> 00:04:54,740
+Dot R Hat على 4π أبسلون نقطة R تربيع إذا الـ
+
+68
+00:04:54,740 --> 00:04:57,660
+Potential الناتج عن الـ Dipole Moment هو قيمة الـ
+
+69
+00:04:57,660 --> 00:05:02,380
+Dipole Dot R Hat على 4π أبسلون نقطة R تربيع 
+
+70
+00:05:04,900 --> 00:05:08,520
+زي ما حكينا اللي هي ال P من السالب للموجب زي
+
+71
+00:05:08,520 --> 00:05:14,350
+الشكل ES طب لو كان الـ dipole مش عند ال origin لو 
+
+72
+00:05:14,350 --> 00:05:17,090
+كان عند أي نقطة في ال space على بعد R' من ال
+
+73
+00:05:17,090 --> 00:05:21,430
+origin هيصير قيمة ال P عبارة عن P dot R minus R 
+
+74
+00:05:21,430 --> 00:05:24,770
+prime على four by epsilon dot R minus R prime لكل
+
+75
+00:05:24,770 --> 00:05:28,270
+cube أو أنا ممكن هدا اسمي ال unit vector R minus R 
+
+76
+00:05:28,270 --> 00:05:31,710
+prime على R minus R prime متذكرين يعني هدول إحنا
+
+77
+00:05:31,710 --> 00:05:34,830
+بقدر نكتبها على شكل نفس القضية على R cube اللي هي 
+
+78
+00:05:34,830 --> 00:05:39,550
+هتكون بدل R hat على R تربيع هتكون R vector على R
+
+79
+00:05:39,550 --> 00:05:44,040
+cube لأن R هتكون هي R vector على R نفس الحاجة هنا
+
+80
+00:05:44,040 --> 00:05:48,920
+هيكون R minus R prime على R minus R prime لكل cube
+
+81
+00:05:48,920 --> 00:05:51,760
+لأن R prime كانت في الحالة الأولى عند مين؟ ال zero
+
+82
+00:05:51,760 --> 00:05:56,260
+خلتها بطلت ال zero صار مكان بعيد عن ال origin تمام 
+
+83
+00:05:59,890 --> 00:06:01,830
+لو أنا بدي ال electric field قلنا إيش ال electric
+
+84
+00:06:01,830 --> 00:06:04,230
+field بيساوي minus ال grade V إحنا أثبتناها في
+
+85
+00:06:04,230 --> 00:06:07,550
+المحاضرة الماضية، أثبتناها بطريقتين، قلنا إن ال
+
+86
+00:06:07,550 --> 00:06:10,990
+electric field بيساوي كيلو ال electric field zero 
+
+87
+00:06:10,990 --> 00:06:15,930
+ال rotational electric field لأن هو ماله؟ عبارة عن
+
+88
+00:06:20,990 --> 00:06:24,190
+فهو ال rotational فهيكون إيه؟ بتساويها نفس grade V
+
+89
+00:06:24,190 --> 00:06:27,090
+وبقدر أجيب ال electric field من ال potential لأن
+
+90
+00:06:27,090 --> 00:06:29,750
+إحنا ال electric field بقدر أجيبه من مين؟ من 
+
+91
+00:06:29,750 --> 00:06:33,130
+column flow, gauss flow ومن ال potential يعني إذا 
+
+92
+00:06:33,130 --> 00:06:36,090
+كنت عارف ال potential ناتج عن ال dipole بقدر أجيب
+
+93
+00:06:36,090 --> 00:06:45,610
+ال electric field اللي ناتج برضه عن a type لو
+
+94
+00:06:45,610 --> 00:06:48,770
+أنا فضلت بطلع معايا الشكل اللي أنا عامله
+
+95
+00:06:55,680 --> 00:06:59,400
+هي الـ electric field هي ساوا بي على four bios ال
+
+96
+00:06:59,400 --> 00:07:04,000
+node R3 في اثنين كسايم ثتا R hat زائد سايم ثتا ثتا
+
+97
+00:07:04,000 --> 00:07:06,900
+hat حيث هنا بي شايفينها بدون vector هي ال
+
+98
+00:07:06,900 --> 00:07:12,040
+magnitude خطة ال vectors برا R hat و theta hat
+
+99
+00:07:20,450 --> 00:07:22,630
+ال point of charge لو بدنا نفكر فيها بنسميها
+
+100
+00:07:22,630 --> 00:07:25,030
+monopole، monopole يعني charge، ما فيش إليها 
+
+101
+00:07:25,030 --> 00:07:28,830
+dipole، يعني dipole يعني اثنتان، mono واحد، فأنا 
+
+102
+00:07:28,830 --> 00:07:31,350
+ممكن أفكر في ال point of charge إنها monopole،
+
+103
+00:07:31,350 --> 00:07:35,410
+monopole يعني pole واحد، إله electric field بتناسب
+
+104
+00:07:35,410 --> 00:07:39,530
+عكسية مع R تربيع، و ال potential مع واحد على R،
+
+105
+00:07:39,530 --> 00:07:42,750
+يعني عندي electric field ناتج عن ال charge واحد
+
+106
+00:07:42,750 --> 00:07:45,910
+على R تربيع، ال potential ناتج عن one charge واحد
+
+107
+00:07:45,910 --> 00:07:48,460
+على R لو فكرت في ال dipole هلاقي إن ال electric
+
+108
+00:07:48,460 --> 00:07:51,220
+field ماله؟ صار واحد على R تكعيب وال potential 
+
+109
+00:07:51,220 --> 00:07:54,200
+واحد على R تربيع وهكذا لو أنا تفكرت في ال
+
+110
+00:07:54,200 --> 00:07:57,680
+higher orders زي ال quadrupole و ال octupole هلاحظ
+
+111
+00:07:57,680 --> 00:08:02,380
+إن ال field هيصير بدل ما هو R تكعيب هيصير R أربعة
+
+112
+00:08:02,380 --> 00:08:05,340
+و R خمسة وهكذا وال potential هيصير R تكعيب R
+
+113
+00:08:05,340 --> 00:08:06,380
+أربعة و R خمسة 
+
+114
+00:08:09,780 --> 00:08:13,020
+نجي لل flux lines إحنا قلنا هنتعلم ال potential و
+
+115
+00:08:13,020 --> 00:08:15,120
+ال flux lines، إيش هو ال electric flux line؟ هو
+
+116
+00:08:15,120 --> 00:08:19,440
+عبارة عن imaginary bus، bus خيالي أو line drawn in
+
+117
+00:08:19,440 --> 00:08:22,080
+such a way that the direction at any point is
+
+118
+00:08:28,430 --> 00:08:31,270
+يعني مثلا هي اللي عندي ال monopole أو ال charge q
+
+119
+00:08:31,270 --> 00:08:35,130
+بصطف معناه ال electric field ماله؟ طالع منها أنا
+
+120
+00:08:35,130 --> 00:08:38,630
+بعبّر عن هذا الخروج بإيش؟ بال electric flux lines
+
+121
+00:08:38,630 --> 00:08:41,630
+هدول ال electric flux lines اللي هي عندها بيكون دي
+
+122
+00:08:41,630 --> 00:08:46,070
+مالها؟ tangential لأن دي هو ال field density بيكون
+
+123
+00:08:46,070 --> 00:08:48,290
+tangential لهم يعني ال electric field في هذا
+
+124
+00:08:48,290 --> 00:08:51,790
+الاتجاه ففي حالة ال monopole هيكون electric field
+
+125
+00:08:51,790 --> 00:08:55,830
+مالها؟ طالع بهذا الشكل ال radially لو كانت سالبة بقى
+
+126
+00:08:55,830 --> 00:09:00,190
+هيكون داخلة هدول المقاطر اللي إحنا شايفينهم حواليها 
+
+127
+00:09:00,190 --> 00:09:02,990
+أو يعني اللي ممكن أقول اللي هي الدوائر العمودية
+
+128
+00:09:02,990 --> 00:09:06,610
+على .. يعني كل لحظة إيش هنلاقي؟ عمودي على هذا الخط اللي 
+
+129
+00:09:06,610 --> 00:09:09,870
+هو ال .. ال circle عمودي على ال flux lines هدول
+
+130
+00:09:09,870 --> 00:09:12,720
+اللي بيسميها equipotential surfaces إيش معنى eco
+
+131
+00:09:12,720 --> 00:09:15,800
+-potential؟ eco-potential يعني متساوي potential
+
+132
+00:09:15,800 --> 00:09:19,080
+اللي هو potential اللي نعرفه الجهود eco-potential
+
+133
+00:09:19,080 --> 00:09:21,340
+يعني عند هدول ال services potential ماله؟ يكون
+
+134
+00:09:21,340 --> 00:09:24,160
+متساوي يعني أنا لو جيبت أداة قياس وقست ال
+
+135
+00:09:24,160 --> 00:09:27,040
+potential على هذا الخط اللي مقطع هلاقي إنه ال
+
+136
+00:09:27,040 --> 00:09:30,900
+potential ماله؟ متساوي أروح على هذا الخط هلاقي ال
+
+137
+00:09:30,900 --> 00:09:34,280
+potential ماله؟ متساوي الدائرة التانية الدائرة
+
+138
+00:09:34,280 --> 00:09:37,300
+التالتة نفس القضية هلاقي إنه ال potential عند نقطة 
+
+139
+00:09:37,590 --> 00:09:41,950
+كل نقطة من النقاط هيكون متساوية، إذا هدول إحنا 
+
+140
+00:09:41,950 --> 00:09:45,950
+نسميهم equipotential surfaces هذا بالنسبة للـ
+
+141
+00:09:45,950 --> 00:09:49,250
+monopole أو one charge، لو أنا رحت للdipole، هذا
+
+142
+00:09:49,250 --> 00:09:52,290
+dipole بس إيش القصة إن رسمها صغيرة كثير زي ما
+
+143
+00:09:52,290 --> 00:09:56,110
+اتفقنا إن المسافة بعيدة كثير، هلاقي إن ال electric
+
+144
+00:09:56,110 --> 00:10:00,090
+lines هتروح من الموجب للسالب، يعني من الموجب 
+
+145
+00:10:00,090 --> 00:10:05,030
+لسالب، من الموجب للسالب، من الموجب للسالب، من
+
+146
+00:10:05,030 --> 00:10:10,320
+الموجب للسالب، صحيح؟ الموجب للسالب هدول ال
+
+147
+00:10:10,320 --> 00:10:14,400
+electric field electric flux lines اللي هو قولنا
+
+148
+00:10:14,400 --> 00:10:17,180
+مالهم؟ imaginary lines اللي بيكون عندهم مدينة له
+
+149
+00:10:17,180 --> 00:10:20,520
+tangential عند كل نقطة من النقطة هيكون ال electric
+
+150
+00:10:20,520 --> 00:10:24,220
+field أو ال dn tangential عند كل نقطة من النقطة 
+
+151
+00:10:24,220 --> 00:10:28,460
+المرسومة على الخط الأزرق نفس الحاجة بقدر أرسمين الـ
+
+152
+00:10:28,460 --> 00:10:31,700
+Equipotential Surfaces اللي هم عموديين عليه للـ
+
+153
+00:10:31,700 --> 00:10:35,120
+line هلاقي دوائر مقطعة هذه هي ال Equipotential
+
+154
+00:10:35,120 --> 00:10:38,100
+Surfaces وقلنا إيش معها Equipotential Surfaces إن
+
+155
+00:10:38,100 --> 00:10:40,600
+عند كل نقطة على هذه الدائرة بيكون ال potential
+
+156
+00:10:40,600 --> 00:10:45,640
+بساوي بعضه يعني لو قست potential هنا هيكون V1 على
+
+157
+00:10:45,640 --> 00:10:49,100
+هذه النقطة هلاقي V1 على هذه نقطة هلاقي V1 عشان هيك
+
+158
+00:10:49,100 --> 00:10:52,480
+إحنا بنسميه Equipotential Equi قلنا متساوي 
+
+159
+00:10:52,480 --> 00:10:56,430
+potential voltage فهدول ال surfaces بيكون عندهم ال
+
+160
+00:10:56,430 --> 00:10:59,790
+potential متساوية هدول على فكرة مش lines هي
+
+161
+00:10:59,790 --> 00:11:08,770
+surfaces بس عشان الرسمة واضحة؟ طيب في استفسار لحد
+
+162
+00:11:08,770 --> 00:11:12,210
+هنا؟ واضح إيش هم ال equipotential surfaces وإيش هم
+
+163
+00:11:12,210 --> 00:11:16,590
+ال flux lines؟
+
+164
+00:11:16,590 --> 00:11:19,330
+كمثال نؤكد إيش هم ال equipotential surfaces هم ال
+
+165
+00:11:19,330 --> 00:11:21,230
+surfaces on which potential is the same
+
+166
+00:11:22,090 --> 00:11:24,590
+intersection of an equipotential surface and a
+
+167
+00:11:24,590 --> 00:11:27,710
+plane results in equipotential lines اللي إحنا 
+
+168
+00:11:27,710 --> 00:11:32,330
+شايفينهم إحنا لإنه إحنا بنرسم على plan فدولها lines
+
+169
+00:11:32,330 --> 00:11:36,510
+لكن هي surfaces يعني بتكون زي shells لكن تقطعها مع 
+
+170
+00:11:36,510 --> 00:11:39,650
+أي plan زي هذا ال plan اللي هو اللي في حالتنا مثلا
+
+171
+00:11:39,650 --> 00:11:43,390
+هذا ممكن يكون ال XZ plan هنلاقي إحنا هنشوف مالهم
+
+172
+00:11:43,390 --> 00:11:46,670
+lines هنشوفهم دوائر مقطعة لكن هم في الواقع زي ما
+
+173
+00:11:46,670 --> 00:11:50,750
+قلنا هي surfaces بس كل دائرة مقطعة جهدها هيغير عن
+
+174
+00:11:50,750 --> 00:11:55,750
+الدائرة؟ طبعا هذه مثلا جهدها V0 هذه جهدها V1 هذه
+
+175
+00:11:55,750 --> 00:12:00,230
+جهدها هيكون V2 بس على طول هيكون الدائرة الدائرة كل
+
+176
+00:12:00,230 --> 00:12:02,810
+ال potentials اللي هو أنا في هذه الحالة هيكون line
+
+177
+00:12:02
+
+201
+00:13:34,420 --> 00:13:39,640
+اتجاهه السالب موجب اتجاه سالب z الموجب اللي هي 9 z
+
+202
+00:13:39,640 --> 00:13:43,320
+hat معناه أنه من السالب موجب اتجاه plus z hat
+
+203
+00:13:49,520 --> 00:13:54,700
+واحد منهم located عند النقطة 00-2 مش قاعد على 00
+
+204
+00:13:54,700 --> 00:13:58,300
+الأصل تبعه لو الأصل تبعه على 0 مش هيكون
+
+205
+00:13:58,300 --> 00:14:03,980
+located عند 000 لكن الأولاني قاعد عند 00-2 والثاني
+
+206
+00:14:03,980 --> 00:14:09,040
+عند 00 plus 3 واضح؟
+
+207
+00:14:09,040 --> 00:14:11,800
+إذا هذول ال diagonals الأصل تبعهم مش قاعد على
+
+208
+00:14:11,800 --> 00:14:19,390
+0 يعني هن دي في R'1 وR'2 معايا؟ إذا هذول الأولاني
+
+209
+00:14:19,390 --> 00:14:24,090
+كانت و-5Z hat نانو كولومبر متر الثاني 9Z hat نانو
+
+210
+00:14:24,090 --> 00:14:28,990
+كولومبر متر located عند النقطة 00-2 الأولاني
+
+211
+00:14:28,990 --> 00:14:34,870
+والثاني عند 003 طالب مني أن أجيب potential عند ال
+
+212
+00:14:34,870 --> 00:14:35,190
+origin
+
+213
+00:14:40,150 --> 00:14:42,630
+طبعًا ال potential مجموعة ال potentials يعني أنا
+
+214
+00:14:42,630 --> 00:14:44,950
+بدي أجيب potential من ال table الأولاني إذا
+
+215
+00:14:44,950 --> 00:14:47,150
+potential من دا قبله الثاني بيعطيني ال total
+
+216
+00:14:47,150 --> 00:14:52,390
+potential عند النقطة المطلوبة ال sum كام من واحد
+
+217
+00:14:52,390 --> 00:14:57,290
+لاثنين PK dot RK على four by epsilon dot RK لكل Q
+
+218
+00:14:57,290 --> 00:15:02,290
+R mean اللي هي المسافة بين ال dipole و ال origin
+
+219
+00:15:03,100 --> 00:15:06,860
+الأولاني يعني R1 المسافة بين dipole الأولاني و ال
+
+220
+00:15:06,860 --> 00:15:10,260
+origin و R2 هي المسافة بين dipole الثاني و ال origin
+
+221
+00:15:10,260 --> 00:15:17,220
+R1 magnitude و R2 magnitude فإذا بنت أجيبهم عندي
+
+222
+00:15:17,220 --> 00:15:19,800
+ال dipole الأولاني أعلنت
+
+223
+00:15:28,210 --> 00:15:31,170
+النقطة اللي بدأيسي عندها ال potential minus r اللي
+
+224
+00:15:31,170 --> 00:15:35,650
+عندها ال source يعني r minus r prime فهذه الحالة
+
+225
+00:15:35,650 --> 00:15:39,990
+مين عند ال r prime بتاعة ال dipole هي 00-2 الفرق
+
+226
+00:15:39,990 --> 00:15:43,410
+بينهم هيعطيني plus 2 z hat بالنسبة لل dipole
+
+227
+00:15:43,410 --> 00:15:43,950
+الثاني
+
+228
+00:15:51,780 --> 00:15:58,290
+المجنوب تبقى R1 هتكون 2 المجنوب تبقى R2 هتكون 3 إذا
+
+229
+00:15:58,290 --> 00:16:02,750
+في إيش هتسوى 1 على 4 by epsilon not في b1 اللي قدش
+
+230
+00:16:02,750 --> 00:16:08,530
+قمت b1 minus 5 في r1 اللي هي 2 يعني نقص 5 في 2 هي
+
+231
+00:16:08,530 --> 00:16:13,110
+minus 10 على r1 ال cube اللي هي 2 ال cube minus b2
+
+232
+00:16:13,110 --> 00:16:19,950
+اللي هي قمتها 9 في r2 هيكون عندي minus 27 على r
+
+233
+00:16:19,950 --> 00:16:25,190
+cubed في 10 هو 9 نقص 9 بس لإنه هي nano هتكون minus
+
+234
+00:16:25,190 --> 00:16:26,370
+9 لأنها في minus
+
+235
+00:16:38,960 --> 00:16:44,500
+هذا هو ال potential اللي عند ال origin الناتج من
+
+236
+00:16:44,500 --> 00:16:48,300
+two dipoles واحد قاعد عند minus 2 زدهاد والثاني
+
+237
+00:16:48,300 --> 00:16:51,000
+قاعد عند plus 3 زدهاد
+
+238
+00:16:53,800 --> 00:16:59,220
+واضح ولا في أي استفسار لحد هنا؟ واضح كلّه؟ طب نيجي
+
+239
+00:16:59,220 --> 00:17:02,420
+ل energy density in electrostatic fields بدي أحسب
+
+240
+00:17:02,420 --> 00:17:07,000
+ال energy density عشان أحسب ال energy density يعني
+
+241
+00:17:07,000 --> 00:17:10,820
+أنا بدي أقرر قداش مجموع ال energy في ال space هناك
+
+242
+00:17:10,820 --> 00:17:12,100
+جاء من وجود بعض ال charges
+
+243
+00:17:15,230 --> 00:17:18,510
+لازم دائمًا أحسب ال work اللي لازمني عشان أنقل
+
+244
+00:17:18,510 --> 00:17:21,390
+واحدة أو charges أو اثنتين أو ثلاث أو عدد من
+
+245
+00:17:21,390 --> 00:17:24,350
+ال charges من ال infinity لنقطة اللي في ال space
+
+246
+00:17:24,350 --> 00:17:27,490
+اللي بتحسب عندها ال energy density عشان أعرف ال
+
+247
+00:17:27,490 --> 00:17:30,450
+energy density لازم أحسب اللي هو ال work و ال work
+
+248
+00:17:30,450 --> 00:17:39,050
+اللي كيف بتحسبه بتحسب قداش ال work اللي
+
+249
+00:17:39,050 --> 00:17:42,370
+لازم لي
+
+250
+00:17:42,370 --> 00:17:45,330
+هو اللي هيخليني أحسب اللي هي ال energy density
+
+251
+00:17:45,330 --> 00:17:50,090
+نبدأ بمين؟ بإن لو أنا بدي أجيب ال charge Q1 و Q2 و
+
+252
+00:17:50,090 --> 00:17:53,370
+Q3 عشان آخذ مثل أما أجيب عدد كبير من ال charges في
+
+253
+00:17:53,370 --> 00:17:57,250
+كم ساعات صعبه نفترض أن عندي ثلاث charges و بدي
+
+254
+00:17:57,250 --> 00:18:00,130
+آخذهم من ال infinity و أحطهم في ال space اللي
+
+255
+00:18:00,130 --> 00:18:03,330
+مدحسب عنده ال energy density لو بدي آخذ ال charge
+
+256
+00:18:03,330 --> 00:18:05,710
+q واحد من ال infinity ل space ماله؟ أنا فرضتها ال
+
+257
+00:18:05,710 --> 00:18:09,970
+space فاضي مش هحتاج أي شي هون ما فيش أي potential
+
+258
+00:18:09,970 --> 00:18:15,120
+ليه ما يكون عكس أو يعمل قوة معك سليقلي وأنا بنقول
+
+259
+00:18:15,120 --> 00:18:19,200
+ال charge من ال infinity للمقطع فإذا ال work اللي
+
+260
+00:18:19,200 --> 00:18:22,260
+لازمني عشان أنقل ال charge الأولى من ال infinity
+
+261
+00:18:22,260 --> 00:18:26,420
+لل space الفاضي لل free space ماله؟ أو free charge
+
+262
+00:18:26,420 --> 00:18:29,420
+space ال charge في free space يعني ما عندي charges
+
+263
+00:18:29,420 --> 00:18:32,840
+هيكون zero ما عندي electric field ناتج عن ال
+
+264
+00:18:32,840 --> 00:18:34,780
+source قاعد بالسماء؟ هل أصلاً عندي charge في ال
+
+265
+00:18:34,780 --> 00:18:38,240
+space؟ أصلاً عندي electric field فلما بدي أنقل
+
+266
+00:18:38,240 --> 00:18:42,650
+charge إيش هيصير في عندي؟ هيبذل ال work بنقول عمال
+
+267
+00:18:42,650 --> 00:18:44,930
+ننتشارج في space female و electric field اللي هو
+
+268
+00:18:44,930 --> 00:18:47,370
+المثال اللي شرحناه في الأول لو كان عندي electric
+
+269
+00:18:47,370 --> 00:18:50,070
+field و عمال نبدأ نقول نقطة من ال infinity ل ال
+
+270
+00:18:50,070 --> 00:18:53,170
+space هذا حتى فرضنا أول نبدأ نقول من نقطة A لنقطة
+
+271
+00:18:53,170 --> 00:18:55,970
+B وبعدين نقول لو فرضنا إيه هي ال infinity هيكون
+
+272
+00:18:55,970 --> 00:19:03,150
+عند الجهود ال work إيش بيساوي؟ هيكون Q2 في V21 V21
+
+273
+00:19:03,150 --> 00:19:07,810
+هو ال potential المبذول على ال charge Q2 من وجود
+
+274
+00:19:07,810 --> 00:19:13,670
+ال charge Q1 هتصار عندي two charges الـ Q الأولى و
+
+275
+00:19:13,670 --> 00:19:17,030
+الـ Q الثانية فعير؟ بدنا نقول ال charge الثالثة
+
+276
+00:19:17,030 --> 00:19:21,110
+هيكون في عندي total potential ناتج من ال charge
+
+277
+00:19:21,110 --> 00:19:24,750
+الأولى و من ال charge الثانية فال charge الثالثة
+
+278
+00:19:24,750 --> 00:19:28,370
+اللي بدنا نقولها هيكون ال work المبذول هو Q ثلاثة
+
+279
+00:19:28,370 --> 00:19:30,750
+في مين؟ في ال two potentials مع مجموع ال two
+
+280
+00:19:30,750 --> 00:19:33,430
+potentials في أي نقطة في ال space لأن هذه هي اللي
+
+281
+00:19:33,430 --> 00:19:38,160
+هتحدد ليه ال work إذا هيكون ال total work هي سواء
+
+282
+00:19:38,160 --> 00:19:44,160
+Q2 V2 1 زائد Q3 في V3 1 زائد V3 2 اللي هم ال
+
+283
+00:19:44,160 --> 00:19:50,040
+potential اللي بتعمله ال Q1 على Q3 و V2 3 اللي هي
+
+284
+00:19:50,040 --> 00:19:53,840
+ال potential اللي ناتج من ال charge الثانية على ال
+
+285
+00:19:53,840 --> 00:19:57,940
+charge الثالثة لو أنا عكست الترتيب يعني قلت أنا
+
+286
+00:19:57,940 --> 00:20:02,040
+بجيب ال charge الثالثة مش من ال charge الأولى
+
+287
+00:20:02,040 --> 00:20:04,900
+ال charge الثالثة هتجي في free space هيكون zero
+
+288
+00:20:04,900 --> 00:20:07,980
+ال charge الثاني هتلاقي اللي هو potential ناتج من
+
+289
+00:20:07,980 --> 00:20:12,360
+ال charge الثالثة هتكون Q2 V32 ال charge الأولى
+
+290
+00:20:12,360 --> 00:20:17,440
+هيكون Q1 V12 V13 لو جمعت الاثنين هدول إيش هيصير
+
+291
+00:20:17,440 --> 00:20:26,340
+عندك اثنين W2E بتاعتها تساوي W1 اللي هي ال zero
+
+292
+00:20:32,460 --> 00:20:38,460
+Q2 مضروبة في V21 زائد V23 إذا ما هي أول حاجة
+
+293
+00:20:38,460 --> 00:20:43,000
+جمعناها Q2 مضروبة في V21 زائد V23 هي ال total
+
+294
+00:20:43,000 --> 00:20:46,160
+potential يمكن أحلم فيه يأثر على Q2 ال potential
+
+295
+00:20:46,160 --> 00:20:51,500
+ناتج من Q1 و ال potential ناتج من Q3 نجمع هنا زائد
+
+296
+00:20:51,500 --> 00:20:56,680
+Q3 مضروبة في V13 زائد V31 زائد V23 اللي هي ال
+
+297
+00:20:56,680 --> 00:20:59,040
+potential ناتج من ال charge الأولى و ال charge الثاني
+
+298
+00:20:59,040 --> 00:21:04,860
+زائد Q1 مضروبة في V12 زائد V13 اللي هو برضه ال
+
+299
+00:21:04,860 --> 00:21:07,980
+total potential ممكن يأثر على Q1 و potential ناتج
+
+300
+00:21:07,980 --> 00:21:14,830
+من ال Q2 و Q3 هذا mean two ال work ضعف ال work إذا
+
+301
+00:21:14,830 --> 00:21:19,650
+الوقش متساوي نص Q1 في ال potential ناتج من ال
+
+302
+00:21:19,650 --> 00:21:21,890
+charge الثانية على ال charge الأولى زاد ال
+
+303
+00:21:21,890 --> 00:21:23,790
+potential ناتج من ال charge الثالثة على ال charge
+
+304
+00:21:23,790 --> 00:21:28,610
+الأولى زاد Q2 في ال potential ناتج من ال charge
+
+305
+00:21:28,610 --> 00:21:30,410
+الأولى على الثانية زاد ال potential ناتج من
+
+306
+00:21:30,410 --> 00:21:34,710
+الثالثة على الثانية زاد Q3 مضروبة في ال potential
+
+307
+00:21:34,710 --> 00:21:37,150
+ناتج من الأولى على الثالثة زاد ال potential ناتج
+
+308
+00:21:37,150 --> 00:21:40,010
+من الثانية على الثالثة يمكن هذه أسهل من الواحد
+
+309
+00:21:40,010 --> 00:21:48,000
+يتذكرها أن ال total potential هي ساول نص V1 V2 V3
+
+310
+00:21:48,000 --> 00:21:51,520
+V4 V5 V6 V7 V8 V9 V10 V11 V12 V13 V14 V15 V16 V17
+
+311
+00:21:51,520 --> 00:21:54,680
+V18 V19 V20 V21 V21 V21 V21 V21 V21 V21 V21 V21
+
+312
+00:21:54,680 --> 00:21:55,320
+V21 V21 V21 V21 V21 V21 V21 V21 V21 V21 V21 V21
+
+313
+00:21:55,320 --> 00:21:55,420
+V21 V21 V21 V21 V21 V21 V21 V21 V21 V21 V21 V21
+
+314
+00:21:55,420 --> 00:21:56,700
+V21 V21 V21 V21 V21 V21 V21 V21 V21 V21 V21 V21
+
+315
+00:21:56,700 --> 00:21:57,960
+V21 V21 V21 V21 V21 V21 V21 V21 V21 V21 V21 V21
+
+316
+00:21:57,960 --> 00:21:58,680
+V21 V21 V21 V21 V21 V21 V21 V21 V21 V21 V21 V21
+
+317
+00:21:58,680 --> 00:21:59,600
+V21 V21 V21 V21 V21 V21 V21 V21 V21 V21 V21 V21
+
+318
+00:21:59,600 --> 00:22:04,860
+V21 V21 V21 V21 V21 V21 V21 V
+
+319
+00:22:07,540 --> 00:22:10,820
+هي الرسمة بتاعتنا يعني عشان بس التذكير أنه أنا جاي
+
+320
+00:22:10,820 --> 00:22:14,140
+من ال infinity و قاعدة بجيب ال charge واحدة بعد
+
+321
+00:22:14,140 --> 00:22:17,840
+الثانية أو أجد مثلًا q واحد من ال infinity ما كانش
+
+322
+00:22:17,840 --> 00:22:21,220
+فيها أي charges هيكون ال work بيساوي zero لما أجيب
+
+323
+00:22:21,220 --> 00:22:23,820
+ال charge الثانية هيكون في عندي electric lines
+
+324
+00:22:23,820 --> 00:22:27,580
+already هيكون في عندي work مبذول نفس الحاجة ل q
+
+325
+00:22:27,580 --> 00:22:31,860
+ثلاثة لكن للتسهيل احنا عشان قلنا أنا بعرف ال total
+
+326
+00:22:31,860 --> 00:22:38,170
+energy أنها نص ال sum من k واحد ل n ك VK أنا كان
+
+327
+00:22:38,170 --> 00:22:41,570
+مثلًا عندي ثلاثة ممكن يكون عندي خمسة ستة ensemble
+
+328
+00:22:41,570 --> 00:22:46,770
+من ال charges يعني عدد كبير منهم فبيكون عندي مجموع
+
+329
+00:22:46,770 --> 00:22:50,270
+ال potentials زي ما عرفناهم اللي هو نص Q واحد V
+
+330
+00:22:50,270 --> 00:22:57,340
+واحد زي نص Q ثانية V ثانية زي نص Q ثلاثة V ثلاثة لو
+
+331
+00:22:57,340 --> 00:23:00,660
+كان عندي continuous charge مش يعني charges يعني
+
+332
+00:23:00,660 --> 00:23:03,920
+عندي body من ال charge هتكون إيش هي ال integral لو
+
+333
+00:23:03,920 --> 00:23:08,820
+كانت line ال charge هيكون نص ال integral رو L VDL
+
+334
+00:23:08,820 --> 00:23:13,660
+ال work على ال مثلًا ال surface charge هيكون نص ال
+
+335
+00:23:13,660 --> 00:23:17,860
+integral رو S VDS لو كان عندي volume ال charge
+
+336
+00:23:17,860 --> 00:23:23,830
+هيكون نص ال integral رو V VDV طب احنا نيجي نأخذ هذه
+
+337
+00:23:23,830 --> 00:23:26,090
+المثال اللي هي تاعت ال volume and charge، إيش
+
+338
+00:23:26,090 --> 00:23:30,110
+هيكون عندي؟ رو V إيش بتساوي؟ diverse D رو V
+
+339
+00:23:30,110 --> 00:23:33,810
+diverse D، متذكرين ال Gauss law؟ رو V بتساوي
+
+340
+00:23:33,810 --> 00:23:37,110
+diverse D أو diverse E بتساوي رو V على إبسلون،
+
+341
+00:23:37,110 --> 00:23:43,040
+صحيح؟ إذا رو V بتساوي diverse V، أعوض في W EW إيش
+
+342
+00:23:43,040 --> 00:23:48,740
+بتأولى نص ال integral على V دايفرش DV DV طبعًا هد V
+
+343
+00:23:48,740 --> 00:23:53,900
+ال potential و هد مين V المعوجة ال volume واضح هد
+
+344
+00:23:53,900 --> 00:23:58,180
+V اللي هي ال volume ال potential زي هنا هد V بس
+
+345
+00:23:58,180 --> 00:24:02,680
+احنا عوضنا عن مين؟ ال integral بدل Q رو مثلًا LDL أو
+
+346
+00:24:02,680 --> 00:24:08,640
+ال integral رو SDS أو ال integral رو V DV لو
+
+347
+00:24:08,640 --> 00:24:11,400
+استخدمنا الـ Row V اللي هي ال charge density الـ
+
+348
+00:24:11,400 --> 00:24:14,760
+Diverge دي في V اللي هو ال potential في DV اللي هو
+
+349
+00:24:14,760 --> 00:24:17,880
+ال volume احنا لو استخدمنا هذه ال identity اللي
+
+350
+00:24:17,880 --> 00:24:21,960
+احنا شفناها في جزء ال calculus ال vector calculus
+
+351
+00:24:21,960 --> 00:24:26,280
+Diverge ال scalar مع vector إيش بنقولنا كأنه بعمل
+
+352
+00:24:26,280 --> 00:24:29,600
+تفاضل ل two quantities واحدة scalar واحدة vector
+
+353
+00:24:29,600 --> 00:24:31,980
+بمعنى التفاضل أول في الثاني زائد أول في تاني في
+
+354
+00:24:31,980 --> 00:24:35,560
+الثاني بس عشان هنا vector بدأ أدبه لو أنا بدأ فاضل
+
+355
+00:24:35,560 --> 00:24:39,650
+V إيش هتصير؟ ال grad ال V؟ يعني هتكون a dot grad
+
+356
+00:24:39,650 --> 00:24:45,630
+of v زائد v diverge ال a أخذنا هذه ال identity أنا
+
+357
+00:24:45,630 --> 00:24:49,950
+مين عندي؟ هذي عندي v في diverge ال a هذي إيش
+
+358
+00:24:49,950 --> 00:24:54,810
+هتساوي؟ diverge ال scalar مع ال vector minus ال
+
+359
+00:24:54,810 --> 00:24:59,950
+vector dot grad ال divergence إذا بعود عن diverge
+
+360
+00:24:59,950 --> 00:25:06,170
+ال d في v لهذه ال quantity مين؟ ال diverge ال
+
+361
+00:25:06,170 --> 00:25:13,220
+scalar مع ال vector minus ال vector dot grad ال V
+
+362
+00:25:13,220 --> 00:25:17,780
+اتعود في هذا ال integral عوضنا هي اسم ال energy
+
+363
+00:25:17,780 --> 00:25:23,900
+هي نص التكامل على ال volume diverse VD DV minus نص
+
+364
+00:25:23,900 --> 00:25:31,000
+integral over VD dot grad V DV ديش الجزء الأولاني
+
+365
+00:25:31,000 --> 00:25:34,720
+طبعًا بقدر أنا استخدم مين؟ اللي هي ال divergence
+
+366
+00:25:34,720 --> 00:25:41,670
+theorem متذكرينها؟ قولنا diverse أي vector a dv
+
+367
+00:25:41,670 --> 00:25:45,970
+بقدر أكمله على ال surface أحوله من اللي هو ال
+
+368
+00:25:45,970 --> 00:25:48,990
+divergence theorem إذا أنتم متذكرينها أو نسينها
+
+369
+00:25:48,990 --> 00:25:53,350
+مفهومكم كل هذا بالذاكرة من الامتحان integral ل
+
+370
+00:25:53,350 --> 00:25:57,270
+diverse أي quantity dv بقدر أقولها تساوي ال close
+
+371
+00:25:57,270 --> 00:26:01,490
+integral على ال surface integral over volume a dot
+
+372
+00:26:01,490 --> 00:26:02,470
+ds
+
+373
+00:26:06,890 --> 00:26:10,810
+أصلًا هي اللي عملناها حولنا من ال volume integral
+
+401
+00:27:55,230 --> 00:27:58,950
+grade V DV بس احنا نتذكر مين الـ grade الـ V بس
+
+402
+00:27:58,950 --> 00:28:03,810
+إطلعوا شفنا مين الـ grade الـ V؟ E E مش بتساوى minus grade 
+
+403
+00:28:03,810 --> 00:28:04,210
+الـ V
+
+404
+00:28:08,160 --> 00:28:11,900
+بتساوي minus grade الـ V قولنا هاي استنتجناها بعد
+
+405
+00:28:11,900 --> 00:28:16,100
+الطرق و أكدت إن العلاقة أن كامل الـ E بتساوي Zero
+
+406
+00:28:16,100 --> 00:28:23,500
+احنا static إذا
+
+407
+00:28:23,500 --> 00:28:26,380
+أنا باخد الـ minus grade الـ V و بقيمها و بحط بدلها
+
+408
+00:28:26,380 --> 00:28:30,820
+mean E إذا أنا عندي نص الـ integral على الـ volume D
+
+409
+00:28:30,820 --> 00:28:36,050
+Dot E DVطب دي و إيه إيش العلاقة بينها؟ إبسلون نوت،
+
+410
+00:28:36,050 --> 00:28:38,750
+لو قلت دي بتساوي إبسلون نوت إيه إيه إيش، هيصير عندي
+
+411
+00:28:38,750 --> 00:28:43,750
+نص الـ integral لإبسلون نوت إيه تربيع في V، هذا مين
+
+412
+00:28:43,750 --> 00:28:51,230
+الـ total work الـ energy density ما هي لـ DWE على
+
+413
+00:28:51,230 --> 00:28:55,630
+DV، فهي الـ energy densityطبعا عندي هذا كله في قلب
+
+414
+00:28:55,630 --> 00:28:58,410
+الـ integral يعني لو أنا فضل دي و by دي و دي و دي
+
+415
+00:28:58,410 --> 00:28:59,070
+و دي و دي و دي و دي و دي و دي و دي و دي و دي و دي
+
+416
+00:28:59,070 --> 00:29:02,850
+و دي و دي و دي و دي و دي و دي و دي و دي و دي و دي
+
+417
+00:29:02,850 --> 00:29:10,110
+و دي و دي و دي و دي و دي و دي و دي و دي و دي و دي
+
+418
+00:29:10,110 --> 00:29:10,130
+و دي و دي و دي و دي و دي و دي و دي و دي و دي و دي
+
+419
+00:29:10,130 --> 00:29:10,890
+و دي و دي و دي و دي و دي و دي و دي و دي و دي و دي
+
+420
+00:29:10,890 --> 00:29:14,990
+و دي و دي و دي 
+
+421
+00:29:21,750 --> 00:29:25,990
+واضح؟ لحد هنا نخلّي الامتحان؟ لحد Gauss؟ آخر إشي لحد
+
+422
+00:29:25,990 --> 00:29:32,140
+Gauss وما دخلش الـ potential؟ طب لحد Gauss امتحانكم
+
+423
+00:29:32,140 --> 00:29:36,880
+لحد go slow طب نيجي نشوف مثال على الـ energy عندي 
+
+424
+00:29:36,880 --> 00:29:41,300
+three pointed charges ثلاث نقاط واحدة عند الـ
+
+425
+00:29:41,300 --> 00:29:45,620
+origin قيمتها minus واحد nano column والثانية عند
+
+426
+00:29:45,620 --> 00:29:51,200
+plus z plus واحد على الـ z axis قيمتها four nano
+
+427
+00:29:51,200 --> 00:29:58,150
+column والثالثة عند الـ x axis واحد x axis قيمتها
+
+428
+00:29:58,150 --> 00:30:01,070
+ثلاثة من الـ column، بده نوجد الـ energy in the
+
+429
+00:30:01,070 --> 00:30:03,150
+system، find the energy in the system، احنا قولنا
+
+430
+00:30:03,150 --> 00:30:06,110
+الـ energy يعني ما فيش حساب من هنا، صرنا حافظينها،
+
+431
+00:30:06,110 --> 00:30:09,970
+يا بستخدم هذا القانون هو Zero, Q, V, N، يا اللي هو
+
+432
+00:30:09,970 --> 00:30:13,690
+نص و أنا حرة مين بدي استخدم ماحدش اللي هو عندي،
+
+433
+00:30:13,690 --> 00:30:17,490
+بحسب الـ total potential على كل واحدة من الـ charges
+
+434
+00:30:17,490 --> 00:30:22,950
+و بقول إن الـ total energy بتساوي نص اللي هو Q1 في
+
+435
+00:30:22,950 --> 00:30:27,830
+V1 زي Q2 في V2 زي Q3 في V3 و بحسب اللي هو الـ
+
+436
+00:30:27,830 --> 00:30:36,130
+potentials الـ total potentials V12 زي V21 زي V23
+
+437
+00:30:36,130 --> 00:30:45,730
+اللي هو لو بده احكي Q1 هتكون V12 V1 V21 بسم الله
+
+438
+00:30:45,730 --> 00:30:56,790
+الرحمن الرحيم V12 و V13 V12 V13
+
+439
+00:30:56,790 --> 00:30:57,270
+V13 V13 V13 V13 V13 V13 V13 V13 V13 V13 V13 V13
+
+440
+00:30:57,270 --> 00:30:57,390
+V13 V13 V13 V13 V13 V13 V13 V13 V13 V13 V13 V13
+
+441
+00:30:57,390 --> 00:30:57,670
+V13 V13 V13 V13 V13 V13 V13 V13 V13 V13 V13 V13
+
+442
+00:30:57,670 --> 00:30:57,990
+V13 V13 V13 V13 V13 V13 V13 V13 V13 V13 V13 V13
+
+443
+00:30:57,990 --> 00:30:58,030
+V13 V13 V13 V13 V13 V13 V13 V13 V13 V13 V13 V13
+
+444
+00:30:58,030 --> 00:30:58,050
+V13 V13 V13 V13 V13 V13 V13 V13 V13 V13 V13 V13
+
+445
+00:30:58,050 --> 00:31:07,310
+V13 V13 V13 V13 V13 V13 V13
+
+446
+00:31:08,110 --> 00:31:11,830
+أو إذا أنا متذكرة و حافظة إن أنا لو جبت الأولى
+
+447
+00:31:11,830 --> 00:31:14,610
+هيكون الـ total work equal to zero الثانية بس هتكون
+
+448
+00:31:14,610 --> 00:31:19,710
+الأولى عليها إذا ما هتكون Q2 V2 1 الثالثة هيكون
+
+449
+00:31:19,710 --> 00:31:26,130
+أندي ثلاثة واحد زائد ثلاثة اثنين
+
+450
+00:31:26,130 --> 00:31:30,110
+يا هيك
+
+451
+00:31:30,110 --> 00:31:32,350
+يا هيك وهذا هو الحل النهائي
+
+452
+00:31:35,030 --> 00:31:37,430
+لو كان عندي charge distribution و الـ spherical
+
+453
+00:31:37,430 --> 00:31:40,390
+symmetry اللي اللي الـ density ρ V بيساوي رو نوت 
+
+454
+00:31:40,390 --> 00:31:44,430
+بالـ R ما بين الـ 0 و الـ R و 0 for R أكبر من R
+
+455
+00:31:44,430 --> 00:31:47,550
+بدنا نجيب الـ potential everywhere و الـ energy
+
+456
+00:31:47,550 --> 00:31:51,610
+stored in the region for R أقل من R أول حاجة بده
+
+457
+00:31:51,610 --> 00:31:54,990
+الـ V everywhere و بعدين بده الـ energy stored في الـ
+
+458
+00:31:54,990 --> 00:31:58,750
+region طبعا الـ potential اللي احنا حكيناه أول إشي
+
+459
+00:31:58,750 --> 00:32:02,610
+فلازم أول حاجة for R أكبر من أو يساوي R إن عندي
+
+460
+00:32:02,610 --> 00:32:08,180
+spherical symmetry وين من R من Zero ل R برا R R
+
+461
+00:32:08,180 --> 00:32:11,800
+أكبر هيكون كل الـ distribution موجودة جوا فبستخدم
+
+462
+00:32:11,800 --> 00:32:15,820
+Gauss law بتجيب الـ electric field فأي نقطة خارج الـ
+
+463
+00:32:15,820 --> 00:32:20,720
+R أكبر من R capital هتكون
+
+464
+00:32:20,720 --> 00:32:24,080
+رو نوت R تكعيب على ثري إبسلون نوت R تربيع R hat هذا
+
+465
+00:32:24,080 --> 00:32:26,420
+المثال اللي أخدته أكيد لما أخدته الـ Gauss
+
+466
+00:32:26,420 --> 00:32:32,500
+distribution يعني دي أنا هاي الـ raw هاي الـ sphere
+
+467
+00:32:32,500 --> 00:32:38,990
+يعني اللي لها charge distribution رو نوت فهي الـ
+
+468
+00:32:38,990 --> 00:32:46,370
+region و برا zero فهي رو V هذي قيمة R برا هيكون كل
+
+469
+00:32:46,370 --> 00:32:50,310
+charge هو أجاوزله clause integral a dot dL بتساوي
+
+470
+00:32:50,310 --> 00:32:55,430
+رو V اللي هيكون رو نوت على epsilon نوت جيبه إن هو
+
+471
+00:32:55,430 --> 00:33:01,210
+الـ integration a dot dR الـ integral a dot dS
+
+472
+00:33:15,930 --> 00:33:19,710
+عشان مش هنعيب يعني هو مفترض إنكوا خلاص ردّينا الحل
+
+473
+00:33:19,710 --> 00:33:24,550
+قبل ليك و استخدمتوه فـ R أكبر من R تساوي R capital هي
+
+474
+00:33:24,550 --> 00:33:28,400
+الـ electric field الـ potential بيساوي معاكس تيجر الـ E 
+
+475
+00:33:28,400 --> 00:33:31,940
+.DL اللي هو ميل أنا الـ E هنا في اتجاه الـ r هو
+
+476
+00:33:31,940 --> 00:33:34,700
+بيحتلّع معاكم في اتجاه الـ r هذا من الـ symmetry و
+
+477
+00:33:34,700 --> 00:33:37,740
+لا كان نادر استخدام Gauss law الـ symmetry أنا عندي
+
+478
+00:33:37,740 --> 00:33:40,880
+spherical الشاشة الـ distribution تبع الـ شاشة
+
+479
+00:33:40,880 --> 00:33:45,720
+symmetrically distributed باستخدام اللي هو Gauss 
+
+480
+00:33:45,720 --> 00:33:49,080
+surface فتخيل إن في عندي surface على شكل مالّه
+
+481
+00:33:49,080 --> 00:33:54,170
+shell محيط اللي هي الـ charge بتاعتي و بحسب الـ
+
+482
+00:33:54,170 --> 00:33:57,630
+clause integer ل a.ds بسونا نوت على ابسلون أخدتوا a
+
+483
+00:33:57,630 --> 00:34:04,870
+ولا أنا حسّاكم مالكم؟ بحسب بيطلع معايا إنه أيضا من
+
+484
+00:34:04,870 --> 00:34:08,170
+الـ symmetry برضه فاتجاه الـ R hat بحسب الـ potential
+
+485
+00:34:08,170 --> 00:34:11,450
+بيطلع معايا الـ potential عند R أكبر من R
+
+486
+00:34:14,480 --> 00:34:16,440
+احنا دائما بنفرض إن الـ potential عن الـ infinity
+
+487
+00:34:16,440 --> 00:34:20,440
+مقلّه بساوي 0 لو أنا أعوض هنا عشان أجيب الـ C1 الـ
+
+488
+00:34:20,440 --> 00:34:23,560
+constant of integration عند الـ infinity هدا هتكون
+
+489
+00:34:23,560 --> 00:34:27,980
+0 و V عند الـ infinity بساوي 0 إذن C1 بساوي 0 إذا
+
+490
+00:34:27,980 --> 00:34:30,700
+أنا باخد الـ reference إنه الـ potential عند الـ
+
+491
+00:34:30,700 --> 00:34:34,780
+infinity بساوي 0 فبالتالي V at R infinity بساوي 0
+
+492
+00:34:34,780 --> 00:34:38,760
+وبالتالي هنا هتكون 0 وهدي بالفعل معوض عن R 
+
+493
+00:34:38,760 --> 00:34:43,790
+infinity مش هتعطيني 0 إذن C1 بساوي 0 إذا V for
+
+494
+00:34:43,790 --> 00:34:52,390
+region R أكبر من R أقل من R أقل
+
+495
+00:34:52,390 --> 00:34:54,950
+من R أقل من R أقل من R أقل من R أقل من R أقل من R
+
+496
+00:34:54,950 --> 00:34:55,270
+من R أقل من R أقل من R أقل من R أقل من R أقل من R
+
+497
+00:34:55,270 --> 00:34:58,910
+أقل من R أقل من R أقل من R أقل من R أقل من R أقل
+
+498
+00:34:58,910 --> 00:35:01,930
+من R أقل من R أقل من R أقل من R أقل من R أقل من R
+
+499
+00:35:01,930 --> 00:35:03,050
+أقل من R أقل من R أقل من R أقل من R أقل من R أقل
+
+500
+00:35:03,050 --> 00:35:03,670
+من R أقل من R أقل من R أقل من R أقل من R أقل من R
+
+501
+00:35:03,670 --> 00:35:11,870
+أقل من R أقل من R أقل تساوي minus rho node R تربيع
+
+502
+00:35:11,870 --> 00:35:18,830
+على 6Y node plus C2 فلقيت
+
+503
+00:35:18,830 --> 00:35:23,270
+احنا كمان لازم يكون في عندنا حاجة مهمة أنا برا داخل
+
+504
+00:35:23,270 --> 00:35:27,910
+في برا هنا عندي الـ region اللي برا اللي أكبر من R
+
+505
+00:35:27,910 --> 00:35:33,190
+و أقدر أروح لحد الـ infinity جوا أنا محصورة من 0 ل R
+
+506
+00:35:33,190 --> 00:35:35,550
+ما أقدرش أقول إن والله الـ reference بتاعتي عند R goes
+
+507
+00:35:35,550 --> 00:35:39,970
+to infinity إن الـ region هاد اللي ما حسبت الـ potential
+
+508
+00:35:39,970 --> 00:35:44,590
+محصورة من 0 ل R هناك من R ل infinity فاستخدمنا
+
+509
+00:35:44,590 --> 00:35:48,670
+نقطة الـ infinity طب جوا كيف بدي أخلص من الـ C2 من
+
+510
+00:35:48,670 --> 00:35:50,590
+الـ boundary condition يعني الـ boundary condition
+
+511
+00:35:50,590 --> 00:35:55,450
+لازم الـ potential عند R بتساوي R capital يعني أسوأ
+
+512
+00:35:55,450 --> 00:36:00,450
+جات من هنا على الـ R أو جات من هنا على الـ R عشان لازم
+
+513
+00:36:00,450 --> 00:36:04,770
+يكون الـ potential بقى المتساوي فمنها بقدر أجيب C2
+
+514
+00:36:09,520 --> 00:36:14,320
+الـ R بتساوي R أعوض عن R بأيش بتساوي رونوت R تربيع
+
+515
+00:36:14,320 --> 00:36:19,360
+على 6 Epsilon Note هذه اللي من هنا واللي من
+
+516
+00:36:19,360 --> 00:36:26,000
+المعادلة اللي السابقة بتعود أعوض عن R بـ R Capital
+
+517
+00:36:26,000 --> 00:36:29,380
+هتسيي رونوت R تربيع على 3 Epsilon Note بسويهم في
+
+518
+00:36:29,380 --> 00:36:35,570
+بعض واضح ليش أنا استخدمت هيك؟ هدول مهمين لأن دائما
+
+519
+00:36:35,570 --> 00:36:39,570
+لازم تعرفيه من C1 و C2 احنا في الـ region اللي برا
+
+520
+00:36:39,570 --> 00:36:45,070
+for R أكبر من R بقدر أروح ل infinity في الـ region
+
+521
+00:36:45,070 --> 00:36:48,850
+اللي جوا وأنا محصورة من الـ zero ل الـ R لازم ألاقي
+
+522
+00:36:48,850 --> 00:36:51,850
+طريقة تانية عشان أجيب اللي هو الـ constant تبعي
+
+523
+00:36:51,850 --> 00:36:54,310
+براه سهل جبت الـ constant قلت عند R goes to
+
+524
+00:36:54,310 --> 00:36:57,410
+infinity الـ reference potential عندي بيساوي zero
+
+525
+00:36:57,410 --> 00:37:01,510
+جوا هقول آه إذا أنا بستخدم boundary كل شي لازم الـ
+
+526
+00:37:01,510 --> 00:37:04,950
+potential عند الـ surface هذا أسوأ يجيله من هنا ولا
+
+527
+00:37:04,950 --> 00:37:08,130
+من هنا يكون واحد مش منطقي يكون feels continuity
+
+528
+00:37:08,130 --> 00:37:13,000
+على الـ surface هكي بقدر أجيب سيقيم الـ C2 و بالتالي
+
+529
+00:37:13,000 --> 00:37:16,140
+بيطلع عندي الـ potential بيساوي رو نوت على 6 epsilon
+
+530
+00:37:16,140 --> 00:37:22,020
+نوت في 3R تكعيب minus R تربيع هيجيبنا V V for R
+
+531
+00:37:22,020 --> 00:37:23,020
+أكبر مساوية R
+
+532
+00:37:49,200 --> 00:37:50,600
+3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r3r
+
+533
+00:37:53,450 --> 00:37:56,250
+لأن highly stored في الجسم يعني فرقار أقل من أو
+
+534
+00:37:56,250 --> 00:38:00,530
+يساوي، واضح؟
+
+535
+00:38:01,900 --> 00:38:05,440
+هيك احنا تقريبا خلصنا الشطر يعني، هنا بعض نص نماذج
+
+536
+00:38:05,440 --> 00:38:09,040
+كيف إن الـ electrostatic بتأثر كثير على الـ
+
+537
+00:38:09,040 --> 00:38:12,500
+components، أي component زي مثلا للمصفد،
+
+538
+00:38:12,500 --> 00:38:15,360
+electrical components اللي أخذتهم في الـ digital
+
+539
+00:38:15,360 --> 00:38:19,820
+electronics، هدول كثير بتأثر وحتى بال .. يعني هي
+
+540
+00:38:19,820 --> 00:38:23,400
+وين بتكون الـ static forces؟ غالبا بتكون في أي جسم،
+
+541
+00:38:23,400 --> 00:38:28,580
+جسم هنا في static force، static energy ف أنا ممكن الـ
+
+542
+00:38:28,580 --> 00:38:31,080
+aesthetic energy اللي في اطراف أصابعي نقشة تسوي و
+
+543
+00:38:31,080 --> 00:38:34,140
+تعمل damage للـ electrical components، فإذا عمركم
+
+544
+00:38:34,140 --> 00:38:37,120
+شفتوا في التلفازيون المصانع وهم بيجيبوهم أحيانا
+
+545
+00:38:37,120 --> 00:38:40,920
+بيجيبوا كيف بيصنعوا أو بيصنعوا اللي هي الـ digital
+
+546
+00:38:40,920 --> 00:38:44,420
+circuits، يبقى غالبا إياه حاطينلهم حاجة على إيدهم
+
+547
+00:38:44,420 --> 00:38:47,600
+عشان تعمل تفريغ للـ aesthetic .. الـ electro
+
+548
+00:38:47,600 --> 00:38:50,700
+-aesthetic forces أو للنساء أحيانا ما بيحبوش النساء
+
+549
+00:38:50,700 --> 00:38:54,260
+يكون حاجة في إيدهم فمحطولهم إياها في رجلهم يعني و
+
+550
+00:38:54,260 --> 00:38:56,780
+برضه ممكن الرجال يحبوا نفس الإشي تكون في رجلهم
+
+551
+00:38:56,780 --> 00:39:01,260
+بيسموها electrostatic band adjustment أسوأ في اللي
+
+552
+00:39:01,260 --> 00:39:05,760
+على الإيد الـ wrists strap أو الـ foot grounder كويس
+
+553
+00:39:05,760 --> 00:39:10,140
+واضحة أكيد حتى ممكن شوفته ممكن في غزة صاروا يعني
+
+554
+00:39:10,140 --> 00:39:12,000
+أصلا يعني يعملوه لإنه كثير صاروا يصاحوا برضه
+
+555
+00:39:12,000 --> 00:39:16,040
+electrostatic أو digital circuits تبقى حتى زي سلك
+
+556
+00:39:16,040 --> 00:39:19,850
+التليفون أحيانا منهم يبقى موصول واحد وإيده طابعة
+
+557
+00:39:19,850 --> 00:39:22,630
+نازلة و ما هي بتقولوش اسمك التليفون هدول بس
+
+558
+00:39:22,630 --> 00:39:27,230
+مالهم discharger لما تكون الدنيا صافية كثير بتحسوا
+
+559
+00:39:27,230 --> 00:39:31,610
+فيها الـ ecostatic force بتحسوا زي كهربا لما تمسكوا
+
+560
+00:39:31,610 --> 00:39:34,590
+قطعة معدنية بتفرغ الـ ecostatic force من إيدك
+
+561
+00:39:34,590 --> 00:39:37,730
+للقطعة المعدنية بتحس زي إيشيلات شدة أحيانا الناس
+
+562
+00:39:37,730 --> 00:39:42,630
+ما بتمش تمسك برد بالسيارة لما تكون الحرارة شوية
+
+563
+00:39:42,630 --> 00:39:47,550
+عالية جفاف يعني لما يكون الجو فيه جفاف بتكون بتحس
+
+564
+00:39:47,550 --> 00:39:51,700
+فيه أعتقد يعطيكوا العافية وإن شاء الله اللقاء
+
+565
+00:39:51,700 --> 00:39:56,440
+القادم بنكمل في الشفطة لغة جديدة وبدي أكمل
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/dU0noz-nJFA.srt b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/dU0noz-nJFA.srt
new file mode 100644
index 0000000000000000000000000000000000000000..9d1e633a9c5a26a320d1c18bcfd602581375dcfb
--- /dev/null
+++ b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/dU0noz-nJFA.srt
@@ -0,0 +1,1945 @@
+1
+00:00:21,040 --> 00:00:23,480
+باسم الله الرحمن الرحيم السلام عليكم ورحمة الله و
+
+2
+00:00:23,480 --> 00:00:26,080
+بركاته  ونحن اليوم إن شاء الله هنكمل في ال
+
+3
+00:00:26,080 --> 00:00:28,580
+coordinate system في المحاضرة الماضية احنا وقفنا 
+
+4
+00:00:28,580 --> 00:00:31,840
+لحد وشفنا إن احنا ممكن نحافظ على حد ال
+
+5
+00:00:31,840 --> 00:00:34,300
+coordinate constant لما نحافظ على حد ال coordinate
+
+6
+00:00:34,300 --> 00:00:36,660
+constant ليه؟ بنتج عنها لأن احنا عندنا space
+
+7
+00:00:36,660 --> 00:00:40,740
+three dimension واحد من الـ three coordinates ثابت 
+
+8
+00:00:40,740 --> 00:00:44,060
+هيعطينا plane فإحنا مثلا عندنا في ال Cartesian
+
+9
+00:00:44,060 --> 00:00:48,700
+coordinate عندنا الـ X Y Z لو أنا مثلا ثبتت الـ Y 
+
+10
+00:00:48,700 --> 00:00:52,660
+ثبتت الـ Y طلع معايا هذا الـ plane بيصير هذا ال
+
+11
+00:00:52,660 --> 00:00:57,980
+plane هذا الـ plane عند Y ثابتة هذا الـ plane وبيكونوا 
+
+12
+00:00:57,980 --> 00:01:02,360
+الـ X تتحرك من ناقص إنفينتي لبلس إنفينتي والـ Z من ناقص
+
+13
+00:01:02,360 --> 00:01:06,620
+إنفينتي لبلس إنفينتي إذا هذا الـ plane بيكون ماله constant y
+
+14
+00:01:06,620 --> 00:01:10,280
+لو أخذنا الـ Z constant هذا اللي من حياتنا معناه
+
+15
+00:01:10,280 --> 00:01:15,160
+هذا الـ plane عن Z ثابتة قيمة مثلا خمسة تلاتة أربعة
+
+16
+00:01:15,160 --> 00:01:19,860
+فبيديني الـ plane موازي للـ XY plane لإن الـ XY plane
+
+17
+00:01:19,860 --> 00:01:24,080
+أصلا ماله عن Z equals zero والـ Y plane اللي توا
+
+18
+00:01:24,080 --> 00:01:27,560
+حكينا عنه اللي عند constant Y plane اللي هو برضه
+
+19
+00:01:27,560 --> 00:01:31,300
+موازي لمين؟ للـ XZ plane بمعنى إن الحالة الخاصة
+
+20
+00:01:31,300 --> 00:01:34,960
+بتكون عند اللي هي Y بتساوي صفر بتكون اللي هو الـ X
+
+21
+00:01:34,960 --> 00:01:38,680
+Z plane  دعنا عند X equal constant اللي هو هذا ال
+
+22
+00:01:38,680 --> 00:01:42,620
+plane عند X equal constant بيعطينا هذا الـ plane اللي
+
+23
+00:01:42,620 --> 00:01:47,980
+فيه بيبقى فيه الـ Y متغيرة والـ Z متغيرة طبعا إذا
+
+24
+00:01:47,980 --> 00:01:52,690
+إن عند constant ككوردينات بتولد عندنا a plane لو نيجي 
+
+25
+00:01:52,690 --> 00:01:55,330
+على الـ cylindrical coordinates فالـ cylindrical
+
+26
+00:01:55,330 --> 00:02:00,870
+coordinates إنها رو وفاى وزد لو احنا ثبتنا رو،
+
+27
+00:02:00,870 --> 00:02:04,850
+رو ثابتة، إيش هيطلع لنا؟ أسطوانة، سطح الأسطوانة، رو 
+
+28
+00:02:04,850 --> 00:02:08,010
+ثابتة هذا اللي على الشكل اللي هو القلم 
+
+29
+00:02:08,010 --> 00:02:10,370
+الرصاص يعني أو يعني المحيط طبعا اللي هو القلم 
+
+30
+00:02:10,370 --> 00:02:15,430
+الرصاص، الأسطوانة هذه رو constant لو أنا ثبتت فاى و
+
+31
+00:02:15,430 --> 00:02:20,470
+خليتها تروح من zero لـ infinity خلت فاى الـ constant و
+
+32
+00:02:20,470 --> 00:02:22,690
+خلت رو تروح من zero لـ infinity وزد من ناقص 
+
+33
+00:02:22,690 --> 00:02:25,670
+infinity لـ infinity هيعطينا هذا الـ plane هذا ال
+
+34
+00:02:25,670 --> 00:02:32,430
+plane هذا الـ plane هيكون في فاى constant هذا
+
+35
+00:02:32,430 --> 00:02:42,330
+الـ plane في فاى constant  رو 
+
+36
+00:02:42,330 --> 00:02:45,690
+تتحرك من zero لـ infinity وزد من ناقص infinity ل
+
+37
+00:02:45,690 --> 00:02:51,110
+بلس infinity طب لو ثبتنا Z، خلينا Z ثابتة، عند Z 
+
+38
+00:02:51,110 --> 00:02:54,670
+بتساوي constant، هيتولد عندي هذا الـ plane هذا ال
+
+39
+00:02:54,670 --> 00:02:57,270
+plane اللي عنده Z constant، لأن Phi هتتغير من Zero 
+
+40
+00:02:57,270 --> 00:03:01,630
+لـ Two Pi، فهتتغير عندي اللي هي رو من Zero ل
+
+41
+00:03:01,630 --> 00:03:06,550
+Infinity، فعندي بتكون Z constant هو plane موازي XY
+
+42
+00:03:06,550 --> 00:03:08,410
+الـ plane، واضح؟
+
+43
+00:03:13,340 --> 00:03:16,600
+نيجي للـ spherical coordinate نفس الشيء ممكن
+
+44
+00:03:16,600 --> 00:03:18,440
+أحصل على الـ planes اللي هي أنا الـ constant 
+
+45
+00:03:18,440 --> 00:03:21,880
+coordinates والـ coordinates كمان مرة هم الـ R والـ
+
+46
+00:03:21,880 --> 00:03:26,700
+theta والفاي طب عند constant R إيش بيطلع لنا؟ 
+
+47
+00:03:26,700 --> 00:03:31,700
+اللي هي sphere سطح sphere shell تبع الـ sphere عند R 
+
+48
+00:03:31,700 --> 00:03:34,220
+constant هيطلع عندي اللي هو الـ shell لأن فاى ثيتا 
+
+49
+00:03:34,220 --> 00:03:39,180
+بتتغير من zero لـ two π وفاى و ثيتا من zero لـ π فتطلع 
+
+50
+00:03:39,180 --> 00:03:43,630
+عندي اللي هي البالونة أو الـ shell تبع الـ sphere فاى 
+
+51
+00:03:43,630 --> 00:03:49,610
+constant هي فاى constant بتتغير عندي ثيتا من π ل 
+
+52
+00:03:49,610 --> 00:03:53,710
+.. من zero لـ π ثيتا بتتغير وعندي الـ R بتتغير من 
+
+53
+00:03:53,710 --> 00:03:57,250
+zero لـ infinity بينما فاى ثابتة على مكان يحدد هي
+
+54
+00:03:57,250 --> 00:04:01,690
+فاى زاوية فاى اللي عاملة مع الـ X axis فهي constant
+
+55
+00:04:01,690 --> 00:04:05,550
+فاى هذه constant فاى تمام هذا الـ plane is a 
+
+56
+00:04:05,550 --> 00:04:10,260
+constant constant ثيتا هيديني cone constant ثيتا
+
+57
+00:04:10,260 --> 00:04:14,060
+لأن فاى ستة هتبقى بتتحرك من zero لـ two π وR من
+
+58
+00:04:14,060 --> 00:04:17,420
+zero لـ infinity فتعطيني cone رأس الـ cone هي قيمة 
+
+59
+00:04:17,420 --> 00:04:22,740
+ثيتا واضح بتخيلينهم؟ إذا إيه الثيتا هذا الـ cone 
+
+60
+00:04:22,740 --> 00:04:27,920
+احنا كم بدناه؟ هذا عند ثيتا constant أنا الثيتا
+
+61
+00:04:27,920 --> 00:04:32,920
+قيمتها ثابتة بينما فاى هتلف من zero لـ two π
+
+62
+00:04:32,920 --> 00:04:39,400
+فتعطيني مسار الـ cone وطبعا المخروطي يعني اه من zero ل
+
+63
+00:04:39,400 --> 00:04:43,980
+infinity معايا؟ لذا لو طلب مني إن أثبت أحد
+
+64
+00:04:43,980 --> 00:04:46,200
+المتغيرات أو أحد الـ coordinate بدي أعرف أنا وين 
+
+65
+00:04:46,200 --> 00:04:49,520
+بحكي يعني لما أقول إن ثيتا constant بقول هتعطول
+
+66
+00:04:49,520 --> 00:04:53,120
+cone في الـ spherical coordinate المخروطي لو أنا بدي
+
+67
+00:04:53,120 --> 00:04:56,420
+أقول إن فاي constant هقول إن في الـ spherical 
+
+68
+00:04:56,420 --> 00:05:00,580
+coordinate هيكون عندي plane اللي هو بيبتدي مع ال 
+
+69
+00:05:00,580 --> 00:05:04,230
+infinity في الـ r وبتغير من ناقص infinity ل
+
+70
+00:05:04,230 --> 00:05:08,090
+بلس infinity في Z direction وعامل فاى ثابتة مع 
+
+71
+00:05:08,090 --> 00:05:12,610
+الـ X direction وهي الـ shell اللي عند R بتساوي ثابت
+
+72
+00:05:14,680 --> 00:05:18,220
+خلينا نشوف أمثلة ناخذ المثال الأول هي uniform
+
+73
+00:05:18,220 --> 00:05:21,760
+vector field طبعا دول الـ vectors احنا بناخدهم لحد 
+
+74
+00:05:21,760 --> 00:05:24,440
+ثلاثة بشكل عام هم vectors بس دول الـ vectors ممكن
+
+75
+00:05:24,440 --> 00:05:27,520
+يكونوا ما هم الـ fields اللي حكينا عنهم إذا scalar 
+
+76
+00:05:27,520 --> 00:05:29,920
+بيكون scalar field إذا vector بيكونوا vector
+
+77
+00:05:29,920 --> 00:05:33,000
+fields وأنواع مختلفة ممكن تكون الـ electric field و
+
+78
+00:05:33,000 --> 00:05:36,680
+magnetic field ورجع نشوف كل هذا الحكي لما نحكي على
+
+79
+00:05:36,680 --> 00:05:41,050
+الـ fields طب لو احنا كنا عندنا two uniform fields
+
+80
+00:05:41,050 --> 00:05:45,250
+vector fields E اللي هو بدلالة الـ cylindrical
+
+81
+00:05:45,250 --> 00:05:48,210
+coordinate وF برضه بدلالة cylindrical coordinate
+
+82
+00:05:48,210 --> 00:05:52,070
+طالب مني إن أجيب الـ cross product تبع E cross F
+
+83
+00:05:52,070 --> 00:05:54,890
+أول حاجة والحاجة الثانية اللي بتدي الـ vector
+
+84
+00:05:54,890 --> 00:06:01,050
+component of E عند اللي هي Phi خمسة رو خمسة وPhi 
+
+85
+00:06:01,050 --> 00:06:05,230
+π على اتنين وZ تلاتة parallel to the line اللي
+
+86
+00:06:05,230 --> 00:06:10,000
+هو X بتساوي اتنين وZ بتساوي تلاتة كمان بتنتمي لـ 
+
+87
+00:06:10,000 --> 00:06:13,460
+الـ E بيعملها مع الـ surface at Z equal تلاتة عند 
+
+88
+00:06:13,460 --> 00:06:16,540
+النقطة B الـ surface عندي Z equal تلاتة احنا قلنا
+
+89
+00:06:16,540 --> 00:06:18,820
+لما يكون constant أحد الـ coordinate احنا ده
+
+90
+00:06:18,820 --> 00:06:21,840
+cylindrical coordinate Z constant إيش بيكون عند
+
+91
+00:06:21,840 --> 00:06:31,140
+surface طب حد يحده يحل حد حاول يحل تعالوا 
+
+92
+00:06:36,070 --> 00:06:38,930
+أول حاجة احنا بنشوف الـ cross product في ال
+
+93
+00:06:38,930 --> 00:06:42,990
+cylindrical coordinate احنا 
+
+94
+00:06:42,990 --> 00:06:45,350
+قلنا الـ cross product هو determinant وبيتبنا ال
+
+95
+00:06:45,350 --> 00:06:54,630
+magnitude احنا تبعه E cross F احنا 
+
+96
+00:06:54,630 --> 00:06:57,070
+أخدناها مع بعض اللي هي determinant تاعة الـ rho وال
+
+97
+00:06:57,070 --> 00:06:57,890
+فاى والـ Z
+
+98
+00:07:12,690 --> 00:07:16,130
+الكتاب بيحط فوقهم vectors عشان بيزهم يعني أنا
+
+99
+00:07:16,130 --> 00:07:19,030
+بشغلكم إياهم إن أنا كنت هو الكتاب بيحطهم both بس
+
+100
+00:07:19,030 --> 00:07:24,470
+احنا بنحط فوقهم vector إذا عندي E x F بس بجيب اللي
+
+101
+00:07:24,470 --> 00:07:25,230
+هو الـ determinant
+
+102
+00:07:33,290 --> 00:07:36,990
+إيه اللي هي الروهات؟ عشرة أقل ما نص ستة ما نص ما
+
+103
+00:07:36,990 --> 00:07:44,890
+نص ستة زاد ما نص ستة زاد اللي هي π component زاد
+
+104
+00:07:44,890 --> 00:07:51,630
+تلاتين نقص تلاتة سالب 
+
+105
+00:07:51,630 --> 00:07:59,330
+عشرة نقص سالب عشرة ما نص ما نص ما نص ما نص
+
+106
+00:08:14,000 --> 00:08:17,820
+مش مشكلة إيه ستة وستين روحها كاملة؟
+
+107
+00:08:43,200 --> 00:08:49,200
+الأخيرة حاجة هي Z hat -11.11.21 Z hat تمام إذا نطلع 
+
+108
+00:08:49,200 --> 00:08:54,820
+معانا .. برضه أول واحدة تالتة يعني .. فإن هي من
+
+109
+00:08:54,820 --> 00:08:56,320
+الانت من الانت من الانت من الانت من الانت من الانت
+
+110
+00:08:56,320 --> 00:08:57,660
+من الانت من الانت من الانت من الانت من الانت من
+
+111
+00:08:57,660 --> 00:08:57,760
+الانت من الانت من الانت من الانت من الانت من الانت
+
+112
+00:08:57,760 --> 00:09:00,360
+من الانت من الانت من الانت من الانت من الانت من
+
+113
+00:09:00,360 --> 00:09:01,360
+الانت من الانت من الانت من الانت من الانت من الانت
+
+114
+00:09:01,360 --> 00:09:01,680
+من الانت من الانت من الانت من الانت من الانت من
+
+115
+00:09:01,680 --> 00:09:01,760
+الانت من الانت من الانت من الانت من الانت من الانت
+
+116
+00:09:01,760 --> 00:09:04,600
+من الانت من الانت من الانت من الانت من الانت من
+
+117
+00:09:04,600 --> 00:09:09,980
+الانت من الانت من الانت من الانت من الانيعني معناه
+
+118
+00:09:09,980 --> 00:09:14,720
+هتكون الـ component الأولى تربية ثم تربية ثم تربية
+
+119
+00:09:14,720 --> 00:09:16,480
+ثم تربية ثم تربية ثم تربية ثم تربية ثم تربية ثم
+
+120
+00:09:16,480 --> 00:09:17,000
+ثم تربية ثم تربية ثم تربية ثم تربية ثم تربية ثم
+
+121
+00:09:17,000 --> 00:09:17,480
+تربية ثم تربية ثم تربية ثم تربية ثم تربية ثم تربية
+
+122
+00:09:17,480 --> 00:09:17,880
+ثم تربية ثم تربية ثم تربية ثم تربية ثم تربية ثم
+
+123
+00:09:17,880 --> 00:09:19,560
+تربية ثم تربية ثم تربية ثم تربية ثم تربية ثم تربية
+
+124
+00:09:19,560 --> 00:09:32,780
+ثم تربية ثم تربية ثم تربية ثم تربية ثم تربية ثم
+
+125
+00:09:32,780 --> 00:09:33,900
+تربية ثم ت
+
+126
+00:09:43,900 --> 00:09:50,640
+بعض الاختصارات الاختصارات الاختصارات
+
+127
+00:09:50,640 --> 00:09:59,080
+الاختصارات
+
+128
+00:09:59,080 --> 00:10:02,620
+الاختصارات
+
+129
+00:10:02,620 --> 00:10:04,070
+الاختصارات الاختصارات الاختصارات الحاجة التانية إيش
+
+130
+00:10:04,070 --> 00:10:11,570
+الـ Y component بتاعتها؟ قد إيه؟ zero في حتة تانية 
+
+131
+00:10:11,570 --> 00:10:15,930
+إنتوا كلام تاني؟ هذا line خط مين الـ constant في
+
+132
+00:10:15,930 --> 00:10:20,450
+هذا الخط؟ قيمة X وزدهم يعطينا X بالساعة الثانية 
+
+133
+00:10:20,450 --> 00:10:24,290
+وزدهم بالساعة تلاتة مين المتغير؟ الـ Y الـ Y بتروح
+
+134
+00:10:24,290 --> 00:10:27,530
+من ناقص infinity لبلس infinity هذا الـ line لو 
+
+135
+00:10:27,530 --> 00:10:28,470
+أنا حكيت على الـ X
+
+136
+00:10:32,470 --> 00:10:40,230
+X,Y,Z عند قيمة X بتساوي 2 وY بتساوي 3 وعند دي 
+
+137
+00:10:40,230 --> 00:10:43,790
+اللي هو الـ line اللي بيروح من ناقص الـ 20 لبلس 
+
+138
+00:10:43,790 --> 00:10:49,330
+الـ 20 sorry عكست الـ coordinate هذا الـ Z اللي موجود
+
+139
+00:10:49,330 --> 00:10:54,490
+يعني ولاش وليس الـ Y X
+
+140
+00:10:54,490 --> 00:11:05,300
+,X,Y,Z يعني X وZ X 2 وZ 3 هذه الـ coordinate والـ 
+
+141
+00:11:05,300 --> 00:11:08,260
+line هيكون Y بتروح ناقص infinity لبلس infinity
+
+142
+00:11:08,260 --> 00:11:12,780
+هاي الـ line اللي عند النقطة سادة أي نقطة على هذا 
+
+143
+00:11:12,780 --> 00:11:17,300
+الـ line هيكون قيمة X فيها 2 وZ 3 وY بتروح ناقص
+
+144
+00:11:17,300 --> 00:11:24,420
+infinity لبلس infinity في حد بيحاول أنا أحله
+
+145
+00:11:24,420 --> 00:11:29,080
+سواه بسيط
+
+146
+00:11:29,080 --> 00:11:34,600
+أبسط من اللي حلتوه لما إذا هو بده الـ vector
+
+147
+00:11:34,600 --> 00:11:39,080
+component عند الخط هذا الموازي لـ vector component 
+
+148
+00:11:39,080 --> 00:11:41,460
+احنا اشتقينا عن أول حاجة إيش الـ component وإيش الـ
+
+149
+00:11:41,460 --> 00:11:44,360
+vector component الذاكرين إنتوا درسنا هذا إيش الـ 
+
+150
+00:11:44,360 --> 00:11:47,020
+component وإيش الـ vector component الـ component 
+
+151
+00:11:47,020 --> 00:11:51,520
+لأي field في اتجاه معين إيش الـ product بتاعه هذا 
+
+152
+00:11:51,520 --> 00:11:55,100
+scalar عشان أجيب الـ vector بتاعه إيش بنسوي بالـ 
+
+153
+00:11:55,100 --> 00:11:59,300
+unit vector في اتجاه هذا المسار فهو بده الـ vector 
+
+154
+00:11:59,300 --> 00:12:02,720
+component اللي موازية للـ line أنا عند الـ field E
+
+155
+00:12:02,720 --> 00:12:04,980
+إنها component في الـ raw واحدة في الـ phi واحدة في 
+
+156
+00:12:04,980 --> 00:12:07,820
+الـ Z three components وإيه اللي أنا بدي الـ
+
+157
+00:12:07,820 --> 00:12:11,660
+component بتاعته اللي هو على هذا الخط الـ component
+
+158
+00:12:11,660 --> 00:12:14,760
+بتاعته فاحنا قلنا إشي في الـ component مش الـ
+
+159
+00:12:14,760 --> 00:12:18,000
+vector component هي dot الـ product ذاكرين؟ dot الـ
+
+160
+00:12:18,000 --> 00:12:21,160
+product لأي field على مثلا الـ X-axis بيديني الـ 
+
+161
+00:12:21,160 --> 00:12:25,720
+component في الـ X-axis dotted لو عملت الـ E dot مع 
+
+162
+00:12:25,720 --> 00:12:29,210
+الـ X-axis حصلتيني الـ component تجاه الـ X-axis هو
+
+163
+00:12:29,210 --> 00:12:31,810
+بيديني المسار اللي بده إياه وين بده الـ component؟
+
+164
+00:12:31,810 --> 00:12:34,190
+بده الـ component على هذا الـ line مش على زي ما
+
+165
+00:12:34,190 --> 00:12:36,650
+احنا شوفنا الأمثلة السابقة كانت مرة على الـ X axis
+
+166
+00:12:36,650 --> 00:12:38,870
+ومرة على الـ Y axis بس بده إياه على هذا الـ axis
+
+167
+00:12:38,870 --> 00:12:44,280
+الجديد اللي هو الـ line اللي له X بتساوي 2 وZ بتساوي
+
+168
+00:12:44,280 --> 00:12:48,040
+3 عشان أخليه vector وإيش كنا نضربه؟ نضربه هذا اللي 
+
+169
+00:12:48,040 --> 00:12:51,660
+عملناه الـ E dot الـ line اللي بدنا فيه اتجاهه في
+
+170
+00:12:51,660 --> 00:12:54,220
+اتجاه الـ line إيش اتجاه الـ line؟ قلنا الـ vector
+
+171
+00:12:54,220 --> 00:12:57,960
+تبع الـ line على الـ unit vector تبع الـ line فهي
+
+172
+00:12:57,960 --> 00:13:02,760
+مهمة بسيطة هو a Y Y hat الـ line تبعنا إيش اتجاهه
+
+173
+00:13:02,760 --> 00:13:07,300
+مش تجاه Y hat احنا
+
+174
+00:13:07,300 --> 00:13:11,090
+تعرفنا على هذا الـ line الـ Y أماله موازي للـ Y إذا 
+
+175
+00:13:11,090 --> 00:13:15,450
+اتجاهه هو Y hat وعشان أعرف الـ component تبع الـ 
+
+176
+00:13:15,450 --> 00:13:18,510
+field في اتجاه هذا الـ line، برضه لو ده بعرف إن أنا
+
+177
+00:13:18,510 --> 00:13:21,8
+
+201
+00:14:34,190 --> 00:14:38,590
+مع بعض إذا كان عندي ال line X بيساوي اثنين و Z ثلاثة
+
+202
+00:14:38,590 --> 00:14:42,130
+هو parallel Y axis هو بيحصل لكم لما يكون اثنين
+
+203
+00:14:42,130 --> 00:14:44,830
+constant في ال space هيكون line
+
+204
+00:14:47,620 --> 00:14:53,060
+لكن لو واحدة constant إيش هيكون؟ ال plane ممتازة
+
+205
+00:14:53,060 --> 00:14:56,440
+يعني إذا كانوا اثنين constant هيكون line أكيد لكن
+
+206
+00:14:56,440 --> 00:14:58,740
+لو واحدة منهم constant coordinates زي المثال اللي
+
+207
+00:14:58,740 --> 00:15:04,080
+شفناها قبل قليل هيكون ال plane عشان أجيب ال E في
+
+208
+00:15:04,080 --> 00:15:07,820
+اتجاه اللي هو ال line اللي وصفناه هيكون E dot A
+
+209
+00:15:07,820 --> 00:15:12,380
+hat في A hat و بتعود عنه في النقطة فيه عند النقطة
+
+210
+00:15:12,380 --> 00:15:15,780
+B إيش ال A y hat A y hat هو طبعا لأن النقطة عندي
+
+211
+00:15:15,780 --> 00:15:19,980
+كله ال field بال raw فائزت بينما ال A y hat ما لها
+
+212
+00:15:20,560 --> 00:15:24,260
+كارتيزيان كوردينت فأول خطوة بتعملها أن أكتب ال a y
+
+213
+00:15:24,260 --> 00:15:27,280
+hat بدلالة ال cylindrical coordinate وهذا شوفناه
+
+214
+00:15:27,280 --> 00:15:30,860
+أعلمكم كيف حتى تجيبوه متذكرين هيكون sin phi rho
+
+215
+00:15:30,860 --> 00:15:34,240
+hat هيكون sin phi phi hat بعود عن phi باي على 
+
+216
+00:15:34,240 --> 00:15:39,100
+اثنين هيطلع معايا أن a y hat بتساوي a rho hat في
+
+217
+00:15:39,100 --> 00:15:44,400
+هذه الحلقة لأن باي على اثنين قد إيش قيمتها باي على اثنين
+
+218
+00:15:44,400 --> 00:15:46,540
+تسعين فإيش أكيد أنه هيكون بالتمام
+
+219
+00:15:50,990 --> 00:15:59,050
+فاي فاي على اثنين و فاي مين هي الزاوية فاي مين هي
+
+220
+00:15:59,050 --> 00:16:04,450
+الزاوية ما بين ال X-axis و ال Y-axis لما تكون فاي 
+
+221
+00:16:04,450 --> 00:16:07,470
+باي على اثنين أكيد تكون الطبق من ال Z-axis مين هي
+
+222
+00:16:07,470 --> 00:16:11,390
+فاي على اثنين فأكيد هيكون ال row فاي في اتجاه ال Z
+
+223
+00:16:11,390 --> 00:16:19,180
+يعني إحنا ال row hat وهي الفلما تكون في بتساوي باي
+
+224
+00:16:19,180 --> 00:16:23,260
+على اثنين الرو hat بتنطبق بالتمام على ال Y hat عرفنا
+
+225
+00:16:23,260 --> 00:16:27,160
+ليش انطبق ال Y hat على ال rho hat و ال rho hat في أي مكان
+
+226
+00:16:27,160 --> 00:16:31,420
+في ال cylindrical coordinate هي في بتغير من zero ل
+
+227
+00:16:31,420 --> 00:16:34,940
+two pi لما في تكون بالتمام باي على اثنين هتكون
+
+228
+00:16:34,940 --> 00:16:38,940
+ال rho hat بتساوي Y hat لما تكون في zero ال rho hat بتساوي
+
+229
+00:16:38,940 --> 00:16:45,520
+X hat معين؟لما تكون الـPhi 0 هيكون الـRowها منطبقة
+
+230
+00:16:45,520 --> 00:16:49,200
+على الـX Axis لما تكون Phi Pi على 2 هتكون الـRow
+
+231
+00:16:49,200 --> 00:16:53,440
+منطبقة بالتمام على الـY Axis ففي هذه الحالة لأن
+
+232
+00:16:53,440 --> 00:16:56,300
+Phi عندي Pi على 2 هلاقي أن الـY hat منطبقة على
+
+233
+00:16:56,300 --> 00:17:02,800
+الـRow hat Ay hat سين الـPhi Row hat زي الـCos Phi
+
+234
+00:17:02,800 --> 00:17:05,620
+Phi hat هذا إحنا شوفناه مع بعض كيف أنتقل من
+
+235
+00:17:05,620 --> 00:17:11,340
+الـCylindrical لالـCartesian ألاحظ أن ال a y hat هي
+
+236
+00:17:11,340 --> 00:17:19,940
+يتنطبق
+
+237
+00:17:19,940 --> 00:17:21,180
+على ال y hat
+
+238
+00:17:24,810 --> 00:17:28,470
+Y hat أو Y hat في Y hat وقلنا ليش نضربها في Y hat
+
+239
+00:17:28,470 --> 00:17:31,430
+عشان هو بده ال vector component مش ال component
+
+240
+00:17:31,430 --> 00:17:35,190
+بده ال vector component E dot row hat في row hat
+
+241
+00:17:35,190 --> 00:17:40,130
+فإذا بتدرج على E و أعملها dot مع ال row hat هال E
+
+242
+00:17:40,130 --> 00:17:42,950
+عندي، عندي واحدة في ال row hat اللي هي minus خمسة
+
+243
+00:17:42,950 --> 00:17:46,090
+و هدول هيكونوا zero لإن بعملها dot مع ال row hat
+
+244
+00:17:48,910 --> 00:17:53,250
+فإذا e dot rho hat اللي هي minus خمسة واتجاهها في
+
+245
+00:17:53,250 --> 00:17:56,070
+اتجاه ال rho hat سبعة فيه من الاتجاه لأنه في اتجاه ال
+
+246
+00:17:56,070 --> 00:17:59,630
+Y hat هو نفسه اتجاه ال rho hat في هذه الحالة الخاصة
+
+247
+00:17:59,630 --> 00:18:04,210
+المطلوب عند نقطة اللي اللي لها ال rho خمسة و Phi Pi
+
+248
+00:18:04,210 --> 00:18:08,130
+على اثنين ففي هذه الحالة هيطبق ال Y hat مع ال rho hat
+
+249
+00:18:08,130 --> 00:18:12,470
+طبعا في طالب إيش كمان
+
+250
+00:18:15,420 --> 00:18:18,580
+الزاوية اللي بيعملها ال field مع ال surface z
+
+251
+00:18:18,580 --> 00:18:22,360
+equal ثلاثة عند النقطة بي يعني أن النقطة بي هذه
+
+252
+00:18:22,360 --> 00:18:26,420
+أنا ثبتت ال z حلتها ثلاثة فصار عندي عند النقطة بي
+
+253
+00:18:26,420 --> 00:18:30,900
+فيه surface z constant معايا إذا هذا ال surface
+
+254
+00:18:30,900 --> 00:18:35,800
+اللي عند z equal ثلاثة اللي عند النقطة five و five
+
+255
+00:18:35,800 --> 00:18:39,680
+على اثنين و ثلاثة سبت الـ z فصار عندي ال surface
+
+256
+00:18:39,680 --> 00:18:43,180
+بيساوي ثلاثة بينما في بتروح من zero to pi أو z
+
+257
+00:18:43,180 --> 00:18:46,900
+minus أنك أنت بتروح من zero ل infinity هذا ال
+
+258
+00:18:46,900 --> 00:18:52,480
+surface عند ال z بتساوي ثلاثة إيش بده الزاوية اللي
+
+259
+00:18:52,480 --> 00:18:57,440
+بيعملها ال field عند هذا ال surface إذا رجعنا ل
+
+260
+00:18:57,440 --> 00:19:00,340
+ال cylindrical coordinate هاي ال surface اللي z
+
+261
+00:19:00,340 --> 00:19:04,940
+فيه constant معايا؟ إيش العمودي عليها هذا الذت؟
+
+262
+00:19:04,940 --> 00:19:10,360
+النورم عليها هذا الذت؟ مين هيكون؟النورم اللي عمودي
+
+263
+00:19:10,360 --> 00:19:16,360
+عليه هذا اتجاه XY صح؟ Z ثابتة لو بتعمل عمودي عليه
+
+264
+00:19:16,360 --> 00:19:21,440
+إيش بيكون اتجاه العمودي عليه؟ Z hat ممتاز إذا
+
+265
+00:19:21,440 --> 00:19:24,460
+العمودي عليه Z hat أنا عندي field موجود في ال
+
+266
+00:19:24,460 --> 00:19:27,680
+space و بدي الزاوية بين هذا ال field و ال z axis و
+
+267
+00:19:27,680 --> 00:19:33,120
+ال plane هذا مش أسهل أعمل الزاوية اللي ما بين ال
+
+268
+00:19:33,120 --> 00:19:36,400
+field و ال z axis و الزاوية اللي طالبها اللي ما بين
+
+269
+00:19:36,400 --> 00:19:40,120
+ال field و اللي ما بين إيش هتكون مكملة إذا بدأ أرجع
+
+270
+00:19:40,120 --> 00:19:42,420
+أتذكر إيش هو ال plane هذا اللي عنده z بتساوي
+
+271
+00:19:42,420 --> 00:19:47,540
+constant هو ال z الموازي لل xy plane معناه إنه أي
+
+272
+00:19:47,540 --> 00:19:52,020
+نوع ما عليها بده يكون في اتجاه ال z axis بالتالي
+
+273
+00:19:52,020 --> 00:19:56,820
+هو طالب مني أجيب الزاوية اللي بين ال field هذا E و
+
+274
+00:19:56,820 --> 00:20:01,740
+ال surface و ال surface هذا فعشان أجيب الزاوية بين
+
+275
+00:20:01,740 --> 00:20:04,500
+a و ال surface أنا عارفة أن هذا ال surface هيكون
+
+276
+00:20:04,500 --> 00:20:07,360
+العمودي عليها يعني اللي هو z hat فبجيب أولا
+
+277
+00:20:07,360 --> 00:20:12,520
+الزاوية بين ال field و ال z hat و بعدين إيش بسوي
+
+278
+00:20:12,520 --> 00:20:16,160
+باخد المكملة يعني هذا اللي هو z طبعا plane أنا ممكن
+
+279
+00:20:16,160 --> 00:20:25,380
+عشان أجيب زاوية عشان
+
+280
+00:20:25,380 --> 00:20:29,570
+إحنا نجيب زاوية بين field و planetجيب الزاوية اللي
+
+281
+00:20:29,570 --> 00:20:33,390
+وحط على ال plane هينا على الزاوية هينا من هذه
+
+282
+00:20:33,390 --> 00:20:42,970
+الزاوية سميها theta E و z بتساوي ثلاثة high ما
+
+283
+00:20:42,970 --> 00:20:50,550
+بين ال acre field و ال 1 z بتساوي ثلاثة قبل ما قصدنا
+
+284
+00:20:50,550 --> 00:20:52,550
+سميها ثلاثة كمية درجة سنة
+
+285
+00:20:56,030 --> 00:21:00,450
+هذه الزاوية عشان نعرف هذه الزاوية أسهلنا لأن أنا
+
+286
+00:21:00,450 --> 00:21:04,330
+بدي أجيب هذا ال vector بدل ما أجيب هذا ال vector و
+
+287
+00:21:04,330 --> 00:21:07,850
+أنا عارفة أن ال norm على هذا ال plane هو مين ال Z
+
+288
+00:21:07,850 --> 00:21:11,770
+hat لأن ال vector العمود على ال plane هو Z hat
+
+289
+00:21:11,770 --> 00:21:15,950
+فإذا جيبت الزاوية اللي ما بين ال field و ال norm
+
+290
+00:21:15,950 --> 00:21:19,410
+بقدر أجيب الزاوية اللي بين ال field و ال plane
+
+291
+00:21:19,410 --> 00:21:23,270
+لأن الزاوية هتكون مكملة للزاوية اللي بين ال field
+
+292
+00:21:23,270 --> 00:21:27,660
+و العمودي هذا اللي عملنا اي دوت زت هات إيش هي عبارة
+
+293
+00:21:27,660 --> 00:21:31,400
+عن مجموعة تبع ال field في مجموعة زت هات هو واحد
+
+294
+00:21:31,400 --> 00:21:34,700
+ال components المكونة اللي ساوية بينهم هو سميها zeta a
+
+295
+00:21:34,700 --> 00:21:42,260
+z اللي هو أضع قيمة اي اللي هي جزر التربية ل 134 و
+
+296
+00:21:42,260 --> 00:21:47,240
+ال dot product للإي و زت إذا رجعنا لل field اي dot
+
+297
+00:21:47,240 --> 00:21:53,360
+مع زت هات three component لل field اللي هو minus
+
+298
+00:21:53,360 --> 00:21:53,840
+five
+
+299
+00:21:56,500 --> 00:22:00,300
+الـ dot مع الـ z hat هيعطيني ثلاثة إذا عندي
+
+300
+00:22:00,300 --> 00:22:00,920
+ثلاثة
+
+301
+00:22:04,550 --> 00:22:08,610
+ثلاثة بتساوي المجنتو التبع ال field اللي هي جزر
+
+302
+00:22:08,610 --> 00:22:14,150
+تربيعي لإي رو تربيع زد إي في تربيع زد إي ز تربيع
+
+303
+00:22:14,150 --> 00:22:17,870
+بتطلع جزر تربيع لمية وأربعة وثلاثين في ال cosine
+
+304
+00:22:17,870 --> 00:22:22,450
+الزاوية اللي بين ال vector و ال z component و z
+
+305
+00:22:22,450 --> 00:22:26,370
+hat بجيب ال z hat بالتالي الزاوية بين ال field و
+
+306
+00:22:26,370 --> 00:22:30,690
+ال surface هتكون تسعين ناقص الزاوية واضح؟
+
+307
+00:22:34,250 --> 00:22:39,470
+بتوقف من هنا ونيجي لل lecture جديدة بتاعة اليوم
+
+308
+00:22:39,470 --> 00:22:45,190
+فيها استفتار بدي أكوا تحلوه تتسيروا يعني تعرفين
+
+309
+00:22:45,190 --> 00:22:48,530
+عليهم يعني تتعودوا عليهم الشيء مش جديد عليكم أنتو
+
+310
+00:22:48,530 --> 00:22:51,570
+حد حكيتولكم ال vector field مش جديد علينا أو ال
+
+311
+00:22:51,570 --> 00:22:54,750
+vector الأساس لكن الجديد أنه التعامل مع ال fields
+
+312
+00:22:54,750 --> 00:22:58,690
+نفهم كيف نتعامل مع ال fields في وجود ال vector
+
+313
+00:22:58,690 --> 00:23:02,550
+كالقلص فبدي أكوا تدرس أول بأول معايا أول بأول
+
+314
+00:23:02,550 --> 00:23:07,730
+انتوا؟ هلقيت إنّي هأجل ال vector calculus
+
+315
+00:23:07,730 --> 00:23:10,630
+differentiation and integration لحد اللي إحنا
+
+316
+00:23:10,630 --> 00:23:14,610
+ما شفناش لا تفاضل ولا تكامل شفنا جميع شفنا
+
+317
+00:23:14,610 --> 00:23:18,610
+cross product و dot product شفنا طرح لكن ما شفناش ال
+
+318
+00:23:18,610 --> 00:23:22,030
+differentiation ولا ال integration هتكمل ال
+
+319
+00:23:22,030 --> 00:23:24,890
+differentiation و ال integration هنشوف إيش معناه
+
+320
+00:23:24,890 --> 00:23:27,550
+هذا الحكي يعني معناه هشوف أنا ال differential
+
+321
+00:23:27,550 --> 00:23:29,470
+links هي المقصود فيها
+
+322
+00:23:42,860 --> 00:23:47,220
+هنشوف ال differential links هنشوف المساحة و نشوف
+
+323
+00:23:47,220 --> 00:23:50,600
+ال volume نبدأ بال Cartesian coordinate لأن هو ال
+
+324
+00:23:50,600 --> 00:23:52,820
+coordinate اللي إحنا بتعودنا عليه هنروح ل ال
+
+325
+00:23:52,820 --> 00:23:54,720
+cylindrical coordinate و بعدين هنروح ل ال
+
+326
+00:23:54,720 --> 00:23:57,520
+spherical coordinate أنتو كان مطلوب منكم تسكين
+
+327
+00:23:57,520 --> 00:24:04,980
+صحيح آه؟ وحاليا أنا عملتلكم this book group آه؟
+
+328
+00:24:04,980 --> 00:24:08,600
+ما انضمتيش؟ اليوم بعد المحاضرة لازم كلكم تنضموا
+
+329
+00:24:08,600 --> 00:24:08,940
+فيها
+
+330
+00:24:24,120 --> 00:24:27,920
+مش مقصود في الـ differential links إحنا بنحكي أول
+
+331
+00:24:27,920 --> 00:24:30,080
+حاجة عن ال differential links إيش المقصود في ال
+
+332
+00:24:30,080 --> 00:24:32,640
+differential links المقصود في ال differential
+
+333
+00:24:32,640 --> 00:24:36,460
+links اللي هو جزء صغير في ال space تبعنا
+
+334
+00:24:36,460 --> 00:24:39,610
+differential يعني جزء يعني لو نحكي على Cartesian
+
+335
+00:24:39,610 --> 00:24:43,790
+coordinates إن dx, y, z هاي نقطة في ال space مثلا
+
+336
+00:24:43,790 --> 00:24:49,030
+بي لها x coordinates و y coordinates و z coordinates لو
+
+337
+00:24:49,030 --> 00:24:52,690
+طبعا هذا المكعب اللي في ال space هذا المكعب في ال
+
+338
+00:24:52,690 --> 00:24:55,610
+space جزء من ال space ال space إن x بتروح minus
+
+339
+00:24:55,610 --> 00:24:58,530
+infinity ل plus infinity و y بتروح minus infinity
+
+340
+00:24:58,530 --> 00:25:00,830
+ل plus infinity و z بال minus infinity ل plus
+
+341
+00:25:00,830 --> 00:25:04,850
+infinity هذا المكعب هو جزء من ال space مربع صغير
+
+342
+00:25:04,850 --> 00:25:09,510
+مكعب قاعد في ال space اللي طول كل ضلع من أضلاعه هو
+
+343
+00:25:09,510 --> 00:25:12,790
+delta من ال space فهذه ال differential matrix إذا
+
+344
+00:25:12,790 --> 00:25:17,230
+طلعتوا عليه هاي الموازي ل X axis اللي هو زي DS وCR
+
+345
+00:25:17,230 --> 00:25:23,170
+هدول طولهم DX الموازين ل Z axis اللي هي زي QR و
+
+346
+00:25:23,170 --> 00:25:29,950
+BC و AD و DS هدول طولهم DZ جزء fraction من ال
+
+347
+00:25:29,950 --> 00:25:34,910
+space جزء من الـ z component و الموازين لل y اللي
+
+348
+00:25:34,910 --> 00:25:41,280
+هم زي a,b و b,q و d,c و s,r طولهم dy إذاً في الـ
+
+349
+00:25:41,280 --> 00:25:44,800
+Cartesian coordinate هيكون لو أنا عند ال space X
+
+350
+00:25:44,800 --> 00:25:48,260
+بروح minus infinity ل plus infinity جزء على هذا ال
+
+351
+00:25:48,260 --> 00:25:52,100
+line هيكون ماله DX لو عند ال Y بروح minus infinity
+
+352
+00:25:52,100 --> 00:25:56,780
+ل plus infinity عين عليه إيش هتكون DY ال Z بروح
+
+353
+00:25:56,780 --> 00:25:59,880
+minus infinity ل plus infinity عين عليه هتكون DZ
+
+354
+00:25:59,880 --> 00:26:06,020
+إذا ال differential X هو DX X hat DY Y hat DZ Z
+
+355
+00:26:06,020 --> 00:26:06,400
+hat
+
+356
+00:26:10,940 --> 00:26:16,080
+لذا عندي DL الـ differential displacement طبعا DL
+
+357
+00:26:16,080 --> 00:26:18,940
+إيش هي؟ displacement ليش هي displacement؟ لأن أنا
+
+358
+00:26:18,940 --> 00:26:21,040
+بروح من نقطة لنقطة عشان هيك بيصير عندي
+
+359
+00:26:21,040 --> 00:26:23,920
+differential links لو أنا عند نقطة سابت أبدا سابت
+
+360
+00:26:23,920 --> 00:26:27,200
+لو كنت على ال X-axis و كنت عند هذه النقطة و تحركت
+
+361
+00:26:27,200 --> 00:26:30,860
+لهذه النقطة مش هيصير عندي Delta X لو أنا على Y
+
+362
+00:26:30,860 --> 00:26:33,160
+-axis و تحركت من هذه النقطة لهذه النقطة مش هيصير
+
+363
+00:26:33,160 --> 00:26:37,220
+عندي Delta Y لو أنا على Z-axis و تحركت Delta Z
+
+364
+00:26:38,050 --> 00:26:46,010
+عشان هي اسمها displacement دلتا ال هي
+
+365
+00:26:46,010 --> 00:26:53,310
+عبارة عن دي اكس دي اكس اكس هات دي واي واي هات دي زي زي
+
+366
+00:26:53,310 --> 00:26:56,170
+هات وهي دلتا ال اللي هتكون تمام زي ما عملنا ال
+
+367
+00:26:56,170 --> 00:26:59,790
+displacement الحقيقية بين نقطتين بس عادي بين
+
+368
+00:26:59,790 --> 00:27:03,050
+differentiation يعني جزء صغير في ال space
+
+369
+00:27:10,060 --> 00:27:13,240
+للقم نحكي على differential surface إذا إحنا شفنا
+
+370
+00:27:13,240 --> 00:27:16,760
+displacement .. differential displacement اللي هي
+
+371
+00:27:16,760 --> 00:27:21,460
+dx, x hat, dy, y hat, dz, z hat ال plane أو ال
+
+372
+00:27:21,460 --> 00:27:25,940
+surface بتغير في coordinate ف أنا بحكي على ال surface
+
+373
+00:27:25,940 --> 00:27:31,160
+عدي مثلا أنا هذا ال surface فيه كان تغير في ال z
+
+374
+00:27:31,160 --> 00:27:34,840
+direction و ال y direction هذا ال plane إيش اللي
+
+375
+00:27:34,840 --> 00:27:37,500
+هيكون العمود عليه زي ال surface اللي توجفناه ال x
+
+376
+00:27:37,500 --> 00:27:40,760
+hat دائما إحنا بناخد لو هذا ال surface جزء من
+
+377
+00:27:40,760 --> 00:27:45,570
+volume بناخد ال norm برا ال volume يعني لو أنا عندي
+
+378
+00:27:45,570 --> 00:27:51,450
+هذا الجزء من .. من مكعبة مكعب هدول من المكعب
+
+401
+00:29:32,980 --> 00:29:35,240
+differential links ال differential links اللي هو
+
+402
+00:29:35,240 --> 00:29:35,700
+dx
+
+403
+00:30:02,700 --> 00:30:04,100
+DxDyDyDyDyDyDyDyDyDyDyDyDyDyDyDyDyDyDyDyDyDyDyDyDyDyDyDyDyDyDyDyDyDyDy
+
+404
+00:30:05,490 --> 00:30:10,090
+الشكل العام للـ DS هي عبارة عن لها magnitude و
+
+405
+00:30:10,090 --> 00:30:14,730
+اتجاه عمودي عليها non vector اللي هي الاتجاه تبعها
+
+406
+00:30:14,730 --> 00:30:16,930
+دايما عمودي على الـ surface يعني إذا بحكي على الـ
+
+407
+00:30:16,930 --> 00:30:20,270
+surface هو الطاولة تعطي اتجاهها اللي هو العمودي 
+408
+00:30:20,270 --> 00:30:22,070
+عليها تمام؟
+
+409
+00:30:32,610 --> 00:30:34,810
+Differential volume عشان نحكي عن الـ differential
+
+410
+00:30:34,810 --> 00:30:37,990
+volume أكيد هتكون بيتغير في الثلاث اتجاهات هتعطيني 
+
+411
+00:30:37,990 --> 00:30:43,310
+في الـ coordinate cube DXDYDZ هتعطيني حجم بكوب
+
+412
+00:30:43,310 --> 00:30:48,170
+بينما الـ area هتكون surface لأحد أو جهة الكيوب
+
+413
+00:30:48,170 --> 00:30:57,990
+يعني إذا رجعنا لكيوب المرسوم هنا هذا
+
+414
+00:30:57,990 --> 00:31:03,450
+الكيوب احنا هذا differential surface مثلا هذا الـ
+
+415
+00:31:03,450 --> 00:31:06,670
+differential surface دي اكس دي واي هذا بالنسبة لنا
+
+416
+00:31:06,670 --> 00:31:10,270
+هيكون دي واي دي زت وكذا كل واحد من هدول الـ
+
+417
+00:31:10,270 --> 00:31:13,510
+surfaces ماله differential surface هذا اتجاهه ايش
+
+418
+00:31:13,510 --> 00:31:19,410
+هيكون مثلا اللي هو a,b,c,d,x hat نجلأ الـ line هذا
+
+419
+00:31:19,410 --> 00:31:24,790
+الجزء اللي هو PQ هذا الـ differential line دي واي
+
+420
+00:31:25,580 --> 00:31:29,200
+هذا qr differential line لكن كله على بعض اللي هو
+
+421
+00:31:29,200 --> 00:31:33,240
+بي كيو بي اي دي دي دي دي دي دي دي دي دي دي دي دي
+
+422
+00:31:33,240 --> 00:31:37,720
+دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي
+
+423
+00:31:37,720 --> 00:31:45,240
+دي دي دي
+
+424
+00:31:47,500 --> 00:31:50,200
+هذا السبب نعرفين إيش هو differential lengths و
+
+425
+00:31:50,200 --> 00:31:53,460
+differential area و الـ area دايما إلها نور يعني
+
+426
+00:31:53,460 --> 00:31:57,720
+اتجاهها عمودي عليها اتجاه تبعها دايما عمودي عليها و
+
+427
+00:31:57,720 --> 00:32:00,440
+عندي الـ differential volume لو حاصل ضرب بثلاثة 
+
+428
+00:32:00,440 --> 00:32:04,630
+coordinateحاجة مهمة كتير نلاحظها إن دي ال مالها
+
+429
+00:32:04,630 --> 00:32:08,370
+احنا كتبناها دي ال مثلا دي displacement دي XX hat
+
+430
+00:32:08,370 --> 00:32:11,690
+دي YY hat، دي ZZ hat displacement في الـ Cartesian
+
+431
+00:32:11,690 --> 00:32:15,130
+coordinate و دي S قلنا دي S magnitude و N hat،
+
+432
+00:32:15,130 --> 00:32:18,770
+N hat عمودي على الـplane تبع الـsurface بينما الـ
+
+433
+00:32:18,770 --> 00:32:23,250
+volume ماله scalar، إذا الـ displacement vector الـ
+
+434
+00:32:23,250 --> 00:32:26,930
+surface vector بينما الـ volume scalar، الـ volume
+
+435
+00:32:26,930 --> 00:32:29,050
+هو DX DY DZ
+
+436
+00:32:33,610 --> 00:32:36,410
+النقطة اللي في الـ space أو الجزء من الـ space هذا
+
+437
+00:32:36,410 --> 00:32:40,550
+هيك بيكون شكله بيكون شكله بهذا الشكل لو أخدت قطعة
+
+438
+00:32:40,550 --> 00:32:43,570
+من الـ cylinder هيكون شكلها بهذا الشكل هيكون هنا
+
+439
+00:32:43,570 --> 00:32:49,650
+ماله أعراض من هنا قطعة شريحة زي هيك لو أنا طلعت
+
+440
+00:32:49,650 --> 00:32:53,390
+عليها جزئية من أسئلة B فإيش هيكون في عندي تغير في
+
+441
+00:32:53,390 --> 00:32:58,430
+تجاه مين الـ raw؟ بس احد اللي هي هنا هذا القطع القطع
+
+442
+00:32:58,430 --> 00:33:03,250
+من الـ السليندر Z عنده ثابتة نقطة في الاسم Z ثابتة و
+
+443
+00:33:03,250 --> 00:33:07,890
+Phi ثابتة وهي قيمة رو مثلا خمسة من أصله بيه ايش هو
+
+444
+00:33:07,890 --> 00:33:13,290
+تغير في رو دلتا رو هتكون دي رو نفس الشيء لـ دي ايه
+
+445
+00:33:13,290 --> 00:33:20,270
+هتكون دي رو RQ دي رو PCP
+
+446
+00:33:20,270 --> 00:33:24,610
+هادي برضه دي رو تمام إذا نهاي جزئية
+
+447
+00:33:28,870 --> 00:33:35,830
+الصغيرة هي الأجزاء هي تغير في دي رو وهي رو وهي دي
+
+448
+00:33:35,830 --> 00:33:39,450
+رو هنا الساوية والزاوية ثابتة على واحد مثلا نفس
+
+449
+00:33:39,450 --> 00:33:45,670
+الأشهر هي دي رو لا ثابت مثلا على قائتين صحيح؟ إذا
+
+450
+00:33:45,670 --> 00:33:50,330
+ما فيه أحدين تغير في رو هنا وهنا وهذا دي رو وهذا
+
+451
+00:33:50,330 --> 00:33:56,570
+دي رو طب نيجي نحكي على إيه شعب الزواياهذا كانت فاي
+
+452
+00:33:56,570 --> 00:34:03,610
+واحد وأنا صارت فاتنين هذا كم يكون دي فاي هذا
+
+453
+00:34:03,610 --> 00:34:11,350
+كله طول ثابت مقطع رو هذا بيساوي هذا صح معين هذا
+
+454
+00:34:11,350 --> 00:34:15,730
+جزئية رو وهذا رو هذا زاوية فاي واحد وهذا زاوية
+
+455
+00:34:15,730 --> 00:34:19,230
+فاتنين بينهم كم يكون دي فاي لماذا هذا القصر مقابل
+
+456
+00:34:19,230 --> 00:34:23,350
+اللي هو كم يكون رو دي فاي لأنه مقابل أي زاوية لدي
+
+457
+00:34:23,350 --> 00:34:32,580
+فايهذه الجزئية وهذه الجزئية دي فاي ليش سميتها دي
+
+458
+00:34:32,580 --> 00:34:37,020
+فاي لأن هذه الزاوية فاي واحد وهذه الزاوية فاي اثنين
+
+459
+00:34:37,020 --> 00:34:44,760
+معايا إذا فاي اثنين وفاي واحد هي دي فاي والقص لقبل
+
+460
+00:34:44,760 --> 00:34:50,660
+أي زاوية متذكرين على الدائرة أنتم؟
+
+461
+00:34:50,660 --> 00:34:56,510
+هذه زاوية ستا وهذا R ايش كنتوا تسموا هذا معاك؟ طول
+
+462
+00:34:56,510 --> 00:35:00,830
+القوس طول القوس نفس الشيء من هنا هنا عندي row و
+
+463
+00:35:00,830 --> 00:35:05,370
+هنا D5 أشهر
+
+464
+00:35:05,370 --> 00:35:10,370
+الحكم row D5 إذا إن احنا فرقنا على هيئها D row
+
+465
+00:35:10,370 --> 00:35:19,850
+وهدول أمامهم row D5 هذي أشهر تكون row plus D row
+
+466
+00:35:19,850 --> 00:35:23,490
+D5 لأن الطول حيسير
+
+467
+00:35:27,210 --> 00:35:31,710
+بشكل عام نسمي هذا الطول هو رو، هذا القوس هو عبارة
+
+468
+00:35:31,710 --> 00:35:38,190
+عن رو دي فاية، طب مش كمان؟ هذه جزئية منها D زت،
+
+469
+00:35:38,190 --> 00:35:43,570
+انتقلت من زت نقطة معينة لزقة نقطة معينة، إذا هدول
+
+470
+00:35:43,570 --> 00:35:47,350
+الـ differential links في الـ cylindrical coordinate
+
+471
+00:35:47,950 --> 00:36:00,370
+هذا هو رو دي فار وهذا هو دي رو وهذا هو دي زد دي
+
+472
+00:36:00,370 --> 00:36:13,130
+الوضع دي الوضع دي الوضع
+
+473
+00:36:13,130 --> 00:36:17,010
+دي الوضع دي الوضع دي الوضع دي الوضع دي الوضع دي
+
+474
+00:36:17,010 --> 00:36:17,270
+الوضع دي الوضع دي الوضع دي ال
+
+475
+00:36:20,490 --> 00:36:24,210
+هذا الاتجاه اللي هو رو هات والعمود اللي عليها فأنا
+
+476
+00:36:24,210 --> 00:36:28,270
+على المنصة اللي بتقرا من هو فاي هات فالتغير عندي
+
+477
+00:36:28,270 --> 00:36:32,250
+لإن فاي بتروح من zero لكو فاي هيكون في اتجاه الـ دي
+
+478
+00:36:32,250 --> 00:36:34,870
+فاي هات الـ دي فاي هيكون في اتجاه الـ دي فاي هات ده ال
+
+479
+00:36:34,870 --> 00:36:40,950
+close to الدي رو دي فاي واتجاه الـ دي فاي هات معين؟
+
+480
+00:36:41,410 --> 00:36:46,110
+بظلمين اللي هو الـ z فعندي dz z hat إذا عندي فيه
+
+481
+00:36:46,110 --> 00:36:48,550
+تغير في تجاه الـ raw بـ raw differential
+
+482
+00:36:48,550 --> 00:36:53,470
+displacement رو هات القوس هيكون رو دي فاي فاي هات
+
+483
+00:36:53,470 --> 00:36:58,170
+وبعدين اللي هو في تجاه الـ z axis اللي هو dz z hat
+
+484
+00:36:58,170 --> 00:37:02,130
+فإنهي
+
+485
+00:37:02,130 --> 00:37:05,210
+الـ displacement الـ differential displacement في الـ
+
+486
+00:37:05,210 --> 00:37:10,250
+cylindrical coordinateبنجي لها الـ area الـ area
+
+487
+00:37:10,250 --> 00:37:13,090
+هتكون حاصل ضرب اثنين من هدول الـ surface اللي
+
+488
+00:37:13,090 --> 00:37:15,670
+احنا شوفناهم يعني اثنين من الـ coordinates يعني لو
+
+489
+00:37:15,670 --> 00:37:18,790
+أنا بحكي على هذا الـ area على هذا الـ surface أو
+
+490
+00:37:18,790 --> 00:37:21,690
+بحكي على هذا الـ surface أو بحكي على هذا الـ surface
+
+491
+00:37:21,690 --> 00:37:25,510
+صحيح؟ ايه الـ surfaces الثلاث؟ يعني مثلا بحكي على
+
+492
+00:37:25,510 --> 00:37:28,570
+هذا الـ surface ايش هيكون اللي عندي؟ هذا dz اللي هو
+
+493
+00:37:28,570 --> 00:37:33,460
+مثلا pq dzو QP اللي هو ماله رو دي فاي اللي هو
+
+494
+00:37:33,460 --> 00:37:38,660
+القوس فالـ area هي ايش هتكون دي زد رو دي فاي رو دي
+
+495
+00:37:38,660 --> 00:37:42,680
+فاي دي زد هذه الـ area لو احنا بنحكي عن هال area
+
+496
+00:37:42,680 --> 00:37:49,660
+اللي هنا اللي هي SPQR مش فيه متغيرات فيها دي رو و
+
+497
+00:37:49,660 --> 00:37:54,700
+دي زد فهي ثابتة فعرف هذا اتجاه ما هو ثابتة
+
+498
+00:37:57,740 --> 00:38:02,340
+بنفس الزاوية دي five في فانها الرومة بس دائرة
+
+499
+00:38:02,340 --> 00:38:07,380
+ثانية و five ثالثة فهذا الـ plan ايش هيكون دي رو دي
+
+500
+00:38:07,380 --> 00:38:12,320
+زت هذا الـ plan ايش هيكون رو دي five في دي زت هذا
+
+501
+00:38:12,320 --> 00:38:17,220
+ايش هيكون رو دي five في مين في دي رو إذا فني دي
+
+502
+00:38:17,220 --> 00:38:21,260
+ثلت surfaces بحوطه جزئيا من الـ aspects اللي في الـ
+
+503
+00:38:21,260 --> 00:38:25,120
+cylindrical coordinate وقيمة كل واحدة فيهم حاصل
+
+504
+00:38:25,120 --> 00:38:29,000
+ضرب الـ two links بتاعونها وكل واحدة مرضوا إليها الـ
+
+505
+00:38:29,000 --> 00:38:33,680
+norm اللي عليها يعني
+
+506
+00:38:33,680 --> 00:38:38,300
+مثلا هذه اللي هي الـ قوص رو D5 في DZ وين هيكون
+
+507
+00:38:38,300 --> 00:38:40,760
+اتجاهها؟ مين اللي سبب في هذه الحالة؟ اللي هو الـ
+
+508
+00:38:40,760 --> 00:38:46,520
+raw hat الـ raw hat يعني مش عليها ليه هذه؟ هذه
+
+509
+00:38:46,520 --> 00:38:52,300
+الشقفة، هذه الجزئية اللي هو DZ وهي رو D5 وين هيكون
+
+510
+00:38:52,300 --> 00:38:55,860
+الـ norm عليها؟ عمودي على هذا هو اتجاه الـ raw hat
+
+511
+00:38:55,860 --> 00:39:02,130
+واضح؟هذه الجزئية اللي هي رو دي رو دي زد هذي أنا 
+
+512
+00:39:02,130 --> 00:39:05,450
+هيقول دي رو وهذا دي زد اللي عاموتي هيكون في تجاه
+
+513
+00:39:05,450 --> 00:39:09,610
+الـ pi hat و اللي فوق اللي هي فرع رو دي في في دي
+
+514
+00:39:09,610 --> 00:39:15,890
+رو هيكون في تجاه الـ z hat واضح؟
+
+515
+00:39:15,890 --> 00:39:19,510
+إذا عندي رو دي في دي زد اتجاهها اتجاه الـ رو hat
+
+516
+00:39:19,510 --> 00:39:23,490
+عندي دي رو دي زد هيكون اتجاهها في الـ pi hat دي رو
+
+517
+00:39:23,490 --> 00:39:29,620
+رو دي في هيكون اتجاه الـ z hatواضح؟ إذا شوفنا الـ
+
+518
+00:39:29,620 --> 00:39:32,420
+differential links و اخرجت شوفنا الـ surface الـ
+
+519
+00:39:32,420 --> 00:39:35,880
+differential surface و اتجاهه اللي هو دايما زي ما
+
+520
+00:39:35,880 --> 00:39:39,720
+اتفقنا عمودي على الـ surface اللي بنحكي عنه فمثلا
+
+521
+00:39:39,720 --> 00:39:44,500
+DS vector هتكون رو D5 و DZ اتجاهها هيكون طبعا
+
+522
+00:39:44,500 --> 00:39:47,160
+أنتم لما تشوفوا D5 و DZ أنتم عارفين مين الثابت
+
+523
+00:39:47,160 --> 00:39:50,600
+اللي هو الـ rawبتجاه الـ rho hat هنا مين السابق الـ
+
+524
+00:39:50,600 --> 00:39:53,780
+d rho d z اللي هي الـ phi تجاه الـ phi hat هنا
+
+525
+00:39:53,780 --> 00:39:57,480
+السابق مين اللي هو الـ z فعندي rho d rho d phi
+
+526
+00:39:57,480 --> 00:40:03,720
+تجاه الـ z hat طيب الـ volume مش هيكون حاصل ضرب
+
+527
+00:40:03,720 --> 00:40:09,400
+بالتلاتة اللي هو rho d rho d phi بـ d z أنا عندي
+
+528
+00:40:09,400 --> 00:40:13,760
+القوس rho d phi وفي عندي اللي هو d rho وفي d z
+
+529
+00:40:13,760 --> 00:40:15,200
+إذا عندي d rho
+
+530
+00:40:22,280 --> 00:40:25,140
+اللقاء القادم إن شاء الله هنعمل هو الـ spherical
+
+531
+00:40:25,140 --> 00:40:28,620
+coordinate نشوف فيه الـ differential displacement و
+
+532
+00:40:28,620 --> 00:40:31,760
+الـ differential area و الـ differential volume
diff --git a/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/dU0noz-nJFA_raw.srt b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/dU0noz-nJFA_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..35072680e16d0868a5ea46127350ebd3810b06aa
--- /dev/null
+++ b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/dU0noz-nJFA_raw.srt
@@ -0,0 +1,2148 @@
+1
+00:00:21,040 --> 00:00:23,480
+باسم الله الرحمن الرحيم السلام عليكم و رحمة الله و
+
+2
+00:00:23,480 --> 00:00:26,080
+بركاته و احنا اليوم ان شاء الله هنكمل في ال
+
+3
+00:00:26,080 --> 00:00:28,580
+coordinate system في المحاضرة الماضية احنا بقفنا
+
+4
+00:00:28,580 --> 00:00:31,840
+لحد و شوفنا ان احنا ممكن نحافظ على حد ال
+
+5
+00:00:31,840 --> 00:00:34,300
+coordinate constant لما نحافظ على حد ال coordinate
+
+6
+00:00:34,300 --> 00:00:36,660
+constant ليه بنتجها اننا لأن احنا عندنا space
+
+7
+00:00:36,660 --> 00:00:40,740
+three dimension واحد من ال three coordinatesسابت
+
+8
+00:00:40,740 --> 00:00:44,060
+هيعطينا plan فإحنا مثلا عندنا في ال Cartesian
+
+9
+00:00:44,060 --> 00:00:48,700
+coordinate عندنا ال X Y Z لو أنا مثلا ثبتت ال Y
+
+10
+00:00:48,700 --> 00:00:52,660
+ثبتت ال Y طلعوا معايا هذا ال plan بيصير هذا ال
+
+11
+00:00:52,660 --> 00:00:57,980
+plan هذا ال plan عند Y ثابتة هذا ال plan و بيكونوا
+
+12
+00:00:57,980 --> 00:01:02,360
+ال Xتتحرك من مناسبتي تلبس انفتي والزد من مناسبتي
+
+13
+00:01:02,360 --> 00:01:06,620
+تلبس انفتي إذا هذا الplane بيكون ماله constant y
+
+14
+00:01:06,620 --> 00:01:10,280
+لو أخدنا ال z constant هذا اللي من حياتنا معناه
+
+15
+00:01:10,280 --> 00:01:15,160
+هذا ال plane عن z ثابتة قيمة مثلا خمسة تلاتة أربعة
+
+16
+00:01:15,160 --> 00:01:19,860
+فبعطيني ال plane موازي لل xy plane لإن ال xy plane
+
+17
+00:01:19,860 --> 00:01:24,080
+أصلا ماله عن z equals zeroوالـ y plan اللى توا
+
+18
+00:01:24,080 --> 00:01:27,560
+حكينا عنه اللى عند constant y plan اللى هو برضه
+
+19
+00:01:27,560 --> 00:01:31,300
+موازي لمين لل x z plan بمعنى ان الحالة الخاصة
+
+20
+00:01:31,300 --> 00:01:34,960
+بتكون عند اللى هي y بتساوى zero بتكون اللى هو ال x
+
+21
+00:01:34,960 --> 00:01:38,680
+z plan دمعنا عند x equal constant اللى هو هذا ال
+
+22
+00:01:38,680 --> 00:01:42,620
+plan عند x equal constant بيعطينا هذا ال plan اللى
+
+23
+00:01:42,620 --> 00:01:47,980
+فيه بيبقى بها ال y متغيرة و ال z متغيرة طبعا إذا
+
+24
+00:01:47,980 --> 00:01:52,690
+ان عند constant كواردينات بتولد عندنا a planلو نجي
+
+25
+00:01:52,690 --> 00:01:55,330
+على الـ cylindrical coordinates فالـ cylindrical
+
+26
+00:01:55,330 --> 00:02:00,870
+coordinates انها رو و فاي و زد لو احنا ثبتنا رو،
+
+27
+00:02:00,870 --> 00:02:04,850
+رو ثابتة، ايش هيطلع عليه؟ سلمدر، سرف السلمدر، رو
+
+28
+00:02:04,850 --> 00:02:08,010
+ثابتة هذا الأزرق اللي على الشكل اللي هو القلم
+
+29
+00:02:08,010 --> 00:02:10,370
+الارصاص يعني أو يعني المحيط طبعا اللي هو القلم
+
+30
+00:02:10,370 --> 00:02:15,430
+الارصاص، السلمدر هذا رو constant لو أنا ثبتت فاي و
+
+31
+00:02:15,430 --> 00:02:20,470
+خلته تروح من zero ل infinityخلّت فاي ال constant و
+
+32
+00:02:20,470 --> 00:02:22,690
+خلّت روت روح من zero ل infinity و set من minus
+
+33
+00:02:22,690 --> 00:02:25,670
+infinity ل infinity هيعطينا هذا ال plan هذا ال
+
+34
+00:02:25,670 --> 00:02:32,430
+plan هذا ال plan هيكون in five constant هذا
+
+35
+00:02:32,430 --> 00:02:42,330
+ال plan in five constant روم
+
+36
+00:02:42,330 --> 00:02:45,690
+تتحرك من zero ل infinity و set من minus infinity ل
+
+37
+00:02:45,690 --> 00:02:51,110
+plus infinityطب لو ثبتنا Z، خلّينا Z ثابتة، عند Z
+
+38
+00:02:51,110 --> 00:02:54,670
+بتساوي constant، هيتولد عندي هذا ال plan هذا ال
+
+39
+00:02:54,670 --> 00:02:57,270
+plan اللي عنده Z constant، لأن Phi هتتغير من Zero
+
+40
+00:02:57,270 --> 00:03:01,630
+ل Two Pi، فهتتغير عندي اللي هي رو من Zero ل
+
+41
+00:03:01,630 --> 00:03:06,550
+Infinity، فعندي بتكون Z constant هو plan موازن XY
+
+42
+00:03:06,550 --> 00:03:08,410
+ال plan، واضح؟
+
+43
+00:03:13,340 --> 00:03:16,600
+ميجي لها ال spherical coordinate نفس الاشي ممكن
+
+44
+00:03:16,600 --> 00:03:18,440
+احصل علي ال plans اللي هي انا ال constant
+
+45
+00:03:18,440 --> 00:03:21,880
+coordinates و ال coordinates كمان مره هم ال R و ال
+
+46
+00:03:21,880 --> 00:03:26,700
+theta و الفاى طب عند constant R ايش بيطلع عليه
+
+47
+00:03:26,700 --> 00:03:31,700
+اللي هي سفير سطح سفير الشل تبع السفير عند R
+
+48
+00:03:31,700 --> 00:03:34,220
+constant هيطلع عندي اللي هو الشل لأن فاى ثتا
+
+49
+00:03:34,220 --> 00:03:39,180
+بتتغير من zero ل two πاى و ثتا من zero ل باى فتطلع
+
+50
+00:03:39,180 --> 00:03:43,630
+عندي اللي هي البلونة او الشل تبع السفيرفاي
+
+51
+00:03:43,630 --> 00:03:49,610
+constant هي فاي constant بتتغير عندى سيتا من باي ل
+
+52
+00:03:49,610 --> 00:03:53,710
+.. من zero ل باي سيتا بتتغير وعندي ال R بتتغير من
+
+53
+00:03:53,710 --> 00:03:57,250
+zero ل infinity بينما فاي ثابتة على مكان يحدد هي
+
+54
+00:03:57,250 --> 00:04:01,690
+فاي زاوية فاي اللى عاملة مع ال x axis فهي constant
+
+55
+00:04:01,690 --> 00:04:05,550
+فاي هذه constant فاي تمام هذا ال plane is a
+
+56
+00:04:05,550 --> 00:04:10,260
+constantconstant theta هيعطيني cone constant theta
+
+57
+00:04:10,260 --> 00:04:14,060
+لأن فاي ستة هتبقى بتتحرك من zero ل two pi وR من
+
+58
+00:04:14,060 --> 00:04:17,420
+zero ل infinity فتعطيني cone رأس الكون هي قيمة
+
+59
+00:04:17,420 --> 00:04:22,740
+theta واضح بتخيلينهم؟ اذا ايه ال theta هذا ال cone
+
+60
+00:04:22,740 --> 00:04:27,920
+احنا كم بدناه هذا عند theta constant انا ال theta
+
+61
+00:04:27,920 --> 00:04:32,920
+قيمتها سابتة بينما فاي هتلف من zero ل two pi
+
+62
+00:04:32,920 --> 00:04:39,400
+فتعطيني مسار الكونوطبعا المخروض يعني اه من zero ل
+
+63
+00:04:39,400 --> 00:04:43,980
+infinity معايا؟ لذا لو طلب مني ان اثبت احد
+
+64
+00:04:43,980 --> 00:04:46,200
+المتغيرات او احد ال coordinate بدي اعرف انا وين
+
+65
+00:04:46,200 --> 00:04:49,520
+بحكي يعني لما اقول انه theta constant بقول هتعطول
+
+66
+00:04:49,520 --> 00:04:53,120
+coin في ال spherical coordinate المخروج لو انا بدي
+
+67
+00:04:53,120 --> 00:04:56,420
+اقول انه phi constant هقول انه في ال spherical
+
+68
+00:04:56,420 --> 00:05:00,580
+coordinate هيكون عندى plane اللي هو بيبتد مع ال
+
+69
+00:05:00,580 --> 00:05:04,230
+infinity في الالـ r و بتغير الـ minus infinity ل
+
+70
+00:05:04,230 --> 00:05:08,090
+plus infinity في z direction و عامل فاي ثابتة مع
+
+71
+00:05:08,090 --> 00:05:12,610
+ال x direction وهي ال shell اللي عند r بتساوي ثابت
+
+72
+00:05:14,680 --> 00:05:18,220
+خلّين نشوف أمثلة ناخد المثال الأول هى uniform
+
+73
+00:05:18,220 --> 00:05:21,760
+vector field طبعا دول ال vectors احنا بناخدهم لحد
+
+74
+00:05:21,760 --> 00:05:24,440
+لتة بشكل عام هم vectors بس دول ال vectors ممكن
+
+75
+00:05:24,440 --> 00:05:27,520
+يكونوا ما هم ال fields اللى حكينا عنهم إذا scalar
+
+76
+00:05:27,520 --> 00:05:29,920
+بيكون scalar field إذا vector بيكونوا vector
+
+77
+00:05:29,920 --> 00:05:33,000
+fields وأنواع مختلفة ممكن تكون ال electric field و
+
+78
+00:05:33,000 --> 00:05:36,680
+magnetic field ورجع نشوف كل هذا الحكي لما نحكي على
+
+79
+00:05:36,680 --> 00:05:41,050
+ال fieldsطب لو احنا كانوا عندنا two uniform fields
+
+80
+00:05:41,050 --> 00:05:45,250
+vector fields E اللي هو بدلة ال cylindrical
+
+81
+00:05:45,250 --> 00:05:48,210
+coordinate و F برضه بدلة cylindrical coordinate
+
+82
+00:05:48,210 --> 00:05:52,070
+طالب مني ان اجيب ال cross product تبع E cross F
+
+83
+00:05:52,070 --> 00:05:54,890
+اول حاجة و الحاجة التانية اللي بتدي ال vector
+
+84
+00:05:54,890 --> 00:06:01,050
+component of E عند اللي هي Phi خمسة رو خمسة و Phi
+
+85
+00:06:01,050 --> 00:06:05,230
+Pi على اتنين و Z تلاتة parallel to the line اللي
+
+86
+00:06:05,230 --> 00:06:10,000
+هو X بتساوي اتنين و Z بتساوي تلاتةكمان بتنزّاوي ال
+
+87
+00:06:10,000 --> 00:06:13,460
+E بيعملها مع ال surface at z equal تلاتة عند
+
+88
+00:06:13,460 --> 00:06:16,540
+النقطة B ال surface عندي z equal تلاتة احنا قولنا
+
+89
+00:06:16,540 --> 00:06:18,820
+لما يكون constant احد ال coordinate احنا ده
+
+90
+00:06:18,820 --> 00:06:21,840
+cylindrical coordinate z constant ايش بيكون عند
+
+91
+00:06:21,840 --> 00:06:31,140
+surface طب حد بحده يحل حد حاول يحل تعالي
+
+92
+00:06:36,070 --> 00:06:38,930
+أول حاجة احنا بنشوف ال cross product في ال
+
+93
+00:06:38,930 --> 00:06:42,990
+cylindrical coordinate احنا
+
+94
+00:06:42,990 --> 00:06:45,350
+قولنا ال cross product هو determinant وبيتنا ال
+
+95
+00:06:45,350 --> 00:06:54,630
+magnitude احنا تبعه E cross F احنا
+
+96
+00:06:54,630 --> 00:06:57,070
+أخدناها مع بعض اللي هي determinant تاعة ال rho و
+
+97
+00:06:57,070 --> 00:06:57,890
+ال phi و ال z
+
+98
+00:07:12,690 --> 00:07:16,130
+الكتاب بيحط فوقهم vectors عشان بيزهم يعني انا
+
+99
+00:07:16,130 --> 00:07:19,030
+بشغلكم اياهم ان انا كنت هو الكتاب بحطهم both بس
+
+100
+00:07:19,030 --> 00:07:24,470
+احنا بنحط فوقهم vector اذا عندي E x F بس بجيب اللي
+
+101
+00:07:24,470 --> 00:07:25,230
+هو ال determinant
+
+102
+00:07:33,290 --> 00:07:36,990
+ايه اللي هي الروحات؟ عشرة أقل ما نص ستة ما نص ما
+
+103
+00:07:36,990 --> 00:07:44,890
+نص ستة زاد ما نص ستة زاد اللي هي πاي كومبونم زاد
+
+104
+00:07:44,890 --> 00:07:51,630
+تلاتين نقص تلاتة سالب
+
+105
+00:07:51,630 --> 00:07:59,330
+عشر نقص سالب عشر ما نص ما نص ما نص ما نص
+
+106
+00:08:14,000 --> 00:08:17,820
+مش مشكلة إيه ستة و ستين روحها كاملة؟
+
+107
+00:08:43,200 --> 00:08:49,200
+الاخر حاجة هي z hat-11.11.21 z hat تمامإذا نطلع
+
+108
+00:08:49,200 --> 00:08:54,820
+معانا .. برضه أول واحدة ثالثة يعني .. فإن هي من
+
+109
+00:08:54,820 --> 00:08:56,320
+الانت من الانت من الانت من الانت من الانت من الانت
+
+110
+00:08:56,320 --> 00:08:57,660
+من الانت من الانت من الانت من الانت من الانت من
+
+111
+00:08:57,660 --> 00:08:57,760
+الانت من الانت من الانت من الانت من الانت من الانت
+
+112
+00:08:57,760 --> 00:09:00,360
+من الانت من الانت من الانت من الانت من الانت من
+
+113
+00:09:00,360 --> 00:09:01,360
+الانت من الانت من الانت من الانت من الانت من الانت
+
+114
+00:09:01,360 --> 00:09:01,680
+من الانت من الانت من الانت من الانت من الانت من
+
+115
+00:09:01,680 --> 00:09:01,760
+الانت من الانت من الانت من الانت من الانت من الانت
+
+116
+00:09:01,760 --> 00:09:04,600
+من الانت من الانت من الانت من الانت من الانت من
+
+117
+00:09:04,600 --> 00:09:09,980
+الانت من الانت من الانت من الانت من الانيعني معناه
+
+118
+00:09:09,980 --> 00:09:14,720
+هتكون ال component الأولى تربية ثم تربية ثم تربية
+
+119
+00:09:14,720 --> 00:09:16,480
+ثم تربية ثم تربية ثم تربية ثم تربية ثم تربية ثم
+
+120
+00:09:16,480 --> 00:09:16,480
+تربية ثم تربية ثم تربية ثم تربية ثم تربية ثم تربية
+
+121
+00:09:16,480 --> 00:09:17,000
+ثم تربية ثم تربية ثم تربية ثم تربية ثم تربية ثم
+
+122
+00:09:17,000 --> 00:09:17,480
+تربية ثم تربية ثم تربية ثم تربية ثم تربية ثم تربية
+
+123
+00:09:17,480 --> 00:09:17,880
+ثم تربية ثم تربية ثم تربية ثم تربية ثم تربية ثم
+
+124
+00:09:17,880 --> 00:09:19,560
+تربية ثم تربية ثم تربية ثم تربية ثم تربية ثم تربية
+
+125
+00:09:19,560 --> 00:09:32,780
+ثم تربية ثم تربية ثم تربية ثم تربية ثم تربية ثم
+
+126
+00:09:32,780 --> 00:09:33,900
+تربية ثم ت
+
+127
+00:09:43,900 --> 00:09:50,640
+بعض الاختصارات الاختصارات الاختصارات
+
+128
+00:09:50,640 --> 00:09:59,080
+الاختصارات
+
+129
+00:09:59,080 --> 00:10:02,620
+الاختصارات
+
+130
+00:10:02,620 --> 00:10:04,070
+الاختصارات الاختصارات الاختصاراتالحاجة التانية ايش
+
+131
+00:10:04,070 --> 00:10:11,570
+ال y component بتاعته؟ كداش؟ zero في حتة تانية
+
+132
+00:10:11,570 --> 00:10:15,930
+انتوا كلام تاني؟ هذا line خط مين ال constant في
+
+133
+00:10:15,930 --> 00:10:20,450
+هذا الحط؟ قيمة x وزدهم يعطينا x بالساعة تانية
+
+134
+00:10:20,450 --> 00:10:24,290
+وزدهم بالساعة تلاتة مين المتغير؟ ال y ال y بتروح
+
+135
+00:10:24,290 --> 00:10:27,530
+من minus infinity ل plus infinity هذا ال line لو
+
+136
+00:10:27,530 --> 00:10:28,470
+انا حكيت على ال x
+
+137
+00:10:32,470 --> 00:10:40,230
+x,y,z عند قيمة x بتساوي 2 و y بتساوي 3 و عند دي
+
+138
+00:10:40,230 --> 00:10:43,790
+اللي هو ال line اللي بيروح من minus ال 20 ل plus
+
+139
+00:10:43,790 --> 00:10:49,330
+ال 20 sorry عكست ال coordinate هذا ال z اللي موجود
+
+140
+00:10:49,330 --> 00:10:54,490
+يعني و لاش و ليس ال y x
+
+141
+00:10:54,490 --> 00:11:05,300
+,x,y,z يعني x و z x 2 و z 3هذه ال coordinate و ال
+
+142
+00:11:05,300 --> 00:11:08,260
+line هيكون y بتروح minus infinity ل plus infinity
+
+143
+00:11:08,260 --> 00:11:12,780
+هاي ال line اللي عند النقطة سادة اي نقطة على هذا
+
+144
+00:11:12,780 --> 00:11:17,300
+ال line هيكون قيمة x فيها 2 و z 3 و y بتروح minus
+
+145
+00:11:17,300 --> 00:11:24,420
+infinity ل plus infinity في حد بيحاول انا احله
+
+146
+00:11:24,420 --> 00:11:29,080
+سواه بسيط
+
+147
+00:11:29,080 --> 00:11:34,600
+أبسط من اللي حلته لماإذا هو بده ال vector
+
+148
+00:11:34,600 --> 00:11:39,080
+component عند الخط هذا الموازي ال vector component
+
+149
+00:11:39,080 --> 00:11:41,460
+احنا اشتفى عن اول حاجة ايش ال component و ايش ال
+
+150
+00:11:41,460 --> 00:11:44,360
+vector component الذاكرين انتوا درسنا هذا ايش ال
+
+151
+00:11:44,360 --> 00:11:47,020
+component و ايش ال vector component ال component
+
+152
+00:11:47,020 --> 00:11:51,520
+لأي field في اتجاه معين ايش ال product بتاعه هذا
+
+153
+00:11:51,520 --> 00:11:55,100
+scalar عشان اجيب ال vector بتاعه ايش بنسوي بال
+
+154
+00:11:55,100 --> 00:11:59,300
+unit vector في اتجاه هذا المصار فهو بده ال vector
+
+155
+00:11:59,300 --> 00:12:02,720
+component اللي موازية لل lineأنا عند ال field E
+
+156
+00:12:02,720 --> 00:12:04,980
+انه component في ال raw واحدة في ال phi واحدة في
+
+157
+00:12:04,980 --> 00:12:07,820
+ال z three components و ايه اللي انا بده ال
+
+158
+00:12:07,820 --> 00:12:11,660
+component بتاعته اللي هو على هذا الحط ال component
+
+159
+00:12:11,660 --> 00:12:14,760
+بتاعته فاحنا قولنا اشي في ال component مش ال
+
+160
+00:12:14,760 --> 00:12:18,000
+vector component هي dot ال product ذاكرين؟ ذت ال
+
+161
+00:12:18,000 --> 00:12:21,160
+product لأي field على مثلا ال x-axis بيبطيني ال
+
+162
+00:12:21,160 --> 00:12:25,720
+component في ال x-axis dotted لو عملت ال E dot مع
+
+163
+00:12:25,720 --> 00:12:29,210
+ال x-axis حصلتيني ال component تجاه ال x-axisهو
+
+164
+00:12:29,210 --> 00:12:31,810
+يعطينا المسار اللى بدهويا وين بدهو ال component؟
+
+165
+00:12:31,810 --> 00:12:34,190
+بدهو ال component على هذا ال line مش على زى ما
+
+166
+00:12:34,190 --> 00:12:36,650
+احنا شوفنا الأمثلة السابقة كانت مره على ال x axis
+
+167
+00:12:36,650 --> 00:12:38,870
+و مره على ال y axis بس بدهويا على هذا ال axis
+
+168
+00:12:38,870 --> 00:12:44,280
+الجديداللي هو ال line اللي له x بساوة 2 و z بساوة
+
+169
+00:12:44,280 --> 00:12:48,040
+3 عشان أخليه vector و إيش كنا نضربه نضربه هذا اللي
+
+170
+00:12:48,040 --> 00:12:51,660
+عملناه ال E dot ال line اللي بدنا فى اتجاهه فى
+
+171
+00:12:51,660 --> 00:12:54,220
+اتجاه ال line إيش اتجاه ال line قولنا ال vector
+
+172
+00:12:54,220 --> 00:12:57,960
+تبع ال line على ال unit vector تبع ال line فهي
+
+173
+00:12:57,960 --> 00:13:02,760
+محالة بسيط هو a y y hat ال line تبعنا إيش اتجاهه
+
+174
+00:13:02,760 --> 00:13:07,300
+مش تجاه y hat احنا
+
+175
+00:13:07,300 --> 00:13:11,090
+تعرفنا عن هذا ال lineالـY أمناه موازي للـY، إذا
+
+176
+00:13:11,090 --> 00:13:15,450
+انتجاهه هو Y hat وعشان أعرف ال component تبع ال
+
+177
+00:13:15,450 --> 00:13:18,510
+field في اتجاه هذا ال line، برضه لو ده بعرف أن أنا
+
+178
+00:13:18,510 --> 00:13:21,870
+بقيت مع ال Y hat، حققنينيها، يعني اللي هيكون عند
+
+179
+00:13:21,870 --> 00:13:26,990
+ال component اللي بدور عليها أولا، هي Y hat، هاي
+
+180
+00:13:26,990 --> 00:13:29,710
+ال component عشان أخليها vector، أقرمها في ال unit
+
+181
+00:13:29,710 --> 00:13:33,030
+vectorباخدناها قبل انكم تذكرين اي component اللى
+
+182
+00:13:33,030 --> 00:13:36,330
+بتبقى بدى يقولها على اتجاه معين بتعمل product مع
+
+183
+00:13:36,330 --> 00:13:38,870
+هذا الاتجاه او مع هذا ال line يعني انتوا اللى
+
+184
+00:13:38,870 --> 00:13:42,570
+اتعودتوا عليه اللى شوفناهم بالامثلة and vector
+
+185
+00:13:42,570 --> 00:13:45,730
+قولنا ال component مثلا في ال X بتذكرينه المثال
+
+186
+00:13:45,730 --> 00:13:49,530
+ايه قولنا a dot x اعطاني ال component لأنها a
+
+187
+00:13:49,530 --> 00:13:52,530
+cosine theta و هذا التحليل اللى اتعودتوا عليه
+
+188
+00:13:52,530 --> 00:13:54,310
+دُغرة كنتوا كتبوا a cosine theta هي ال component
+
+189
+00:13:54,310 --> 00:13:57,730
+في ال X direction عشان اعطيه vector C شكل vector
+
+190
+00:13:57,730 --> 00:14:03,150
+ال component اللى هى a X عشان بتساويإيه مغنيتو
+
+191
+00:14:03,150 --> 00:14:05,490
+يتبع إيه؟ cosine مثال ثانوية ثانوية ثانوية ثانوية
+
+192
+00:14:05,490 --> 00:14:06,410
+ثانوية ثانوية ثانوية ثانوية ثانوية ثانوية ثانوية
+
+193
+00:14:06,410 --> 00:14:07,570
+ثانوية ثانوية ثانوية ثانوية ثانوية ثانوية ثانوية
+
+194
+00:14:07,570 --> 00:14:08,950
+ثانوية ثانوية ثانوية ثانوية ثانوية ثانوية ثانوية
+
+195
+00:14:08,950 --> 00:14:11,030
+ثانوية ثانوية ثانوية ثانوية ثانوية ثانوية ثانوية
+
+196
+00:14:11,030 --> 00:14:13,330
+ثانوية ثانوية ثانوية ثانوية ثانوية ثانوية ثانوية
+
+197
+00:14:13,330 --> 00:14:16,930
+ثانوية ثانوية ثانوية ثانوية ثانوية ثانوية ثانوية
+
+198
+00:14:16,930 --> 00:14:20,330
+ثانوية ثانوية ثانوية ثانوية ثانوية ثهيكون E اللى
+
+199
+00:14:20,330 --> 00:14:24,330
+هى ال vector مطنية ال vector field doted مع اللى
+
+200
+00:14:24,330 --> 00:14:30,150
+هو ال A hat و بدي اعوض عن القيم بعدها بRaw خمسة و
+
+201
+00:14:30,150 --> 00:14:34,190
+Phi Pi على اتنين و Z تلاتة اذا نشوف اش اللى عملناه
+
+202
+00:14:34,190 --> 00:14:38,590
+مع بعض اذا ان عندي ال line X بيساوى تنين و Z تلاتة
+
+203
+00:14:38,590 --> 00:14:42,130
+هو parallel Y axis هو بيحصل لكم لما يكون تنين
+
+204
+00:14:42,130 --> 00:14:44,830
+constant فى ال space هيكون line
+
+205
+00:14:47,620 --> 00:14:53,060
+لكن لو واحدة constant إيش هيكون؟ ال plan ممتازة
+
+206
+00:14:53,060 --> 00:14:56,440
+يعني إذا كانوا جنين constant هيكون line أكيد لكن
+
+207
+00:14:56,440 --> 00:14:58,740
+لو واحدة منهم constant coordinates زي الأمثل اللي
+
+208
+00:14:58,740 --> 00:15:04,080
+شفناها قبل قليل هيكون ال planعشان اجيب ال E في
+
+209
+00:15:04,080 --> 00:15:07,820
+اتجاه اللي هو ال line اللي واصفنايا هيكون E dot A
+
+210
+00:15:07,820 --> 00:15:12,380
+hat في A hat و بتعود عنه في النقطة فيه عند النقطة
+
+211
+00:15:12,380 --> 00:15:15,780
+B ايش ال A y hat A y hat هو طبعا لان النقطة عندى
+
+212
+00:15:15,780 --> 00:15:19,980
+كله ال field بال raw فائزت بينما ال A y hat مالها
+
+213
+00:15:20,560 --> 00:15:24,260
+كاوتيشن كواردينت فأول خطوة بتعملها ان اكتب ال a y
+
+214
+00:15:24,260 --> 00:15:27,280
+hat بدلالة ال cylindrical coordinate و هذا شوفناه
+
+215
+00:15:27,280 --> 00:15:30,860
+اعلنكم كيف حتى تجيبوه متذكرين هيكون sin phi rho
+
+216
+00:15:30,860 --> 00:15:34,240
+hat هيكون sin phi phi hat بعود عن phi باي على
+
+217
+00:15:34,240 --> 00:15:39,100
+اتنين هيطلع معايا ان a y hat بتساوي a rho hat في
+
+218
+00:15:39,100 --> 00:15:44,400
+هالحلقة لأن باي على اتنين قدش قمتها باي على اتنين
+
+219
+00:15:44,400 --> 00:15:46,540
+تسعين فإيش اكيد انه هيكون بالتمام
+
+220
+00:15:50,990 --> 00:15:59,050
+فاي فاي على اتنين و فاي مين هي الزاوية فاي مين هي
+
+221
+00:15:59,050 --> 00:16:04,450
+الزاوية ما بين ال X-axis و ال Y-axis لما تكون فاي
+
+222
+00:16:04,450 --> 00:16:07,470
+باع على اتنين أكيد تكون الطبق من ال Z-axis مين يه
+
+223
+00:16:07,470 --> 00:16:11,390
+فاي على اتنين فأكيد هيكون ال row فاي في اتجاه ال Z
+
+224
+00:16:11,390 --> 00:16:19,180
+يعني احنا ال row هات وهي الفلما تكون في بتساوي باي
+
+225
+00:16:19,180 --> 00:16:23,260
+على اتنين الروحة بتنطبق بالتنين على ال Y hat عرفنا
+
+226
+00:16:23,260 --> 00:16:27,160
+ليش انطبق ال Y hat على ال روحة و الروحة في اي مكان
+
+227
+00:16:27,160 --> 00:16:31,420
+في ال cylindrical coordinate هي في بتغير من zero ل
+
+228
+00:16:31,420 --> 00:16:34,940
+two pi لما في تكون بالتمام باي على اتنين هتكون
+
+229
+00:16:34,940 --> 00:16:38,940
+الروحة بتساوي Y hat لما تكون في zero الروحة بتساوي
+
+230
+00:16:38,940 --> 00:16:45,520
+X hat معين؟لما تكون الـPhi 0 هيكون الـRowها منطبقة
+
+231
+00:16:45,520 --> 00:16:49,200
+على الـX Axis لما تكون Phi Pi على 2 هتكون الـRow
+
+232
+00:16:49,200 --> 00:16:53,440
+منطبقة بالتمام على الـY Axis ففي هذه الحالة لأن
+
+233
+00:16:53,440 --> 00:16:56,300
+Phi عندي Pi على 2 هلاقي أن الـY hat منطبقة على
+
+234
+00:16:56,300 --> 00:17:02,800
+الـRow hat Ay hat سين الـPhi Row hat زي الـCos Phi
+
+235
+00:17:02,800 --> 00:17:05,620
+Phi hat هذا احنا شوفناه مع بعض كيف أنتقل من
+
+236
+00:17:05,620 --> 00:17:11,340
+الـCylindrical لالـCartesianألاحظ ان ال a y hat هي
+
+237
+00:17:11,340 --> 00:17:19,940
+يتنطبق
+
+238
+00:17:19,940 --> 00:17:21,180
+على ال y hat
+
+239
+00:17:24,810 --> 00:17:28,470
+Y hat أو Y hat في Y hat وقلنا ليش نضره في Y hat
+
+240
+00:17:28,470 --> 00:17:31,430
+عشان هو بده ال vector component مش ال component
+
+241
+00:17:31,430 --> 00:17:35,190
+بده ال vector component E dot row hat في row hat
+
+242
+00:17:35,190 --> 00:17:40,130
+فإذا بتدرج على E و أعملها dot مع ال row hat هال E
+
+243
+00:17:40,130 --> 00:17:42,950
+عندي، عندي واحدة في ال row hat اللي هي minus خمسة
+
+244
+00:17:42,950 --> 00:17:46,090
+و هدوله هيكونوا zero لإن بعملها dot مع ال row hat
+
+245
+00:17:48,910 --> 00:17:53,250
+فإذا e dot rho hat اللي هي minus خمسة واتجاه في
+
+246
+00:17:53,250 --> 00:17:56,070
+اتجاه الروهات سبعة فيه من الاتجاه لأنه في اتجاه ال
+
+247
+00:17:56,070 --> 00:17:59,630
+Y hat هو نفسه اتجاه الروهات في هذه الحالة الخاصة
+
+248
+00:17:59,630 --> 00:18:04,210
+المطالب عند نقطة اللي اللي لها الروه خمسة و Phi Pi
+
+249
+00:18:04,210 --> 00:18:08,130
+على اتنين ففي هذه الحالة هيطبق ال Y hat مع الروهات
+
+250
+00:18:08,130 --> 00:18:12,470
+طبعا في طالب أيش كمان
+
+251
+00:18:15,420 --> 00:18:18,580
+الزاوية اللى بيعملها ال field مع ال surface z
+
+252
+00:18:18,580 --> 00:18:22,360
+equal تلاتة عند النقطة بي يعني ان النقطة بي هذه
+
+253
+00:18:22,360 --> 00:18:26,420
+انا ثبتت ال z حلتها تلاتة فصار عندى عند النقطة بي
+
+254
+00:18:26,420 --> 00:18:30,900
+فيه surface z constant معايا اذا هذا ال surface
+
+255
+00:18:30,900 --> 00:18:35,800
+اللى عند z equal تلاتة اللى عند النقطة five و five
+
+256
+00:18:35,800 --> 00:18:39,680
+على اتنين و تلاتةسبت الـ z فصار عندى ال surface
+
+257
+00:18:39,680 --> 00:18:43,180
+بيسوى تلاتة بينما في بتروح من zero to pi او z
+
+258
+00:18:43,180 --> 00:18:46,900
+minus انك انت بتروح من zero ل infinity هذا ال
+
+259
+00:18:46,900 --> 00:18:52,480
+surface عند ال z بتسوى تلاتة ايش بده الزاوية اللى
+
+260
+00:18:52,480 --> 00:18:57,440
+بيعملها ال field عند هذا ال surface اذا رجعنا ده
+
+261
+00:18:57,440 --> 00:19:00,340
+ال cylindrical coordinate هاي ال surface اللى z
+
+262
+00:19:00,340 --> 00:19:04,940
+فيه constantمعايا؟ إيش العمودي عليها ده الذت؟
+
+263
+00:19:04,940 --> 00:19:10,360
+النورم عليها ده الذت؟ مين هيكون؟النورم اللي عمودي
+
+264
+00:19:10,360 --> 00:19:16,360
+عليه هذا اتجاه XY صح؟ Z ثابتة لو بتعمل عمودي عليه
+
+265
+00:19:16,360 --> 00:19:21,440
+إيش بيكون اتجاه العمودي عليه؟ Z hat ممتاز إذا
+
+266
+00:19:21,440 --> 00:19:24,460
+العمودي عليه Z hat أنا عندي field موجود في ال
+
+267
+00:19:24,460 --> 00:19:27,680
+space و بدي الزاوية بين هذا ال field و ال z axis و
+
+268
+00:19:27,680 --> 00:19:33,120
+ال plane هذا مش أسهل أعمل الزاوية اللي مابين ال
+
+269
+00:19:33,120 --> 00:19:36,400
+field و ال z axis و الزاوية اللي طالبها اللي مابين
+
+270
+00:19:36,400 --> 00:19:40,120
+ال field و اللي مابين ايش هتكون مكملةأذا بدأ أرجع
+
+271
+00:19:40,120 --> 00:19:42,420
+أتذكر إيش هو ال plan هذا اللي عنده z بتساوي
+
+272
+00:19:42,420 --> 00:19:47,540
+constant هو ال z الموازي لل xy plan معناه إنه أي
+
+273
+00:19:47,540 --> 00:19:52,020
+نوع ما عليها بده يكون في اتجاه ال z axis بالتالي
+
+274
+00:19:52,020 --> 00:19:56,820
+هو طالب مني أجيب الزاوية اللي بين ال field هذا E و
+
+275
+00:19:56,820 --> 00:20:01,740
+ال surfaceو ال surface هذا فعشان اجيب الزاوية بين
+
+276
+00:20:01,740 --> 00:20:04,500
+a و ال surface انا عارفة ان هذا ال surface هيكون
+
+277
+00:20:04,500 --> 00:20:07,360
+العمودي عليها mean اللي هو z hat فبجيب اولا
+
+278
+00:20:07,360 --> 00:20:12,520
+الزاوية بين ال field و ال z hat و بعدين ايش بسوي
+
+279
+00:20:12,520 --> 00:20:16,160
+باخد المكملة يعني هذا اللي هو z طبعا plan انا ممكن
+
+280
+00:20:16,160 --> 00:20:25,380
+عشان اجيب زواية عشان
+
+281
+00:20:25,380 --> 00:20:29,570
+احنا نجيب زاوية بين field و planتجيب اللغة اللي
+
+282
+00:20:29,570 --> 00:20:33,390
+وحط علي ال plan هينا على الزاوية هينا من هذه
+
+283
+00:20:33,390 --> 00:20:42,970
+الزاوية ساميها theta E و z بتساوي تلاتة high ما
+
+284
+00:20:42,970 --> 00:20:50,550
+بين ال acre field و 1 z بتساوي تلاتة قبل ما قصدنا
+
+285
+00:20:50,550 --> 00:20:52,550
+ساميها ثلاثة كمية درجة سنة
+
+286
+00:20:56,030 --> 00:21:00,450
+هذه الزاوية عشان نعرف هذه الزاوية أسهلنا لإن انا
+
+287
+00:21:00,450 --> 00:21:04,330
+بدي أجيب هذا ال vector بدل ما أجيب هذا ال vector و
+
+288
+00:21:04,330 --> 00:21:07,850
+أنا عارفة ان ال norm على هذا ال plane هو مين ال Z
+
+289
+00:21:07,850 --> 00:21:11,770
+hat لأن ال vector العمود على ال plane هو Z hat
+
+290
+00:21:11,770 --> 00:21:15,950
+فإذا جيبت الزاوية اللي ما بين ال field و ال norm
+
+291
+00:21:15,950 --> 00:21:19,410
+بقدر أجيب الزاوية اللي بين ال field و ال plane
+
+292
+00:21:19,410 --> 00:21:23,270
+لأنه الزاوية هتكون مكملة للزاوية اللي بين ال field
+
+293
+00:21:23,270 --> 00:21:27,660
+و العمودفهذا اللي عملنا اي دوت زت هات إيش هي عبارة
+
+294
+00:21:27,660 --> 00:21:31,400
+عن مجموعة تبع ال field في المجموعة زت هات هو واحد
+
+295
+00:21:31,400 --> 00:21:34,700
+ال chips المقتنع اللي ساوية بينهم هو سميها zeta a
+
+296
+00:21:34,700 --> 00:21:42,260
+z اللي هو اوضع قيمة اي اللي هي جزر التربية ل134 و
+
+297
+00:21:42,260 --> 00:21:47,240
+ال dot product للإي و زت إذا رجعنا لل field اي dot
+
+298
+00:21:47,240 --> 00:21:53,360
+مع زت هات three component لل field اللي هو minus
+
+299
+00:21:53,360 --> 00:21:53,840
+five
+
+300
+00:21:56,500 --> 00:22:00,300
+الـ dot مع الـ z ده هاتيش هيعطيني تلاتة اذا عندي
+
+301
+00:22:00,300 --> 00:22:00,920
+تلاتة
+
+302
+00:22:04,550 --> 00:22:08,610
+تلاتة بتتساوي المجنتو التبع ال field اللى هى جزر
+
+303
+00:22:08,610 --> 00:22:14,150
+تربيعى لإي رو تربيع زد إي في تربيع زد إي ز تربيع
+
+304
+00:22:14,150 --> 00:22:17,870
+بتطلع جزر تربيع لمية و أربعة و تلاتين في ال cosine
+
+305
+00:22:17,870 --> 00:22:22,450
+الزاوية اللى بين ال vector و ال z component و z
+
+306
+00:22:22,450 --> 00:22:26,370
+hat بجيب ال set هات بالتالى الزاوية بين ال field و
+
+307
+00:22:26,370 --> 00:22:30,690
+ال surface هتكون تسعين مقص الزاوية واضح؟
+
+308
+00:22:34,250 --> 00:22:39,470
+بتوقف من هنا و نيجي لل lecture جديدة بتاعة اليوم
+
+309
+00:22:39,470 --> 00:22:45,190
+فيها استفتار بدي أكوا تحلوه تتسيروا يعني تعرفين
+
+310
+00:22:45,190 --> 00:22:48,530
+عليهم يعني تتعودوا عليهم الاشي مش جديد عليكم انتوا
+
+311
+00:22:48,530 --> 00:22:51,570
+حد حكيتوليا ال vector field مش جديد علينا او ال
+
+312
+00:22:51,570 --> 00:22:54,750
+vector الاساس لكن الجديد انه التعامل مع ال fields
+
+313
+00:22:54,750 --> 00:22:58,690
+نفهم كيف نتعامل مع ال fields في وجود ال vector
+
+314
+00:22:58,690 --> 00:23:02,550
+كالقلص فبدي أكوا تدرس أول بأول معايا أول بأول
+
+315
+00:23:02,550 --> 00:23:07,730
+انتوا؟هلقيت اني جلع ال vector calculus
+
+316
+00:23:07,730 --> 00:23:10,630
+differentiation and integration لحد اللي احنا
+
+317
+00:23:10,630 --> 00:23:14,610
+ماشوفناش لا تفاضل ولا اتكامل شوفنا جميع شوفنا
+
+318
+00:23:14,610 --> 00:23:18,610
+cross product و product شوفنا طريح لكن ماشوفناش ال
+
+319
+00:23:18,610 --> 00:23:22,030
+differentiation ولا ال integration هتكمل ال
+
+320
+00:23:22,030 --> 00:23:24,890
+differentiation و ال integration هنشوف ايش معناه
+
+321
+00:23:24,890 --> 00:23:27,550
+هذا الحكي يعني معناه هشوف انا ال differential
+
+322
+00:23:27,550 --> 00:23:29,470
+links هي المقصود فيها
+
+323
+00:23:42,860 --> 00:23:47,220
+هنشوف ال differential links هنشوف المساحة و نشوف
+
+324
+00:23:47,220 --> 00:23:50,600
+ال volume نبدأ بال Cartesian coordinate لإن هو ال
+
+325
+00:23:50,600 --> 00:23:52,820
+coordinate اللى احنا بتعودى عليه هنروح ل ال
+
+326
+00:23:52,820 --> 00:23:54,720
+cylindrical coordinate و بعدين هنروح ل ال
+
+327
+00:23:54,720 --> 00:23:57,520
+spherical coordinate انتوا كان مطلوب منكم تسكين
+
+328
+00:23:57,520 --> 00:24:04,980
+صحيح اه؟ و حاليا انا عملتلكم this book group اه؟
+
+329
+00:24:04,980 --> 00:24:08,600
+مانضمتيش؟ اليوم بعد المحاضرة لازم كلكوا تنضموا
+
+330
+00:24:08,600 --> 00:24:08,940
+فيها
+
+331
+00:24:24,120 --> 00:24:27,920
+مش مقصود في الـ differential links احنا بنحكي اول
+
+332
+00:24:27,920 --> 00:24:30,080
+حاجة عن ال differential links ايش المقصود في ال
+
+333
+00:24:30,080 --> 00:24:32,640
+differential links المقصود في ال differential
+
+334
+00:24:32,640 --> 00:24:36,460
+links اللي هو جزء صغير فيها ال space تبعنا
+
+335
+00:24:36,460 --> 00:24:39,610
+differential يعني جزءيعني لو نحكي ع كارتيشن
+
+336
+00:24:39,610 --> 00:24:43,790
+كواردينات ان دي x, y, z هاي نقطة في ال space مثلا
+
+337
+00:24:43,790 --> 00:24:49,030
+بي لها x كواردينات و y كواردينات و z كواردينات لو
+
+338
+00:24:49,030 --> 00:24:52,690
+طبعا هذا المكعب اللي في ال space هذا المكعب في ال
+
+339
+00:24:52,690 --> 00:24:55,610
+space جزء من ال space ال space ان x بتروح minus
+
+340
+00:24:55,610 --> 00:24:58,530
+infinity ل plus infinity و y بتروح minus infinity
+
+341
+00:24:58,530 --> 00:25:00,830
+ل plus infinity و z بال minus infinity ل plus
+
+342
+00:25:00,830 --> 00:25:04,850
+infinityهذا المكعب هو جزء من ال space مربع صغير
+
+343
+00:25:04,850 --> 00:25:09,510
+مكعب قاعد في ال space اللى طول كل ضلع من أضلعه هو
+
+344
+00:25:09,510 --> 00:25:12,790
+delta من ال space فهذه ال differential matrix اذا
+
+345
+00:25:12,790 --> 00:25:17,230
+طلعتوا عليه هاي الموازي ل X axis اللى هو زي DS وCR
+
+346
+00:25:17,230 --> 00:25:23,170
+هدولة طولهم DX الموازين ل Z axis اللى هي زي QR و
+
+347
+00:25:23,170 --> 00:25:29,950
+BC و AD و DS هدولة طولهم DZ جزء fraction من الالـ
+
+348
+00:25:29,950 --> 00:25:34,910
+space جزء من الـ z component و الموازين لل y اللي
+
+349
+00:25:34,910 --> 00:25:41,280
+هم زي a,b و b,q و d,c و s,r طولهم dyإذاً في الـ
+
+350
+00:25:41,280 --> 00:25:44,800
+Cartesian coordinate هيكون لو أنا عند ال space X
+
+351
+00:25:44,800 --> 00:25:48,260
+بروح minus infinity ل plus infinity جزء على هذا ال
+
+352
+00:25:48,260 --> 00:25:52,100
+line هيكون ماله DX لو عند ال Y بروح minus infinity
+
+353
+00:25:52,100 --> 00:25:56,780
+ل plus infinity عين عليه ايش هتكون DY ال Z بروح
+
+354
+00:25:56,780 --> 00:25:59,880
+minus infinity ل plus infinity عين عليه هتكون DZ
+
+355
+00:25:59,880 --> 00:26:06,020
+إذا ال differential X هو DX X hat DY Y hat DZ Z
+
+356
+00:26:06,020 --> 00:26:06,400
+hat
+
+357
+00:26:10,940 --> 00:26:16,080
+لذن عندي DL الـ differential displacement طبعا DL
+
+358
+00:26:16,080 --> 00:26:18,940
+ايش هي؟ displacement ليش هي displacement؟ لأن أنا
+
+359
+00:26:18,940 --> 00:26:21,040
+بروح من نقطة لنقطة عشان هيك بيصير عندي
+
+360
+00:26:21,040 --> 00:26:23,920
+differential links لو أنا عند نقطة سابت أبدا سابت
+
+361
+00:26:23,920 --> 00:26:27,200
+لو كنت على ال X-axis و كنت عند هذه النقطة و اتحركت
+
+362
+00:26:27,200 --> 00:26:30,860
+لهذه النقطة مش هيصير عندي Delta X لو أنا على Y
+
+363
+00:26:30,860 --> 00:26:33,160
+-axis و اتحركت من هذه النقطة لهذه النقطة مش هيصير
+
+364
+00:26:33,160 --> 00:26:37,220
+عندي Delta Y لو أنا على Z-axis و اتحركت Delta Z
+
+365
+00:26:38,050 --> 00:26:46,010
+عشان هي اسمها displacement دلت أل هي
+
+366
+00:26:46,010 --> 00:26:53,310
+عبارة عن دي اكس دي اكس اكسات دي وي وي هات دي زي زي
+
+367
+00:26:53,310 --> 00:26:56,170
+هات وهي دلت أل اللي هتكون تمام زي ما عملنا ال
+
+368
+00:26:56,170 --> 00:26:59,790
+displacement الحقيقية بين مقطتين بس عادى بين
+
+369
+00:26:59,790 --> 00:27:03,050
+differentiation يعني جزء صغير في ال space
+
+370
+00:27:10,060 --> 00:27:13,240
+لقم نحكي على differential surface إذا إحنا شفنا
+
+371
+00:27:13,240 --> 00:27:16,760
+displacement .. differential displacementاللي هي
+
+372
+00:27:16,760 --> 00:27:21,460
+dx, x hat, dy, y hat, z, z hat ال plan او ال
+
+373
+00:27:21,460 --> 00:27:25,940
+surface بتغير في coordinate فانا بحكي ع ال surface
+
+374
+00:27:25,940 --> 00:27:31,160
+عدي مثلا انا هذا ال surface فيه كان تغير في ال z
+
+375
+00:27:31,160 --> 00:27:34,840
+direction و ال y direction هذا ال plan ايش اللي
+
+376
+00:27:34,840 --> 00:27:37,500
+هيكون العمود عليه زي ال surface اللي توجفناه ال x
+
+377
+00:27:37,500 --> 00:27:40,760
+hat دائما احنا بناخد لو هذا ال surface جزء من
+
+378
+00:27:40,760 --> 00:27:45,570
+volume بناخد ال norm برا ال volumeيعني لو أنا عندي
+
+379
+00:27:45,570 --> 00:27:51,450
+هذا الجزء من .. من مكعةمكعب هدوجي من المكعب باخد
+
+380
+00:27:51,450 --> 00:27:55,470
+ال norm اللي عليه مرة المكعب مش في قلب المكعب هذا
+
+381
+00:27:55,470 --> 00:27:59,110
+يعني convention دايما بكون العمودي مرة المكعب
+
+382
+00:27:59,110 --> 00:28:03,070
+فعندي مثلا هذا ال surface اللي هو دي إيه عبارة عن
+
+383
+00:28:03,070 --> 00:28:06,490
+دي زت في دي واي ال area هنا ال differential area
+
+384
+00:28:06,490 --> 00:28:10,890
+دي إيه هتكون دي واي في دي زت هنا مين اللي ثابت و
+
+385
+00:28:10,890 --> 00:28:14,550
+مين متغير هنا عندي اللي متغير ال X و ال Z عندي دي
+
+386
+00:28:14,550 --> 00:28:20,030
+X و دي Z والثابت هو ال Yفهذا ما يلو ال norm تبعه
+
+387
+00:28:20,030 --> 00:28:25,030
+عمودي على ال y عند ال x متغيرة و ال z متغيرة فعند
+
+388
+00:28:25,030 --> 00:28:28,050
+ال plane هذا جزء من ال plane ما يلو اللي فيه z
+
+389
+00:28:28,050 --> 00:28:31,750
+constant هذا جزء من ال plane اللي فيه ال y قبل
+
+390
+00:28:31,750 --> 00:28:35,350
+تأسفه constant و ال norm تبعه هيكون y hat هذا ال
+
+391
+00:28:35,350 --> 00:28:39,520
+plane اللي هو في ال z yجزء هذا الـ differential من
+
+392
+00:28:39,520 --> 00:28:44,120
+الـ plane عنده الـ X ثابتة يمكن أن تكون X0,5,6 أو
+
+393
+00:28:44,120 --> 00:28:48,280
+ماينوس تلاتة ماينوس أربعة و النور تتجاه ال X axis
+
+394
+00:28:48,280 --> 00:28:54,000
+هنا ال X و ال Z متغيرين ان هو عند surface عنده ال
+
+395
+00:28:54,000 --> 00:28:59,780
+Y ثابتة و النور تبع تجاه ال Y hatهنا عندى dx dy
+
+396
+00:28:59,780 --> 00:29:04,260
+مين اللى ثابت؟ z, z constant و هيكون ال north تجاه
+
+397
+00:29:04,260 --> 00:29:07,300
+ال z hat إذا ال differential area هنا إيش هتكون؟
+
+398
+00:29:07,300 --> 00:29:16,420
+dz dy هنا هتكون dx dz هنا dx dy DS
+
+399
+00:29:16,420 --> 00:29:21,560
+as a vector هتكون في هالحالة dy dz و تجاه مين؟ ال
+
+400
+00:29:21,560 --> 00:29:29,380
+x hatانها هتكون dx dz y hat هدى هتكون dx dy z hat
+
+401
+00:29:29,380 --> 00:29:32,980
+اذا عرفنا اش هو ال differential line او ال
+
+402
+00:29:32,980 --> 00:29:35,240
+differential links ال differential links اللى هو
+
+403
+00:29:35,240 --> 00:29:35,700
+dx
+
+404
+00:30:02,700 --> 00:30:04,100
+DxDyDyDyDyDyDyDyDyDyDyDyDyDyDyDyDyDyDyDyDyDyDyDyDyDyDyDyDyDyDyDyDyDyDyDy
+
+405
+00:30:05,490 --> 00:30:10,090
+الشكل العام ال DS هي عبارة عن إلها magnitude و
+
+406
+00:30:10,090 --> 00:30:14,730
+اتجاه عمودي عليها non vector اللي هي الاتجاه دبعها
+
+407
+00:30:14,730 --> 00:30:16,930
+دايما عمودي على ال surface يعني إذا بحكي على ال
+
+408
+00:30:16,930 --> 00:30:20,270
+surface هو الطاولة تعطي اتجاهها اللي هو العمودي
+
+409
+00:30:20,270 --> 00:30:22,070
+عليها تمام؟
+
+410
+00:30:32,610 --> 00:30:34,810
+Differential volume عشان نحكي عن الـ differential
+
+411
+00:30:34,810 --> 00:30:37,990
+volume أكيد هتكون بيتغير في التلات اتجاهات هتعطيني
+
+412
+00:30:37,990 --> 00:30:43,310
+في ال coordinate cube DXDYDZ هتعطيني حجم بكيوب
+
+413
+00:30:43,310 --> 00:30:48,170
+بينما ال area هتكون surface لأحد أو جهة الكيوب
+
+414
+00:30:48,170 --> 00:30:57,990
+يعني إذا رجعنا لكيوب المرسوم هنا هذا
+
+415
+00:30:57,990 --> 00:31:03,450
+الكيوب احنا هذا differential surface مثلاهذا الـ
+
+416
+00:31:03,450 --> 00:31:06,670
+differential surface دي اكس دي واي هذا بالنسبالنا
+
+417
+00:31:06,670 --> 00:31:10,270
+هيكون دي واي دي زت وكذا كل واحد من هدولة ال
+
+418
+00:31:10,270 --> 00:31:13,510
+surfaces ماله differential surface هذا اتجاهه ايش
+
+419
+00:31:13,510 --> 00:31:19,410
+هيكون مثلا اللي هو a,b,c,d,x hat نجلأ ال line هذا
+
+420
+00:31:19,410 --> 00:31:24,790
+الجزء اللي هو PQ هذا ال differential line دي واي
+
+421
+00:31:25,580 --> 00:31:29,200
+هذا qr differential line لكن كله على بعض اللي هو
+
+422
+00:31:29,200 --> 00:31:33,240
+بي كيو بي اي دي دي دي دي دي دي دي دي دي دي دي دي
+
+423
+00:31:33,240 --> 00:31:37,720
+دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي دي
+
+424
+00:31:37,720 --> 00:31:45,240
+دي دي دي
+
+425
+00:31:47,500 --> 00:31:50,200
+هذا السبب نعرفين إيش هو differential lengths و
+
+426
+00:31:50,200 --> 00:31:53,460
+differential area و ال area دايما إلها نور يعني
+
+427
+00:31:53,460 --> 00:31:57,720
+اتجاهه عمودي عليها اتجاه تبعها دايما عمودي عليها و
+
+428
+00:31:57,720 --> 00:32:00,440
+عندي ال differential volume لو حاصل ضرب ب three
+
+429
+00:32:00,440 --> 00:32:04,630
+coordinateحاجة مهمة كتير نلاحظها ان دي ال مالها
+
+430
+00:32:04,630 --> 00:32:08,370
+احنا اكتبناها دي ال مثلا دي displacement دي XX hat
+
+431
+00:32:08,370 --> 00:32:11,690
+دي YY hat، دي ZZ hat displacement في الـ Cartesian
+
+432
+00:32:11,690 --> 00:32:15,130
+coordinate و دي S قولنا دي S magnitude و N hat،
+
+433
+00:32:15,130 --> 00:32:18,770
+نهات عمودي على الـplane تبع الـsurface بينما ال
+
+434
+00:32:18,770 --> 00:32:23,250
+volume ماله scalar، اذا ال displacement vector ال
+
+435
+00:32:23,250 --> 00:32:26,930
+surface vector بينما ال volume scalar، ال volume
+
+436
+00:32:26,930 --> 00:32:29,050
+هو DX DY DZ
+
+437
+00:32:33,610 --> 00:32:36,410
+النقطة اللي في ال space أو الجزء من ال space هذا
+
+438
+00:32:36,410 --> 00:32:40,550
+هيك بيكون شكله بيكون شكله بهذا الشكل لو أخدت قطعة
+
+439
+00:32:40,550 --> 00:32:43,570
+من ال cylinder هيكون شكلها بهذا الشكل هيكون هنا
+
+440
+00:32:43,570 --> 00:32:49,650
+ماله أعراض من هنا قطعة شريحة زي هيك لو أنا طلعت
+
+441
+00:32:49,650 --> 00:32:53,390
+عها جزئية من أسلة B فإيش هيكون في عندي تغير في
+
+442
+00:32:53,390 --> 00:32:58,430
+تجاه مين ال raw؟بس احد اللي هي هنا هذا القطع القطع
+
+443
+00:32:58,430 --> 00:33:03,250
+من السليندر Z عنده ثابتة نقطة في الاسم Z ثابتة و
+
+444
+00:33:03,250 --> 00:33:07,890
+Phi ثابتة وهي قيمة رو مثلا خمسة من أصله بيه ايش هو
+
+445
+00:33:07,890 --> 00:33:13,290
+تغير في رو دلتا رو هتكون دي رو نفس الاشي ل دي ايه
+
+446
+00:33:13,290 --> 00:33:20,270
+هتكون دي رو RQ دي رو PCP
+
+447
+00:33:20,270 --> 00:33:24,610
+هادي برضه دي رو تمام اذا نهاي جزئية
+
+448
+00:33:28,870 --> 00:33:35,830
+الصغيرة هي الأجزة هي تغير في دي رو وهي رو وهي دي
+
+449
+00:33:35,830 --> 00:33:39,450
+رو هنا الساوية و الزاوية ثابتة على واحد مثلا نفس
+
+450
+00:33:39,450 --> 00:33:45,670
+الأشهر هي دي رو لا ثابت مثلا على قائتين صحيح؟ إذا
+
+451
+00:33:45,670 --> 00:33:50,330
+مافيه أحدين تغير في رو هنا و هنا وهذا دي رو وهذا
+
+452
+00:33:50,330 --> 00:33:56,570
+دي رو طب نيجي نحكي على إيه شعب الزواياهذا كانت فاي
+
+453
+00:33:56,570 --> 00:34:03,610
+واحد و أنا صارت فاتنين هذا كم يكون دي فاي هذا
+
+454
+00:34:03,610 --> 00:34:11,350
+كله طول ثابت مقطع رو هذا بيساوي هذا صح معين هذا
+
+455
+00:34:11,350 --> 00:34:15,730
+جزئية رو وهذا رو هذا زاوية فاي واحد و هذا زاوية
+
+456
+00:34:15,730 --> 00:34:19,230
+فاتنين بينهم كم يكون دي فاي لماذا هذا القصر مقابل
+
+457
+00:34:19,230 --> 00:34:23,350
+اللي هو كم يكون رو دي فاي لأنه مقابل أي زاوية لدي
+
+458
+00:34:23,350 --> 00:34:32,580
+فايهذه الجزئية وهذه الجزئية دي فاي ليش سميتها دي
+
+459
+00:34:32,580 --> 00:34:37,020
+فاي لأن هذه الزاوية فاي واحد وهذه الزاوية فاي تنين
+
+460
+00:34:37,020 --> 00:34:44,760
+معايا اذا فاي تنين وفاي واحد هي دي فاي والقص لقبل
+
+461
+00:34:44,760 --> 00:34:50,660
+اي زاوية متذكرين على الدائرة انتوا؟
+
+462
+00:34:50,660 --> 00:34:56,510
+هذه زاوية ستا وهذا R ايش كنتوا تسموا هذا معاك؟طول
+
+463
+00:34:56,510 --> 00:35:00,830
+القوس طول القوس نفس الاشي من هنا هنا عندي row و
+
+464
+00:35:00,830 --> 00:35:05,370
+هنا D5 اشهر
+
+465
+00:35:05,370 --> 00:35:10,370
+الحكم row D5 اذا ان احنا فرقنا على هيئها D row
+
+466
+00:35:10,370 --> 00:35:19,850
+وهدول امامهم row D5 هذي اشهر تكون row plus D row
+
+467
+00:35:19,850 --> 00:35:23,490
+D5 لان القطول حيسير
+
+468
+00:35:27,210 --> 00:35:31,710
+بشكل عام نسمي هذا الطول هو رو، هذا القوس هو عبارة
+
+469
+00:35:31,710 --> 00:35:38,190
+عن رو دي فاية، طب مش كمان؟ هذه جزئية منها D زت،
+
+470
+00:35:38,190 --> 00:35:43,570
+انتقلت من زت نقطة معينة لزقة نقطة معينة، اذا هدول
+
+471
+00:35:43,570 --> 00:35:47,350
+ال differential links في ال cylindrical coordinate
+
+472
+00:35:47,950 --> 00:36:00,370
+هذا هو رو دي فار وهذا هو دي رو وهذا هو دي زد دي
+
+473
+00:36:00,370 --> 00:36:13,130
+الوضع دي الوضع دي الوضع
+
+474
+00:36:13,130 --> 00:36:17,010
+دي الوضع دي الوضع دي الوضع دي الوضع دي الوضع دي
+
+475
+00:36:17,010 --> 00:36:17,010
+الوضع دي الوضع دي الوضع دي الوضع دي الوضع دي الوضع
+
+476
+00:36:17,010 --> 00:36:17,010
+دي الوضع دي الوضع دي الوضع دي الوضع دي الوضع دي
+
+477
+00:36:17,010 --> 00:36:17,010
+الوضع دي الوضع دي الوضع دي الوضع دي الوضع دي الوضع
+
+478
+00:36:17,010 --> 00:36:17,010
+دي الوضع دي الوضع دي الوضع دي الوضع دي الوضع دي
+
+479
+00:36:17,010 --> 00:36:17,270
+الوضع دي الوضع دي الوضع دي ال
+
+480
+00:36:20,490 --> 00:36:24,210
+هذا الاتجاه اللي هو رو هات والعمود اللي عليها فانا
+
+481
+00:36:24,210 --> 00:36:28,270
+علي المنصة اللي بتقرا من هو فاي هات فالتغير عندي
+
+482
+00:36:28,270 --> 00:36:32,250
+لإن فاي بتروح من zero لكو فاي هيكون في اتجاه الدي
+
+483
+00:36:32,250 --> 00:36:34,870
+فاي هات الدي فاي هيكون في اتجاه الدي فاي هات ده ال
+
+484
+00:36:34,870 --> 00:36:40,950
+close to الدي رو دي فاي واتجاه الدي فاي هات معين؟
+
+485
+00:36:41,410 --> 00:36:46,110
+بظلمين اللي هو ال z فعندي dz z hat اذا عندي فيه
+
+486
+00:36:46,110 --> 00:36:48,550
+تغير في تجاه ال raw ب raw differential
+
+487
+00:36:48,550 --> 00:36:53,470
+displacement رو هات القوس هيكون رو دي فاي فاي هات
+
+488
+00:36:53,470 --> 00:36:58,170
+وبعدين اللي هو في تجاه ال z axis اللي هو dz z hat
+
+489
+00:36:58,170 --> 00:37:02,130
+فانهي
+
+490
+00:37:02,130 --> 00:37:05,210
+ال displacement ال differential displacement في ال
+
+491
+00:37:05,210 --> 00:37:10,250
+cylindrical coordinateبنجي لها ال area ال area
+
+492
+00:37:10,250 --> 00:37:13,090
+هتكون حاصل طارب اتنين من هدولة ال surface اللي
+
+493
+00:37:13,090 --> 00:37:15,670
+احنا شوفناهم يعني اتنين من ال coordinates يعني لو
+
+494
+00:37:15,670 --> 00:37:18,790
+انا بحكي على هذا ال area على هذا ال surface او
+
+495
+00:37:18,790 --> 00:37:21,690
+بحكي على هذا ال surface او بحكي على هذا ال surface
+
+496
+00:37:21,690 --> 00:37:25,510
+صحيح؟ ايه ال surfaces التلاتة؟ يعني مثلا بحكي على
+
+497
+00:37:25,510 --> 00:37:28,570
+هذا ال surface ايش هيكون اللي عندي؟ هذا dz اللي هو
+
+498
+00:37:28,570 --> 00:37:33,460
+مثلا pq dzو QP اللي هو ماله رو دي فاي اللي هو
+
+499
+00:37:33,460 --> 00:37:38,660
+القوس فال area هي ايش هتكون دي زد رو دي فاي رو دي
+
+500
+00:37:38,660 --> 00:37:42,680
+فاي دي زد هذه ال area لو احنا بنحكي عن هال area
+
+501
+00:37:42,680 --> 00:37:49,660
+اللي هنا اللي هي SPQR مش فيه متغيرات فيها دي رو و
+
+502
+00:37:49,660 --> 00:37:54,700
+دي زد فهي ثابتة فعرف هذا اتجاه ما هو ثابتة
+
+503
+00:37:57,740 --> 00:38:02,340
+بنفس الزاوية دي five في فانها الرومة بس دائرة
+
+504
+00:38:02,340 --> 00:38:07,380
+تانية و five ثالثة فهذا ال plan إيش هيكون دي رو دي
+
+505
+00:38:07,380 --> 00:38:12,320
+زت هذا ال plan إيش هيكون رو دي five في دي زت هذا
+
+506
+00:38:12,320 --> 00:38:17,220
+إيش هيكون رو دي five في مين في دي رو إذا فني دي
+
+507
+00:38:17,220 --> 00:38:21,260
+تلت surfaces بحوطه جزئيا من ال aspects اللي في ال
+
+508
+00:38:21,260 --> 00:38:25,120
+cylindrical coordinate و قيمة كل واحدة فيهم حاصل
+
+509
+00:38:25,120 --> 00:38:29,000
+ضل ال two links بتاعونهاوكل واحدة مرضوا إليها ال
+
+510
+00:38:29,000 --> 00:38:33,680
+norm اللي عليها يعني
+
+511
+00:38:33,680 --> 00:38:38,300
+مثلا هذه اللي هي ال قوص رو D5 في DZ وين هيكون
+
+512
+00:38:38,300 --> 00:38:40,760
+اتجاهها؟ مين اللي سبب في هذه الحالة؟ اللي هو ال
+
+513
+00:38:40,760 --> 00:38:46,520
+raw hat ال raw hat يعني مش عليها ليه هذه؟ هذه
+
+514
+00:38:46,520 --> 00:38:52,300
+الشقفة، هذه الجزئية اللي هو DZ وهي رو D5 وين هيكون
+
+515
+00:38:52,300 --> 00:38:55,860
+ال norm عليها؟ عمودي على هذا هو اتجاه ال raw hat
+
+516
+00:38:55,860 --> 00:39:02,130
+واضح؟هذه الجزئية اللي هي رو دي رو دي زد هذي انا
+
+517
+00:39:02,130 --> 00:39:05,450
+هيقول دي رو و هذا دي زد اللي عاموتي هيكون في تجاه
+
+518
+00:39:05,450 --> 00:39:09,610
+الـ pi hat و اللي فوق اللي هي فرع رو دي في في دي
+
+519
+00:39:09,610 --> 00:39:15,890
+رو هيكون في تجاه الـ z hat واضح؟
+
+520
+00:39:15,890 --> 00:39:19,510
+اذا عندي رو دي في دي زد اتجاهها اتجاه الـ رو hat
+
+521
+00:39:19,510 --> 00:39:23,490
+عندي دي رو دي زد هيكون اتجاهها في الـ pi hat دي رو
+
+522
+00:39:23,490 --> 00:39:29,620
+رو دي في هيكون اتجاه الـ z hatواضح؟ اذا شوفنا ال
+
+523
+00:39:29,620 --> 00:39:32,420
+differential links و اخرجت شوفنا ال surface ال
+
+524
+00:39:32,420 --> 00:39:35,880
+differential surface و اتجاهه اللى هو دايما زى ما
+
+525
+00:39:35,880 --> 00:39:39,720
+اتفقنا عمودي على ال surface اللى بنحكى عنه فمثلا
+
+526
+00:39:39,720 --> 00:39:44,500
+DS vector هتكون رو D5 و DZ اتجاهها هيكون طبعا
+
+527
+00:39:44,500 --> 00:39:47,160
+انتوا لما تشوفوا D5 و DZ انتوا عارفين مين الثابت
+
+528
+00:39:47,160 --> 00:39:50,600
+اللى هو ال rawبتجاه الـ rho hat هنا مين السابق الـ
+
+529
+00:39:50,600 --> 00:39:53,780
+d rho d z اللي هي الـ phi تجاه الـ phi hat هنا
+
+530
+00:39:53,780 --> 00:39:57,480
+السابق مين اللي هو الـ z فعندي rho d rho d phi
+
+531
+00:39:57,480 --> 00:40:03,720
+تجاه الـ z hat طيب ال volume مش هيكون حاصل ضغط
+
+532
+00:40:03,720 --> 00:40:09,400
+بالتلاتة اللي هو rho d rho d phi ب d z أنا عندي
+
+533
+00:40:09,400 --> 00:40:13,760
+القوس rho d phi وفي عندي اللي هو d rho و في d z
+
+534
+00:40:13,760 --> 00:40:15,200
+إذا عندي d rho
+
+535
+00:40:22,280 --> 00:40:25,140
+اللقاء القادم ان شاء الله هنعمل هو الـ spherical
+
+536
+00:40:25,140 --> 00:40:28,620
+coordinate نشوف فيه ال differential displacement و
+
+537
+00:40:28,620 --> 00:40:31,760
+ال differential area و ال differential volume
+
diff --git a/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/iWj--QJF6uM_postprocess.srt b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/iWj--QJF6uM_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..b989bb93b33c7f3272a871d1db758d0225dd25c4
--- /dev/null
+++ b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/iWj--QJF6uM_postprocess.srt
@@ -0,0 +1,2680 @@
+1
+00:00:12,710 --> 00:00:15,490
+بسم الله الرحمن الرحيم السلام عليكم ورحمة الله
+
+2
+00:00:15,490 --> 00:00:20,550
+وبركاته احنا اليوم هناخد بيو سفارت لاو و أمبرز لاو
+
+3
+00:00:20,550 --> 00:00:23,870
+كم مرة أمبرز لاو احنا مرق علينا هناخده كم مرة لكن
+
+4
+00:00:23,870 --> 00:00:27,450
+بيو سفارت لاو اول مرة هناخده احنا اذا بدنا من هاي
+
+5
+00:00:27,450 --> 00:00:31,010
+المعادلة بي kill ال A احنا يعني ماعنها مين هي kill
+
+6
+00:00:31,010 --> 00:00:36,140
+ال B صح؟كرل كرل ال A اللي هي كرل ال B هذه معادلة
+
+7
+00:00:36,140 --> 00:00:39,280
+شفناها قبل هيك لما أخدنا ال calculus لما كرل كرل
+
+8
+00:00:39,280 --> 00:00:42,340
+ال B ومتذكرين قلتلكوا كرل كرل انا أشعر ان انتوا
+
+9
+00:00:42,340 --> 00:00:46,160
+بتدل ال diversity لما ينزل تربية M متذكرينها
+
+10
+00:00:46,160 --> 00:00:50,160
+فزنعيلنا هاي المعادلة وكمان احنا هنبدأ من عشان
+
+11
+00:00:50,160 --> 00:00:53,740
+نشتق بياصورت لو انا مش هشتقه بس هحكي على السريع ان
+
+12
+00:00:53,740 --> 00:00:58,090
+B هي أدوة عن كرل ال A لو بدأنا من هناو اشتغلنا
+
+13
+00:00:58,090 --> 00:01:02,630
+شوية على ال curve و شوية على تعريفاتها احصلوا على
+
+14
+00:01:02,630 --> 00:01:05,930
+اللي هو bios of our plot مجرد من curve ال A بداية
+
+15
+00:01:05,930 --> 00:01:09,510
+من curve ال A اعوض عن A اللي هي mu not I دي ال ال
+
+16
+00:01:09,510 --> 00:01:13,850
+prime على four by R واخد ال curve لواحد على R لإنه
+
+17
+00:01:13,850 --> 00:01:18,930
+curve بس بيأثر على مين؟ على R، R فيها X وY وZفدلبس
+
+18
+00:01:18,930 --> 00:01:24,870
+باصلة R بستخدم identity اللى هى علاقة بالcurve و
+
+19
+00:01:24,870 --> 00:01:29,370
+بجيب اللى هى القيم اللى بعوض مجرد تعويض مباشر بحصل
+
+20
+00:01:29,370 --> 00:01:33,150
+على اللى هو بيو سفرتلو مش بتطلب منه اشتقاق بيو
+
+21
+00:01:33,150 --> 00:01:36,870
+سفرتلو بقولنا ان ال magnetic field بساوة mu node
+
+22
+00:01:36,870 --> 00:01:42,070
+على 4pi ال line integral ل IDL اللى هو ال element
+
+23
+00:01:42,430 --> 00:01:45,650
+من الـ Filament اللي مضروف فيها تيار مضروف في تيار
+
+24
+00:01:45,650 --> 00:01:49,430
+مضروف في هذا الـ Filament الـ cross R hat اللي هو
+
+25
+00:01:49,430 --> 00:01:52,610
+ال unit vector من ال element هذا للنقطة الباقية
+
+26
+00:01:52,610 --> 00:01:56,210
+ساعدها الوطن شرك ال cross R hat على R تربيهة و
+
+27
+00:01:56,210 --> 00:01:59,370
+احنا شوفناها قبلها كده المعادلة هذه اللي هي curl
+
+28
+00:01:59,370 --> 00:02:03,470
+بيه انها بتساوي curl curl A بتذكرينها يعني curl
+
+29
+00:02:03,470 --> 00:02:06,770
+curl A بتساوي grade divergence A minus delta بيه R
+
+30
+00:02:06,770 --> 00:02:11,420
+إذا أخدنا ان divergence A بيساوي Zeroفي هذه الحالة
+
+31
+00:02:11,420 --> 00:02:15,680
+بيكون عندنا دل تربيع ايه ايش بتساوي سالب curl ال B
+
+32
+00:02:15,680 --> 00:02:21,820
+اللي هي سالب ميو curl ال H لأن بي بتساوي ميو نوض H
+
+33
+00:02:21,820 --> 00:02:24,560
+ميو نوض اللي هي في ال free space ميو نوض بقالها
+
+34
+00:02:24,560 --> 00:02:27,780
+isotropic constant في ال free space فهي هم جنس
+
+35
+00:02:27,780 --> 00:02:31,220
+isotropic والاخر يعني فدل تربيع هتساوي minus ميو
+
+36
+00:02:31,220 --> 00:02:36,530
+نوض curl ال H وcurl ال H بتساوي Jفإذا دي التربيع A
+
+37
+00:02:36,530 --> 00:02:40,690
+بيساوي minus الـ mu0 J وهدي عبارة عن vector بس هو
+
+38
+00:02:40,690 --> 00:02:45,050
+equation مش vector لإن ال A vector field وJ ال
+
+39
+00:02:45,050 --> 00:02:49,390
+vector field هدي
+
+40
+00:02:49,390 --> 00:02:54,570
+عبارة عن دي التربيع ل A vector يعني A XXH زائد
+
+41
+00:02:54,570 --> 00:03:04,380
+AYYH زائد AZZH ده تساوي minus ال mu0 وهدي J XXHزي
+
+42
+00:03:04,380 --> 00:03:09,600
+جي وي وي هت زي جي وزي زي وزي كمان احنا بتقدر نقسم
+
+43
+00:03:09,600 --> 00:03:14,460
+المعادلة لثلاث معادلات ال X component لازم تسوى X
+
+44
+00:03:14,460 --> 00:03:16,460
+component ال Y component لازم تسوى Y component
+
+45
+00:03:16,460 --> 00:03:25,800
+فبقدر اقسمها ل three scalar components واضح؟
+
+46
+00:03:36,780 --> 00:03:40,740
+واضح؟ في أسف سلحتنا؟ إذا إحنا ال vector basal
+
+47
+00:03:40,740 --> 00:03:45,100
+equation بتسير إلينا اللي هي بقدر أكتبها أشكل ال
+
+48
+00:03:45,100 --> 00:03:48,780
+components فبتكون three scalar equations
+
+49
+00:03:53,840 --> 00:03:58,480
+أحنا متذكرين ان ال close line integral ل H.DL بقدر
+
+50
+00:03:58,480 --> 00:04:02,080
+استخدم stock theorem تعطينا surface integral لكل H
+
+51
+00:04:02,080 --> 00:04:08,940
+.DS وكل ال H منها 1 على new node B فبتصير كل ال B
+
+52
+00:04:09,660 --> 00:04:13,980
+كل كل ال a واضح بيقولها ايجت h هي واحدة ع ال mu
+
+53
+00:04:13,980 --> 00:04:18,700
+not b فh بتسوى بي بتسوى كل a فهي هتكون واحدة ع ال
+
+54
+00:04:18,700 --> 00:04:22,080
+mu ال surface integral كل كل ال a دلوقتي اصلا كل
+
+55
+00:04:22,080 --> 00:04:25,260
+كل ال a احنا قولنا في حالة diverge a بتسوى zero
+
+56
+00:04:25,260 --> 00:04:30,540
+بتسوى هذه المعادلة كل كل a بتسوى minus delta b a
+
+57
+00:04:31,960 --> 00:04:36,320
+بعود مباشرة عن كرر
+
+58
+00:04:36,320 --> 00:04:42,160
+كرر ل A بقاش من ميو
+
+59
+00:04:42,160 --> 00:04:50,440
+نوت جيال
+
+60
+00:04:50,440 --> 00:04:53,880
+ميو نوت بتروح مع ميو نوت هتصبح ال surface integral
+
+61
+00:04:53,880 --> 00:04:57,390
+ل جهد ال DSالـ service integral دي أسمين هي
+
+62
+00:04:57,390 --> 00:04:59,890
+التيارة اذا ال numbers دول اللي احنا شفناها قبل
+
+63
+00:04:59,890 --> 00:05:02,250
+هيك ال line enclosed line integral اتش و ال dl
+
+64
+00:05:02,250 --> 00:05:08,830
+بتساوي ال enclosed كمان فاضح؟ احنا بنكون خلصمهم
+
+65
+00:05:08,830 --> 00:05:14,810
+الجرئية هاي من الشبتر او يعني ما هتمن هذا الشبتر
+
+66
+00:05:14,810 --> 00:05:18,530
+بيبقى علينا المبدأ ان شاء الله شبتر تمانين اذا
+
+67
+00:05:18,530 --> 00:05:22,530
+مافيش اي استفسار في اي استفسار؟
+
+68
+00:05:25,500 --> 00:05:31,200
+الشبطر 8 هو magnetic force سنركز
+
+69
+00:05:31,200 --> 00:05:34,340
+على magnetic force في هذا الشبطر
+
+70
+00:05:42,290 --> 00:05:45,890
+يا أستاذ بس هدأ نقوله magnetic force و لا انوان
+
+71
+00:05:45,890 --> 00:05:49,130
+هيكون الدكتورة هل جيتها في chapter 7 شرحت اللي
+
+72
+00:05:49,130 --> 00:05:52,290
+عندى slide 55 اللي الباقى مش مطلوب ولا عادى؟ لأ
+
+73
+00:05:52,290 --> 00:05:55,830
+الباقى أنا كنت حاطة اللي هى الأمثلة و أسئلة و
+
+74
+00:05:55,830 --> 00:06:04,550
+مركزة بس خلاص هيك اه اللي هو magnetic force اذا ان
+
+75
+00:06:04,550 --> 00:06:06,690
+شاء الله اليوم احنا هنبدأ ال magnetic force
+
+76
+00:06:06,690 --> 00:06:10,410
+يابنخلصها يا ان شاء الله لازم ده كمان محاضرة
+
+77
+00:06:12,240 --> 00:06:15,600
+إذا بدنا نحسب ال force due to magnetic field، فيه
+
+78
+00:06:15,600 --> 00:06:19,200
+هنا تلت طرُب اللي ممكن نحسب فيها ال magnetic force
+
+79
+00:06:19,200 --> 00:06:22,100
+أو يعني اللي نحكي فيها عن magnetic force ناتجة عن
+
+80
+00:06:22,100 --> 00:06:25,290
+magnetic field، يعني لو أنا دي magnetic fieldو في
+
+81
+00:06:25,290 --> 00:06:28,130
+عندى charge فى قلب هذا ال magnetic field بتتحرك
+
+82
+00:06:28,130 --> 00:06:30,910
+بيكون فى عندى force على ال charge اللى بتتحرك هى
+
+83
+00:06:30,910 --> 00:06:34,490
+أول نوع اذا في الأول افترض ان بدي magnetic field
+
+84
+00:06:34,490 --> 00:06:36,610
+بدي أشوف ايش القوة اللى بتأثر فيها ال magnetic
+
+85
+00:06:36,610 --> 00:06:40,430
+field على إيش و كيف أحسبها فعندي تلت أنواع انه
+
+86
+00:06:40,430 --> 00:06:43,670
+يكون عندى magnetic field بت charge بتتحرك لازم
+
+87
+00:06:43,670 --> 00:06:47,410
+تكون تتحرك اذا ساكنة مش هعندي force لازم تكون
+
+88
+00:06:47,410 --> 00:06:50,550
+تتحرك اذا فى عندى moving charge بيكون عندى force
+
+89
+00:06:50,550 --> 00:06:53,630
+متولدة على هى ال moving charge نتيجة وجود ال
+
+90
+00:06:53,630 --> 00:06:58,050
+magnetic fieldالتانى لو كان عندى current element
+
+91
+00:06:58,050 --> 00:07:02,610
+أسوأ يعني line ولا surface plane ولا volume و هذا
+
+92
+00:07:02,610 --> 00:07:08,830
+ال element موجودفى external field برضه هنقيص القوة
+
+93
+00:07:08,830 --> 00:07:12,270
+على ال current ال current بمعنى load charge متحركة
+
+94
+00:07:12,270 --> 00:07:15,730
+هيكون هذا القانون أعمل من moving charge moving
+
+95
+00:07:15,730 --> 00:07:20,070
+charge بحكي عنه charge واحدة ال current تدفق من ال
+
+96
+00:07:20,070 --> 00:07:23,650
+charges يعني لازم احنا بنحكي عن charges متحركة
+
+97
+00:07:23,650 --> 00:07:27,270
+أسوأ في filament أو في surface أو في volume ايش
+
+98
+00:07:27,270 --> 00:07:30,890
+القوة اللى بتأثر على هذا ال current نتيجة وجوده فى
+
+99
+00:07:30,890 --> 00:07:37,030
+ال magnetic fieldاخر واحدة طيارين، بس هو في .. في
+
+100
+00:07:37,030 --> 00:07:40,290
+خطين، في two filaments أو في two planes أو في two
+
+101
+00:07:40,290 --> 00:07:43,530
+volumes، إذا بتحركوا يعني ال current مدافي،
+
+102
+00:07:43,530 --> 00:07:45,990
+current يعملها تشارج اسمها اللي هم تحركها، إيش
+
+103
+00:07:45,990 --> 00:07:49,490
+القوة اللي بتنتج على واحد من هدولة ال filaments،
+
+104
+00:07:49,490 --> 00:07:52,810
+نتيجة وجوده في المجال المواطيسي للfilament التاني؟
+
+105
+00:07:52,810 --> 00:07:55,510
+هنا مابنحكيش على external field، ملاحظين؟ الحل
+
+106
+00:07:55,510 --> 00:07:59,490
+قولنا إنه moving chargeفى magnetic field التانى
+
+107
+00:07:59,490 --> 00:08:01,850
+قولنا current فى external التالت قولنا two
+
+108
+00:08:01,850 --> 00:08:05,590
+currents واحد منهم هيولد magnetic field هتكون فى
+
+109
+00:08:05,590 --> 00:08:08,530
+قوة تولد على التانى نتيجة من ال magnetic field
+
+110
+00:08:08,530 --> 00:08:12,470
+اللى نتاج من الأول واضح؟طب إذا ما بنحكي عن القوة
+
+111
+00:08:12,470 --> 00:08:15,470
+بنحكي عن هاي التلات حلوة نبدأ في مين في اللي هي
+
+112
+00:08:15,470 --> 00:08:19,670
+moving charge قل قلنا إذا في عندي magnetic field
+
+113
+00:08:19,670 --> 00:08:23,310
+وفي عندي charge اللي بتتحرك بتتحرك في وجود ال
+
+114
+00:08:23,310 --> 00:08:28,450
+magnetic field هيتولد عندي magnetic force بتساوي Q
+
+115
+00:08:28,450 --> 00:08:31,810
+اللي هي قيمة ال charge V ال volume بتاع ال charge
+
+116
+00:08:31,810 --> 00:08:39,950
+cross B إذا القوة هذه هتكون Q في V cross Bمالها
+
+117
+00:08:39,950 --> 00:08:42,970
+إيش هتكون نوع ال force عمودية لأنها دي مالها right
+
+118
+00:08:42,970 --> 00:08:48,250
+hand rule P X P هتكون F صح؟ إذا هيتولد عندي قوة
+
+119
+00:08:48,250 --> 00:08:52,450
+عمودية على حركة ال particle و على magnetic field
+
+120
+00:08:52,450 --> 00:08:57,230
+إذا هدولة التلت components عمودين على بعض ال
+
+121
+00:08:57,230 --> 00:09:01,170
+velocity و ال magnetic field و ال force الناتجة
+
+122
+00:09:01,170 --> 00:09:05,550
+إذا بيستنتج إنه ال magnetic force هذي رمز منها
+
+123
+00:09:05,550 --> 00:09:09,830
+يعني magnetic force فيه معناه أفعىالـ magnet force
+
+124
+00:09:09,830 --> 00:09:12,770
+بتولدش عنها work، فانا بذكرى إيش ال work اللي احنا
+
+125
+00:09:12,770 --> 00:09:18,830
+قولنا هو F d work مثلا F دو ال DL أو التكامل line
+
+126
+00:09:18,830 --> 00:09:22,150
+integral F دو ال DL ال force مالهبش في اتجاه
+
+127
+00:09:22,150 --> 00:09:25,750
+الحركة عمودية عليها فF دو ال DR إيش بده تساوي؟
+
+128
+00:09:25,750 --> 00:09:30,170
+Zero ال velocity فين؟ اتجاه و القوة عمودية عليها
+
+129
+00:09:30,170 --> 00:09:35,090
+فF دو ال DL إيش بده تساوي؟ Zero إذا ال work الناقش
+
+130
+00:09:35,090 --> 00:09:37,150
+من القوة المواطية بساوة Zero
+
+131
+00:09:43,260 --> 00:09:49,080
+غالبا بيكون ال magnitude لل magnetic force مهمل
+
+132
+00:09:49,080 --> 00:09:55,660
+جنب القوة بتاعة ال electric field و طبعا اول حاجة
+
+133
+00:09:55,660 --> 00:09:59,160
+انه ال magnetic force بتتولد فقط عند moving charge
+
+134
+00:09:59,160 --> 00:10:03,500
+يعني انا لو عندي charge في electric field هيتولد
+
+135
+00:10:03,500 --> 00:10:08,980
+عندي force، force بالساوة Q في E، صح؟لو اتحركت ال
+
+136
+00:10:08,980 --> 00:10:12,260
+charge في وجود ال magnetic field هيتولد اندي كمان
+
+137
+00:10:12,260 --> 00:10:15,340
+قوة ناتجة من magnetic field بس ما تتحرك من ال
+
+138
+00:10:15,340 --> 00:10:18,340
+charge هتفترض ان في اندي electric field و magnetic
+
+139
+00:10:18,340 --> 00:10:21,600
+field و اتولد اندي two قوة ال F electric اللي هي
+
+140
+00:10:21,600 --> 00:10:24,560
+القوة الناتجة على ال charge نتيجة وجودها في ال
+
+141
+00:10:24,560 --> 00:10:27,420
+electric field و عاملها بتتحرك و في magnetic field
+
+142
+00:10:27,420 --> 00:10:30,320
+فكمان اندي كمان قوة بتأثر عليها نتيجة وجودها في
+
+143
+00:10:30,320 --> 00:10:33,580
+magnetic field دائما بتكون القوة اللي ناتجة من
+
+144
+00:10:33,580 --> 00:10:36,240
+magnetic field أقل بكتير من ناتجة من ال electric
+
+145
+00:10:36,240 --> 00:10:41,990
+fieldتهبل في .. لأن غالبا بتكون ال velocity صغيرة
+
+146
+00:10:41,990 --> 00:10:46,390
+كتير لكن لو كانت ال velocity قريبة من سرعة الضوء
+
+147
+00:10:46,390 --> 00:10:49,950
+تلاتة فعاشرة قوة تمانية قريبة منها ساعتها ماقدرش
+
+148
+00:10:49,950 --> 00:10:54,450
+أحمل ال magnetic force لكن بشكل عام بتكون ال
+
+149
+00:10:54,450 --> 00:10:58,550
+magnetic force صغيرة مقارنة مع ال electric force
+
+150
+00:10:58,550 --> 00:11:00,970
+صح؟
+
+151
+00:11:03,880 --> 00:11:08,820
+E عبارة عن KQ نخدة أبسط حاجة KQ1 KQ2 على 4 بي أرثر
+
+152
+00:11:08,820 --> 00:11:15,060
+بي اللي قبل كيو طلعناها فهتكون KQ1 مثلا اللي نجم
+
+153
+00:11:15,060 --> 00:11:17,400
+ال electric field نجم نفترض انه جامن point of
+
+154
+00:11:17,400 --> 00:11:23,120
+charge قمتها كيو واحد فهتكون E KQ1 على أو واحد على
+
+155
+00:11:23,120 --> 00:11:27,800
+4 بي إبسلنون KQ على أرثر بيه صح او الواحد على 4 بي
+
+156
+00:11:27,800 --> 00:11:30,820
+إبسلنون مش هي K 9 constant 9 فعشان قوة 9
+
+157
+00:11:35,740 --> 00:11:39,620
+مقارنة مع ان هي ال magnetic field اللى بتتعداش
+
+158
+00:11:39,620 --> 00:11:42,560
+يعني a few values يعني بتكون صغير كتير ال magnetic
+
+159
+00:11:42,560 --> 00:11:47,280
+field نجي
+
+160
+00:11:47,280 --> 00:11:50,480
+لقى ال force بشكل عام ماقدر أكتبها بدلالة ال
+
+161
+00:11:50,480 --> 00:11:54,700
+electric force و ال magnetic force فإذا F بتساوي Q
+
+162
+00:11:54,700 --> 00:11:58,960
+في E اللى هي ال electric force زائد U cross B اللى
+
+163
+00:11:58,960 --> 00:12:02,360
+هي ال magnetic force هذه كلها بنسميها Lorentz
+
+164
+00:12:02,360 --> 00:12:06,880
+forceلما نحكي عشان أسألك امتحان ايش هي ال lawrence
+
+165
+00:12:06,880 --> 00:12:09,440
+force ال lawrence force هي مجموعة electric و
+
+166
+00:12:09,440 --> 00:12:14,600
+magnetic forces طبعا force بشكل عام على moving
+
+167
+00:12:14,600 --> 00:12:22,000
+object او على اللي اللي له كتلة هو m dv by dt صح؟
+
+168
+00:12:22,000 --> 00:12:26,400
+mdv by dt اذا ال total force هي م ايه؟ اللي هي ال
+
+169
+00:12:26,400 --> 00:12:31,080
+acceleration هي dv by dt بتسوى q في e plus v cross
+
+170
+00:12:31,080 --> 00:12:31,340
+b
+
+171
+00:12:34,630 --> 00:12:42,630
+لو كانت قوة
+
+172
+00:12:42,630 --> 00:12:53,170
+قوة
+
+173
+00:12:53,170 --> 00:12:57,250
+قوة
+
+174
+00:12:57,250 --> 00:13:02,350
+قوة قوة قوة قوة قوة قوة قوة قوة قوة قوة قوة قوة
+
+175
+00:13:02,350 --> 00:13:06,560
+قوة قوة قوة قوة قوة قوة قوةلو كانت moving فهيكون
+
+176
+00:13:06,560 --> 00:13:09,420
+فى عندى electric field force ناجة من ال electric
+
+177
+00:13:09,420 --> 00:13:12,740
+field QE أو force ناجة من ال magnetic field هي QV
+
+178
+00:13:12,740 --> 00:13:19,440
+cross P و ال total اللى هى لورانز force نيجي
+
+179
+00:13:19,440 --> 00:13:24,960
+لفورس الناجة من ال current filament طبعا أنا مش
+
+180
+00:13:24,960 --> 00:13:28,880
+هاقود كتير فى الإشتقال بس البساطة هي عشان نربط ال
+
+181
+00:13:28,880 --> 00:13:34,870
+twoالمعادلات لان احنا عارفين ان ال current density
+
+182
+00:13:34,870 --> 00:13:40,470
+بتساوره في V طبعا هبقدر اشتغل ال forces اللي ناتجة
+
+183
+00:13:40,470 --> 00:13:44,790
+على filament اللي موجود فيها طيار من القانون QV
+
+184
+00:13:44,790 --> 00:13:52,550
+cross B بيناقول ان DF بدل ما اقول QV ايش هتكون IDL
+
+185
+00:13:52,550 --> 00:13:54,210
+cross B
+
+186
+00:13:58,310 --> 00:14:04,230
+العلاقة بين I D L و V D Q مثلا V D Q تصبح I D L
+
+187
+00:14:04,230 --> 00:14:09,890
+أسوأ للـ line أو ال surface أو ال volume I D L
+
+188
+00:14:09,890 --> 00:14:14,910
+بتسوء K D S بتسوء J D V وهذا ال I D L لو عوضناه عن
+
+189
+00:14:14,910 --> 00:14:20,710
+I بنها J باليونة volume أو باليونة surface هتكون
+
+190
+00:14:20,710 --> 00:14:26,850
+رو في V D Vبدل مقاومة عوض عنها لإن بدنا ال J اللي
+
+191
+00:14:26,850 --> 00:14:34,030
+هي رو في V اللي يمينها دي I في DS صح ف ID او IDL
+
+192
+00:14:34,030 --> 00:14:39,210
+رو V دي U هتكون انها اللي هي رو V دي V بدل ال
+
+193
+00:14:39,210 --> 00:14:42,110
+current استخدامنا ال current DC اللي هي J دي V
+
+194
+00:14:42,110 --> 00:14:47,150
+هيكون انها اللي هي V دي Q اللي هي مين رو دي V رو
+
+195
+00:14:47,150 --> 00:14:52,970
+دي V اللي هي DQ صح؟فانا مش هاطلب منكم تاخدوا
+
+196
+00:14:52,970 --> 00:14:55,910
+التفاصيل بتاعة الاشتقاق لكن ان احنا بساطة علاقة
+
+197
+00:14:55,910 --> 00:14:58,470
+ممكن نبدأها من ان ما ان ال current density
+
+198
+00:14:58,470 --> 00:15:02,630
+بتساوروا في V ممكن استخدمها عشان احصل على القوة
+
+199
+00:15:02,630 --> 00:15:07,270
+الناتجة على فعلا ما تمبر فيها ال current في وجود
+
+200
+00:15:07,270 --> 00:15:09,110
+ال magnetic field يعني ان عندي magnetic field
+
+201
+00:15:09,110 --> 00:15:13,460
+موجودوفي عندى element بيبور في التيار فهتتولد على
+
+202
+00:15:13,460 --> 00:15:17,620
+هذا ال element قوة مقدرها ال close line integral I
+
+203
+00:15:17,620 --> 00:15:22,900
+DL DL هنا vector cross B vector و ال force بتكون
+
+204
+00:15:22,900 --> 00:15:27,180
+اللى عموديه على ال filament و المجنون فيه لو كانت
+
+205
+00:15:27,180 --> 00:15:31,360
+surface يعني عندى plane و مافيه current هتكون Kds
+
+206
+00:15:31,360 --> 00:15:35,480
+cross B او لو كانت عندى اللى هي volume هيكون ال
+
+207
+00:15:35,480 --> 00:15:39,240
+volume integral لGDV cross B واضح؟
+
+208
+00:15:42,860 --> 00:15:45,840
+أحيانا الناس بتسمي ال magnetic fields هو ال force
+
+209
+00:15:45,840 --> 00:15:51,820
+per unit current element يعني ال current element F
+
+210
+00:15:51,820 --> 00:15:56,640
+على IDL هاي ال B force per unit current element أو
+
+211
+00:15:56,640 --> 00:16:00,600
+يعني B بيسوا F على GV أو F على KDS
+
+212
+00:16:06,110 --> 00:16:09,330
+أحنا شفنا ال force انها جامن اللى هو ال magnetic
+
+213
+00:16:09,330 --> 00:16:12,010
+field على point of charge انه بتساوي افضل تساوي qv
+
+214
+00:16:12,010 --> 00:16:16,290
+cross b ال force اللى بنتجها ال magnetic field على
+
+215
+00:16:16,290 --> 00:16:19,670
+filament او plane او volume اللى بتساوي ال force
+
+216
+00:16:19,670 --> 00:16:28,390
+بتساوي ال line integral idl cross b اوI D L X B او
+
+217
+00:16:28,390 --> 00:16:34,090
+K D S X B او J D V X B طب لو كانوا two lines مثلا
+
+218
+00:16:34,090 --> 00:16:36,970
+كل واحد مور فيه تيار زى ما انتوا شايفين هنا و انا
+
+219
+00:16:36,970 --> 00:16:41,170
+اتجيب القوة اللى على ال line الاول اللى ناتجه من
+
+220
+00:16:41,170 --> 00:16:45,690
+مرور التيار فى ال line التانى هناخدله elements ان
+
+221
+00:16:45,690 --> 00:16:50,130
+ال element تبعنا I 1 D I 1 و ال element التانى I 2
+
+222
+00:16:50,130 --> 00:16:55,920
+D I 2 القوة اللى ناتجه على ال element الاولاللي هو
+
+223
+00:16:55,920 --> 00:17:02,520
+I1D1 من مرشود من مرور الطيارة في ال element I2DI2
+
+224
+00:17:04,620 --> 00:17:08,600
+I1TI1 cross mean DB2 اللي هو ال magnetic field
+
+225
+00:17:08,600 --> 00:17:13,240
+الناتج من ال element I2DI2 يعني باختصار أنا بجيب
+
+226
+00:17:13,240 --> 00:17:17,600
+القوة على ال element اللي أنا مسميها واحد ال مورفي
+
+227
+00:17:17,600 --> 00:17:22,380
+تيار نتيجة ال magnetic field اللي ناتجة من مرور
+
+228
+00:17:22,380 --> 00:17:25,620
+التيار في ال element التاني فالقوة الناتجة between
+
+229
+00:17:25,620 --> 00:17:29,100
+two current elements هي ببساطة بقدر ابسطها اقول ان
+
+230
+00:17:29,100 --> 00:17:31,700
+هي القوة الناتجة على ال element الأول او ال
+
+231
+00:17:31,700 --> 00:17:36,030
+element الأول نتيجة مرورنتيجة ال magnetic field
+
+232
+00:17:36,030 --> 00:17:39,750
+المتولدة من مرور التيار في ال element التاني لو
+
+233
+00:17:39,750 --> 00:17:44,690
+عوضنا بيوسفر بلو HDB بالساوية ميو نوت اي تنين دي
+
+234
+00:17:44,690 --> 00:17:49,690
+اي تنين اكروس ارهاد على four by ار تربيع وين هي ار
+
+235
+00:17:49,690 --> 00:17:53,530
+هي المسافة ما بين ال element اللي بيولد ال
+
+236
+00:17:53,530 --> 00:17:56,410
+magnetic field و النقطة اللي انا بحسب عندها ال
+
+237
+00:17:56,410 --> 00:18:01,170
+forceيعني في ال space إيش بكون بحط حط ال position
+
+238
+00:18:01,170 --> 00:18:06,810
+تبع هذا هيكون R1 ال position تبع هذا R2 وR21 هي
+
+239
+00:18:06,810 --> 00:18:11,490
+عبارة عن المسافة بين ال source اللي هو ال element
+
+240
+00:18:11,490 --> 00:18:14,670
+اللي بولد المجد فيه و المكان اللي بقي اسم منه let
+
+241
+00:18:14,670 --> 00:18:20,900
+charge اللي هو هسميه R21 لو عوضت عن اللي هو DB2في
+
+242
+00:18:20,900 --> 00:18:25,200
+المعادلة بتاعتي هيكون عندي ميو نوت اي واحد دي
+
+243
+00:18:25,200 --> 00:18:29,540
+الواحد ال cross عند cross product اي تانين دي اي
+
+244
+00:18:29,540 --> 00:18:35,030
+تانين cross are hat على four by are تربيةأذا عندي
+
+245
+00:18:35,030 --> 00:18:38,970
+بقدر أقول ال total force هي double انتيجرة عندي دي
+
+246
+00:18:38,970 --> 00:18:42,510
+I1 و دي I2 اذا عندي double انتيجرة اذا اقف واحد
+
+247
+00:18:42,510 --> 00:18:46,910
+منه I1 I2 بطلعهم برا على 4πI ال double integer
+
+248
+00:18:46,910 --> 00:18:51,090
+المر على اللوب الأول و مر على اللوب التاني طبعا
+
+249
+00:18:51,090 --> 00:18:53,870
+حتى اللوب التاني بيعطيني كل الماجنة تفيد انها تجمد
+
+250
+00:18:53,870 --> 00:18:56,980
+مرور تيار في كل ال elementsلو أخد قطعة صغيرة قطعة
+
+251
+00:18:56,980 --> 00:18:59,800
+صغيرة بدي أكمل عليهم كلهم بيعطيني ال magnitude
+
+252
+00:18:59,800 --> 00:19:04,280
+الناتج من كل ال loop و لما أكمل على الواحد ايش
+
+253
+00:19:04,280 --> 00:19:08,420
+بيعطيني اول حاجة لما أخد قطعة هنا أكمل كليا بقول
+
+254
+00:19:08,420 --> 00:19:11,220
+كل القوة الناتجة من كل ال elements على هذا ال loop
+
+255
+00:19:11,220 --> 00:19:15,040
+على هذا ال element I1DI1 لما أكمل على ال loop
+
+256
+00:19:15,040 --> 00:19:18,280
+التاني بيعطيني كل القوة الناتجة على هذا ال loop من
+
+257
+00:19:18,280 --> 00:19:22,540
+نتيجة اللي هو ال loop التاني واضح؟هيكون دي الواحد
+
+258
+00:19:22,540 --> 00:19:27,420
+cross دي الاتنين cross R ها على R اتنين واحد تربيه
+
+259
+00:19:27,420 --> 00:19:31,320
+طبعا لو انا بد القوة اللى بيأثرها ال element واحد
+
+260
+00:19:31,320 --> 00:19:34,220
+او ال filament واحد على اتنين هتكون بتساوى بال
+
+261
+00:19:34,220 --> 00:19:36,800
+تمام في المقدار القوة اللى بيأثرها ال filament
+
+262
+00:19:36,800 --> 00:19:39,640
+اتنين على واحد بس بتعكسها باتجاهها زى ما انتوا
+
+263
+00:19:39,640 --> 00:19:42,860
+شايفين هذه هتكون اتجاهها هيك بينما اتجاه التاني
+
+264
+00:19:42,860 --> 00:19:47,320
+هيك يعني دي F واحد هي اتجاهها دي F تاني هتكون
+
+265
+00:19:47,320 --> 00:19:49,780
+العكس يعني دي F واحد
+
+266
+00:19:58,850 --> 00:20:05,040
+خلصنا القوانينأخر واحد هو يمكن البس أطولهم بس كنت
+
+267
+00:20:05,040 --> 00:20:09,760
+بتذكروهم مجرد اللي هو اضعف بيو سوبرت لو على I DL
+
+268
+00:20:09,760 --> 00:20:14,120
+هذا هى بس بنكامل طبعا عشان نجيب ال total force و
+
+269
+00:20:14,120 --> 00:20:17,080
+بنكامل على بيو سوبرت لو اذا أف و أح سو نيون اي
+
+270
+00:20:17,080 --> 00:20:20,360
+واحد اي اتين اربع اربع اي دوبل انتيجرة DL واحد
+
+271
+00:20:20,360 --> 00:20:23,280
+across DL تانين across R hat اللي هو ال unit
+
+272
+00:20:23,280 --> 00:20:26,260
+vector بين ال two elements على اللي هو R تانين
+
+273
+00:20:26,260 --> 00:20:31,630
+واحد تانينفنبدأ أول حاجة على ال point of charge لو
+
+274
+00:20:31,630 --> 00:20:37,050
+كان عندك charge particle of mass 2 kilogram يعني
+
+275
+00:20:37,050 --> 00:20:41,730
+قيمتها ال charge هذه لها كتلة مقدارها 3 kilogram و
+
+276
+00:20:41,730 --> 00:20:46,990
+لها charge 2 kilogram و لها charge 3 column starts
+
+277
+00:20:46,990 --> 00:20:50,390
+at a point يعني بدأت في ال space عند نطة مقدار
+
+278
+00:20:50,390 --> 00:20:53,790
+موجودة 1 مقاس 2 0 يعني وين هي موجودة في ال XY
+
+279
+00:20:53,790 --> 00:20:54,190
+plane
+
+280
+00:21:04,290 --> 00:21:16,710
+X مقدارها 1 و Y قدرها X و Y قدرها Z يعني
+
+281
+00:21:16,710 --> 00:21:20,150
+هنا بدأت الموضوع عند X واحد و ثالث تانية طبعا اليم
+
+282
+00:21:20,150 --> 00:21:23,710
+موجودة وين؟ في ال XY plane لأن مزيد بتسوء Zero
+
+283
+00:21:23,710 --> 00:21:32,930
+الماس بتسوء 2 كيلو اجرام والتشاش بتسوء تلاتةهي كل
+
+284
+00:21:32,930 --> 00:21:36,230
+معلومات عن ال point in charge ايش كمان قايلة انها
+
+285
+00:21:36,230 --> 00:21:38,690
+بدت ال velocity يعني هاي الموضوع ال initial
+
+286
+00:21:38,690 --> 00:21:41,930
+position بدت من هذا ال position ال initial
+
+287
+00:21:41,930 --> 00:21:52,030
+velocity V0 بتساوي 4X hat plus 3Z hat قدش ال meter
+
+288
+00:21:52,030 --> 00:21:57,650
+per second initial position initial velocity في
+
+289
+00:21:57,650 --> 00:22:04,060
+وجود electric field في وجود electric fieldاللي
+
+290
+00:22:04,060 --> 00:22:13,340
+قيمته 12x hat plus 10y hat ضهده موجود في ال XY
+
+291
+00:22:13,340 --> 00:22:18,900
+plane Electric field موجود في ال XY plane ان اتناش
+
+292
+00:22:18,900 --> 00:22:27,520
+اتجاهه 12x hat و 10y hat Electric field في اتجاهه
+
+293
+00:22:27,520 --> 00:22:33,830
+في هذا المصاريموجود في ال X Y يعني يكون موازن هذا
+
+294
+00:22:33,830 --> 00:22:37,970
+الحط يعني لو حطينا أول حط عشرة electric field فهذا
+
+295
+00:22:37,970 --> 00:22:43,550
+متشابه طبعا عرفنا ال electric field وين هو موجود
+
+296
+00:22:43,550 --> 00:22:46,250
+في ال X Y plane اللي component في ال X مقدارها
+
+297
+00:22:46,250 --> 00:22:51,130
+اتناش وفي ال Z مقدارها عشرة volt per meter طبعا وي
+
+298
+00:22:51,130 --> 00:22:55,230
+end الزمن T واحد T بيساوا واحد second انتهى اللحظة
+
+299
+00:22:55,230 --> 00:23:00,510
+ان T بيساوا واحد secondبدنا نقرر التالي اذا احنا
+
+300
+00:23:00,510 --> 00:23:03,430
+قولنا initially يعني عند t equal zero كان عندنا
+
+301
+00:23:03,430 --> 00:23:06,610
+initial position اللي هو عند x يتساوى واحد و y
+
+302
+00:23:06,610 --> 00:23:09,830
+minus اتنين عندنا initial velocity اللي هي اربعة x
+
+303
+00:23:09,830 --> 00:23:14,460
+hat زي تلاتة z hatفي اللى هو ال electric field
+
+304
+00:23:14,460 --> 00:23:18,320
+اللى مقداره 12 اكساد زي 10 وايهات عند اللحظة
+
+305
+00:23:18,320 --> 00:23:21,480
+السؤال بقول ليه عند اللحظة T بيسأل واحد second قرر
+
+306
+00:23:21,480 --> 00:23:24,940
+اللى التانى ال acceleration of the particle احنا
+
+307
+00:23:24,940 --> 00:23:28,240
+طالما بنعرف انه مدام ها دى ناسق الجسم اللى كتلة
+
+308
+00:23:28,240 --> 00:23:32,440
+جسم اللى كتلة و بتتحرك اذا فى عندى فرصة فى
+
+309
+00:23:32,440 --> 00:23:36,200
+acceleration فى وجود فى عندى قوة خارجية اول حاجة
+
+310
+00:23:36,200 --> 00:23:38,280
+هى اللى هى القوة الخارجية هى ال electric field
+
+311
+00:23:38,280 --> 00:23:42,140
+وجود highlight charge في مجال ال electric field
+
+312
+00:23:42,460 --> 00:23:49,980
+هيعطينا قوة مقدارها Q في E وهي أول حاجة وهذه ال
+
+313
+00:23:49,980 --> 00:23:54,040
+force هتولق يعني ال force هذي بتساوي MA اللي هو
+
+314
+00:23:54,040 --> 00:23:58,260
+مين ال mutant second one انتوا شايفين قدامكم على
+
+315
+00:23:58,260 --> 00:24:03,580
+ال slide إذا القوة اللي exerted على ال object تبعي
+
+316
+00:24:03,580 --> 00:24:07,280
+على ال chargeناتجة من وجودها في مجال الـ electric
+
+317
+00:24:07,280 --> 00:24:10,880
+field بتساوي Q في E والقوة من الـ Newton's law
+
+318
+00:24:10,880 --> 00:24:14,560
+بتساوي M تقرر إذا ال acceleration إيش بصدها ساوي
+
+319
+00:24:14,560 --> 00:24:19,900
+القوة على ال mass ال Q في E على M ال Q مقطعها
+
+320
+00:24:19,900 --> 00:24:24,700
+تلاتة كولو E مقليها اتناش اكساد زي الأشهر Y على ال
+
+321
+00:24:24,700 --> 00:24:27,240
+mass اللي هي اتنين كيلو وبالتالي حصلت على ال
+
+322
+00:24:27,240 --> 00:24:29,840
+acceleration واضح؟
+
+323
+00:24:31,300 --> 00:24:34,760
+تانية it's velocity مقعطين ال acceleration و بدهوا
+
+324
+00:24:34,760 --> 00:24:37,000
+ال velocity ايش العلاقة بال acceleration و ال
+
+325
+00:24:37,000 --> 00:24:41,900
+velocity ال acceleration dv by dt صح اذا بقدر
+
+326
+00:24:41,900 --> 00:24:44,320
+استخدم هاي العلاقة ان اقول ال acceleration هاي
+
+327
+00:24:44,320 --> 00:24:49,380
+بتما بتساوي dv by dt بتساوي 18x hat زي 15y hat و
+
+328
+00:24:49,380 --> 00:24:54,180
+كامل اذا عندي ال acceleration بتساوي dv by dt اللي
+
+329
+00:24:54,180 --> 00:24:59,100
+هي d by dt لمين Vx hat Vx x hat Vy y hat
+
+330
+00:25:06,810 --> 00:25:11,050
+بتساوي 18x hat زي 15 y hat ايش تفاعله ابن الكابل
+
+331
+00:25:11,050 --> 00:25:13,730
+طبعا ال x component هتساوي ال x component و ال y
+
+332
+00:25:13,730 --> 00:25:15,530
+component هتساوي ال y component و ال z component
+
+333
+00:25:15,530 --> 00:25:18,690
+هتساوي ال z component ال x component بيقول ال dvx
+
+334
+00:25:18,690 --> 00:25:23,050
+by dt بتساوي 18 ال y component بيقول ال dvy by dt
+
+335
+00:25:23,050 --> 00:25:27,350
+بتساوي 15 بينما ال z component dvz by dt بتساوي 0
+
+336
+00:25:28,150 --> 00:25:31,790
+طبعا هاي اذا الاول واحدة اللى دى vx by dt بالساوية
+
+337
+00:25:31,790 --> 00:25:36,410
+18 هكامل vx مش بالساوية 18t زايد some constant
+
+338
+00:25:36,410 --> 00:25:42,530
+اكامل التانية اللى دى vy by dt بالساوية 15 هتعطينى
+
+339
+00:25:42,530 --> 00:25:48,050
+vy بالساوية 15t زايد bDvz by dt بتسوى 0 إذا vz
+
+340
+00:25:48,050 --> 00:25:52,270
+بتسوى constant من هنا بدأ أجيب قيم a و b و c من ال
+
+341
+00:25:52,270 --> 00:25:56,890
+initial conditions قال يعني t equals 0 الفرصة v
+
+342
+00:25:56,890 --> 00:26:02,920
+not بتسوى 4x hat ساعة تلاتة z hatInitially كان
+
+343
+00:26:02,920 --> 00:26:06,460
+الجسم بتحرك ب initial velocity أو ال charge
+
+344
+00:26:06,460 --> 00:26:10,760
+بتاعتي، الكتلة اللي عليها ال charge بتتحرك ب
+
+345
+00:26:10,760 --> 00:26:14,740
+initial velocity مقار 4x plus 3 زي ذلك، معناه ال X
+
+346
+00:26:14,740 --> 00:26:19,790
+componentاللي هى initial value يعني T equal 0 إيش
+
+347
+00:26:19,790 --> 00:26:25,710
+بتساوي 4 إذا new x at T بتساوي 0 بتساوي إيه لإن 18
+
+348
+00:26:25,710 --> 00:26:30,710
+في 0 سفر إذا new x at T equal 0 بتساوي 4 given
+
+349
+00:26:30,710 --> 00:26:36,750
+إلنا بتساوي إيه إذا إيه بتساوي 4 عرفنا إيهY ال
+
+350
+00:26:36,750 --> 00:26:41,210
+component لل velocity initial بتساوي تلاتة يعني VY
+
+351
+00:26:41,210 --> 00:26:45,050
+at zero بتساوي B بتساوي قداش تلاتة اذا B بتساوي
+
+352
+00:26:45,050 --> 00:26:49,550
+تلاتة Zero بتاسوة Zero هاد ال Z component ال Y
+
+353
+00:26:49,550 --> 00:26:53,070
+component لأ ال velocity بتساوي Zero اذا VY at
+
+354
+00:26:53,070 --> 00:26:56,610
+zero بتساوي Zero اذا B بتساوي Zero ال Z component
+
+355
+00:26:56,610 --> 00:27:02,500
+بتساوي تلاتة اذا U VZ at zeroبتساوى C بتساوى تلاتة
+
+356
+00:27:02,500 --> 00:27:06,360
+زى ان C بتساوى تلاتة اذا نعرفنا ان ال A بتساوى
+
+357
+00:27:06,360 --> 00:27:10,440
+اربعة ال B بتساوى سفر و ال C بتساوى تلاتة فبعود عن
+
+358
+00:27:10,440 --> 00:27:16,690
+ال velocity U of T اللى هي UX UY UZ او VXVXيعني
+
+359
+00:27:16,690 --> 00:27:20,650
+الطريقتين ممكن اكتبهم ال X component هي طمن طعش T
+
+360
+00:27:20,650 --> 00:27:24,410
+زا قد A اللي طلعناها أربعة ال Y component خمس طعش
+
+361
+00:27:24,410 --> 00:27:27,950
+T لأنه بيه Zero و ال Z component تساوية تلاتة
+
+362
+00:27:27,950 --> 00:27:30,970
+تمام؟ اذا هلقيته جيبنا ال acceleration و جيبنا ال
+
+363
+00:27:30,970 --> 00:27:35,450
+velocity عند أي لحظة it's kinetic energy مش نص ك
+
+364
+00:27:35,450 --> 00:27:39,890
+نص M V تربية اه؟ اذا ال kinetic energy اهم متحركة
+
+365
+00:27:39,890 --> 00:27:42,130
+مافيش potential energy ال total energy هنا kinetic
+
+366
+00:27:42,130 --> 00:27:48,830
+energy نص M V تربيةالـ V تربيع في مقدارها dot ال
+
+367
+00:27:48,830 --> 00:27:51,750
+product في نفسها تحت جزر التربيع ماشي خلّال ال
+
+368
+00:27:51,750 --> 00:27:56,750
+magnitude إذا حتساوى نص اتنين اتنين و عشرين تربيع
+
+369
+00:27:56,750 --> 00:28:01,550
+ازاد خمساش تربيع ازاد تلات تربيع تحت الجزر التربيع
+
+370
+00:28:01,550 --> 00:28:04,050
+لكل تربيع بتصير اتنين و عشرين تربيع ازاد خمساش
+
+371
+00:28:04,050 --> 00:28:07,190
+تربيع ازاد تلات تربيع ال magnitude هو جزر التربيع
+
+372
+00:28:07,190 --> 00:28:08,910
+ل U dot U
+
+373
+00:28:11,650 --> 00:28:14,390
+هى اللى بتتبعها مع بعضها تحسس الترفيه بتوطين ال
+
+374
+00:28:14,390 --> 00:28:19,010
+magnitude ترفيها برفع فبروح الجزر الترفيه فقدر
+
+375
+00:28:19,010 --> 00:28:21,610
+احسبها اللى كانت كده يوم سبعمية و تمانية عشو
+
+376
+00:28:24,630 --> 00:28:28,050
+it's position بدو الموقع احنا جبنا الفلس ت والفلس
+
+377
+00:28:28,050 --> 00:28:30,830
+ت مش علاقتها و ال position الفلس ت بتساوي d
+
+378
+00:28:30,830 --> 00:28:36,630
+position by dt اذا هى ال position اللى هى dL by dt
+
+379
+00:28:36,630 --> 00:28:40,070
+او dR by dt ايش بيكونوا يسموه مش مشكلة مش هنخلف
+
+380
+00:28:40,070 --> 00:28:44,310
+عليها اذا الفلس ت بتساوي d by dt لمين ل X Y و Z
+
+381
+00:28:44,310 --> 00:28:50,590
+اللى هى قدش كمة الفلس ت حسبناها مع بعض 18 T زاد 4
+
+382
+00:28:50,590 --> 00:28:55,720
+هو 13 T و 3نفس القضية ال x component لا تساوي ال x
+
+383
+00:28:55,720 --> 00:28:58,220
+component ال y component تساوي ال y component ال z
+
+384
+00:28:58,220 --> 00:29:00,900
+component لا تساوي ال z component دي x by دي t إيش
+
+385
+00:29:00,900 --> 00:29:05,400
+بتساوي؟ و x ليه 18t زاد 4 بالكامل، x إيش بيبقى
+
+386
+00:29:05,400 --> 00:29:10,520
+تساوي 18 على 2t تربيه، يعني 9 على 2 تربيه زاد 4 في
+
+387
+00:29:10,520 --> 00:29:14,140
+t زاد a واحد، بسميها a واحد عشان تخلف عن a اللي
+
+388
+00:29:14,140 --> 00:29:19,810
+قبلك احضر معاهأذا عندي x صارت 9t تربيع زي 4t زي a1
+
+389
+00:29:19,810 --> 00:29:28,090
+dy by dt 15t بكامل هضطيني y بتساوي 15t تربيع على 2
+
+390
+00:29:28,090 --> 00:29:32,610
+يعني سبعة و نص تربيع زي b1 dz by dt بتساوي تلاتة
+
+391
+00:29:32,610 --> 00:29:37,550
+اذا زدتش بتساوي تلاتة t زي c1 a1 و b1 و c1 نجيبها
+
+392
+00:29:37,550 --> 00:29:39,570
+من ال initial position نعطينا ال initial position
+
+393
+00:29:39,570 --> 00:29:43,010
+معينة ايه انا حاططه على اسمة واحد و ماعناه اثنين
+
+394
+00:29:43,970 --> 00:29:48,070
+إذا إحنا عارفين ال initial يعني T equals 0 X
+
+395
+00:29:48,070 --> 00:29:51,610
+initialي إيش كانت بتساوي واحد إذاً A واحد مش
+
+396
+00:29:51,610 --> 00:29:57,070
+بتساوي واحد Y and T equals 0 بتساوي ثالث تنين إذاً
+
+397
+00:29:57,070 --> 00:30:00,510
+B واحد بتساوي تنين Z initialي بتساوي سفر إذاً C
+
+398
+00:30:00,510 --> 00:30:05,310
+واحد بتساوي Zero واضح؟ إذا بقدر أجيب اللي هو ال ..
+
+399
+00:30:05,310 --> 00:30:08,990
+ال position تبعنا ال X Y Z بيساوي تسعة T تربية زد
+
+400
+00:30:08,990 --> 00:30:14,990
+أربعة T زادزائد واحد زائد واحد وعندي اللي هو ال y
+
+401
+00:30:14,990 --> 00:30:18,610
+component سبعة و نص تتربيه minus تانين و z
+
+402
+00:30:18,610 --> 00:30:23,170
+component تلاتة T بدوياها عند اللحظة T بتساوي واحد
+
+403
+00:30:23,170 --> 00:30:27,110
+second بعود عن T بواحد second بحصل على ال position
+
+404
+00:30:27,110 --> 00:30:33,650
+and height اللحظة طبعا في حاجة طالما خلصناها S
+
+405
+00:30:33,650 --> 00:30:37,430
+position سهل السؤال صح يعني كل الحاجة الجديدة فيه
+
+406
+00:30:37,430 --> 00:30:42,110
+ان اجيب ال force Q V cross Pبس هناك ال electric
+
+407
+00:30:42,110 --> 00:30:47,270
+field Q في E بس و بعدين كله Newton's law ده كان
+
+408
+00:30:47,270 --> 00:30:51,050
+بلعته الجبرة هنا طبعا في وجود magnetic field شفنا
+
+409
+00:30:51,050 --> 00:30:55,050
+غير المثال كان في وجود ال electric field حسبنا ال
+
+410
+00:30:55,050 --> 00:30:58,270
+force و جيبنا منها ال acceleration و الposition و
+
+411
+00:30:58,270 --> 00:31:01,590
+ال kinetic energy لو كان عندي charged particle
+
+412
+00:31:01,590 --> 00:31:08,420
+وزنها 2 kilogramلها واحد column ال charge بدأت عند
+
+413
+00:31:08,420 --> 00:31:11,920
+ال origin هنا بدأت عند ال zero zero zero initially
+
+414
+00:31:11,920 --> 00:31:15,660
+وين كانت؟ واحد ثمانية ثمانية ثمانية ثمانية zero
+
+415
+00:31:15,660 --> 00:31:19,420
+zero zero هنا initial هنا الكتلة بتاعتها او برضه
+
+416
+00:31:19,420 --> 00:31:26,900
+تن كيلو واحد column هنا واحد column بدأت
+
+417
+00:31:26,900 --> 00:31:32,190
+هنا عند ال originstart at the origin with velocity
+
+418
+00:31:32,190 --> 00:31:40,010
+initial velocity تلاتة y hat
+
+419
+00:31:40,010 --> 00:31:47,610
+متر per second هاي
+
+420
+00:31:47,610 --> 00:31:50,810
+عرفنا ال initial velocity and travels in the
+
+421
+00:31:50,810 --> 00:31:53,130
+region of the four magnetic field in the magnetic
+
+422
+00:31:53,130 --> 00:31:57,530
+field بيساوي
+
+423
+00:31:57,530 --> 00:31:59,250
+عشر زدها
+
+424
+00:32:01,730 --> 00:32:08,190
+والدور درمتر تربيه بدنا
+
+425
+00:32:08,190 --> 00:32:11,950
+عند اللحظة T بتساوي أربع ساكن تحسب التالي كلها نفس
+
+426
+00:32:11,950 --> 00:32:15,430
+الفكرة يعني احنا لاقيها هنا بس ناقص كانت Q في E
+
+427
+00:32:15,430 --> 00:32:19,870
+هنا هتسيب فيها ماكروس صفر ده دي اول حاجة طالب مننا
+
+428
+00:32:19,870 --> 00:32:23,570
+ال force و ال acceleration of the particle بدنا ال
+
+429
+00:32:23,570 --> 00:32:25,650
+acceleration هو اللي بتجيبها من ال force يعني ال
+
+430
+00:32:25,650 --> 00:32:28,430
+force مش بتساوي القوة اللي على الجسم يعني الجسم
+
+431
+00:32:28,430 --> 00:32:32,610
+اللي كتلة اتنين كيلو جرام تساوي انفقانبتساوي Q في
+
+432
+00:32:32,610 --> 00:32:37,310
+V X B لأنها موجودة في مجال مع مطيسي في اتجاه ال Z
+
+433
+00:32:37,310 --> 00:32:42,030
+axis والفلوس بتاعتنا في اي اتجاه في اتجاه ال Y
+
+434
+00:32:42,030 --> 00:32:49,910
+axis ال acceleration قلنا هي Q على M V X B
+
+435
+00:32:50,830 --> 00:32:55,410
+الأكسلاريشن هي eq على n v cross b لو أنا استخدمت
+
+436
+00:32:55,410 --> 00:32:59,770
+ال cross product هيكون نص x hat y hat z hat الفلوس
+
+437
+00:32:59,770 --> 00:33:05,610
+اللى بتحسبها vx vy vz اللى مش عارفاها وعندي المادة
+
+438
+00:33:05,610 --> 00:33:10,390
+تكفي دوا انتجاهه في اتجاه z هذا بتعطيني ال cross
+
+439
+00:33:10,390 --> 00:33:14,690
+product بيعطيني قيمين اللى هي eq على n v cross b
+
+440
+00:33:14,690 --> 00:33:17,810
+طبعا عشان أربط فلوسي ففلوسي فبعوض عن ال
+
+441
+00:33:17,810 --> 00:33:21,480
+acceleration dv by dtهنا عندى اكسر ال velocity
+
+442
+00:33:21,480 --> 00:33:24,600
+فبعود بال velocity و بجيب اول ال velocity و منها
+
+443
+00:33:24,600 --> 00:33:27,540
+برجع بجيب ال acceleration هو بده اتنين بس و ال
+
+444
+00:33:27,540 --> 00:33:30,680
+acceleration اذا انا لما اجيب ال cross product لك
+
+445
+00:33:30,680 --> 00:33:34,360
+V cross P بطلع النتيجة بدلات ال velocity اللى يمين
+
+446
+00:33:34,360 --> 00:33:38,140
+بطلع افضل لان الوحيد اللى بسوي الصفر اللى هو ال Z
+
+447
+00:33:38,140 --> 00:33:44,100
+component فهيكون دايما عند ال X component هي 10 في
+
+448
+00:33:44,100 --> 00:33:48,400
+Y hat على 2 طبعا لان المص اللى جاى من Mهيعطيني
+
+449
+00:33:48,400 --> 00:33:52,400
+خمسة هى ال واحد ال component هو ال X hat والتانية
+
+450
+00:33:52,400 --> 00:33:58,740
+اللى هى ال Y hat لكن Z hat هتكون سفر سفر، صح؟ فD
+
+451
+00:33:58,740 --> 00:34:05,080
+by DT VX X hat زي VY Y hat زي VZ Z hat بسوى ال X
+
+452
+00:34:05,080 --> 00:34:07,860
+component مع بعض و ال Y component مع بعض و ال Z
+
+453
+00:34:07,860 --> 00:34:11,240
+component مع بعض، هيكون عندى DVX by DT بتسوى خمسة
+
+454
+00:34:11,240 --> 00:34:18,100
+VYدى vy by dt بتسوى minus خمسة vx ودى vz by dt
+
+455
+00:34:18,100 --> 00:34:22,400
+بتسوى سفر هى المعادلات التلاتة اللى معناها بدى
+
+456
+00:34:22,400 --> 00:34:25,600
+اجيبهم من اين ال .. ال .. ال .. ال .. ال c node
+
+457
+00:34:25,600 --> 00:34:27,500
+هدا طبعا من ال initial condition و هدول بدي اشوف
+
+458
+00:34:27,500 --> 00:34:30,360
+كيف بدي احلهم اولا بدي افكر في ال c node يعنى ال z
+
+459
+00:34:30,360 --> 00:34:33,740
+component initially قدش كانت الفلسطين initially
+
+460
+00:34:33,740 --> 00:34:41,210
+كانت تلاتة y hat اذا لو انا حطت vz at zeroبتكون V
+
+461
+00:34:41,210 --> 00:34:44,450
+total يعني مافيش ال DZ component اللي هي صفر فإذا
+
+462
+00:34:44,450 --> 00:34:48,710
+C not بتساوي صفر كيف بدأ أحلها دولة ال two
+
+463
+00:34:48,710 --> 00:34:53,850
+equations هاد ال X مربوطة بال Y و هنا ال Y مربوطة
+
+464
+00:34:53,850 --> 00:34:58,410
+بال X الحل الواحد ان أخد الكمان مرة يعني ال D2 ب X
+
+465
+00:34:58,410 --> 00:35:05,510
+by DT تربيه بتساوي 5 DBY by DTو DV بي وي وDT
+
+466
+00:35:05,510 --> 00:35:09,230
+مربوطة بين VX فبصير المعادلة تفاضليها من درجة
+
+467
+00:35:09,230 --> 00:35:14,090
+تانية تربط VX مع بعض واضح؟ اذا بفاضل كمان مرة
+
+468
+00:35:14,090 --> 00:35:19,630
+بيصير D2VX بي DT بيساوي 5DVY بي DT اللي بتساوي منص
+
+469
+00:35:19,630 --> 00:35:27,510
+5VX فبتطلع عندي D2VX بي DT تربيه بتساوي منص 25VX
+
+470
+00:35:27,510 --> 00:35:32,650
+لو عملت نفس الحكي هنا إيش هيكون D2VY بي D2
+
+471
+00:35:55,230 --> 00:35:58,690
+طبعا هذه احنا شوفناها في الدوائر و اكيد شوفتها في
+
+472
+00:35:58,690 --> 00:36:03,670
+ال differential و بتعرفوا كيف تحلوها ولا لافها دي
+
+473
+00:36:03,670 --> 00:36:07,070
+oscillator اه اللي هي ها دي بتكون على شكل E to the
+
+474
+00:36:07,070 --> 00:36:14,450
+J خمسة X T ليش؟ افعض الأول مرة بتعطيني اللي هي
+
+475
+00:36:14,450 --> 00:36:18,630
+الخمسة و كمان مرة بتعطيني كمان J في J بتعطيني ال
+
+476
+00:36:18,630 --> 00:36:23,310
+minus صح؟ لإن لو قلت E to the minus خمسة T أول مرة
+
+477
+00:36:23,310 --> 00:36:25,230
+بتعطيني ال minus خمسة و أول مرة minus خمسة تصير ال
+
+478
+00:36:25,230 --> 00:36:31,510
+plus فهي لازم تكون على شكل E to the J خمسة Tطبعا
+
+479
+00:36:31,510 --> 00:36:35,910
+او بعضرتها بشكل Cos وSin ياسي واحد E to the plus J
+
+480
+00:36:35,910 --> 00:36:39,650
+plus C تنين E to the minus J خمسة T او بشكل Sin
+
+481
+00:36:39,650 --> 00:36:43,830
+وCos فإذا ان الناتج تبعنا ل UX بسوء C واحد Cos
+
+482
+00:36:43,830 --> 00:36:53,790
+خمسة T زي C تنين Sin الخمسة T طيب هذه أول حاجة
+
+483
+00:36:53,790 --> 00:36:59,010
+بالنسبة لل X ال Y نفس الحاجة اللي عملنا بيعطيناأو
+
+484
+00:36:59,010 --> 00:37:02,450
+ايش كمان ممكن استخدم عشان اجيب ال Y ان عندي
+
+485
+00:37:02,450 --> 00:37:06,910
+المعادلة ان متفاضل ال X بالنسبالتي ايش تعطيني خمسة
+
+486
+00:37:06,910 --> 00:37:13,490
+VY وانا جبت الجوار تبع ال VX لو فضلتها دي VX by دي
+
+487
+00:37:13,490 --> 00:37:17,850
+VY بتعطيني خمسة VY بحصل على VY مباشرة او زي ما
+
+488
+00:37:17,850 --> 00:37:20,710
+قلتلكوا بفاضل مرة تانية بحصل على معادلة تاعة ال Y
+
+489
+00:37:20,710 --> 00:37:25,690
+يا هيك يا هيك بتنصحي اذا انا عرفت قيمة ال VX وعرفت
+
+490
+00:37:25,690 --> 00:37:32,870
+قيمة ال VYواضال علينا ان اجيب قيم
+
+491
+00:37:32,870 --> 00:37:37,330
+C1 و C2 ان هما دولة مجاهيل بالنسبالي و ال solution
+
+492
+00:37:37,330 --> 00:37:41,930
+ماله مش كامل الا انا اعرف قيم C1 و C2 عشان اجيبهم
+
+493
+00:37:41,930 --> 00:37:43,970
+هنا و اجيبهم ال initial value ال initial value ان
+
+494
+00:37:43,970 --> 00:37:48,570
+T equal 0 و V اتجاهها في ال Y direction قيمتها 3
+
+495
+00:37:48,570 --> 00:37:54,520
+اذا نقول ان V X هو 0جبتها من الـ 0 و 1 صين الـ 00ش
+
+496
+00:37:54,520 --> 00:38:00,600
+بيضل عند Vx الـ 0 C1 بتسوى 0 if C1 is 0 بيضل عند
+
+497
+00:38:00,600 --> 00:38:06,440
+Vx بتسوى C2 sin 5T صح؟ الحاجة التانية المهمة اللي
+
+498
+00:38:06,440 --> 00:38:10,540
+بيجيب الـ C2 من Vy Vy اللي لها قيمة بتسوى قداش
+
+499
+00:38:10,540 --> 00:38:16,460
+تلاتة يعني T equals 0 صين الـ 00و جبتها من الـ 0 و
+
+500
+00:38:16,460 --> 00:38:20,200
+1 فهتكون C تلين إيش بتساوي تلاتة إذا يعرفنا C1
+
+501
+00:38:20,200 --> 00:38:23,080
+بتساوي صفر من و جيبناها من و VX إيش هي اللي كانت
+
+502
+00:38:23,080 --> 00:38:27,820
+Zero واضح أعملهم على اللوح و لا واضح أكتب و لا
+
+503
+00:38:27,820 --> 00:38:33,180
+واضح يعني VX أت Zero Zero جبتها من ال Zero واحد
+
+504
+00:38:33,180 --> 00:38:38,230
+صالي Zero Zero إذا هتظل عندي Zero بتساوي C1اذا
+
+505
+00:38:38,230 --> 00:38:43,490
+عرفنا c1 سوى 0 من ال y component y at 0 بتساوي 3
+
+506
+00:38:43,490 --> 00:38:49,250
+sin 0 هذا المقدر 0 لكن جبتها من 0 و 1 حتى c2 سوى 3
+
+507
+00:38:49,250 --> 00:38:56,350
+اذا c1 0 c2 3 و c تقولنا 0 لأن z component مش اللي
+
+508
+00:38:56,350 --> 00:38:59,930
+كانت 0 احنا عملناها من بدري اذا ايش هيكون vx
+
+509
+00:38:59,930 --> 00:39:03,890
+بتساوي c1 0 هتروح من هنا و من هنا هيكون vx بتساوي
+
+510
+00:39:03,890 --> 00:39:11,180
+3 sin 5tو Vy ايش بتساوي تلاتة كوصين خمسة T و Vz
+
+511
+00:39:11,180 --> 00:39:15,520
+ايش بتساوي Zero احنا طلعناها constant و ال
+
+512
+00:39:15,520 --> 00:39:19,980
+constant طلعناها تساوي Zero اذا هى ال volumetric
+
+513
+00:39:19,980 --> 00:39:24,080
+step تلاتة كوصين الخمسة T تلاتة كوصين الخمسة T و
+
+514
+00:39:24,080 --> 00:39:29,290
+Zero بده عند اللحظة T بالساوية أربعة بعوضأيش كمان
+
+515
+00:39:29,290 --> 00:39:32,870
+طالب منها ال acceleration ال acceleration هي dP by
+
+516
+00:39:32,870 --> 00:39:37,070
+dt بفضل بحصل على ال acceleration عند ال T بتسوء
+
+517
+00:39:37,070 --> 00:39:40,710
+أربع هي تفضل بال sign خمسة cosine تفضل cosine
+
+518
+00:39:40,710 --> 00:39:45,630
+minus طبعا خمسة في sign الخمسة T فهتصير هنا minus
+
+519
+00:39:45,630 --> 00:39:50,090
+خمس عشر فهيصير خلاص خمس عشر واضح تفضل ال sign
+
+520
+00:39:50,090 --> 00:39:53,670
+بplus cosine تفضل cosine minus sign هي ال
+
+521
+00:39:53,670 --> 00:39:56,370
+acceleration يعني أربعة بعوض عن T أربعة و بحصل على
+
+522
+00:39:56,370 --> 00:40:02,080
+ال accelerationالفرق ال B واضح انه طالب القوة اللى
+
+523
+00:40:02,080 --> 00:40:08,920
+بتأثر ال magnetic force on it عند اللحظة T
+
+524
+00:40:08,920 --> 00:40:12,680
+بالساوية أربعة second احنا عارفين ان ال force
+
+525
+00:40:12,680 --> 00:40:15,700
+بالساوية أمبر ايه و احنا جيبنا ال acceleration عند
+
+526
+00:40:15,700 --> 00:40:18,800
+اللحظة T بالساوية أربعة فبس بدروبها اعطي الكتلة
+
+527
+00:40:18,800 --> 00:40:22,520
+اللى هو في اتنينبعدين تطلب مننا ال kinetic energy
+
+528
+00:40:22,520 --> 00:40:26,700
+عند T بالسوء 4 نص mv تربيع و احنا عارفين ال
+
+529
+00:40:26,700 --> 00:40:31,760
+velocity عند ال 4 بس بربع هاي مربع هاي بحصل على ال
+
+530
+00:40:31,760 --> 00:40:35,360
+kinetic energy عند اللحظة T بالسوء 4 هي لحد ال
+
+531
+00:40:35,360 --> 00:40:38,820
+point T بعدين تطلب انه بدنا ال particles
+
+532
+00:40:38,820 --> 00:40:41,980
+trajectory بيقلمنات ال T ال particles trajectory
+
+533
+00:40:41,980 --> 00:40:46,100
+يعني بدي ال X و ال Y بدون الاعتمادية على ال T حالة
+
+534
+00:40:46,100 --> 00:40:51,630
+trajectoryمساره مساره في ال X و Y يعني لو انا بس
+
+535
+00:40:51,630 --> 00:40:56,110
+حطيت XYZ احصل على المسار بدلت ال X و Y و Z بدون ما
+
+536
+00:40:56,110 --> 00:41:00,470
+انه يكون لإنه احنا عندنا لحد ال اتا ال X ال
+
+537
+00:41:00,470 --> 00:41:02,890
+velocity بدلت ال T و ال acceleration بدلت ال T
+
+538
+00:41:02,890 --> 00:41:06,410
+باتنمين المسار يعني عندنا ال X و Y و Z طبعا ال
+
+539
+00:41:06,410 --> 00:41:11,550
+velocity بتساوي DL by DT فباخد اللي هي ال X
+
+540
+00:41:11,550 --> 00:41:16,130
+component على طول مباشرة يعني ال X component مش
+
+541
+00:41:16,130 --> 00:41:21,850
+هتساويDx by Dt هي الـ x component للفلوس تي تلاتة
+
+542
+00:41:21,850 --> 00:41:26,090
+صين خمسة T وDy by Dt هي ال Y component للفلوس تي
+
+543
+00:41:26,090 --> 00:41:30,910
+تلاتة صين خمسة Tدى z by dt اللى هى ال velocity فى
+
+544
+00:41:30,910 --> 00:41:34,530
+z direction بتساوى 0 عشان أجيب ال x بدى أكامل
+
+545
+00:41:34,530 --> 00:41:38,390
+فهتكون ماينوس تلاتة على خمسة كساين خمسة t زاية بي
+
+546
+00:41:38,390 --> 00:41:42,350
+واحد ال y هتعطيى تلاتة على خمسة sin خمسة t زاية
+
+547
+00:41:42,350 --> 00:41:45,590
+بيتنين و ال z هتعطيى some constant مهم نجيبهم ال
+
+548
+00:41:45,590 --> 00:41:48,530
+initial بصش ال initial potential I1 at الناعم دى
+
+549
+00:41:48,530 --> 00:41:54,500
+ال origin اذا ال x at zeroبتساوى zero جبت وامي
+
+550
+00:41:54,500 --> 00:41:57,600
+zero واحد هتكون إيش بتساوى minus خمسة تلاتة على
+
+551
+00:41:57,600 --> 00:42:00,380
+خمسة زائد بي واحد بتساوى صفر إذاً بي واحد إيش
+
+552
+00:42:00,380 --> 00:42:05,900
+بتساوى تلاتة على خمسة y at zero بتساوى zero صين ال
+
+553
+00:42:05,900 --> 00:42:10,140
+zero zero إذاً y at zero بتساوى بي تنين إيش بتساوى
+
+554
+00:42:10,140 --> 00:42:14,300
+zero إذاً بي تنين صفر z at zero بتساوى zero بتساوى
+
+555
+00:42:14,300 --> 00:42:17,920
+بي تلاتة زائد بي تلاتة zero إذاً عندي بقدر أقول إن
+
+556
+00:42:17,920 --> 00:42:23,640
+xyz إيش بتساوى minus إيه نص cosineالخمسة T ذات P
+
+557
+00:42:23,640 --> 00:42:27,040
+واحدة اش أمنا بتساوي تلتة على خمسة اللي هي برضه
+
+558
+00:42:27,040 --> 00:42:29,960
+ستة من عشرة فإذا بتقدر تعوض عنها ستة من عشرة minus
+
+559
+00:42:29,960 --> 00:42:34,780
+ستة من عشرة قصارى خمسة T هل ال X component لأ ال
+
+560
+00:42:34,780 --> 00:42:40,820
+position ال Y.6 sin 5t لأن P2 هو صفر و Z هو صفر
+
+561
+00:42:40,820 --> 00:42:45,000
+اذا انا انا اولا عندي ال component انت في ال X و Y
+
+562
+00:42:45,000 --> 00:42:49,340
+فقط ال particle تبعي في ال X و Y بس كمان بدويا عن
+
+563
+00:42:49,340 --> 00:42:53,280
+T equal 4 حسابنا لابسش ان عن T equal 4 و بده ال
+
+564
+00:42:53,280 --> 00:42:56,860
+trajectory بدون ما انه يكون فيه اعتمادية على الزمن
+
+565
+00:42:56,860 --> 00:43:04,100
+كيف بده اعمل هذا انا عند ال X component عند
+
+566
+00:43:04,100 --> 00:43:12,870
+ال X component بتساوي6 من 10-6 من 10 cos 5t و ال y
+
+567
+00:43:12,870 --> 00:43:21,990
+component تساوي 6 من 10 sin 5t لو أنا قلت x-6 من
+
+568
+00:43:21,990 --> 00:43:28,770
+10 بتساوي-6 من 10 cos 5t وهي عندي ال two
+
+569
+00:43:28,770 --> 00:43:33,650
+components لو ربعت هاي و ربعت هاي و جماعة مبقى خلص
+
+570
+00:43:33,650 --> 00:43:39,580
+من دي dependency لأن هاي مربعهابتعطيني X minus أنا
+
+571
+00:43:39,580 --> 00:43:43,060
+بالتأسفة ماجبتش القلم الأسود و هذا الأزرق فات كتير
+
+572
+00:43:43,060 --> 00:43:49,900
+مش كمان ولا حتناسي القلم هو واضح على الشاشة؟ واضحة
+
+573
+00:43:49,900 --> 00:43:55,440
+في الجرار بس واضح الخط ولا مش واضح؟
+
+574
+00:43:55,440 --> 00:44:03,120
+اذا
+
+575
+00:44:03,120 --> 00:44:08,500
+عندنا ال Xالـ X-6
+
+576
+00:44:08,500 --> 00:44:13,120
+من 10 يكون تربيه زائد Y تربيه اشهد السؤال هاي
+
+577
+00:44:13,120 --> 00:44:19,040
+تربيها 0.6 يكون تربيه minus تربيها plus cosine
+
+578
+00:44:19,040 --> 00:44:26,400
+تربيه الخمسة T زائد نص تربيه sin تربيه الخمسة T لو
+
+579
+00:44:26,400 --> 00:44:31,820
+أحطت 6 من 10 تربيها من المشترك هيصير cosine تربيه
+
+580
+00:44:33,790 --> 00:44:38,150
+خمسة T زائد ساعة تربيع الخمسة T ايش بتساوي واحد
+
+581
+00:44:38,150 --> 00:44:42,390
+هيك انا بكون عملت elimination لمين للاعتمادية على
+
+582
+00:44:42,390 --> 00:44:47,450
+الزمن خلصت من الاعتمادية على الزمن و السعر عندي X
+
+583
+00:44:47,450 --> 00:44:50,930
+minus ستة من عشرة تربيع زائد واحد تربيع بتساوي ستة
+
+584
+00:44:50,930 --> 00:44:58,070
+من عشرة تربيع أعرفين ليش هاد؟ X minus ستة من عشرة
+
+585
+00:44:58,070 --> 00:45:05,040
+كل تربيع زائدي ترمير برساوي 6 من 10 لكل ترمير هذه
+
+586
+00:45:05,040 --> 00:45:10,140
+دائرة اللي ال origin تبعها عند x equals 6 من 10 و
+
+587
+00:45:10,140 --> 00:45:14,440
+y صفر هي ال origin تبعها و ال radius تبعها 6 من 10
+
+588
+00:45:14,440 --> 00:45:20,960
+واضح؟
+
+589
+00:45:20,960 --> 00:45:24,480
+اذا هذه الدائرة بتاعتنا هي ال trajectory تبعنا اذا
+
+590
+00:45:24,480 --> 00:45:27,080
+ال particle تبعنا اللي قاعد في المجنك ينقش بيعمل
+
+591
+00:45:27,080 --> 00:45:32,900
+دائرةزى ما صار الباطكال فى المجال مع ناطيسيا عمودي
+
+592
+00:45:32,900 --> 00:45:36,420
+عليا لإن هما متعمدين احنا قشعنا الباطكال بتعمل ال
+
+593
+00:45:36,420 --> 00:45:40,480
+XY plane و المجلد فيه جوية تجاه ال Z
+
+594
+00:45:46,900 --> 00:45:51,340
+تجهزت ال magnet field تجهز ال axis و ال particle
+
+595
+00:45:51,340 --> 00:45:54,780
+تبعي بتحرك في ال x و عكسي في اتجاه الترجيبتور اللي
+
+596
+00:45:54,780 --> 00:45:57,700
+صرتوا عارفينه هلقيته لو انسألتوا ايش هيكون circle
+
+597
+00:45:57,700 --> 00:46:02,260
+لو عندى charge قاعدة بتتحرك في مجال معناطيسي ايش
+
+598
+00:46:02,260 --> 00:46:07,720
+بتقول الترجيب تبعها دائرة أثبتناها لازم اي charge
+
+599
+00:46:07,720 --> 00:46:12,440
+بحكي عنها وجودة في مجال معناطيسي هيكون ال
+
+600
+00:46:12,440 --> 00:46:14,280
+trajectory او مسارها دائر
+
+601
+00:46:20,100 --> 00:46:25,440
+طالب مننا بعدين احنا جيبنا ال trajectory، اخر حاجة
+
+602
+00:46:25,440 --> 00:46:28,940
+طالب مننا ال magnetic field ال .. ال .. ال kinetic
+
+603
+00:46:28,940 --> 00:46:30,220
+energy بشكل عام
+
+604
+00:46:32,840 --> 00:46:36,480
+أخر حاجة show that it's the kinetic energy remains
+
+605
+00:46:36,480 --> 00:46:39,900
+constant احنا جيبنا ال kinetic energy عن T بساوة
+
+606
+00:46:39,900 --> 00:46:43,700
+أربع صح هلأ تبقولنا بشكل عام انا بدي أثبت انها
+
+607
+00:46:43,700 --> 00:46:46,780
+constant بتبقى اذا بدي استخدم مين الفلسطين بشكل
+
+608
+00:46:46,780 --> 00:46:49,840
+عام ليه هى تعرف الفلسطين احنا مش بنعرف الفلسطين
+
+609
+00:46:54,860 --> 00:47:03,660
+باربعها و باربعها و باربعها و باربعها
+
+610
+00:47:03,660 --> 00:47:05,980
+و باربعها و باربعها
+
+611
+00:47:07,910 --> 00:47:10,910
+طبعا في الناس اللي هي اتنين كيلو والنص بيروحوا مع
+
+612
+00:47:10,910 --> 00:47:13,850
+بعض و بيبقوا عندى تسعة dual اللي هي نفس اللي حصلنا
+
+613
+00:47:13,850 --> 00:47:17,650
+عندها عن T بالساوة أربع نفس اللي هحصل عليها عن T
+
+614
+00:47:17,650 --> 00:47:21,030
+equal zero وعند Zero هاي واحد وهاي واحد نفس الحاجة
+
+615
+00:47:21,030 --> 00:47:24,290
+إذا اللي كانت ال energy مالها بتضلها constant لل
+
+616
+00:47:24,290 --> 00:47:28,130
+particle إذا معناها كمان مرة بنقول إن مافيش عندنا
+
+617
+00:47:28,130 --> 00:47:31,410
+اللي هو work مقبول لأنه ماتتغيرش Delta K بالساوة
+
+618
+00:47:31,410 --> 00:47:36,770
+صفرأول حاجة تفتحها من أفضل DL بتساوية Zero لإن ال
+
+619
+00:47:36,770 --> 00:47:41,110
+force عمودية على ال particle دائما لإن ال force هي
+
+620
+00:47:41,110 --> 00:47:45,230
+cross product V cross B فدائما عمودية عليهم فأخدت
+
+621
+00:47:45,230 --> 00:47:49,410
+المصار السودان سفر اتجاه ال velocity و ال force
+
+622
+00:47:49,410 --> 00:47:55,200
+عمودية فمصارها و ال force عموديفازن دائما ال work
+
+623
+00:47:55,200 --> 00:47:57,480
+بيساوي صفر كمان و مرة اصلا اننا حسبنا ال kinetic
+
+624
+00:47:57,480 --> 00:48:00,880
+energy عند اي لحظة انها constant فدالة كامة لها
+
+625
+00:48:00,880 --> 00:48:04,100
+صفر اللي هي بيساوي ال work لإذا مافيش عندي work
+
+626
+00:48:04,100 --> 00:48:05,680
+اكيد من مرة تانية حسبناها
+
+627
+00:48:08,660 --> 00:48:11,700
+طبعا هاي معلومات إضافية اللي هى إيش بقولنا انه ال
+
+628
+00:48:11,700 --> 00:48:15,940
+angular velocity omega اللى هى الحمسة هدى احنا
+
+629
+00:48:15,940 --> 00:48:18,540
+بنتحكى عنها angular rhythm الذاكرين ال cosine ال
+
+630
+00:48:18,540 --> 00:48:22,280
+omega T و ال sine ال omega T هى الخمسة هى ال
+
+631
+00:48:22,280 --> 00:48:25,640
+angular velocity rate per second صح هدى مالها
+
+632
+00:48:25,640 --> 00:48:30,400
+بقولنا بشكل عام بتساوي Q في P على M احنا كانت
+
+633
+00:48:30,400 --> 00:48:34,060
+عاملنا خمسة لما حسبنا ال trajectory او لما حسبنا
+
+634
+00:48:34,060 --> 00:48:36,600
+ال velocity و كله طلعت معانا omega بتساوي خمسة
+
+635
+00:48:39,810 --> 00:48:43,950
+بس هو بيقولك بشكل عام هاي الوميجا اللي هي طلعت
+
+636
+00:48:43,950 --> 00:48:51,710
+معنا بتساوي خمس قرار per second بشكل عام بتساوي Q
+
+637
+00:48:51,710 --> 00:48:57,270
+في B على M يعني لو حد سألك ايش قيمة ال radial
+
+638
+00:48:57,270 --> 00:49:00,850
+frequency فيها Q في B في A على M نشوف من المثال
+
+639
+00:49:00,850 --> 00:49:04,770
+تبعنا، تبعطينا خمسة ولا أحد حافظين الأرقام؟
+
+640
+00:49:08,300 --> 00:49:15,880
+وحدي مقدارها قداش عشرة وعلى أمني قداش اتنين
+
+641
+00:49:21,660 --> 00:49:25,300
+QPR اذا ال radian frequency اللي هي ال frequency
+
+642
+00:49:25,300 --> 00:49:28,120
+اللي عمال ماله و بارتك ال ماله بلوف فيها يعني،
+
+643
+00:49:28,120 --> 00:49:32,700
+عندي واحدة sinusoidal في axis و cosine في axis، ال
+
+644
+00:49:32,700 --> 00:49:34,900
+cosine و ال cosine اللي انت خدته برضه على ال
+
+645
+00:49:34,900 --> 00:49:37,020
+oscilloscope و شفت انه هذا بيعطينا اللي هو نفس ال
+
+646
+00:49:37,020 --> 00:49:39,880
+frequency و في نفس ال phase بيعطينا دائرة، لو كان
+
+647
+00:49:39,880 --> 00:49:42,380
+out of phase مش بيعطينا ellipse، هاي ال
+
+648
+00:49:42,380 --> 00:49:45,660
+trajectorism، تذكرين؟ أخدتهوا هذا أكيد، حلصته من
+
+649
+00:49:45,660 --> 00:49:50,060
+زمان يعنيالتراجيكتوريس فإذا هنا قلنا ال frequency
+
+650
+00:49:50,060 --> 00:49:56,040
+بشكل عام اللي هي Q بيلعب وال radius of the orbit
+
+651
+00:49:56,040 --> 00:50:00,780
+ال radius أقل عن ال initial velocity على Omega
+
+652
+00:50:00,780 --> 00:50:04,700
+قداش ال initial velocity اللي كان في المثال
+
+653
+00:50:04,700 --> 00:50:13,240
+initial velocity تلقتك قلنا ال radius قلنا ال
+
+654
+00:50:13,240 --> 00:50:14,800
+initial velocity على R
+
+655
+00:50:18,110 --> 00:50:26,610
+على اوميجا تلاتة
+
+656
+00:50:26,610 --> 00:50:29,850
+على حمسة يعني ادنى 618
+
+657
+00:50:32,350 --> 00:50:34,910
+مش هيك طالع معنا؟ ال radius تبع ال trajectory
+
+658
+00:50:34,910 --> 00:50:39,510
+تمام؟ و قبل هاي النقطة، هاي ممكن تسأله فيهم يعنى،
+
+659
+00:50:39,510 --> 00:50:42,830
+إيش هي ال frequency اللي بلوف فيها ال particle، ال
+
+660
+00:50:42,830 --> 00:50:46,610
+trajectory تبعه، اللي هي الدائرة تاعته، كيف شكلها،
+
+661
+00:50:46,610 --> 00:50:49,450
+إيش ال radius تبعها، طبعا هذا ما أعطينا مثال اللي
+
+662
+00:50:49,450 --> 00:50:52,360
+هي ال cathode ray tubeلأ اللي هو ال electron اللي
+
+663
+00:50:52,360 --> 00:50:56,080
+بتحرك من النقطة high إلى النقطة اللي هي على الشاشة
+
+664
+00:50:56,080 --> 00:50:59,600
+اللي بيكون حامل معلومات عن الصورة موجود في مجال
+
+665
+00:50:59,600 --> 00:51:02,900
+magnetic field هيكون ال trajectory لو أنت طلعت على
+
+666
+00:51:02,900 --> 00:51:05,420
+ال screen اللي هي ال trajectories بتاعتهم اللي هي
+
+667
+00:51:05,420 --> 00:51:10,840
+الدوائر، واضح؟ المثال
+
+668
+00:51:10,840 --> 00:51:14,640
+التاني هيكون اللقاء القادم ان شاء الله و معاكم
+
+669
+00:51:14,640 --> 00:51:20,300
+بقينيعطيك العافية ان شاء الله يعطيك العافية ان شاء
+
+670
+00:51:20,300 --> 00:51:21,500
+الله بنكمل اللقاء القادر
+
diff --git a/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/iWj--QJF6uM_raw.json b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/iWj--QJF6uM_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..3b837037b68ce78043eff1b1a79b10d1053dcffa
--- /dev/null
+++ b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/iWj--QJF6uM_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 3245, "start": 12.71, "end": 32.45, "text": "بسم الله الرحمن الرحيم السلام عليكم ورحمة الله وبركاته احنا اليوم هناخد بيو سفارت لاو و أمبرز لاو كم مرة أمبرز لاو احنا مرق علينا هناخده كم مرة لكن بيو سفارت لاو اول مرة هناخده احنا اذا بدنا من هاي المعادلة بي kill ال A احنا يعني ماعنها مين هي kill ال B صح؟", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 21136, 37440, 25894, 24793, 4032, 2288, 35571, 3660, 21984, 4032, 26890, 4117, 9307, 3224, 1975, 5016, 8315, 45595, 20498, 8032, 1863, 47283, 3215, 4724, 1829, 2407, 8608, 5172, 9640, 2655, 20193, 2407, 4032, 5551, 2304, 26890, 11622, 20193, 2407, 9122, 2304, 3714, 25720, 5551, 2304, 26890, 11622, 20193, 2407, 1975, 5016, 8315, 3714, 2288, 4587, 25894, 8315, 8032, 1863, 47283, 3215, 3224, 9122, 2304, 3714, 25720, 44381, 4724, 1829, 2407, 8608, 5172, 9640, 2655, 20193, 2407, 1975, 12610, 3714, 25720, 8032, 1863, 47283, 3215, 3224, 1975, 5016, 8315, 1975, 15730, 47525, 8315, 9154, 8032, 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"probability": 0.992919921875}, {"start": 25.19, "end": 26.23, "word": " هناخده", "probability": 0.9912109375}, {"start": 26.23, "end": 26.51, "word": " احنا", "probability": 0.9378255208333334}, {"start": 26.51, "end": 26.69, "word": " اذا", "probability": 0.835205078125}, {"start": 26.69, "end": 27.07, "word": " بدنا", "probability": 0.803955078125}, {"start": 27.07, "end": 27.23, "word": " من", "probability": 0.98828125}, {"start": 27.23, "end": 27.45, "word": " هاي", "probability": 0.576171875}, {"start": 27.45, "end": 28.53, "word": " المعادلة", "probability": 0.9893798828125}, {"start": 28.53, "end": 28.81, "word": " بي", "probability": 0.3048095703125}, {"start": 28.81, "end": 29.09, "word": " kill", "probability": 0.544921875}, {"start": 29.09, "end": 29.51, "word": " ال", "probability": 0.53759765625}, {"start": 29.51, "end": 29.67, "word": " A", "probability": 0.48779296875}, {"start": 29.67, "end": 29.93, "word": " احنا", "probability": 0.8942057291666666}, {"start": 29.93, "end": 30.13, "word": " يعني", "probability": 0.910400390625}, {"start": 30.13, "end": 30.37, "word": " ماعنها", "probability": 0.575775146484375}, {"start": 30.37, "end": 30.61, "word": " مين", "probability": 0.7203369140625}, {"start": 30.61, "end": 30.73, "word": " هي", "probability": 0.35498046875}, {"start": 30.73, "end": 31.01, "word": " kill", "probability": 0.8359375}, {"start": 31.01, "end": 31.15, "word": " ال", "probability": 0.9853515625}, {"start": 31.15, "end": 31.39, "word": " B", "probability": 0.943359375}, {"start": 31.39, "end": 32.45, "word": " صح؟", "probability": 0.9348958333333334}], "temperature": 1.0}, {"id": 2, "seek": 5678, "start": 32.82, "end": 56.78, "text": "كرل كرل ال A اللي هي كرل ال B هذه معادلة شفناها قبل هيك لما أخدنا ال calculus لما كرل كرل ال B ومتذكرين قلتلكوا كرل كرل انا أشعر ان انتوا بتدل ال diversity لما ينزل تربية M متذكرينها فزنعيلنا هاي المعادلة وكمان احنا هنبدأ من عشان نشتق بياصورت لو انا مش هشتقه بس هحكي على السريع ان B هي أدوة عن كرل ال A 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54.68, "word": " أدوة", "probability": 0.6533203125}, {"start": 54.68, "end": 54.9, "word": " عن", "probability": 0.95263671875}, {"start": 54.9, "end": 55.16, "word": " كرل", "probability": 0.97265625}, {"start": 55.16, "end": 55.28, "word": " ال", "probability": 0.8974609375}, {"start": 55.28, "end": 55.42, "word": " A", "probability": 0.92724609375}, {"start": 55.42, "end": 56.04, "word": " لو", "probability": 0.93212890625}, {"start": 56.04, "end": 56.4, "word": " بدأنا", "probability": 0.654296875}, {"start": 56.4, "end": 56.54, "word": " من", "probability": 0.994140625}, {"start": 56.54, "end": 56.78, "word": " هنا", "probability": 0.98974609375}], "temperature": 1.0}, {"id": 3, "seek": 7703, "start": 57.51, "end": 77.03, "text": "و اشتغلنا شوية على ال curve و شوية على تعريفاتها احصلوا على اللي هو bios of our plot مجرد من curve ال A بداية من curve ال A اعوض عن A اللي هي mu not I دي ال ال prime على four by R واخد ال curve لواحد على R لإنه curve بس بيأثر على مين؟ على R، R فيها X وY 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isotropic constant في ال free space فهي هم جنس isotropic والاخر يعني فدل تربيع هتساوي minus ميو نوض curl ال H وcurl ال H بتساوي J", "tokens": [41185, 29538, 21542, 6027, 3660, 4724, 1829, 30544, 43242, 8315, 11778, 1211, 6055, 2288, 21292, 3615, 1975, 1829, 3224, 1975, 1829, 8592, 39894, 3794, 995, 45865, 8608, 6027, 3555, 22591, 2423, 363, 13672, 1829, 39896, 8608, 6027, 3555, 3714, 1829, 2407, 22591, 2423, 389, 5296, 33456, 4724, 1829, 39894, 3794, 995, 45865, 3714, 1829, 2407, 8717, 2407, 11242, 389, 3714, 1829, 2407, 8717, 2407, 11242, 13672, 1829, 39896, 8978, 2423, 1737, 1901, 3714, 1829, 2407, 8717, 2407, 11242, 4724, 4587, 6027, 11296, 307, 310, 39173, 5754, 8978, 2423, 1737, 1901, 6156, 3224, 1829, 8032, 2304, 10874, 1863, 3794, 307, 310, 39173, 16070, 47283, 2288, 37495, 22653, 6156, 3215, 1211, 6055, 2288, 21292, 3615, 8032, 2655, 3794, 995, 45865, 3175, 3714, 1829, 2407, 8717, 2407, 11242, 22591, 2423, 389, 4032, 14112, 75, 2423, 389, 39894, 3794, 995, 45865, 508], 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0.8605143229166666}, {"start": 148.28, "end": 148.76, "word": " والاخر", "probability": 0.6228841145833334}, {"start": 148.76, "end": 149.34, "word": " يعني", "probability": 0.78271484375}, {"start": 149.34, "end": 149.74, "word": " فدل", "probability": 0.95947265625}, {"start": 149.74, "end": 150.18, "word": " تربيع", "probability": 0.906982421875}, {"start": 150.18, "end": 150.54, "word": " هتساوي", "probability": 0.8322265625}, {"start": 150.54, "end": 150.84, "word": " minus", "probability": 0.76123046875}, {"start": 150.84, "end": 151.22, "word": " ميو", "probability": 0.8600260416666666}, {"start": 151.22, "end": 151.58, "word": " نوض", "probability": 0.9817708333333334}, {"start": 151.58, "end": 152.26, "word": " curl", "probability": 0.9306640625}, {"start": 152.26, "end": 152.36, "word": " ال", "probability": 0.86328125}, {"start": 152.36, "end": 152.52, "word": " H", "probability": 0.95263671875}, {"start": 152.52, "end": 152.8, "word": " وcurl", "probability": 0.715576171875}, {"start": 152.8, "end": 152.88, "word": " ال", "probability": 0.951171875}, {"start": 152.88, "end": 153.02, "word": " H", "probability": 0.97802734375}, {"start": 153.02, "end": 153.72, "word": " بتساوي", "probability": 0.9473876953125}, {"start": 153.72, "end": 154.12, "word": " J", "probability": 0.67236328125}], "temperature": 1.0}, {"id": 7, "seek": 18363, "start": 155.35, "end": 183.63, "text": "فإذا دي التربيع A بيساوي minus الـ mu0 J وهدي عبارة عن vector بس هو equation مش vector لإن ال A vector field وJ ال vector field هدي عبارة عن دي التربيع ل A vector يعني A XXH زائد AYYH زائد AZZH ده تساوي minus ال mu0 وهدي J XXH", "tokens": [5172, 28814, 15730, 11778, 1829, 16712, 2288, 21292, 3615, 316, 4724, 1829, 3794, 995, 45865, 3175, 2423, 39184, 2992, 15, 508, 37037, 16254, 6225, 3555, 9640, 3660, 18871, 8062, 4724, 3794, 31439, 5367, 37893, 8062, 5296, 28814, 1863, 2423, 316, 8062, 2519, 4032, 41, 2423, 8062, 2519, 8032, 16254, 6225, 3555, 9640, 3660, 18871, 11778, 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1349.02, "text": "اللي قيمته 12x hat plus 10y hat ضهده موجود في ال XY plane Electric field موجود في ال XY plane ان اتناش اتجاهه 12x hat و 10y hat Electric field في اتجاهه في هذا المصاري", "tokens": [6027, 20292, 12174, 32640, 47395, 2272, 87, 2385, 1804, 1266, 88, 2385, 48812, 3224, 3215, 3224, 3714, 29245, 23328, 8978, 2423, 48826, 5720, 24677, 2519, 3714, 29245, 23328, 8978, 2423, 48826, 5720, 16472, 1975, 2655, 1863, 33599, 1975, 2655, 7435, 40294, 3224, 2272, 87, 2385, 4032, 1266, 88, 2385, 24677, 2519, 8978, 1975, 2655, 7435, 40294, 3224, 8978, 23758, 9673, 9381, 9640, 1829], "avg_logprob": -0.3420410016551614, "compression_ratio": 1.6, "no_speech_prob": 2.562999725341797e-06, "words": [{"start": 1322.42, "end": 1324.06, "word": "اللي", "probability": 0.193878173828125}, {"start": 1324.06, "end": 1324.6, "word": " قيمته", "probability": 0.82861328125}, {"start": 1324.6, "end": 1325.82, "word": " 12x", "probability": 0.40234375}, {"start": 1325.82, "end": 1326.42, "word": " hat", 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"word": " جبتها", "probability": 0.920166015625}, {"start": 2326.89, "end": 2326.97, "word": " من", "probability": 0.9892578125}, {"start": 2326.97, "end": 2327.29, "word": " 0", "probability": 0.4072265625}, {"start": 2327.29, "end": 2327.41, "word": " و", "probability": 0.5986328125}, {"start": 2327.41, "end": 2327.63, "word": " 1", "probability": 0.8056640625}, {"start": 2327.63, "end": 2327.97, "word": " حتى", "probability": 0.810302734375}, {"start": 2327.97, "end": 2328.57, "word": " c2", "probability": 0.855224609375}, {"start": 2328.57, "end": 2328.89, "word": " سوى", "probability": 0.7714029947916666}, {"start": 2328.89, "end": 2329.25, "word": " 3", "probability": 0.9775390625}, {"start": 2329.25, "end": 2330.37, "word": " اذا", "probability": 0.789794921875}, {"start": 2330.37, "end": 2330.87, "word": " c1", "probability": 0.80322265625}, {"start": 2330.87, "end": 2331.31, "word": " 0", "probability": 0.32470703125}, {"start": 2331.31, "end": 2332.13, "word": " c2", 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0.8173828125}, {"start": 2336.83, "end": 2337.05, "word": " احنا", "probability": 0.935546875}, {"start": 2337.05, "end": 2337.61, "word": " عملناها", "probability": 0.9908447265625}, {"start": 2337.61, "end": 2337.95, "word": " من", "probability": 0.9658203125}, {"start": 2337.95, "end": 2338.33, "word": " بدري", "probability": 0.70458984375}, {"start": 2338.33, "end": 2339.05, "word": " اذا", "probability": 0.883056640625}, {"start": 2339.05, "end": 2339.21, "word": " ايش", "probability": 0.8074544270833334}, {"start": 2339.21, "end": 2339.55, "word": " هيكون", "probability": 0.902587890625}, {"start": 2339.55, "end": 2339.93, "word": " vx", "probability": 0.830810546875}, {"start": 2339.93, "end": 2340.35, "word": " بتساوي", "probability": 0.9566650390625}, {"start": 2340.35, "end": 2340.87, "word": " c1", "probability": 0.62939453125}, {"start": 2340.87, "end": 2341.25, "word": " 0", "probability": 0.916015625}, {"start": 2341.25, "end": 2341.71, "word": " هتروح", "probability": 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"و Vy ايش بتساوي تلاتة كوصين خمسة T و Vz ايش بتساوي Zero احنا طلعناها constant و ال constant طلعناها تساوي Zero اذا هى ال volumetric step تلاتة كوصين الخمسة T تلاتة كوصين الخمسة T و Zero بده عند اللحظة T بالساوية أربعة بعوض", "tokens": [2407, 691, 88, 1975, 1829, 8592, 39894, 3794, 995, 45865, 6055, 1211, 9307, 3660, 9122, 2407, 9381, 9957, 16490, 2304, 3794, 3660, 314, 4032, 691, 89, 1975, 1829, 8592, 39894, 3794, 995, 45865, 17182, 1975, 5016, 8315, 23032, 1211, 3615, 8315, 11296, 5754, 4032, 2423, 5754, 23032, 1211, 3615, 8315, 11296, 6055, 3794, 995, 45865, 17182, 1975, 15730, 8032, 7578, 2423, 1996, 449, 17475, 1823, 6055, 1211, 9307, 3660, 9122, 2407, 9381, 9957, 33962, 2304, 3794, 3660, 314, 6055, 1211, 9307, 3660, 9122, 2407, 9381, 9957, 33962, 2304, 3794, 3660, 314, 4032, 17182, 47525, 3224, 43242, 13672, 5016, 19913, 3660, 314, 20666, 3794, 995, 2407, 10632, 5551, 25513, 27884, 45030, 2407, 11242], "avg_logprob": -0.30282080067997486, "compression_ratio": 1.95, 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"word": " بتساوي", "probability": 0.9892578125}, {"start": 2351.76, "end": 2352.12, "word": " Zero", "probability": 0.74462890625}, {"start": 2352.12, "end": 2354.3, "word": " احنا", "probability": 0.7255452473958334}, {"start": 2354.3, "end": 2354.82, "word": " طلعناها", "probability": 0.9734375}, {"start": 2354.82, "end": 2355.2, "word": " constant", "probability": 0.51806640625}, {"start": 2355.2, "end": 2355.44, "word": " و", "probability": 0.74267578125}, {"start": 2355.44, "end": 2355.52, "word": " ال", "probability": 0.69287109375}, {"start": 2355.52, "end": 2355.78, "word": " constant", "probability": 0.93017578125}, {"start": 2355.78, "end": 2356.28, "word": " طلعناها", "probability": 0.9359375}, {"start": 2356.28, "end": 2356.52, "word": " تساوي", "probability": 0.80731201171875}, {"start": 2356.52, "end": 2356.82, "word": " Zero", "probability": 0.64111328125}, {"start": 2356.82, "end": 2359.04, "word": " اذا", "probability": 0.81640625}, {"start": 2359.04, "end": 2359.34, "word": " هى", "probability": 0.44873046875}, {"start": 2359.34, "end": 2359.52, "word": " ال", "probability": 0.96533203125}, {"start": 2359.52, "end": 2359.98, "word": " volumetric", "probability": 0.1925048828125}, {"start": 2359.98, "end": 2360.04, "word": " step", "probability": 0.78173828125}, {"start": 2360.04, "end": 2361.08, "word": " تلاتة", "probability": 0.95263671875}, {"start": 2361.08, "end": 2361.26, "word": " كوصين", "probability": 0.7656402587890625}, {"start": 2361.26, "end": 2361.72, "word": " الخمسة", "probability": 0.9083251953125}, {"start": 2361.72, "end": 2361.94, "word": " T", "probability": 0.97412109375}, {"start": 2361.94, "end": 2362.66, "word": " تلاتة", "probability": 0.890380859375}, {"start": 2362.66, "end": 2363.14, "word": " كوصين", "probability": 0.9759521484375}, {"start": 2363.14, "end": 2363.78, "word": " الخمسة", "probability": 0.98095703125}, {"start": 2363.78, "end": 2363.9, "word": " T", "probability": 0.48486328125}, {"start": 2363.9, "end": 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الخمسة T فهتصير هنا minus خمس عشر فهيصير خلاص خمس عشر واضح تفضل ال sign بplus cosine تفضل cosine minus sign هي ال acceleration يعني أربعة بعوض عن T أربعة و بحصل على ال acceleration", "tokens": [10721, 1829, 8592, 9122, 2304, 7649, 23032, 6027, 3555, 9154, 11296, 2423, 17162, 2423, 17162, 39896, 274, 47, 538, 36423, 4724, 5172, 11242, 1211, 4724, 5016, 36520, 15844, 2423, 17162, 43242, 2423, 314, 39894, 3794, 2407, 38207, 5551, 25513, 3615, 39896, 6055, 5172, 11242, 1211, 20666, 1465, 16490, 2304, 3794, 3660, 23565, 6055, 5172, 11242, 1211, 23565, 3175, 23032, 3555, 3615, 995, 16490, 2304, 3794, 3660, 8978, 1465, 33962, 2304, 3794, 3660, 314, 6156, 3224, 2655, 9381, 13546, 34105, 3175, 16490, 2304, 3794, 6225, 46309, 6156, 3224, 1829, 9381, 13546, 16490, 1211, 33546, 16490, 2304, 3794, 6225, 46309, 4032, 46958, 5016, 6055, 5172, 11242, 1211, 2423, 1465, 4724, 18954, 23565, 6055, 5172, 11242, 1211, 23565, 3175, 1465, 39896, 2423, 17162, 37495, 22653, 5551, 25513, 27884, 45030, 2407, 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"word": " فيها", "probability": 0.98974609375}, {"start": 3041.87, "end": 3042.09, "word": " ال", "probability": 0.97998046875}, {"start": 3042.09, "end": 3042.71, "word": " particle،", "probability": 0.830322265625}, {"start": 3042.71, "end": 3042.83, "word": " ال", "probability": 0.9072265625}, {"start": 3042.83, "end": 3043.31, "word": " trajectory", "probability": 0.97900390625}, {"start": 3043.31, "end": 3044.53, "word": " تبعه،", "probability": 0.93515625}, {"start": 3044.53, "end": 3044.67, "word": " اللي", "probability": 0.974609375}, {"start": 3044.67, "end": 3044.73, "word": " هي", "probability": 0.80517578125}, {"start": 3044.73, "end": 3045.15, "word": " الدائرة", "probability": 0.95947265625}, {"start": 3045.15, "end": 3045.53, "word": " تاعته،", "probability": 0.777734375}, {"start": 3045.53, "end": 3045.65, "word": " كيف", "probability": 0.958984375}, {"start": 3045.65, "end": 3046.61, "word": " شكلها،", "probability": 0.9215087890625}, {"start": 3046.61, "end": 3046.79, "word": " إيش", "probability": 0.9807942708333334}, {"start": 3046.79, "end": 3046.91, "word": " ال", "probability": 0.9892578125}, {"start": 3046.91, "end": 3047.17, "word": " radius", "probability": 0.970703125}, {"start": 3047.17, "end": 3047.69, "word": " تبعها،", "probability": 0.84814453125}, {"start": 3047.69, "end": 3047.83, "word": " طبعا", "probability": 0.896484375}, {"start": 3047.83, "end": 3048.07, "word": " هذا", "probability": 0.6181640625}, {"start": 3048.07, "end": 3048.21, "word": " ما", "probability": 0.5498046875}, {"start": 3048.21, "end": 3048.45, "word": " أعطينا", "probability": 0.87646484375}, {"start": 3048.45, "end": 3048.99, "word": " مثال", "probability": 0.899658203125}, {"start": 3048.99, "end": 3049.45, "word": " اللي", "probability": 0.8681640625}, {"start": 3049.45, "end": 3049.57, "word": " هي", "probability": 0.60400390625}, {"start": 3049.57, "end": 3049.69, "word": " ال", "probability": 0.4384765625}, {"start": 3049.69, "end": 3050.03, "word": " cathode", "probability": 0.667724609375}, {"start": 3050.03, "end": 3050.21, "word": " ray", "probability": 0.79541015625}, {"start": 3050.21, "end": 3050.57, "word": " tube", "probability": 0.94384765625}], "temperature": 1.0}, {"id": 125, "seek": 307530, "start": 3050.78, "end": 3075.3, "text": "لأ اللي هو ال electron اللي بتحرك من النقطة high إلى النقطة اللي هي على الشاشة اللي بيكون حامل معلومات عن الصورة موجود في مجال magnetic field هيكون ال trajectory لو أنت طلعت على ال screen اللي هي ال trajectories بتاعتهم اللي هي الدوائر، واضح؟ المثال التاني هيكون اللقاء القادم ان شاء الله و معاكم بقين", "tokens": [1211, 10721, 13672, 1829, 31439, 2423, 6084, 13672, 1829, 39894, 5016, 31747, 9154, 28239, 47432, 3660, 1090, 30731, 28239, 47432, 3660, 13672, 1829, 39896, 15844, 25124, 33599, 3660, 13672, 1829, 4724, 1829, 30544, 11331, 10943, 1211, 20449, 1211, 20498, 9307, 18871, 31767, 13063, 3660, 3714, 29245, 23328, 8978, 3714, 7435, 6027, 12688, 2519, 39896, 30544, 2423, 21512, 45164, 14739, 2655, 23032, 1211, 34268, 15844, 2423, 2568, 13672, 1829, 39896, 2423, 18257, 2083, 39894, 995, 34268, 16095, 13672, 1829, 39896, 32748, 2407, 16373, 2288, 12399, 4032, 46958, 5016, 22807, 9673, 12984, 6027, 16712, 7649, 1829, 39896, 30544, 13672, 4587, 16606, 25062, 18513, 2304, 16472, 13412, 16606, 21984, 4032, 20449, 995, 24793, 4724, 4587, 9957], "avg_logprob": -0.22807018197419351, "compression_ratio": 1.9, "no_speech_prob": 8.344650268554688e-06, "words": [{"start": 3050.78, "end": 3051.22, "word": "لأ", "probability": 0.75244140625}, {"start": 3051.22, "end": 3051.36, "word": " اللي", "probability": 0.6824951171875}, {"start": 3051.36, "end": 3051.54, "word": " هو", "probability": 0.97119140625}, {"start": 3051.54, "end": 3051.7, "word": " ال", "probability": 0.96826171875}, {"start": 3051.7, "end": 3052.1, "word": " electron", "probability": 0.62109375}, {"start": 3052.1, "end": 3052.36, "word": " اللي", "probability": 0.886962890625}, {"start": 3052.36, "end": 3052.96, "word": 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حامل", "probability": 0.9781901041666666}, {"start": 3057.02, "end": 3057.52, "word": " معلومات", "probability": 0.968017578125}, {"start": 3057.52, "end": 3057.68, "word": " عن", "probability": 0.9921875}, {"start": 3057.68, "end": 3058.32, "word": " الصورة", "probability": 0.9833984375}, {"start": 3058.32, "end": 3059.12, "word": " موجود", "probability": 0.96630859375}, {"start": 3059.12, "end": 3059.22, "word": " في", "probability": 0.5126953125}, {"start": 3059.22, "end": 3059.6, "word": " مجال", "probability": 0.9720052083333334}, {"start": 3059.6, "end": 3060.32, "word": " magnetic", "probability": 0.94580078125}, {"start": 3060.32, "end": 3060.72, "word": " field", "probability": 0.91357421875}, {"start": 3060.72, "end": 3061.42, "word": " هيكون", "probability": 0.648193359375}, {"start": 3061.42, "end": 3061.52, "word": " ال", "probability": 0.94775390625}, {"start": 3061.52, "end": 3061.88, "word": " trajectory", "probability": 0.83251953125}, {"start": 3061.88, "end": 3062.1, "word": " لو", "probability": 0.90283203125}, {"start": 3062.1, "end": 3062.3, "word": " أنت", "probability": 0.763427734375}, {"start": 3062.3, "end": 3062.74, "word": " طلعت", "probability": 0.9697265625}, {"start": 3062.74, "end": 3062.9, "word": " على", "probability": 0.5458984375}, {"start": 3062.9, "end": 3063.04, "word": " ال", "probability": 0.8466796875}, {"start": 3063.04, "end": 3063.4, "word": " screen", "probability": 0.857421875}, {"start": 3063.4, "end": 3063.92, "word": " اللي", "probability": 0.7919921875}, {"start": 3063.92, "end": 3064.02, "word": " هي", "probability": 0.93359375}, {"start": 3064.02, "end": 3064.12, "word": " ال", "probability": 0.734375}, {"start": 3064.12, "end": 3064.6, "word": " trajectories", "probability": 0.943603515625}, {"start": 3064.6, "end": 3065.04, "word": " بتاعتهم", "probability": 0.8216552734375}, {"start": 3065.04, "end": 3065.2, "word": " اللي", "probability": 0.78564453125}, {"start": 3065.2, "end": 3065.42, "word": " هي", "probability": 0.81494140625}, {"start": 3065.42, "end": 3066.18, "word": " الدوائر،", "probability": 0.6685546875}, {"start": 3066.18, "end": 3066.8, "word": " واضح؟", "probability": 0.950927734375}, {"start": 3066.8, "end": 3070.84, "word": " المثال", "probability": 0.7378743489583334}, {"start": 3070.84, "end": 3071.46, "word": " التاني", "probability": 0.9132486979166666}, {"start": 3071.46, "end": 3071.92, "word": " هيكون", "probability": 0.966064453125}, {"start": 3071.92, "end": 3072.34, "word": " اللقاء", "probability": 0.9910481770833334}, {"start": 3072.34, "end": 3072.76, "word": " القادم", "probability": 0.994140625}, {"start": 3072.76, "end": 3072.9, "word": " ان", "probability": 0.48486328125}, {"start": 3072.9, "end": 3073.08, "word": " شاء", "probability": 0.9736328125}, {"start": 3073.08, "end": 3073.36, "word": " الله", "probability": 0.96875}, {"start": 3073.36, "end": 3073.98, "word": " و", "probability": 0.26611328125}, {"start": 3073.98, "end": 3074.64, "word": " معاكم", "probability": 0.6422526041666666}, {"start": 3074.64, "end": 3075.3, "word": " بقين", "probability": 0.4635416666666667}], "temperature": 1.0}, {"id": 126, "seek": 308150, "start": 3076.42, "end": 3081.5, "text": "يعطيك العافية ان شاء الله يعطيك العافية ان شاء الله بنكمل اللقاء القادر", "tokens": [40228, 9566, 1829, 4117, 18863, 31845, 10632, 16472, 13412, 16606, 21984, 37495, 9566, 1829, 4117, 18863, 31845, 10632, 16472, 13412, 16606, 21984, 44945, 24793, 1211, 13672, 4587, 16606, 25062, 18513, 2288], "avg_logprob": -0.23144530830904841, "compression_ratio": 1.7808219178082192, "no_speech_prob": 0.0001647472381591797, "words": [{"start": 3076.42, "end": 3077.14, "word": "يعطيك", "probability": 0.8935546875}, {"start": 3077.14, "end": 3077.54, "word": " العافية", "probability": 0.5588175455729166}, {"start": 3077.54, "end": 3077.68, "word": " ان", "probability": 0.7646484375}, {"start": 3077.68, "end": 3077.84, "word": " شاء", "probability": 0.977783203125}, {"start": 3077.84, "end": 3078.08, "word": " الله", "probability": 0.9677734375}, {"start": 3078.08, "end": 3078.72, "word": " يعطيك", "probability": 0.78973388671875}, {"start": 3078.72, "end": 3079.36, "word": " العافية", "probability": 0.939453125}, {"start": 3079.36, "end": 3080.14, "word": " ان", "probability": 0.517578125}, {"start": 3080.14, "end": 3080.3, "word": " شاء", "probability": 0.9921875}, {"start": 3080.3, "end": 3080.38, "word": " الله", "probability": 0.9228515625}, {"start": 3080.38, "end": 3080.84, "word": " بنكمل", "probability": 0.8470052083333334}, {"start": 3080.84, "end": 3081.2, "word": " اللقاء", "probability": 0.9794921875}, {"start": 3081.2, "end": 3081.5, "word": " القادر", "probability": 0.8473307291666666}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 3082.0775, "duration_after_vad": 2933.558124999992}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/iWj--QJF6uM_raw.srt b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/iWj--QJF6uM_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..b989bb93b33c7f3272a871d1db758d0225dd25c4
--- /dev/null
+++ b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/iWj--QJF6uM_raw.srt
@@ -0,0 +1,2680 @@
+1
+00:00:12,710 --> 00:00:15,490
+بسم الله الرحمن الرحيم السلام عليكم ورحمة الله
+
+2
+00:00:15,490 --> 00:00:20,550
+وبركاته احنا اليوم هناخد بيو سفارت لاو و أمبرز لاو
+
+3
+00:00:20,550 --> 00:00:23,870
+كم مرة أمبرز لاو احنا مرق علينا هناخده كم مرة لكن
+
+4
+00:00:23,870 --> 00:00:27,450
+بيو سفارت لاو اول مرة هناخده احنا اذا بدنا من هاي
+
+5
+00:00:27,450 --> 00:00:31,010
+المعادلة بي kill ال A احنا يعني ماعنها مين هي kill
+
+6
+00:00:31,010 --> 00:00:36,140
+ال B صح؟كرل كرل ال A اللي هي كرل ال B هذه معادلة
+
+7
+00:00:36,140 --> 00:00:39,280
+شفناها قبل هيك لما أخدنا ال calculus لما كرل كرل
+
+8
+00:00:39,280 --> 00:00:42,340
+ال B ومتذكرين قلتلكوا كرل كرل انا أشعر ان انتوا
+
+9
+00:00:42,340 --> 00:00:46,160
+بتدل ال diversity لما ينزل تربية M متذكرينها
+
+10
+00:00:46,160 --> 00:00:50,160
+فزنعيلنا هاي المعادلة وكمان احنا هنبدأ من عشان
+
+11
+00:00:50,160 --> 00:00:53,740
+نشتق بياصورت لو انا مش هشتقه بس هحكي على السريع ان
+
+12
+00:00:53,740 --> 00:00:58,090
+B هي أدوة عن كرل ال A لو بدأنا من هناو اشتغلنا
+
+13
+00:00:58,090 --> 00:01:02,630
+شوية على ال curve و شوية على تعريفاتها احصلوا على
+
+14
+00:01:02,630 --> 00:01:05,930
+اللي هو bios of our plot مجرد من curve ال A بداية
+
+15
+00:01:05,930 --> 00:01:09,510
+من curve ال A اعوض عن A اللي هي mu not I دي ال ال
+
+16
+00:01:09,510 --> 00:01:13,850
+prime على four by R واخد ال curve لواحد على R لإنه
+
+17
+00:01:13,850 --> 00:01:18,930
+curve بس بيأثر على مين؟ على R، R فيها X وY وZفدلبس
+
+18
+00:01:18,930 --> 00:01:24,870
+باصلة R بستخدم identity اللى هى علاقة بالcurve و
+
+19
+00:01:24,870 --> 00:01:29,370
+بجيب اللى هى القيم اللى بعوض مجرد تعويض مباشر بحصل
+
+20
+00:01:29,370 --> 00:01:33,150
+على اللى هو بيو سفرتلو مش بتطلب منه اشتقاق بيو
+
+21
+00:01:33,150 --> 00:01:36,870
+سفرتلو بقولنا ان ال magnetic field بساوة mu node
+
+22
+00:01:36,870 --> 00:01:42,070
+على 4pi ال line integral ل IDL اللى هو ال element
+
+23
+00:01:42,430 --> 00:01:45,650
+من الـ Filament اللي مضروف فيها تيار مضروف في تيار
+
+24
+00:01:45,650 --> 00:01:49,430
+مضروف في هذا الـ Filament الـ cross R hat اللي هو
+
+25
+00:01:49,430 --> 00:01:52,610
+ال unit vector من ال element هذا للنقطة الباقية
+
+26
+00:01:52,610 --> 00:01:56,210
+ساعدها الوطن شرك ال cross R hat على R تربيهة و
+
+27
+00:01:56,210 --> 00:01:59,370
+احنا شوفناها قبلها كده المعادلة هذه اللي هي curl
+
+28
+00:01:59,370 --> 00:02:03,470
+بيه انها بتساوي curl curl A بتذكرينها يعني curl
+
+29
+00:02:03,470 --> 00:02:06,770
+curl A بتساوي grade divergence A minus delta بيه R
+
+30
+00:02:06,770 --> 00:02:11,420
+إذا أخدنا ان divergence A بيساوي Zeroفي هذه الحالة
+
+31
+00:02:11,420 --> 00:02:15,680
+بيكون عندنا دل تربيع ايه ايش بتساوي سالب curl ال B
+
+32
+00:02:15,680 --> 00:02:21,820
+اللي هي سالب ميو curl ال H لأن بي بتساوي ميو نوض H
+
+33
+00:02:21,820 --> 00:02:24,560
+ميو نوض اللي هي في ال free space ميو نوض بقالها
+
+34
+00:02:24,560 --> 00:02:27,780
+isotropic constant في ال free space فهي هم جنس
+
+35
+00:02:27,780 --> 00:02:31,220
+isotropic والاخر يعني فدل تربيع هتساوي minus ميو
+
+36
+00:02:31,220 --> 00:02:36,530
+نوض curl ال H وcurl ال H بتساوي Jفإذا دي التربيع A
+
+37
+00:02:36,530 --> 00:02:40,690
+بيساوي minus الـ mu0 J وهدي عبارة عن vector بس هو
+
+38
+00:02:40,690 --> 00:02:45,050
+equation مش vector لإن ال A vector field وJ ال
+
+39
+00:02:45,050 --> 00:02:49,390
+vector field هدي
+
+40
+00:02:49,390 --> 00:02:54,570
+عبارة عن دي التربيع ل A vector يعني A XXH زائد
+
+41
+00:02:54,570 --> 00:03:04,380
+AYYH زائد AZZH ده تساوي minus ال mu0 وهدي J XXHزي
+
+42
+00:03:04,380 --> 00:03:09,600
+جي وي وي هت زي جي وزي زي وزي كمان احنا بتقدر نقسم
+
+43
+00:03:09,600 --> 00:03:14,460
+المعادلة لثلاث معادلات ال X component لازم تسوى X
+
+44
+00:03:14,460 --> 00:03:16,460
+component ال Y component لازم تسوى Y component
+
+45
+00:03:16,460 --> 00:03:25,800
+فبقدر اقسمها ل three scalar components واضح؟
+
+46
+00:03:36,780 --> 00:03:40,740
+واضح؟ في أسف سلحتنا؟ إذا إحنا ال vector basal
+
+47
+00:03:40,740 --> 00:03:45,100
+equation بتسير إلينا اللي هي بقدر أكتبها أشكل ال
+
+48
+00:03:45,100 --> 00:03:48,780
+components فبتكون three scalar equations
+
+49
+00:03:53,840 --> 00:03:58,480
+أحنا متذكرين ان ال close line integral ل H.DL بقدر
+
+50
+00:03:58,480 --> 00:04:02,080
+استخدم stock theorem تعطينا surface integral لكل H
+
+51
+00:04:02,080 --> 00:04:08,940
+.DS وكل ال H منها 1 على new node B فبتصير كل ال B
+
+52
+00:04:09,660 --> 00:04:13,980
+كل كل ال a واضح بيقولها ايجت h هي واحدة ع ال mu
+
+53
+00:04:13,980 --> 00:04:18,700
+not b فh بتسوى بي بتسوى كل a فهي هتكون واحدة ع ال
+
+54
+00:04:18,700 --> 00:04:22,080
+mu ال surface integral كل كل ال a دلوقتي اصلا كل
+
+55
+00:04:22,080 --> 00:04:25,260
+كل ال a احنا قولنا في حالة diverge a بتسوى zero
+
+56
+00:04:25,260 --> 00:04:30,540
+بتسوى هذه المعادلة كل كل a بتسوى minus delta b a
+
+57
+00:04:31,960 --> 00:04:36,320
+بعود مباشرة عن كرر
+
+58
+00:04:36,320 --> 00:04:42,160
+كرر ل A بقاش من ميو
+
+59
+00:04:42,160 --> 00:04:50,440
+نوت جيال
+
+60
+00:04:50,440 --> 00:04:53,880
+ميو نوت بتروح مع ميو نوت هتصبح ال surface integral
+
+61
+00:04:53,880 --> 00:04:57,390
+ل جهد ال DSالـ service integral دي أسمين هي
+
+62
+00:04:57,390 --> 00:04:59,890
+التيارة اذا ال numbers دول اللي احنا شفناها قبل
+
+63
+00:04:59,890 --> 00:05:02,250
+هيك ال line enclosed line integral اتش و ال dl
+
+64
+00:05:02,250 --> 00:05:08,830
+بتساوي ال enclosed كمان فاضح؟ احنا بنكون خلصمهم
+
+65
+00:05:08,830 --> 00:05:14,810
+الجرئية هاي من الشبتر او يعني ما هتمن هذا الشبتر
+
+66
+00:05:14,810 --> 00:05:18,530
+بيبقى علينا المبدأ ان شاء الله شبتر تمانين اذا
+
+67
+00:05:18,530 --> 00:05:22,530
+مافيش اي استفسار في اي استفسار؟
+
+68
+00:05:25,500 --> 00:05:31,200
+الشبطر 8 هو magnetic force سنركز
+
+69
+00:05:31,200 --> 00:05:34,340
+على magnetic force في هذا الشبطر
+
+70
+00:05:42,290 --> 00:05:45,890
+يا أستاذ بس هدأ نقوله magnetic force و لا انوان
+
+71
+00:05:45,890 --> 00:05:49,130
+هيكون الدكتورة هل جيتها في chapter 7 شرحت اللي
+
+72
+00:05:49,130 --> 00:05:52,290
+عندى slide 55 اللي الباقى مش مطلوب ولا عادى؟ لأ
+
+73
+00:05:52,290 --> 00:05:55,830
+الباقى أنا كنت حاطة اللي هى الأمثلة و أسئلة و
+
+74
+00:05:55,830 --> 00:06:04,550
+مركزة بس خلاص هيك اه اللي هو magnetic force اذا ان
+
+75
+00:06:04,550 --> 00:06:06,690
+شاء الله اليوم احنا هنبدأ ال magnetic force
+
+76
+00:06:06,690 --> 00:06:10,410
+يابنخلصها يا ان شاء الله لازم ده كمان محاضرة
+
+77
+00:06:12,240 --> 00:06:15,600
+إذا بدنا نحسب ال force due to magnetic field، فيه
+
+78
+00:06:15,600 --> 00:06:19,200
+هنا تلت طرُب اللي ممكن نحسب فيها ال magnetic force
+
+79
+00:06:19,200 --> 00:06:22,100
+أو يعني اللي نحكي فيها عن magnetic force ناتجة عن
+
+80
+00:06:22,100 --> 00:06:25,290
+magnetic field، يعني لو أنا دي magnetic fieldو في
+
+81
+00:06:25,290 --> 00:06:28,130
+عندى charge فى قلب هذا ال magnetic field بتتحرك
+
+82
+00:06:28,130 --> 00:06:30,910
+بيكون فى عندى force على ال charge اللى بتتحرك هى
+
+83
+00:06:30,910 --> 00:06:34,490
+أول نوع اذا في الأول افترض ان بدي magnetic field
+
+84
+00:06:34,490 --> 00:06:36,610
+بدي أشوف ايش القوة اللى بتأثر فيها ال magnetic
+
+85
+00:06:36,610 --> 00:06:40,430
+field على إيش و كيف أحسبها فعندي تلت أنواع انه
+
+86
+00:06:40,430 --> 00:06:43,670
+يكون عندى magnetic field بت charge بتتحرك لازم
+
+87
+00:06:43,670 --> 00:06:47,410
+تكون تتحرك اذا ساكنة مش هعندي force لازم تكون
+
+88
+00:06:47,410 --> 00:06:50,550
+تتحرك اذا فى عندى moving charge بيكون عندى force
+
+89
+00:06:50,550 --> 00:06:53,630
+متولدة على هى ال moving charge نتيجة وجود ال
+
+90
+00:06:53,630 --> 00:06:58,050
+magnetic fieldالتانى لو كان عندى current element
+
+91
+00:06:58,050 --> 00:07:02,610
+أسوأ يعني line ولا surface plane ولا volume و هذا
+
+92
+00:07:02,610 --> 00:07:08,830
+ال element موجودفى external field برضه هنقيص القوة
+
+93
+00:07:08,830 --> 00:07:12,270
+على ال current ال current بمعنى load charge متحركة
+
+94
+00:07:12,270 --> 00:07:15,730
+هيكون هذا القانون أعمل من moving charge moving
+
+95
+00:07:15,730 --> 00:07:20,070
+charge بحكي عنه charge واحدة ال current تدفق من ال
+
+96
+00:07:20,070 --> 00:07:23,650
+charges يعني لازم احنا بنحكي عن charges متحركة
+
+97
+00:07:23,650 --> 00:07:27,270
+أسوأ في filament أو في surface أو في volume ايش
+
+98
+00:07:27,270 --> 00:07:30,890
+القوة اللى بتأثر على هذا ال current نتيجة وجوده فى
+
+99
+00:07:30,890 --> 00:07:37,030
+ال magnetic fieldاخر واحدة طيارين، بس هو في .. في
+
+100
+00:07:37,030 --> 00:07:40,290
+خطين، في two filaments أو في two planes أو في two
+
+101
+00:07:40,290 --> 00:07:43,530
+volumes، إذا بتحركوا يعني ال current مدافي،
+
+102
+00:07:43,530 --> 00:07:45,990
+current يعملها تشارج اسمها اللي هم تحركها، إيش
+
+103
+00:07:45,990 --> 00:07:49,490
+القوة اللي بتنتج على واحد من هدولة ال filaments،
+
+104
+00:07:49,490 --> 00:07:52,810
+نتيجة وجوده في المجال المواطيسي للfilament التاني؟
+
+105
+00:07:52,810 --> 00:07:55,510
+هنا مابنحكيش على external field، ملاحظين؟ الحل
+
+106
+00:07:55,510 --> 00:07:59,490
+قولنا إنه moving chargeفى magnetic field التانى
+
+107
+00:07:59,490 --> 00:08:01,850
+قولنا current فى external التالت قولنا two
+
+108
+00:08:01,850 --> 00:08:05,590
+currents واحد منهم هيولد magnetic field هتكون فى
+
+109
+00:08:05,590 --> 00:08:08,530
+قوة تولد على التانى نتيجة من ال magnetic field
+
+110
+00:08:08,530 --> 00:08:12,470
+اللى نتاج من الأول واضح؟طب إذا ما بنحكي عن القوة
+
+111
+00:08:12,470 --> 00:08:15,470
+بنحكي عن هاي التلات حلوة نبدأ في مين في اللي هي
+
+112
+00:08:15,470 --> 00:08:19,670
+moving charge قل قلنا إذا في عندي magnetic field
+
+113
+00:08:19,670 --> 00:08:23,310
+وفي عندي charge اللي بتتحرك بتتحرك في وجود ال
+
+114
+00:08:23,310 --> 00:08:28,450
+magnetic field هيتولد عندي magnetic force بتساوي Q
+
+115
+00:08:28,450 --> 00:08:31,810
+اللي هي قيمة ال charge V ال volume بتاع ال charge
+
+116
+00:08:31,810 --> 00:08:39,950
+cross B إذا القوة هذه هتكون Q في V cross Bمالها
+
+117
+00:08:39,950 --> 00:08:42,970
+إيش هتكون نوع ال force عمودية لأنها دي مالها right
+
+118
+00:08:42,970 --> 00:08:48,250
+hand rule P X P هتكون F صح؟ إذا هيتولد عندي قوة
+
+119
+00:08:48,250 --> 00:08:52,450
+عمودية على حركة ال particle و على magnetic field
+
+120
+00:08:52,450 --> 00:08:57,230
+إذا هدولة التلت components عمودين على بعض ال
+
+121
+00:08:57,230 --> 00:09:01,170
+velocity و ال magnetic field و ال force الناتجة
+
+122
+00:09:01,170 --> 00:09:05,550
+إذا بيستنتج إنه ال magnetic force هذي رمز منها
+
+123
+00:09:05,550 --> 00:09:09,830
+يعني magnetic force فيه معناه أفعىالـ magnet force
+
+124
+00:09:09,830 --> 00:09:12,770
+بتولدش عنها work، فانا بذكرى إيش ال work اللي احنا
+
+125
+00:09:12,770 --> 00:09:18,830
+قولنا هو F d work مثلا F دو ال DL أو التكامل line
+
+126
+00:09:18,830 --> 00:09:22,150
+integral F دو ال DL ال force مالهبش في اتجاه
+
+127
+00:09:22,150 --> 00:09:25,750
+الحركة عمودية عليها فF دو ال DR إيش بده تساوي؟
+
+128
+00:09:25,750 --> 00:09:30,170
+Zero ال velocity فين؟ اتجاه و القوة عمودية عليها
+
+129
+00:09:30,170 --> 00:09:35,090
+فF دو ال DL إيش بده تساوي؟ Zero إذا ال work الناقش
+
+130
+00:09:35,090 --> 00:09:37,150
+من القوة المواطية بساوة Zero
+
+131
+00:09:43,260 --> 00:09:49,080
+غالبا بيكون ال magnitude لل magnetic force مهمل
+
+132
+00:09:49,080 --> 00:09:55,660
+جنب القوة بتاعة ال electric field و طبعا اول حاجة
+
+133
+00:09:55,660 --> 00:09:59,160
+انه ال magnetic force بتتولد فقط عند moving charge
+
+134
+00:09:59,160 --> 00:10:03,500
+يعني انا لو عندي charge في electric field هيتولد
+
+135
+00:10:03,500 --> 00:10:08,980
+عندي force، force بالساوة Q في E، صح؟لو اتحركت ال
+
+136
+00:10:08,980 --> 00:10:12,260
+charge في وجود ال magnetic field هيتولد اندي كمان
+
+137
+00:10:12,260 --> 00:10:15,340
+قوة ناتجة من magnetic field بس ما تتحرك من ال
+
+138
+00:10:15,340 --> 00:10:18,340
+charge هتفترض ان في اندي electric field و magnetic
+
+139
+00:10:18,340 --> 00:10:21,600
+field و اتولد اندي two قوة ال F electric اللي هي
+
+140
+00:10:21,600 --> 00:10:24,560
+القوة الناتجة على ال charge نتيجة وجودها في ال
+
+141
+00:10:24,560 --> 00:10:27,420
+electric field و عاملها بتتحرك و في magnetic field
+
+142
+00:10:27,420 --> 00:10:30,320
+فكمان اندي كمان قوة بتأثر عليها نتيجة وجودها في
+
+143
+00:10:30,320 --> 00:10:33,580
+magnetic field دائما بتكون القوة اللي ناتجة من
+
+144
+00:10:33,580 --> 00:10:36,240
+magnetic field أقل بكتير من ناتجة من ال electric
+
+145
+00:10:36,240 --> 00:10:41,990
+fieldتهبل في .. لأن غالبا بتكون ال velocity صغيرة
+
+146
+00:10:41,990 --> 00:10:46,390
+كتير لكن لو كانت ال velocity قريبة من سرعة الضوء
+
+147
+00:10:46,390 --> 00:10:49,950
+تلاتة فعاشرة قوة تمانية قريبة منها ساعتها ماقدرش
+
+148
+00:10:49,950 --> 00:10:54,450
+أحمل ال magnetic force لكن بشكل عام بتكون ال
+
+149
+00:10:54,450 --> 00:10:58,550
+magnetic force صغيرة مقارنة مع ال electric force
+
+150
+00:10:58,550 --> 00:11:00,970
+صح؟
+
+151
+00:11:03,880 --> 00:11:08,820
+E عبارة عن KQ نخدة أبسط حاجة KQ1 KQ2 على 4 بي أرثر
+
+152
+00:11:08,820 --> 00:11:15,060
+بي اللي قبل كيو طلعناها فهتكون KQ1 مثلا اللي نجم
+
+153
+00:11:15,060 --> 00:11:17,400
+ال electric field نجم نفترض انه جامن point of
+
+154
+00:11:17,400 --> 00:11:23,120
+charge قمتها كيو واحد فهتكون E KQ1 على أو واحد على
+
+155
+00:11:23,120 --> 00:11:27,800
+4 بي إبسلنون KQ على أرثر بيه صح او الواحد على 4 بي
+
+156
+00:11:27,800 --> 00:11:30,820
+إبسلنون مش هي K 9 constant 9 فعشان قوة 9
+
+157
+00:11:35,740 --> 00:11:39,620
+مقارنة مع ان هي ال magnetic field اللى بتتعداش
+
+158
+00:11:39,620 --> 00:11:42,560
+يعني a few values يعني بتكون صغير كتير ال magnetic
+
+159
+00:11:42,560 --> 00:11:47,280
+field نجي
+
+160
+00:11:47,280 --> 00:11:50,480
+لقى ال force بشكل عام ماقدر أكتبها بدلالة ال
+
+161
+00:11:50,480 --> 00:11:54,700
+electric force و ال magnetic force فإذا F بتساوي Q
+
+162
+00:11:54,700 --> 00:11:58,960
+في E اللى هي ال electric force زائد U cross B اللى
+
+163
+00:11:58,960 --> 00:12:02,360
+هي ال magnetic force هذه كلها بنسميها Lorentz
+
+164
+00:12:02,360 --> 00:12:06,880
+forceلما نحكي عشان أسألك امتحان ايش هي ال lawrence
+
+165
+00:12:06,880 --> 00:12:09,440
+force ال lawrence force هي مجموعة electric و
+
+166
+00:12:09,440 --> 00:12:14,600
+magnetic forces طبعا force بشكل عام على moving
+
+167
+00:12:14,600 --> 00:12:22,000
+object او على اللي اللي له كتلة هو m dv by dt صح؟
+
+168
+00:12:22,000 --> 00:12:26,400
+mdv by dt اذا ال total force هي م ايه؟ اللي هي ال
+
+169
+00:12:26,400 --> 00:12:31,080
+acceleration هي dv by dt بتسوى q في e plus v cross
+
+170
+00:12:31,080 --> 00:12:31,340
+b
+
+171
+00:12:34,630 --> 00:12:42,630
+لو كانت قوة
+
+172
+00:12:42,630 --> 00:12:53,170
+قوة
+
+173
+00:12:53,170 --> 00:12:57,250
+قوة
+
+174
+00:12:57,250 --> 00:13:02,350
+قوة قوة قوة قوة قوة قوة قوة قوة قوة قوة قوة قوة
+
+175
+00:13:02,350 --> 00:13:06,560
+قوة قوة قوة قوة قوة قوة قوةلو كانت moving فهيكون
+
+176
+00:13:06,560 --> 00:13:09,420
+فى عندى electric field force ناجة من ال electric
+
+177
+00:13:09,420 --> 00:13:12,740
+field QE أو force ناجة من ال magnetic field هي QV
+
+178
+00:13:12,740 --> 00:13:19,440
+cross P و ال total اللى هى لورانز force نيجي
+
+179
+00:13:19,440 --> 00:13:24,960
+لفورس الناجة من ال current filament طبعا أنا مش
+
+180
+00:13:24,960 --> 00:13:28,880
+هاقود كتير فى الإشتقال بس البساطة هي عشان نربط ال
+
+181
+00:13:28,880 --> 00:13:34,870
+twoالمعادلات لان احنا عارفين ان ال current density
+
+182
+00:13:34,870 --> 00:13:40,470
+بتساوره في V طبعا هبقدر اشتغل ال forces اللي ناتجة
+
+183
+00:13:40,470 --> 00:13:44,790
+على filament اللي موجود فيها طيار من القانون QV
+
+184
+00:13:44,790 --> 00:13:52,550
+cross B بيناقول ان DF بدل ما اقول QV ايش هتكون IDL
+
+185
+00:13:52,550 --> 00:13:54,210
+cross B
+
+186
+00:13:58,310 --> 00:14:04,230
+العلاقة بين I D L و V D Q مثلا V D Q تصبح I D L
+
+187
+00:14:04,230 --> 00:14:09,890
+أسوأ للـ line أو ال surface أو ال volume I D L
+
+188
+00:14:09,890 --> 00:14:14,910
+بتسوء K D S بتسوء J D V وهذا ال I D L لو عوضناه عن
+
+189
+00:14:14,910 --> 00:14:20,710
+I بنها J باليونة volume أو باليونة surface هتكون
+
+190
+00:14:20,710 --> 00:14:26,850
+رو في V D Vبدل مقاومة عوض عنها لإن بدنا ال J اللي
+
+191
+00:14:26,850 --> 00:14:34,030
+هي رو في V اللي يمينها دي I في DS صح ف ID او IDL
+
+192
+00:14:34,030 --> 00:14:39,210
+رو V دي U هتكون انها اللي هي رو V دي V بدل ال
+
+193
+00:14:39,210 --> 00:14:42,110
+current استخدامنا ال current DC اللي هي J دي V
+
+194
+00:14:42,110 --> 00:14:47,150
+هيكون انها اللي هي V دي Q اللي هي مين رو دي V رو
+
+195
+00:14:47,150 --> 00:14:52,970
+دي V اللي هي DQ صح؟فانا مش هاطلب منكم تاخدوا
+
+196
+00:14:52,970 --> 00:14:55,910
+التفاصيل بتاعة الاشتقاق لكن ان احنا بساطة علاقة
+
+197
+00:14:55,910 --> 00:14:58,470
+ممكن نبدأها من ان ما ان ال current density
+
+198
+00:14:58,470 --> 00:15:02,630
+بتساوروا في V ممكن استخدمها عشان احصل على القوة
+
+199
+00:15:02,630 --> 00:15:07,270
+الناتجة على فعلا ما تمبر فيها ال current في وجود
+
+200
+00:15:07,270 --> 00:15:09,110
+ال magnetic field يعني ان عندي magnetic field
+
+201
+00:15:09,110 --> 00:15:13,460
+موجودوفي عندى element بيبور في التيار فهتتولد على
+
+202
+00:15:13,460 --> 00:15:17,620
+هذا ال element قوة مقدرها ال close line integral I
+
+203
+00:15:17,620 --> 00:15:22,900
+DL DL هنا vector cross B vector و ال force بتكون
+
+204
+00:15:22,900 --> 00:15:27,180
+اللى عموديه على ال filament و المجنون فيه لو كانت
+
+205
+00:15:27,180 --> 00:15:31,360
+surface يعني عندى plane و مافيه current هتكون Kds
+
+206
+00:15:31,360 --> 00:15:35,480
+cross B او لو كانت عندى اللى هي volume هيكون ال
+
+207
+00:15:35,480 --> 00:15:39,240
+volume integral لGDV cross B واضح؟
+
+208
+00:15:42,860 --> 00:15:45,840
+أحيانا الناس بتسمي ال magnetic fields هو ال force
+
+209
+00:15:45,840 --> 00:15:51,820
+per unit current element يعني ال current element F
+
+210
+00:15:51,820 --> 00:15:56,640
+على IDL هاي ال B force per unit current element أو
+
+211
+00:15:56,640 --> 00:16:00,600
+يعني B بيسوا F على GV أو F على KDS
+
+212
+00:16:06,110 --> 00:16:09,330
+أحنا شفنا ال force انها جامن اللى هو ال magnetic
+
+213
+00:16:09,330 --> 00:16:12,010
+field على point of charge انه بتساوي افضل تساوي qv
+
+214
+00:16:12,010 --> 00:16:16,290
+cross b ال force اللى بنتجها ال magnetic field على
+
+215
+00:16:16,290 --> 00:16:19,670
+filament او plane او volume اللى بتساوي ال force
+
+216
+00:16:19,670 --> 00:16:28,390
+بتساوي ال line integral idl cross b اوI D L X B او
+
+217
+00:16:28,390 --> 00:16:34,090
+K D S X B او J D V X B طب لو كانوا two lines مثلا
+
+218
+00:16:34,090 --> 00:16:36,970
+كل واحد مور فيه تيار زى ما انتوا شايفين هنا و انا
+
+219
+00:16:36,970 --> 00:16:41,170
+اتجيب القوة اللى على ال line الاول اللى ناتجه من
+
+220
+00:16:41,170 --> 00:16:45,690
+مرور التيار فى ال line التانى هناخدله elements ان
+
+221
+00:16:45,690 --> 00:16:50,130
+ال element تبعنا I 1 D I 1 و ال element التانى I 2
+
+222
+00:16:50,130 --> 00:16:55,920
+D I 2 القوة اللى ناتجه على ال element الاولاللي هو
+
+223
+00:16:55,920 --> 00:17:02,520
+I1D1 من مرشود من مرور الطيارة في ال element I2DI2
+
+224
+00:17:04,620 --> 00:17:08,600
+I1TI1 cross mean DB2 اللي هو ال magnetic field
+
+225
+00:17:08,600 --> 00:17:13,240
+الناتج من ال element I2DI2 يعني باختصار أنا بجيب
+
+226
+00:17:13,240 --> 00:17:17,600
+القوة على ال element اللي أنا مسميها واحد ال مورفي
+
+227
+00:17:17,600 --> 00:17:22,380
+تيار نتيجة ال magnetic field اللي ناتجة من مرور
+
+228
+00:17:22,380 --> 00:17:25,620
+التيار في ال element التاني فالقوة الناتجة between
+
+229
+00:17:25,620 --> 00:17:29,100
+two current elements هي ببساطة بقدر ابسطها اقول ان
+
+230
+00:17:29,100 --> 00:17:31,700
+هي القوة الناتجة على ال element الأول او ال
+
+231
+00:17:31,700 --> 00:17:36,030
+element الأول نتيجة مرورنتيجة ال magnetic field
+
+232
+00:17:36,030 --> 00:17:39,750
+المتولدة من مرور التيار في ال element التاني لو
+
+233
+00:17:39,750 --> 00:17:44,690
+عوضنا بيوسفر بلو HDB بالساوية ميو نوت اي تنين دي
+
+234
+00:17:44,690 --> 00:17:49,690
+اي تنين اكروس ارهاد على four by ار تربيع وين هي ار
+
+235
+00:17:49,690 --> 00:17:53,530
+هي المسافة ما بين ال element اللي بيولد ال
+
+236
+00:17:53,530 --> 00:17:56,410
+magnetic field و النقطة اللي انا بحسب عندها ال
+
+237
+00:17:56,410 --> 00:18:01,170
+forceيعني في ال space إيش بكون بحط حط ال position
+
+238
+00:18:01,170 --> 00:18:06,810
+تبع هذا هيكون R1 ال position تبع هذا R2 وR21 هي
+
+239
+00:18:06,810 --> 00:18:11,490
+عبارة عن المسافة بين ال source اللي هو ال element
+
+240
+00:18:11,490 --> 00:18:14,670
+اللي بولد المجد فيه و المكان اللي بقي اسم منه let
+
+241
+00:18:14,670 --> 00:18:20,900
+charge اللي هو هسميه R21 لو عوضت عن اللي هو DB2في
+
+242
+00:18:20,900 --> 00:18:25,200
+المعادلة بتاعتي هيكون عندي ميو نوت اي واحد دي
+
+243
+00:18:25,200 --> 00:18:29,540
+الواحد ال cross عند cross product اي تانين دي اي
+
+244
+00:18:29,540 --> 00:18:35,030
+تانين cross are hat على four by are تربيةأذا عندي
+
+245
+00:18:35,030 --> 00:18:38,970
+بقدر أقول ال total force هي double انتيجرة عندي دي
+
+246
+00:18:38,970 --> 00:18:42,510
+I1 و دي I2 اذا عندي double انتيجرة اذا اقف واحد
+
+247
+00:18:42,510 --> 00:18:46,910
+منه I1 I2 بطلعهم برا على 4πI ال double integer
+
+248
+00:18:46,910 --> 00:18:51,090
+المر على اللوب الأول و مر على اللوب التاني طبعا
+
+249
+00:18:51,090 --> 00:18:53,870
+حتى اللوب التاني بيعطيني كل الماجنة تفيد انها تجمد
+
+250
+00:18:53,870 --> 00:18:56,980
+مرور تيار في كل ال elementsلو أخد قطعة صغيرة قطعة
+
+251
+00:18:56,980 --> 00:18:59,800
+صغيرة بدي أكمل عليهم كلهم بيعطيني ال magnitude
+
+252
+00:18:59,800 --> 00:19:04,280
+الناتج من كل ال loop و لما أكمل على الواحد ايش
+
+253
+00:19:04,280 --> 00:19:08,420
+بيعطيني اول حاجة لما أخد قطعة هنا أكمل كليا بقول
+
+254
+00:19:08,420 --> 00:19:11,220
+كل القوة الناتجة من كل ال elements على هذا ال loop
+
+255
+00:19:11,220 --> 00:19:15,040
+على هذا ال element I1DI1 لما أكمل على ال loop
+
+256
+00:19:15,040 --> 00:19:18,280
+التاني بيعطيني كل القوة الناتجة على هذا ال loop من
+
+257
+00:19:18,280 --> 00:19:22,540
+نتيجة اللي هو ال loop التاني واضح؟هيكون دي الواحد
+
+258
+00:19:22,540 --> 00:19:27,420
+cross دي الاتنين cross R ها على R اتنين واحد تربيه
+
+259
+00:19:27,420 --> 00:19:31,320
+طبعا لو انا بد القوة اللى بيأثرها ال element واحد
+
+260
+00:19:31,320 --> 00:19:34,220
+او ال filament واحد على اتنين هتكون بتساوى بال
+
+261
+00:19:34,220 --> 00:19:36,800
+تمام في المقدار القوة اللى بيأثرها ال filament
+
+262
+00:19:36,800 --> 00:19:39,640
+اتنين على واحد بس بتعكسها باتجاهها زى ما انتوا
+
+263
+00:19:39,640 --> 00:19:42,860
+شايفين هذه هتكون اتجاهها هيك بينما اتجاه التاني
+
+264
+00:19:42,860 --> 00:19:47,320
+هيك يعني دي F واحد هي اتجاهها دي F تاني هتكون
+
+265
+00:19:47,320 --> 00:19:49,780
+العكس يعني دي F واحد
+
+266
+00:19:58,850 --> 00:20:05,040
+خلصنا القوانينأخر واحد هو يمكن البس أطولهم بس كنت
+
+267
+00:20:05,040 --> 00:20:09,760
+بتذكروهم مجرد اللي هو اضعف بيو سوبرت لو على I DL
+
+268
+00:20:09,760 --> 00:20:14,120
+هذا هى بس بنكامل طبعا عشان نجيب ال total force و
+
+269
+00:20:14,120 --> 00:20:17,080
+بنكامل على بيو سوبرت لو اذا أف و أح سو نيون اي
+
+270
+00:20:17,080 --> 00:20:20,360
+واحد اي اتين اربع اربع اي دوبل انتيجرة DL واحد
+
+271
+00:20:20,360 --> 00:20:23,280
+across DL تانين across R hat اللي هو ال unit
+
+272
+00:20:23,280 --> 00:20:26,260
+vector بين ال two elements على اللي هو R تانين
+
+273
+00:20:26,260 --> 00:20:31,630
+واحد تانينفنبدأ أول حاجة على ال point of charge لو
+
+274
+00:20:31,630 --> 00:20:37,050
+كان عندك charge particle of mass 2 kilogram يعني
+
+275
+00:20:37,050 --> 00:20:41,730
+قيمتها ال charge هذه لها كتلة مقدارها 3 kilogram و
+
+276
+00:20:41,730 --> 00:20:46,990
+لها charge 2 kilogram و لها charge 3 column starts
+
+277
+00:20:46,990 --> 00:20:50,390
+at a point يعني بدأت في ال space عند نطة مقدار
+
+278
+00:20:50,390 --> 00:20:53,790
+موجودة 1 مقاس 2 0 يعني وين هي موجودة في ال XY
+
+279
+00:20:53,790 --> 00:20:54,190
+plane
+
+280
+00:21:04,290 --> 00:21:16,710
+X مقدارها 1 و Y قدرها X و Y قدرها Z يعني
+
+281
+00:21:16,710 --> 00:21:20,150
+هنا بدأت الموضوع عند X واحد و ثالث تانية طبعا اليم
+
+282
+00:21:20,150 --> 00:21:23,710
+موجودة وين؟ في ال XY plane لأن مزيد بتسوء Zero
+
+283
+00:21:23,710 --> 00:21:32,930
+الماس بتسوء 2 كيلو اجرام والتشاش بتسوء تلاتةهي كل
+
+284
+00:21:32,930 --> 00:21:36,230
+معلومات عن ال point in charge ايش كمان قايلة انها
+
+285
+00:21:36,230 --> 00:21:38,690
+بدت ال velocity يعني هاي الموضوع ال initial
+
+286
+00:21:38,690 --> 00:21:41,930
+position بدت من هذا ال position ال initial
+
+287
+00:21:41,930 --> 00:21:52,030
+velocity V0 بتساوي 4X hat plus 3Z hat قدش ال meter
+
+288
+00:21:52,030 --> 00:21:57,650
+per second initial position initial velocity في
+
+289
+00:21:57,650 --> 00:22:04,060
+وجود electric field في وجود electric fieldاللي
+
+290
+00:22:04,060 --> 00:22:13,340
+قيمته 12x hat plus 10y hat ضهده موجود في ال XY
+
+291
+00:22:13,340 --> 00:22:18,900
+plane Electric field موجود في ال XY plane ان اتناش
+
+292
+00:22:18,900 --> 00:22:27,520
+اتجاهه 12x hat و 10y hat Electric field في اتجاهه
+
+293
+00:22:27,520 --> 00:22:33,830
+في هذا المصاريموجود في ال X Y يعني يكون موازن هذا
+
+294
+00:22:33,830 --> 00:22:37,970
+الحط يعني لو حطينا أول حط عشرة electric field فهذا
+
+295
+00:22:37,970 --> 00:22:43,550
+متشابه طبعا عرفنا ال electric field وين هو موجود
+
+296
+00:22:43,550 --> 00:22:46,250
+في ال X Y plane اللي component في ال X مقدارها
+
+297
+00:22:46,250 --> 00:22:51,130
+اتناش وفي ال Z مقدارها عشرة volt per meter طبعا وي
+
+298
+00:22:51,130 --> 00:22:55,230
+end الزمن T واحد T بيساوا واحد second انتهى اللحظة
+
+299
+00:22:55,230 --> 00:23:00,510
+ان T بيساوا واحد secondبدنا نقرر التالي اذا احنا
+
+300
+00:23:00,510 --> 00:23:03,430
+قولنا initially يعني عند t equal zero كان عندنا
+
+301
+00:23:03,430 --> 00:23:06,610
+initial position اللي هو عند x يتساوى واحد و y
+
+302
+00:23:06,610 --> 00:23:09,830
+minus اتنين عندنا initial velocity اللي هي اربعة x
+
+303
+00:23:09,830 --> 00:23:14,460
+hat زي تلاتة z hatفي اللى هو ال electric field
+
+304
+00:23:14,460 --> 00:23:18,320
+اللى مقداره 12 اكساد زي 10 وايهات عند اللحظة
+
+305
+00:23:18,320 --> 00:23:21,480
+السؤال بقول ليه عند اللحظة T بيسأل واحد second قرر
+
+306
+00:23:21,480 --> 00:23:24,940
+اللى التانى ال acceleration of the particle احنا
+
+307
+00:23:24,940 --> 00:23:28,240
+طالما بنعرف انه مدام ها دى ناسق الجسم اللى كتلة
+
+308
+00:23:28,240 --> 00:23:32,440
+جسم اللى كتلة و بتتحرك اذا فى عندى فرصة فى
+
+309
+00:23:32,440 --> 00:23:36,200
+acceleration فى وجود فى عندى قوة خارجية اول حاجة
+
+310
+00:23:36,200 --> 00:23:38,280
+هى اللى هى القوة الخارجية هى ال electric field
+
+311
+00:23:38,280 --> 00:23:42,140
+وجود highlight charge في مجال ال electric field
+
+312
+00:23:42,460 --> 00:23:49,980
+هيعطينا قوة مقدارها Q في E وهي أول حاجة وهذه ال
+
+313
+00:23:49,980 --> 00:23:54,040
+force هتولق يعني ال force هذي بتساوي MA اللي هو
+
+314
+00:23:54,040 --> 00:23:58,260
+مين ال mutant second one انتوا شايفين قدامكم على
+
+315
+00:23:58,260 --> 00:24:03,580
+ال slide إذا القوة اللي exerted على ال object تبعي
+
+316
+00:24:03,580 --> 00:24:07,280
+على ال chargeناتجة من وجودها في مجال الـ electric
+
+317
+00:24:07,280 --> 00:24:10,880
+field بتساوي Q في E والقوة من الـ Newton's law
+
+318
+00:24:10,880 --> 00:24:14,560
+بتساوي M تقرر إذا ال acceleration إيش بصدها ساوي
+
+319
+00:24:14,560 --> 00:24:19,900
+القوة على ال mass ال Q في E على M ال Q مقطعها
+
+320
+00:24:19,900 --> 00:24:24,700
+تلاتة كولو E مقليها اتناش اكساد زي الأشهر Y على ال
+
+321
+00:24:24,700 --> 00:24:27,240
+mass اللي هي اتنين كيلو وبالتالي حصلت على ال
+
+322
+00:24:27,240 --> 00:24:29,840
+acceleration واضح؟
+
+323
+00:24:31,300 --> 00:24:34,760
+تانية it's velocity مقعطين ال acceleration و بدهوا
+
+324
+00:24:34,760 --> 00:24:37,000
+ال velocity ايش العلاقة بال acceleration و ال
+
+325
+00:24:37,000 --> 00:24:41,900
+velocity ال acceleration dv by dt صح اذا بقدر
+
+326
+00:24:41,900 --> 00:24:44,320
+استخدم هاي العلاقة ان اقول ال acceleration هاي
+
+327
+00:24:44,320 --> 00:24:49,380
+بتما بتساوي dv by dt بتساوي 18x hat زي 15y hat و
+
+328
+00:24:49,380 --> 00:24:54,180
+كامل اذا عندي ال acceleration بتساوي dv by dt اللي
+
+329
+00:24:54,180 --> 00:24:59,100
+هي d by dt لمين Vx hat Vx x hat Vy y hat
+
+330
+00:25:06,810 --> 00:25:11,050
+بتساوي 18x hat زي 15 y hat ايش تفاعله ابن الكابل
+
+331
+00:25:11,050 --> 00:25:13,730
+طبعا ال x component هتساوي ال x component و ال y
+
+332
+00:25:13,730 --> 00:25:15,530
+component هتساوي ال y component و ال z component
+
+333
+00:25:15,530 --> 00:25:18,690
+هتساوي ال z component ال x component بيقول ال dvx
+
+334
+00:25:18,690 --> 00:25:23,050
+by dt بتساوي 18 ال y component بيقول ال dvy by dt
+
+335
+00:25:23,050 --> 00:25:27,350
+بتساوي 15 بينما ال z component dvz by dt بتساوي 0
+
+336
+00:25:28,150 --> 00:25:31,790
+طبعا هاي اذا الاول واحدة اللى دى vx by dt بالساوية
+
+337
+00:25:31,790 --> 00:25:36,410
+18 هكامل vx مش بالساوية 18t زايد some constant
+
+338
+00:25:36,410 --> 00:25:42,530
+اكامل التانية اللى دى vy by dt بالساوية 15 هتعطينى
+
+339
+00:25:42,530 --> 00:25:48,050
+vy بالساوية 15t زايد bDvz by dt بتسوى 0 إذا vz
+
+340
+00:25:48,050 --> 00:25:52,270
+بتسوى constant من هنا بدأ أجيب قيم a و b و c من ال
+
+341
+00:25:52,270 --> 00:25:56,890
+initial conditions قال يعني t equals 0 الفرصة v
+
+342
+00:25:56,890 --> 00:26:02,920
+not بتسوى 4x hat ساعة تلاتة z hatInitially كان
+
+343
+00:26:02,920 --> 00:26:06,460
+الجسم بتحرك ب initial velocity أو ال charge
+
+344
+00:26:06,460 --> 00:26:10,760
+بتاعتي، الكتلة اللي عليها ال charge بتتحرك ب
+
+345
+00:26:10,760 --> 00:26:14,740
+initial velocity مقار 4x plus 3 زي ذلك، معناه ال X
+
+346
+00:26:14,740 --> 00:26:19,790
+componentاللي هى initial value يعني T equal 0 إيش
+
+347
+00:26:19,790 --> 00:26:25,710
+بتساوي 4 إذا new x at T بتساوي 0 بتساوي إيه لإن 18
+
+348
+00:26:25,710 --> 00:26:30,710
+في 0 سفر إذا new x at T equal 0 بتساوي 4 given
+
+349
+00:26:30,710 --> 00:26:36,750
+إلنا بتساوي إيه إذا إيه بتساوي 4 عرفنا إيهY ال
+
+350
+00:26:36,750 --> 00:26:41,210
+component لل velocity initial بتساوي تلاتة يعني VY
+
+351
+00:26:41,210 --> 00:26:45,050
+at zero بتساوي B بتساوي قداش تلاتة اذا B بتساوي
+
+352
+00:26:45,050 --> 00:26:49,550
+تلاتة Zero بتاسوة Zero هاد ال Z component ال Y
+
+353
+00:26:49,550 --> 00:26:53,070
+component لأ ال velocity بتساوي Zero اذا VY at
+
+354
+00:26:53,070 --> 00:26:56,610
+zero بتساوي Zero اذا B بتساوي Zero ال Z component
+
+355
+00:26:56,610 --> 00:27:02,500
+بتساوي تلاتة اذا U VZ at zeroبتساوى C بتساوى تلاتة
+
+356
+00:27:02,500 --> 00:27:06,360
+زى ان C بتساوى تلاتة اذا نعرفنا ان ال A بتساوى
+
+357
+00:27:06,360 --> 00:27:10,440
+اربعة ال B بتساوى سفر و ال C بتساوى تلاتة فبعود عن
+
+358
+00:27:10,440 --> 00:27:16,690
+ال velocity U of T اللى هي UX UY UZ او VXVXيعني
+
+359
+00:27:16,690 --> 00:27:20,650
+الطريقتين ممكن اكتبهم ال X component هي طمن طعش T
+
+360
+00:27:20,650 --> 00:27:24,410
+زا قد A اللي طلعناها أربعة ال Y component خمس طعش
+
+361
+00:27:24,410 --> 00:27:27,950
+T لأنه بيه Zero و ال Z component تساوية تلاتة
+
+362
+00:27:27,950 --> 00:27:30,970
+تمام؟ اذا هلقيته جيبنا ال acceleration و جيبنا ال
+
+363
+00:27:30,970 --> 00:27:35,450
+velocity عند أي لحظة it's kinetic energy مش نص ك
+
+364
+00:27:35,450 --> 00:27:39,890
+نص M V تربية اه؟ اذا ال kinetic energy اهم متحركة
+
+365
+00:27:39,890 --> 00:27:42,130
+مافيش potential energy ال total energy هنا kinetic
+
+366
+00:27:42,130 --> 00:27:48,830
+energy نص M V تربيةالـ V تربيع في مقدارها dot ال
+
+367
+00:27:48,830 --> 00:27:51,750
+product في نفسها تحت جزر التربيع ماشي خلّال ال
+
+368
+00:27:51,750 --> 00:27:56,750
+magnitude إذا حتساوى نص اتنين اتنين و عشرين تربيع
+
+369
+00:27:56,750 --> 00:28:01,550
+ازاد خمساش تربيع ازاد تلات تربيع تحت الجزر التربيع
+
+370
+00:28:01,550 --> 00:28:04,050
+لكل تربيع بتصير اتنين و عشرين تربيع ازاد خمساش
+
+371
+00:28:04,050 --> 00:28:07,190
+تربيع ازاد تلات تربيع ال magnitude هو جزر التربيع
+
+372
+00:28:07,190 --> 00:28:08,910
+ل U dot U
+
+373
+00:28:11,650 --> 00:28:14,390
+هى اللى بتتبعها مع بعضها تحسس الترفيه بتوطين ال
+
+374
+00:28:14,390 --> 00:28:19,010
+magnitude ترفيها برفع فبروح الجزر الترفيه فقدر
+
+375
+00:28:19,010 --> 00:28:21,610
+احسبها اللى كانت كده يوم سبعمية و تمانية عشو
+
+376
+00:28:24,630 --> 00:28:28,050
+it's position بدو الموقع احنا جبنا الفلس ت والفلس
+
+377
+00:28:28,050 --> 00:28:30,830
+ت مش علاقتها و ال position الفلس ت بتساوي d
+
+378
+00:28:30,830 --> 00:28:36,630
+position by dt اذا هى ال position اللى هى dL by dt
+
+379
+00:28:36,630 --> 00:28:40,070
+او dR by dt ايش بيكونوا يسموه مش مشكلة مش هنخلف
+
+380
+00:28:40,070 --> 00:28:44,310
+عليها اذا الفلس ت بتساوي d by dt لمين ل X Y و Z
+
+381
+00:28:44,310 --> 00:28:50,590
+اللى هى قدش كمة الفلس ت حسبناها مع بعض 18 T زاد 4
+
+382
+00:28:50,590 --> 00:28:55,720
+هو 13 T و 3نفس القضية ال x component لا تساوي ال x
+
+383
+00:28:55,720 --> 00:28:58,220
+component ال y component تساوي ال y component ال z
+
+384
+00:28:58,220 --> 00:29:00,900
+component لا تساوي ال z component دي x by دي t إيش
+
+385
+00:29:00,900 --> 00:29:05,400
+بتساوي؟ و x ليه 18t زاد 4 بالكامل، x إيش بيبقى
+
+386
+00:29:05,400 --> 00:29:10,520
+تساوي 18 على 2t تربيه، يعني 9 على 2 تربيه زاد 4 في
+
+387
+00:29:10,520 --> 00:29:14,140
+t زاد a واحد، بسميها a واحد عشان تخلف عن a اللي
+
+388
+00:29:14,140 --> 00:29:19,810
+قبلك احضر معاهأذا عندي x صارت 9t تربيع زي 4t زي a1
+
+389
+00:29:19,810 --> 00:29:28,090
+dy by dt 15t بكامل هضطيني y بتساوي 15t تربيع على 2
+
+390
+00:29:28,090 --> 00:29:32,610
+يعني سبعة و نص تربيع زي b1 dz by dt بتساوي تلاتة
+
+391
+00:29:32,610 --> 00:29:37,550
+اذا زدتش بتساوي تلاتة t زي c1 a1 و b1 و c1 نجيبها
+
+392
+00:29:37,550 --> 00:29:39,570
+من ال initial position نعطينا ال initial position
+
+393
+00:29:39,570 --> 00:29:43,010
+معينة ايه انا حاططه على اسمة واحد و ماعناه اثنين
+
+394
+00:29:43,970 --> 00:29:48,070
+إذا إحنا عارفين ال initial يعني T equals 0 X
+
+395
+00:29:48,070 --> 00:29:51,610
+initialي إيش كانت بتساوي واحد إذاً A واحد مش
+
+396
+00:29:51,610 --> 00:29:57,070
+بتساوي واحد Y and T equals 0 بتساوي ثالث تنين إذاً
+
+397
+00:29:57,070 --> 00:30:00,510
+B واحد بتساوي تنين Z initialي بتساوي سفر إذاً C
+
+398
+00:30:00,510 --> 00:30:05,310
+واحد بتساوي Zero واضح؟ إذا بقدر أجيب اللي هو ال ..
+
+399
+00:30:05,310 --> 00:30:08,990
+ال position تبعنا ال X Y Z بيساوي تسعة T تربية زد
+
+400
+00:30:08,990 --> 00:30:14,990
+أربعة T زادزائد واحد زائد واحد وعندي اللي هو ال y
+
+401
+00:30:14,990 --> 00:30:18,610
+component سبعة و نص تتربيه minus تانين و z
+
+402
+00:30:18,610 --> 00:30:23,170
+component تلاتة T بدوياها عند اللحظة T بتساوي واحد
+
+403
+00:30:23,170 --> 00:30:27,110
+second بعود عن T بواحد second بحصل على ال position
+
+404
+00:30:27,110 --> 00:30:33,650
+and height اللحظة طبعا في حاجة طالما خلصناها S
+
+405
+00:30:33,650 --> 00:30:37,430
+position سهل السؤال صح يعني كل الحاجة الجديدة فيه
+
+406
+00:30:37,430 --> 00:30:42,110
+ان اجيب ال force Q V cross Pبس هناك ال electric
+
+407
+00:30:42,110 --> 00:30:47,270
+field Q في E بس و بعدين كله Newton's law ده كان
+
+408
+00:30:47,270 --> 00:30:51,050
+بلعته الجبرة هنا طبعا في وجود magnetic field شفنا
+
+409
+00:30:51,050 --> 00:30:55,050
+غير المثال كان في وجود ال electric field حسبنا ال
+
+410
+00:30:55,050 --> 00:30:58,270
+force و جيبنا منها ال acceleration و الposition و
+
+411
+00:30:58,270 --> 00:31:01,590
+ال kinetic energy لو كان عندي charged particle
+
+412
+00:31:01,590 --> 00:31:08,420
+وزنها 2 kilogramلها واحد column ال charge بدأت عند
+
+413
+00:31:08,420 --> 00:31:11,920
+ال origin هنا بدأت عند ال zero zero zero initially
+
+414
+00:31:11,920 --> 00:31:15,660
+وين كانت؟ واحد ثمانية ثمانية ثمانية ثمانية zero
+
+415
+00:31:15,660 --> 00:31:19,420
+zero zero هنا initial هنا الكتلة بتاعتها او برضه
+
+416
+00:31:19,420 --> 00:31:26,900
+تن كيلو واحد column هنا واحد column بدأت
+
+417
+00:31:26,900 --> 00:31:32,190
+هنا عند ال originstart at the origin with velocity
+
+418
+00:31:32,190 --> 00:31:40,010
+initial velocity تلاتة y hat
+
+419
+00:31:40,010 --> 00:31:47,610
+متر per second هاي
+
+420
+00:31:47,610 --> 00:31:50,810
+عرفنا ال initial velocity and travels in the
+
+421
+00:31:50,810 --> 00:31:53,130
+region of the four magnetic field in the magnetic
+
+422
+00:31:53,130 --> 00:31:57,530
+field بيساوي
+
+423
+00:31:57,530 --> 00:31:59,250
+عشر زدها
+
+424
+00:32:01,730 --> 00:32:08,190
+والدور درمتر تربيه بدنا
+
+425
+00:32:08,190 --> 00:32:11,950
+عند اللحظة T بتساوي أربع ساكن تحسب التالي كلها نفس
+
+426
+00:32:11,950 --> 00:32:15,430
+الفكرة يعني احنا لاقيها هنا بس ناقص كانت Q في E
+
+427
+00:32:15,430 --> 00:32:19,870
+هنا هتسيب فيها ماكروس صفر ده دي اول حاجة طالب مننا
+
+428
+00:32:19,870 --> 00:32:23,570
+ال force و ال acceleration of the particle بدنا ال
+
+429
+00:32:23,570 --> 00:32:25,650
+acceleration هو اللي بتجيبها من ال force يعني ال
+
+430
+00:32:25,650 --> 00:32:28,430
+force مش بتساوي القوة اللي على الجسم يعني الجسم
+
+431
+00:32:28,430 --> 00:32:32,610
+اللي كتلة اتنين كيلو جرام تساوي انفقانبتساوي Q في
+
+432
+00:32:32,610 --> 00:32:37,310
+V X B لأنها موجودة في مجال مع مطيسي في اتجاه ال Z
+
+433
+00:32:37,310 --> 00:32:42,030
+axis والفلوس بتاعتنا في اي اتجاه في اتجاه ال Y
+
+434
+00:32:42,030 --> 00:32:49,910
+axis ال acceleration قلنا هي Q على M V X B
+
+435
+00:32:50,830 --> 00:32:55,410
+الأكسلاريشن هي eq على n v cross b لو أنا استخدمت
+
+436
+00:32:55,410 --> 00:32:59,770
+ال cross product هيكون نص x hat y hat z hat الفلوس
+
+437
+00:32:59,770 --> 00:33:05,610
+اللى بتحسبها vx vy vz اللى مش عارفاها وعندي المادة
+
+438
+00:33:05,610 --> 00:33:10,390
+تكفي دوا انتجاهه في اتجاه z هذا بتعطيني ال cross
+
+439
+00:33:10,390 --> 00:33:14,690
+product بيعطيني قيمين اللى هي eq على n v cross b
+
+440
+00:33:14,690 --> 00:33:17,810
+طبعا عشان أربط فلوسي ففلوسي فبعوض عن ال
+
+441
+00:33:17,810 --> 00:33:21,480
+acceleration dv by dtهنا عندى اكسر ال velocity
+
+442
+00:33:21,480 --> 00:33:24,600
+فبعود بال velocity و بجيب اول ال velocity و منها
+
+443
+00:33:24,600 --> 00:33:27,540
+برجع بجيب ال acceleration هو بده اتنين بس و ال
+
+444
+00:33:27,540 --> 00:33:30,680
+acceleration اذا انا لما اجيب ال cross product لك
+
+445
+00:33:30,680 --> 00:33:34,360
+V cross P بطلع النتيجة بدلات ال velocity اللى يمين
+
+446
+00:33:34,360 --> 00:33:38,140
+بطلع افضل لان الوحيد اللى بسوي الصفر اللى هو ال Z
+
+447
+00:33:38,140 --> 00:33:44,100
+component فهيكون دايما عند ال X component هي 10 في
+
+448
+00:33:44,100 --> 00:33:48,400
+Y hat على 2 طبعا لان المص اللى جاى من Mهيعطيني
+
+449
+00:33:48,400 --> 00:33:52,400
+خمسة هى ال واحد ال component هو ال X hat والتانية
+
+450
+00:33:52,400 --> 00:33:58,740
+اللى هى ال Y hat لكن Z hat هتكون سفر سفر، صح؟ فD
+
+451
+00:33:58,740 --> 00:34:05,080
+by DT VX X hat زي VY Y hat زي VZ Z hat بسوى ال X
+
+452
+00:34:05,080 --> 00:34:07,860
+component مع بعض و ال Y component مع بعض و ال Z
+
+453
+00:34:07,860 --> 00:34:11,240
+component مع بعض، هيكون عندى DVX by DT بتسوى خمسة
+
+454
+00:34:11,240 --> 00:34:18,100
+VYدى vy by dt بتسوى minus خمسة vx ودى vz by dt
+
+455
+00:34:18,100 --> 00:34:22,400
+بتسوى سفر هى المعادلات التلاتة اللى معناها بدى
+
+456
+00:34:22,400 --> 00:34:25,600
+اجيبهم من اين ال .. ال .. ال .. ال .. ال c node
+
+457
+00:34:25,600 --> 00:34:27,500
+هدا طبعا من ال initial condition و هدول بدي اشوف
+
+458
+00:34:27,500 --> 00:34:30,360
+كيف بدي احلهم اولا بدي افكر في ال c node يعنى ال z
+
+459
+00:34:30,360 --> 00:34:33,740
+component initially قدش كانت الفلسطين initially
+
+460
+00:34:33,740 --> 00:34:41,210
+كانت تلاتة y hat اذا لو انا حطت vz at zeroبتكون V
+
+461
+00:34:41,210 --> 00:34:44,450
+total يعني مافيش ال DZ component اللي هي صفر فإذا
+
+462
+00:34:44,450 --> 00:34:48,710
+C not بتساوي صفر كيف بدأ أحلها دولة ال two
+
+463
+00:34:48,710 --> 00:34:53,850
+equations هاد ال X مربوطة بال Y و هنا ال Y مربوطة
+
+464
+00:34:53,850 --> 00:34:58,410
+بال X الحل الواحد ان أخد الكمان مرة يعني ال D2 ب X
+
+465
+00:34:58,410 --> 00:35:05,510
+by DT تربيه بتساوي 5 DBY by DTو DV بي وي وDT
+
+466
+00:35:05,510 --> 00:35:09,230
+مربوطة بين VX فبصير المعادلة تفاضليها من درجة
+
+467
+00:35:09,230 --> 00:35:14,090
+تانية تربط VX مع بعض واضح؟ اذا بفاضل كمان مرة
+
+468
+00:35:14,090 --> 00:35:19,630
+بيصير D2VX بي DT بيساوي 5DVY بي DT اللي بتساوي منص
+
+469
+00:35:19,630 --> 00:35:27,510
+5VX فبتطلع عندي D2VX بي DT تربيه بتساوي منص 25VX
+
+470
+00:35:27,510 --> 00:35:32,650
+لو عملت نفس الحكي هنا إيش هيكون D2VY بي D2
+
+471
+00:35:55,230 --> 00:35:58,690
+طبعا هذه احنا شوفناها في الدوائر و اكيد شوفتها في
+
+472
+00:35:58,690 --> 00:36:03,670
+ال differential و بتعرفوا كيف تحلوها ولا لافها دي
+
+473
+00:36:03,670 --> 00:36:07,070
+oscillator اه اللي هي ها دي بتكون على شكل E to the
+
+474
+00:36:07,070 --> 00:36:14,450
+J خمسة X T ليش؟ افعض الأول مرة بتعطيني اللي هي
+
+475
+00:36:14,450 --> 00:36:18,630
+الخمسة و كمان مرة بتعطيني كمان J في J بتعطيني ال
+
+476
+00:36:18,630 --> 00:36:23,310
+minus صح؟ لإن لو قلت E to the minus خمسة T أول مرة
+
+477
+00:36:23,310 --> 00:36:25,230
+بتعطيني ال minus خمسة و أول مرة minus خمسة تصير ال
+
+478
+00:36:25,230 --> 00:36:31,510
+plus فهي لازم تكون على شكل E to the J خمسة Tطبعا
+
+479
+00:36:31,510 --> 00:36:35,910
+او بعضرتها بشكل Cos وSin ياسي واحد E to the plus J
+
+480
+00:36:35,910 --> 00:36:39,650
+plus C تنين E to the minus J خمسة T او بشكل Sin
+
+481
+00:36:39,650 --> 00:36:43,830
+وCos فإذا ان الناتج تبعنا ل UX بسوء C واحد Cos
+
+482
+00:36:43,830 --> 00:36:53,790
+خمسة T زي C تنين Sin الخمسة T طيب هذه أول حاجة
+
+483
+00:36:53,790 --> 00:36:59,010
+بالنسبة لل X ال Y نفس الحاجة اللي عملنا بيعطيناأو
+
+484
+00:36:59,010 --> 00:37:02,450
+ايش كمان ممكن استخدم عشان اجيب ال Y ان عندي
+
+485
+00:37:02,450 --> 00:37:06,910
+المعادلة ان متفاضل ال X بالنسبالتي ايش تعطيني خمسة
+
+486
+00:37:06,910 --> 00:37:13,490
+VY وانا جبت الجوار تبع ال VX لو فضلتها دي VX by دي
+
+487
+00:37:13,490 --> 00:37:17,850
+VY بتعطيني خمسة VY بحصل على VY مباشرة او زي ما
+
+488
+00:37:17,850 --> 00:37:20,710
+قلتلكوا بفاضل مرة تانية بحصل على معادلة تاعة ال Y
+
+489
+00:37:20,710 --> 00:37:25,690
+يا هيك يا هيك بتنصحي اذا انا عرفت قيمة ال VX وعرفت
+
+490
+00:37:25,690 --> 00:37:32,870
+قيمة ال VYواضال علينا ان اجيب قيم
+
+491
+00:37:32,870 --> 00:37:37,330
+C1 و C2 ان هما دولة مجاهيل بالنسبالي و ال solution
+
+492
+00:37:37,330 --> 00:37:41,930
+ماله مش كامل الا انا اعرف قيم C1 و C2 عشان اجيبهم
+
+493
+00:37:41,930 --> 00:37:43,970
+هنا و اجيبهم ال initial value ال initial value ان
+
+494
+00:37:43,970 --> 00:37:48,570
+T equal 0 و V اتجاهها في ال Y direction قيمتها 3
+
+495
+00:37:48,570 --> 00:37:54,520
+اذا نقول ان V X هو 0جبتها من الـ 0 و 1 صين الـ 00ش
+
+496
+00:37:54,520 --> 00:38:00,600
+بيضل عند Vx الـ 0 C1 بتسوى 0 if C1 is 0 بيضل عند
+
+497
+00:38:00,600 --> 00:38:06,440
+Vx بتسوى C2 sin 5T صح؟ الحاجة التانية المهمة اللي
+
+498
+00:38:06,440 --> 00:38:10,540
+بيجيب الـ C2 من Vy Vy اللي لها قيمة بتسوى قداش
+
+499
+00:38:10,540 --> 00:38:16,460
+تلاتة يعني T equals 0 صين الـ 00و جبتها من الـ 0 و
+
+500
+00:38:16,460 --> 00:38:20,200
+1 فهتكون C تلين إيش بتساوي تلاتة إذا يعرفنا C1
+
+501
+00:38:20,200 --> 00:38:23,080
+بتساوي صفر من و جيبناها من و VX إيش هي اللي كانت
+
+502
+00:38:23,080 --> 00:38:27,820
+Zero واضح أعملهم على اللوح و لا واضح أكتب و لا
+
+503
+00:38:27,820 --> 00:38:33,180
+واضح يعني VX أت Zero Zero جبتها من ال Zero واحد
+
+504
+00:38:33,180 --> 00:38:38,230
+صالي Zero Zero إذا هتظل عندي Zero بتساوي C1اذا
+
+505
+00:38:38,230 --> 00:38:43,490
+عرفنا c1 سوى 0 من ال y component y at 0 بتساوي 3
+
+506
+00:38:43,490 --> 00:38:49,250
+sin 0 هذا المقدر 0 لكن جبتها من 0 و 1 حتى c2 سوى 3
+
+507
+00:38:49,250 --> 00:38:56,350
+اذا c1 0 c2 3 و c تقولنا 0 لأن z component مش اللي
+
+508
+00:38:56,350 --> 00:38:59,930
+كانت 0 احنا عملناها من بدري اذا ايش هيكون vx
+
+509
+00:38:59,930 --> 00:39:03,890
+بتساوي c1 0 هتروح من هنا و من هنا هيكون vx بتساوي
+
+510
+00:39:03,890 --> 00:39:11,180
+3 sin 5tو Vy ايش بتساوي تلاتة كوصين خمسة T و Vz
+
+511
+00:39:11,180 --> 00:39:15,520
+ايش بتساوي Zero احنا طلعناها constant و ال
+
+512
+00:39:15,520 --> 00:39:19,980
+constant طلعناها تساوي Zero اذا هى ال volumetric
+
+513
+00:39:19,980 --> 00:39:24,080
+step تلاتة كوصين الخمسة T تلاتة كوصين الخمسة T و
+
+514
+00:39:24,080 --> 00:39:29,290
+Zero بده عند اللحظة T بالساوية أربعة بعوضأيش كمان
+
+515
+00:39:29,290 --> 00:39:32,870
+طالب منها ال acceleration ال acceleration هي dP by
+
+516
+00:39:32,870 --> 00:39:37,070
+dt بفضل بحصل على ال acceleration عند ال T بتسوء
+
+517
+00:39:37,070 --> 00:39:40,710
+أربع هي تفضل بال sign خمسة cosine تفضل cosine
+
+518
+00:39:40,710 --> 00:39:45,630
+minus طبعا خمسة في sign الخمسة T فهتصير هنا minus
+
+519
+00:39:45,630 --> 00:39:50,090
+خمس عشر فهيصير خلاص خمس عشر واضح تفضل ال sign
+
+520
+00:39:50,090 --> 00:39:53,670
+بplus cosine تفضل cosine minus sign هي ال
+
+521
+00:39:53,670 --> 00:39:56,370
+acceleration يعني أربعة بعوض عن T أربعة و بحصل على
+
+522
+00:39:56,370 --> 00:40:02,080
+ال accelerationالفرق ال B واضح انه طالب القوة اللى
+
+523
+00:40:02,080 --> 00:40:08,920
+بتأثر ال magnetic force on it عند اللحظة T
+
+524
+00:40:08,920 --> 00:40:12,680
+بالساوية أربعة second احنا عارفين ان ال force
+
+525
+00:40:12,680 --> 00:40:15,700
+بالساوية أمبر ايه و احنا جيبنا ال acceleration عند
+
+526
+00:40:15,700 --> 00:40:18,800
+اللحظة T بالساوية أربعة فبس بدروبها اعطي الكتلة
+
+527
+00:40:18,800 --> 00:40:22,520
+اللى هو في اتنينبعدين تطلب مننا ال kinetic energy
+
+528
+00:40:22,520 --> 00:40:26,700
+عند T بالسوء 4 نص mv تربيع و احنا عارفين ال
+
+529
+00:40:26,700 --> 00:40:31,760
+velocity عند ال 4 بس بربع هاي مربع هاي بحصل على ال
+
+530
+00:40:31,760 --> 00:40:35,360
+kinetic energy عند اللحظة T بالسوء 4 هي لحد ال
+
+531
+00:40:35,360 --> 00:40:38,820
+point T بعدين تطلب انه بدنا ال particles
+
+532
+00:40:38,820 --> 00:40:41,980
+trajectory بيقلمنات ال T ال particles trajectory
+
+533
+00:40:41,980 --> 00:40:46,100
+يعني بدي ال X و ال Y بدون الاعتمادية على ال T حالة
+
+534
+00:40:46,100 --> 00:40:51,630
+trajectoryمساره مساره في ال X و Y يعني لو انا بس
+
+535
+00:40:51,630 --> 00:40:56,110
+حطيت XYZ احصل على المسار بدلت ال X و Y و Z بدون ما
+
+536
+00:40:56,110 --> 00:41:00,470
+انه يكون لإنه احنا عندنا لحد ال اتا ال X ال
+
+537
+00:41:00,470 --> 00:41:02,890
+velocity بدلت ال T و ال acceleration بدلت ال T
+
+538
+00:41:02,890 --> 00:41:06,410
+باتنمين المسار يعني عندنا ال X و Y و Z طبعا ال
+
+539
+00:41:06,410 --> 00:41:11,550
+velocity بتساوي DL by DT فباخد اللي هي ال X
+
+540
+00:41:11,550 --> 00:41:16,130
+component على طول مباشرة يعني ال X component مش
+
+541
+00:41:16,130 --> 00:41:21,850
+هتساويDx by Dt هي الـ x component للفلوس تي تلاتة
+
+542
+00:41:21,850 --> 00:41:26,090
+صين خمسة T وDy by Dt هي ال Y component للفلوس تي
+
+543
+00:41:26,090 --> 00:41:30,910
+تلاتة صين خمسة Tدى z by dt اللى هى ال velocity فى
+
+544
+00:41:30,910 --> 00:41:34,530
+z direction بتساوى 0 عشان أجيب ال x بدى أكامل
+
+545
+00:41:34,530 --> 00:41:38,390
+فهتكون ماينوس تلاتة على خمسة كساين خمسة t زاية بي
+
+546
+00:41:38,390 --> 00:41:42,350
+واحد ال y هتعطيى تلاتة على خمسة sin خمسة t زاية
+
+547
+00:41:42,350 --> 00:41:45,590
+بيتنين و ال z هتعطيى some constant مهم نجيبهم ال
+
+548
+00:41:45,590 --> 00:41:48,530
+initial بصش ال initial potential I1 at الناعم دى
+
+549
+00:41:48,530 --> 00:41:54,500
+ال origin اذا ال x at zeroبتساوى zero جبت وامي
+
+550
+00:41:54,500 --> 00:41:57,600
+zero واحد هتكون إيش بتساوى minus خمسة تلاتة على
+
+551
+00:41:57,600 --> 00:42:00,380
+خمسة زائد بي واحد بتساوى صفر إذاً بي واحد إيش
+
+552
+00:42:00,380 --> 00:42:05,900
+بتساوى تلاتة على خمسة y at zero بتساوى zero صين ال
+
+553
+00:42:05,900 --> 00:42:10,140
+zero zero إذاً y at zero بتساوى بي تنين إيش بتساوى
+
+554
+00:42:10,140 --> 00:42:14,300
+zero إذاً بي تنين صفر z at zero بتساوى zero بتساوى
+
+555
+00:42:14,300 --> 00:42:17,920
+بي تلاتة زائد بي تلاتة zero إذاً عندي بقدر أقول إن
+
+556
+00:42:17,920 --> 00:42:23,640
+xyz إيش بتساوى minus إيه نص cosineالخمسة T ذات P
+
+557
+00:42:23,640 --> 00:42:27,040
+واحدة اش أمنا بتساوي تلتة على خمسة اللي هي برضه
+
+558
+00:42:27,040 --> 00:42:29,960
+ستة من عشرة فإذا بتقدر تعوض عنها ستة من عشرة minus
+
+559
+00:42:29,960 --> 00:42:34,780
+ستة من عشرة قصارى خمسة T هل ال X component لأ ال
+
+560
+00:42:34,780 --> 00:42:40,820
+position ال Y.6 sin 5t لأن P2 هو صفر و Z هو صفر
+
+561
+00:42:40,820 --> 00:42:45,000
+اذا انا انا اولا عندي ال component انت في ال X و Y
+
+562
+00:42:45,000 --> 00:42:49,340
+فقط ال particle تبعي في ال X و Y بس كمان بدويا عن
+
+563
+00:42:49,340 --> 00:42:53,280
+T equal 4 حسابنا لابسش ان عن T equal 4 و بده ال
+
+564
+00:42:53,280 --> 00:42:56,860
+trajectory بدون ما انه يكون فيه اعتمادية على الزمن
+
+565
+00:42:56,860 --> 00:43:04,100
+كيف بده اعمل هذا انا عند ال X component عند
+
+566
+00:43:04,100 --> 00:43:12,870
+ال X component بتساوي6 من 10-6 من 10 cos 5t و ال y
+
+567
+00:43:12,870 --> 00:43:21,990
+component تساوي 6 من 10 sin 5t لو أنا قلت x-6 من
+
+568
+00:43:21,990 --> 00:43:28,770
+10 بتساوي-6 من 10 cos 5t وهي عندي ال two
+
+569
+00:43:28,770 --> 00:43:33,650
+components لو ربعت هاي و ربعت هاي و جماعة مبقى خلص
+
+570
+00:43:33,650 --> 00:43:39,580
+من دي dependency لأن هاي مربعهابتعطيني X minus أنا
+
+571
+00:43:39,580 --> 00:43:43,060
+بالتأسفة ماجبتش القلم الأسود و هذا الأزرق فات كتير
+
+572
+00:43:43,060 --> 00:43:49,900
+مش كمان ولا حتناسي القلم هو واضح على الشاشة؟ واضحة
+
+573
+00:43:49,900 --> 00:43:55,440
+في الجرار بس واضح الخط ولا مش واضح؟
+
+574
+00:43:55,440 --> 00:44:03,120
+اذا
+
+575
+00:44:03,120 --> 00:44:08,500
+عندنا ال Xالـ X-6
+
+576
+00:44:08,500 --> 00:44:13,120
+من 10 يكون تربيه زائد Y تربيه اشهد السؤال هاي
+
+577
+00:44:13,120 --> 00:44:19,040
+تربيها 0.6 يكون تربيه minus تربيها plus cosine
+
+578
+00:44:19,040 --> 00:44:26,400
+تربيه الخمسة T زائد نص تربيه sin تربيه الخمسة T لو
+
+579
+00:44:26,400 --> 00:44:31,820
+أحطت 6 من 10 تربيها من المشترك هيصير cosine تربيه
+
+580
+00:44:33,790 --> 00:44:38,150
+خمسة T زائد ساعة تربيع الخمسة T ايش بتساوي واحد
+
+581
+00:44:38,150 --> 00:44:42,390
+هيك انا بكون عملت elimination لمين للاعتمادية على
+
+582
+00:44:42,390 --> 00:44:47,450
+الزمن خلصت من الاعتمادية على الزمن و السعر عندي X
+
+583
+00:44:47,450 --> 00:44:50,930
+minus ستة من عشرة تربيع زائد واحد تربيع بتساوي ستة
+
+584
+00:44:50,930 --> 00:44:58,070
+من عشرة تربيع أعرفين ليش هاد؟ X minus ستة من عشرة
+
+585
+00:44:58,070 --> 00:45:05,040
+كل تربيع زائدي ترمير برساوي 6 من 10 لكل ترمير هذه
+
+586
+00:45:05,040 --> 00:45:10,140
+دائرة اللي ال origin تبعها عند x equals 6 من 10 و
+
+587
+00:45:10,140 --> 00:45:14,440
+y صفر هي ال origin تبعها و ال radius تبعها 6 من 10
+
+588
+00:45:14,440 --> 00:45:20,960
+واضح؟
+
+589
+00:45:20,960 --> 00:45:24,480
+اذا هذه الدائرة بتاعتنا هي ال trajectory تبعنا اذا
+
+590
+00:45:24,480 --> 00:45:27,080
+ال particle تبعنا اللي قاعد في المجنك ينقش بيعمل
+
+591
+00:45:27,080 --> 00:45:32,900
+دائرةزى ما صار الباطكال فى المجال مع ناطيسيا عمودي
+
+592
+00:45:32,900 --> 00:45:36,420
+عليا لإن هما متعمدين احنا قشعنا الباطكال بتعمل ال
+
+593
+00:45:36,420 --> 00:45:40,480
+XY plane و المجلد فيه جوية تجاه ال Z
+
+594
+00:45:46,900 --> 00:45:51,340
+تجهزت ال magnet field تجهز ال axis و ال particle
+
+595
+00:45:51,340 --> 00:45:54,780
+تبعي بتحرك في ال x و عكسي في اتجاه الترجيبتور اللي
+
+596
+00:45:54,780 --> 00:45:57,700
+صرتوا عارفينه هلقيته لو انسألتوا ايش هيكون circle
+
+597
+00:45:57,700 --> 00:46:02,260
+لو عندى charge قاعدة بتتحرك في مجال معناطيسي ايش
+
+598
+00:46:02,260 --> 00:46:07,720
+بتقول الترجيب تبعها دائرة أثبتناها لازم اي charge
+
+599
+00:46:07,720 --> 00:46:12,440
+بحكي عنها وجودة في مجال معناطيسي هيكون ال
+
+600
+00:46:12,440 --> 00:46:14,280
+trajectory او مسارها دائر
+
+601
+00:46:20,100 --> 00:46:25,440
+طالب مننا بعدين احنا جيبنا ال trajectory، اخر حاجة
+
+602
+00:46:25,440 --> 00:46:28,940
+طالب مننا ال magnetic field ال .. ال .. ال kinetic
+
+603
+00:46:28,940 --> 00:46:30,220
+energy بشكل عام
+
+604
+00:46:32,840 --> 00:46:36,480
+أخر حاجة show that it's the kinetic energy remains
+
+605
+00:46:36,480 --> 00:46:39,900
+constant احنا جيبنا ال kinetic energy عن T بساوة
+
+606
+00:46:39,900 --> 00:46:43,700
+أربع صح هلأ تبقولنا بشكل عام انا بدي أثبت انها
+
+607
+00:46:43,700 --> 00:46:46,780
+constant بتبقى اذا بدي استخدم مين الفلسطين بشكل
+
+608
+00:46:46,780 --> 00:46:49,840
+عام ليه هى تعرف الفلسطين احنا مش بنعرف الفلسطين
+
+609
+00:46:54,860 --> 00:47:03,660
+باربعها و باربعها و باربعها و باربعها
+
+610
+00:47:03,660 --> 00:47:05,980
+و باربعها و باربعها
+
+611
+00:47:07,910 --> 00:47:10,910
+طبعا في الناس اللي هي اتنين كيلو والنص بيروحوا مع
+
+612
+00:47:10,910 --> 00:47:13,850
+بعض و بيبقوا عندى تسعة dual اللي هي نفس اللي حصلنا
+
+613
+00:47:13,850 --> 00:47:17,650
+عندها عن T بالساوة أربع نفس اللي هحصل عليها عن T
+
+614
+00:47:17,650 --> 00:47:21,030
+equal zero وعند Zero هاي واحد وهاي واحد نفس الحاجة
+
+615
+00:47:21,030 --> 00:47:24,290
+إذا اللي كانت ال energy مالها بتضلها constant لل
+
+616
+00:47:24,290 --> 00:47:28,130
+particle إذا معناها كمان مرة بنقول إن مافيش عندنا
+
+617
+00:47:28,130 --> 00:47:31,410
+اللي هو work مقبول لأنه ماتتغيرش Delta K بالساوة
+
+618
+00:47:31,410 --> 00:47:36,770
+صفرأول حاجة تفتحها من أفضل DL بتساوية Zero لإن ال
+
+619
+00:47:36,770 --> 00:47:41,110
+force عمودية على ال particle دائما لإن ال force هي
+
+620
+00:47:41,110 --> 00:47:45,230
+cross product V cross B فدائما عمودية عليهم فأخدت
+
+621
+00:47:45,230 --> 00:47:49,410
+المصار السودان سفر اتجاه ال velocity و ال force
+
+622
+00:47:49,410 --> 00:47:55,200
+عمودية فمصارها و ال force عموديفازن دائما ال work
+
+623
+00:47:55,200 --> 00:47:57,480
+بيساوي صفر كمان و مرة اصلا اننا حسبنا ال kinetic
+
+624
+00:47:57,480 --> 00:48:00,880
+energy عند اي لحظة انها constant فدالة كامة لها
+
+625
+00:48:00,880 --> 00:48:04,100
+صفر اللي هي بيساوي ال work لإذا مافيش عندي work
+
+626
+00:48:04,100 --> 00:48:05,680
+اكيد من مرة تانية حسبناها
+
+627
+00:48:08,660 --> 00:48:11,700
+طبعا هاي معلومات إضافية اللي هى إيش بقولنا انه ال
+
+628
+00:48:11,700 --> 00:48:15,940
+angular velocity omega اللى هى الحمسة هدى احنا
+
+629
+00:48:15,940 --> 00:48:18,540
+بنتحكى عنها angular rhythm الذاكرين ال cosine ال
+
+630
+00:48:18,540 --> 00:48:22,280
+omega T و ال sine ال omega T هى الخمسة هى ال
+
+631
+00:48:22,280 --> 00:48:25,640
+angular velocity rate per second صح هدى مالها
+
+632
+00:48:25,640 --> 00:48:30,400
+بقولنا بشكل عام بتساوي Q في P على M احنا كانت
+
+633
+00:48:30,400 --> 00:48:34,060
+عاملنا خمسة لما حسبنا ال trajectory او لما حسبنا
+
+634
+00:48:34,060 --> 00:48:36,600
+ال velocity و كله طلعت معانا omega بتساوي خمسة
+
+635
+00:48:39,810 --> 00:48:43,950
+بس هو بيقولك بشكل عام هاي الوميجا اللي هي طلعت
+
+636
+00:48:43,950 --> 00:48:51,710
+معنا بتساوي خمس قرار per second بشكل عام بتساوي Q
+
+637
+00:48:51,710 --> 00:48:57,270
+في B على M يعني لو حد سألك ايش قيمة ال radial
+
+638
+00:48:57,270 --> 00:49:00,850
+frequency فيها Q في B في A على M نشوف من المثال
+
+639
+00:49:00,850 --> 00:49:04,770
+تبعنا، تبعطينا خمسة ولا أحد حافظين الأرقام؟
+
+640
+00:49:08,300 --> 00:49:15,880
+وحدي مقدارها قداش عشرة وعلى أمني قداش اتنين
+
+641
+00:49:21,660 --> 00:49:25,300
+QPR اذا ال radian frequency اللي هي ال frequency
+
+642
+00:49:25,300 --> 00:49:28,120
+اللي عمال ماله و بارتك ال ماله بلوف فيها يعني،
+
+643
+00:49:28,120 --> 00:49:32,700
+عندي واحدة sinusoidal في axis و cosine في axis، ال
+
+644
+00:49:32,700 --> 00:49:34,900
+cosine و ال cosine اللي انت خدته برضه على ال
+
+645
+00:49:34,900 --> 00:49:37,020
+oscilloscope و شفت انه هذا بيعطينا اللي هو نفس ال
+
+646
+00:49:37,020 --> 00:49:39,880
+frequency و في نفس ال phase بيعطينا دائرة، لو كان
+
+647
+00:49:39,880 --> 00:49:42,380
+out of phase مش بيعطينا ellipse، هاي ال
+
+648
+00:49:42,380 --> 00:49:45,660
+trajectorism، تذكرين؟ أخدتهوا هذا أكيد، حلصته من
+
+649
+00:49:45,660 --> 00:49:50,060
+زمان يعنيالتراجيكتوريس فإذا هنا قلنا ال frequency
+
+650
+00:49:50,060 --> 00:49:56,040
+بشكل عام اللي هي Q بيلعب وال radius of the orbit
+
+651
+00:49:56,040 --> 00:50:00,780
+ال radius أقل عن ال initial velocity على Omega
+
+652
+00:50:00,780 --> 00:50:04,700
+قداش ال initial velocity اللي كان في المثال
+
+653
+00:50:04,700 --> 00:50:13,240
+initial velocity تلقتك قلنا ال radius قلنا ال
+
+654
+00:50:13,240 --> 00:50:14,800
+initial velocity على R
+
+655
+00:50:18,110 --> 00:50:26,610
+على اوميجا تلاتة
+
+656
+00:50:26,610 --> 00:50:29,850
+على حمسة يعني ادنى 618
+
+657
+00:50:32,350 --> 00:50:34,910
+مش هيك طالع معنا؟ ال radius تبع ال trajectory
+
+658
+00:50:34,910 --> 00:50:39,510
+تمام؟ و قبل هاي النقطة، هاي ممكن تسأله فيهم يعنى،
+
+659
+00:50:39,510 --> 00:50:42,830
+إيش هي ال frequency اللي بلوف فيها ال particle، ال
+
+660
+00:50:42,830 --> 00:50:46,610
+trajectory تبعه، اللي هي الدائرة تاعته، كيف شكلها،
+
+661
+00:50:46,610 --> 00:50:49,450
+إيش ال radius تبعها، طبعا هذا ما أعطينا مثال اللي
+
+662
+00:50:49,450 --> 00:50:52,360
+هي ال cathode ray tubeلأ اللي هو ال electron اللي
+
+663
+00:50:52,360 --> 00:50:56,080
+بتحرك من النقطة high إلى النقطة اللي هي على الشاشة
+
+664
+00:50:56,080 --> 00:50:59,600
+اللي بيكون حامل معلومات عن الصورة موجود في مجال
+
+665
+00:50:59,600 --> 00:51:02,900
+magnetic field هيكون ال trajectory لو أنت طلعت على
+
+666
+00:51:02,900 --> 00:51:05,420
+ال screen اللي هي ال trajectories بتاعتهم اللي هي
+
+667
+00:51:05,420 --> 00:51:10,840
+الدوائر، واضح؟ المثال
+
+668
+00:51:10,840 --> 00:51:14,640
+التاني هيكون اللقاء القادم ان شاء الله و معاكم
+
+669
+00:51:14,640 --> 00:51:20,300
+بقينيعطيك العافية ان شاء الله يعطيك العافية ان شاء
+
+670
+00:51:20,300 --> 00:51:21,500
+الله بنكمل اللقاء القادر
+
diff --git a/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/j0dzFrOg0yk_postprocess.srt b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/j0dzFrOg0yk_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..7eb56d030bf9a693904d2a0d19cec042b4aec88c
--- /dev/null
+++ b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/j0dzFrOg0yk_postprocess.srt
@@ -0,0 +1,2028 @@
+1
+00:00:20,720 --> 00:00:23,460
+بسم الله الرحمن الرحيم السلام عليكم ورحمة الله
+
+2
+00:00:23,460 --> 00:00:26,240
+وبركاته احنا اليوم ان شاء الله هنتبع موضوعنا اللي
+
+3
+00:00:26,240 --> 00:00:29,480
+هو ال feels او ال feels in matters احنا قدام
+
+4
+00:00:29,480 --> 00:00:33,140
+المحاضرة الماضية عرفنا ايش هو التيار كيف نحسن
+
+5
+00:00:33,140 --> 00:00:38,060
+التيار اللي مدفق في قلب ال media اليوم هنتبع ونشوف
+
+6
+00:00:38,060 --> 00:00:42,400
+اللي هو ال polarizationin dielectrics احنا عرفنا
+
+7
+00:00:42,400 --> 00:00:44,820
+ال dielectrics اللي هي ال materials اللي مش metals
+
+8
+00:00:44,820 --> 00:00:48,120
+ال metals قلنا اللي هي conductors و المحاضرات
+
+9
+00:00:48,120 --> 00:00:50,540
+الماضية ركزنا أكتر على ال conductors و كيف ال
+
+10
+00:00:50,540 --> 00:00:53,000
+current بتدفق تقل بال conductor أسوأ هو في free
+
+11
+00:00:53,000 --> 00:00:58,080
+space و صعب تحت تأثير الكثير أو احنا وصلنا by
+
+12
+00:00:58,080 --> 00:01:01,540
+brute force يعني بسلك مع اللي هو دائرة كهربائية و
+
+13
+00:01:01,540 --> 00:01:05,060
+لاحظنا لما يكون في free space و يحطه في وجود
+
+14
+00:01:05,060 --> 00:01:08,860
+المجال الكهربائيبصير اش معلو عامل زي echo
+
+15
+00:01:08,860 --> 00:01:11,260
+potential surface يعني ال electric field معلو جوا
+
+16
+00:01:11,260 --> 00:01:16,080
+zero و potential zero دلتا v بيتساوة zero echo
+
+17
+00:01:16,080 --> 00:01:20,220
+potential surface وبالتالي raw جوا zero لأنه لجاسو
+
+18
+00:01:20,220 --> 00:01:24,060
+اش بيسور بيقول close integral a dot ds بتساوي raw
+
+19
+00:01:24,060 --> 00:01:28,840
+enclosed او q enclosed فبما انه ال electric field
+
+20
+00:01:28,840 --> 00:01:32,300
+زيرو جوا معناه انه q enclosed زيرو هذا احنا فهمناه
+
+21
+00:01:32,300 --> 00:01:35,120
+لأن كل ال charges معلها بتروح على ال surfaces
+
+22
+00:01:35,120 --> 00:01:40,080
+صحيح؟طبعا احنا اليوم هنحكي عن حاجة تانية اللي هي
+
+23
+00:01:40,080 --> 00:01:42,800
+ال dialectics و إيش بيصير لل dialectics عندكوا في
+
+24
+00:01:42,800 --> 00:01:45,820
+وجود ال electric field كانت two types من ال
+
+25
+00:01:45,820 --> 00:01:50,080
+dialectics منهم اللي هي أصلا أساسا هي non-polar
+
+26
+00:01:50,080 --> 00:01:55,760
+يعني مافيها polarity و ناس منهم هي polar خلّيني
+
+27
+00:01:55,760 --> 00:01:58,980
+أبدأ بتعريف أنه لو كان عندى positive charge موجودة
+
+28
+00:01:58,980 --> 00:02:02,680
+في وجود اللي هي ال electric field إيش بيصير لها؟
+
+29
+00:02:02,680 --> 00:02:08,100
+بيصير تحت تأثير force موجبةاللي بتقوللي انه ال
+
+30
+00:02:08,100 --> 00:02:11,580
+charge مالها هتمشي مع اتجاه ال electric field يعني
+
+31
+00:02:11,580 --> 00:02:15,780
+هيكون ال plus ال QE لو كانت minus ال Q موجودة في
+
+32
+00:02:15,780 --> 00:02:19,280
+مجال ال electric field هتكون ال negative او ال
+
+33
+00:02:19,280 --> 00:02:22,660
+force بتأثر عليها مالها في اتجاه معاكس لل electric
+
+34
+00:02:22,660 --> 00:02:29,970
+field اللي هي QE او minus QE لو بدأت هتبقى أكثرفال
+
+35
+00:02:29,970 --> 00:02:33,050
+dipole إيش هو ال dipole؟ عشان نحكي أنه أنواع ال ..
+
+36
+00:02:33,050 --> 00:02:35,630
+ال material يا ما ال dipole يا ال dipole خلّيني
+
+37
+00:02:35,630 --> 00:02:39,290
+أعرف إيش هو ال dipole ال dipole هو الفندق يعني أنه
+
+38
+00:02:39,290 --> 00:02:42,130
+بيصير displacement لل charges بيصير عندي
+
+39
+00:02:42,130 --> 00:02:45,950
+displacement و جزءه بيصير كأنه حامل شحنات موجبة و
+
+40
+00:02:45,950 --> 00:02:50,570
+جزءه كأنه حامل شحنات ثالثة و بيصير أنه اللي عندنا
+
+41
+00:02:50,570 --> 00:02:55,050
+ال electric أنه إيش ماله polarizedنفرق بين اللي هي
+
+42
+00:02:55,050 --> 00:02:58,250
+ال polarized و ال electrically neutral ال atom
+
+43
+00:02:58,250 --> 00:03:01,050
+بوضعها الطبيعي لما يكون فاش electric field يعني
+
+44
+00:03:01,050 --> 00:03:05,410
+تكون المجال الكهربائي حوالها سكر تكون منها ال
+
+45
+00:03:05,410 --> 00:03:09,970
+neutral و شكلها زي الطبق التبعي كرامو الشحنة
+
+46
+00:03:09,970 --> 00:03:15,290
+الموجة بقى في ال nucleus مركزها و حواليها ال
+
+47
+00:03:15,290 --> 00:03:18,810
+clouds من ال electrons حدثي neutral atom اللي
+
+48
+00:03:18,810 --> 00:03:23,210
+مجموع الشحنات بساوة zeroلو كان في اندي الكرة كثير،
+
+49
+00:03:23,210 --> 00:03:27,790
+ده يسوى zero، بحدث اللي أمامنا، بيصير زي إنبعادش،
+
+50
+00:03:27,790 --> 00:03:32,210
+بيصير إعادة توزيع للشحنات، هذا إعادة التوزيع هي
+
+51
+00:03:32,210 --> 00:03:36,550
+اللي بتخليها بطلت تحافظ على شكلها الكراوة، لازالت
+
+52
+00:03:36,550 --> 00:03:40,170
+ال neutral يعني، بس صار إيش عندي؟ إعادة توزيع
+
+53
+00:03:40,170 --> 00:03:45,010
+للشحنات، بعبر عنه إن هاي ال polarized atom كأنها
+
+54
+00:03:45,010 --> 00:03:49,360
+ال neutral atom زائد dipoleمجموعة لولا اتنين
+
+55
+00:03:49,360 --> 00:03:52,660
+بيعادل ال polarized atom ال superposition ما بين
+
+56
+00:03:52,660 --> 00:03:57,020
+ال neutral atom و ال dipole بيعطيني مين اللي هو ال
+
+57
+00:03:57,020 --> 00:04:03,940
+polarized atom لو كان عندي N من ال dipoles مش واحد
+
+58
+00:04:03,940 --> 00:04:10,520
+بس اللي هو نتج من انه من اتم واحدة عندي N منهم N
+
+59
+00:04:10,520 --> 00:04:15,770
+من ال dipolesمعناه انه هيكون في عندى total dipole
+
+60
+00:04:15,770 --> 00:04:18,270
+moment مش dipole moment واحد ال Q في دى هيكون عندى
+
+61
+00:04:18,270 --> 00:04:22,010
+عدد منهم فالdipole moment الكلي هيكون ال summation
+
+62
+00:04:22,010 --> 00:04:27,350
+من K واحد ل N في اللي هم عددهم مثلا KQ وDQ اللي هو
+
+63
+00:04:27,350 --> 00:04:32,230
+ال dipole moment عشان
+
+64
+00:04:32,230 --> 00:04:37,700
+احنا نقيصشدت ال polarization او يعني قدش ان ال
+
+65
+00:04:37,700 --> 00:04:40,860
+dipole moment بدنا نلجأ لحاجة بنسميها polarization
+
+66
+00:04:40,860 --> 00:04:47,340
+ال polarization بساطة اللي هي dB by dV او يعني ال
+
+67
+00:04:47,340 --> 00:04:51,440
+dipole moment per unit volume فاحنا السونا قسمنا
+
+68
+00:04:51,440 --> 00:04:54,280
+ال dipole على ال volume هاي بتعطينا ال
+
+69
+00:04:54,280 --> 00:04:57,220
+polarization polarization capital P و ال dipole
+
+70
+00:04:57,220 --> 00:04:59,920
+بالعمر هقلنها ب small p عشان تميزوا عنهم في
+
+71
+00:04:59,920 --> 00:05:06,110
+المحاضرة small p ال dipole momentالـ dipole moment
+
+72
+00:05:06,110 --> 00:05:12,030
+في الـ unit area الـ polarization إذا
+
+73
+00:05:12,030 --> 00:05:17,250
+لما احنا يكون عندنا electric field موجودهيسويش
+
+74
+00:05:17,250 --> 00:05:21,870
+بيعمل في الزراعات، بيعمل لهم قاعدة تنظيم او ال
+
+75
+00:05:21,870 --> 00:05:25,430
+dipoles الموجودين في ال atoms بيقدم منها alignment
+
+76
+00:05:25,430 --> 00:05:28,490
+انها تسير تجاه ال electric field ال center تبعها
+
+77
+00:05:28,490 --> 00:05:32,370
+بيصير aligned يعني موازي لل electric field هذا
+
+78
+00:05:32,370 --> 00:05:34,890
+اللي بيسوي ال electric field عندي انا ال atom
+
+79
+00:05:35,150 --> 00:05:38,430
+هيتكون عندى كوجود ال electric field قاعد التوزيع
+
+80
+00:05:38,430 --> 00:05:41,850
+قولنا إيش بنسميها قاعد التوزيع ال neutral atom
+
+81
+00:05:41,850 --> 00:05:45,110
+كإنه neutral atom أو ال diverse هدول ال diverse
+
+82
+00:05:45,110 --> 00:05:48,050
+بكونوا aligned مع ال electric field بنظمهم ال
+
+83
+00:05:48,050 --> 00:05:53,440
+electric field بكونوا في اتجاهها هذا النوع منالـ
+
+84
+00:05:53,440 --> 00:05:56,820
+dielectrics بنسميه non-polar اللي بنعدله بـ atom و
+
+85
+00:05:56,820 --> 00:06:01,320
+dipole هو أساساً بيكون non-polar مافيه أي polarity
+
+86
+00:06:01,320 --> 00:06:04,700
+منهم ال hydrogen atom و ال oxygen و ال nitrogen و
+
+87
+00:06:04,700 --> 00:06:07,320
+ال rare gases هدولة كلهم non-polar لما بحط
+
+88
+00:06:07,320 --> 00:06:10,880
+electric field بيصير إعادة التوزيع بتصير كأنها
+
+89
+00:06:10,880 --> 00:06:14,460
+معادلة ل neutral atom زي ال dipoles هدولة ال
+
+90
+00:06:14,460 --> 00:06:18,880
+dipoles موزعين في اتجاه ال electric field ال
+
+91
+00:06:18,880 --> 00:06:21,680
+dipole atoms في الواقع هي بتكون already ع شكل
+
+92
+00:06:21,680 --> 00:06:26,660
+dipoleهم بيكونوا لهم dipole يعني لها positive
+
+93
+00:06:26,660 --> 00:06:30,260
+charge و negative charge و بينهم distance D يعني
+
+94
+00:06:30,260 --> 00:06:32,940
+هي already بتكون ع شكل دايبل ال atoms هدولة
+
+95
+00:06:32,940 --> 00:06:37,900
+بيسميهم دايبل دا electric لكن بيكونوا بدون وجود ال
+
+96
+00:06:37,900 --> 00:06:40,700
+electric field يعني هاي الحالة A ال electric field
+
+97
+00:06:40,700 --> 00:06:45,440
+بيساو Zero بدون وجود خطوط المجال بتخترقها بيكونوا
+
+98
+00:06:45,440 --> 00:06:49,660
+موزعين بشكل عشوائي العشوائي اللي موزعين فيها بتقول
+
+99
+00:06:49,660 --> 00:06:54,810
+ان مجموعة دولة دايبل بيكون Zeroتوزيهم بيكون عشوائي
+
+100
+00:06:54,810 --> 00:06:57,610
+لكن في وجهة ال electric field ايش بيعملهم ال
+
+101
+00:06:57,610 --> 00:07:00,190
+electric field؟ هو alignment ال phosphate charges
+
+102
+00:07:00,190 --> 00:07:04,350
+بتصير فيها قوة في اتجاه ال electric field و السابق
+
+103
+00:07:04,350 --> 00:07:09,170
+في قوة في معاكس اتجاه ال electric field و بترتبوا
+
+104
+00:07:09,170 --> 00:07:12,530
+موازين مع ال electric field بيبطل ال die ball
+
+105
+00:07:12,530 --> 00:07:16,840
+مجموع بساوة zeroزي مين اللي أصلا dyebul دا
+
+106
+00:07:16,840 --> 00:07:19,820
+electric الميه أكيد بتعرفوا عن الميه خصائصها ال
+
+107
+00:07:19,820 --> 00:07:23,120
+dyebul atoms خدتواها في المثلقات كيميا أو ده أخرى
+
+108
+00:07:23,120 --> 00:07:28,880
+sulfur dioxide هيدرولكاسيد طبعا
+
+109
+00:07:28,880 --> 00:07:32,660
+العملية اللي بتخلي هدول ال dyebul يصلهم alignment
+
+110
+00:07:32,660 --> 00:07:35,540
+مع ال electric field هو torque لإن هنا فيه قوة
+
+111
+00:07:35,540 --> 00:07:39,400
+موجبة وهو قوة سالبة ال torque هو اللي بيظبطهم لحين
+
+112
+00:07:39,400 --> 00:07:41,040
+بيسيروا في اتجاه ال electric field
+
+113
+00:07:44,180 --> 00:07:47,060
+إذا نقول ال permanent dipole لما يكون في شكل ال
+
+114
+00:07:47,060 --> 00:07:50,120
+electric field بساوة 0 لأنه السبب إن هم aligned
+
+115
+00:07:50,120 --> 00:07:53,860
+مالهم بشكل عشوائي فمجموعهم محالتين Zero في وجود ال
+
+116
+00:07:53,860 --> 00:07:57,600
+electric field بيسمحوا كلهم alignment في اتجاه ال
+
+117
+00:07:57,600 --> 00:08:02,560
+electric field و يبطل ال dipole بساوة Zero طب احنا
+
+118
+00:08:02,560 --> 00:08:05,460
+أخذنا المحاضرة اللي في الشكل الماضي إن ال
+
+119
+00:08:05,460 --> 00:08:09,060
+potential الناتج من ال dipole moment هو عبارة عن B
+
+120
+00:08:09,060 --> 00:08:15,640
+اللي هو ال dipole اللي هو Q في D.rh تعرفنا مين هى
+
+121
+00:08:16,860 --> 00:08:19,940
+بتجاه اللي ما بين الـ center تبع الـ dipole و
+
+122
+00:08:19,940 --> 00:08:21,660
+النقطة البقية عندها الـ electric field أو الـ
+
+123
+00:08:21,660 --> 00:08:25,320
+potential ماذا ذاكرينه الرسمى كان احنا فرضينه اول
+
+124
+00:08:25,320 --> 00:08:29,820
+حاجة انه ال center تبعه unlined عن zero و R hat هو
+
+125
+00:08:29,820 --> 00:08:33,740
+اتجاه ال line اللي وفق ال center تبع ال dipole مع
+
+126
+00:08:33,740 --> 00:08:38,160
+النقطة البقية عندها ال potential و عملنا يعني
+
+127
+00:08:38,160 --> 00:08:40,880
+حسبنا قيمة ال potential لقينا انه بالنهاية بساوة
+
+128
+00:08:40,880 --> 00:08:46,230
+بي اللي هي ال dipole اللي هي Q في Rاللي هي R
+
+129
+00:08:46,230 --> 00:08:50,250
+المسافة اللي بينهم vector dot R hat اللي هي
+
+130
+00:08:50,250 --> 00:08:52,270
+المسافة بين ال center ونقطة بأيه ساعتها ال
+
+131
+00:08:52,270 --> 00:08:56,410
+potential على four pi اسم ال node R تربيع وR تربيع
+
+132
+00:08:56,410 --> 00:09:00,390
+اللي هي قيمة المسافة بين ال center ونقطة بأيه
+
+133
+00:09:00,390 --> 00:09:04,370
+ساعتها ال potential مش ذاكرين وحدة بحكي اه ان شاء
+
+134
+00:09:04,370 --> 00:09:04,550
+الله
+
+135
+00:09:07,730 --> 00:09:10,990
+طب لو بدي اكتب دلالة الـPolarization دلالة
+
+136
+00:09:10,990 --> 00:09:13,670
+الـdipole احنا قولنا الـPolarization ايش بتساوي؟
+
+137
+00:09:13,670 --> 00:09:19,230
+الـPolarization هي capital B بتساوي DB by DV اللي
+
+138
+00:09:19,230 --> 00:09:24,450
+هي mean ال volume يعني هنا الـPolarization
+
+139
+00:09:24,450 --> 00:09:31,910
+هي capital B بتساوي DB by DV مثلا لو أخدناها D برا
+
+140
+00:09:34,320 --> 00:09:37,900
+فإذا ال potential اللي احنا كنا كتبينه ده تتضايقه
+
+141
+00:09:37,900 --> 00:09:44,460
+dot r hat على four by epsilon نُزعى التبنيه بقدر
+
+142
+00:09:44,460 --> 00:09:47,900
+اكتبه او اكتب ان هو ال friendship تبع ال potential
+
+143
+00:09:47,900 --> 00:09:54,680
+ناتج من element dv بساوي ال polarization dot r hat
+
+144
+00:09:54,680 --> 00:10:00,080
+من dv prime هال volume على four by epsilon نُزعى
+
+145
+00:10:04,430 --> 00:10:14,870
+مش فارق الـ R هنا بس
+
+146
+00:10:14,870 --> 00:10:19,050
+تعريف الـ R اللي هي ما بين R-R' يقولوا لو ماكنش
+
+147
+00:10:19,050 --> 00:10:26,330
+هان بالسيطر تمام هاي R صارت جديدة بس هو أكبر طلقة
+
+148
+00:10:26,330 --> 00:10:32,430
+واسمه هنا اللي هي الفرق ما بين R-R' تمام هى R أو
+
+149
+00:10:32,430 --> 00:10:33,390
+يعني يخليني عشان
+
+150
+00:10:37,810 --> 00:10:42,390
+عشان يكون هنا r hat عشان
+
+151
+00:10:42,390 --> 00:10:45,770
+انه ليس عند ال center بشكل عام يعني لو عند ال
+
+152
+00:10:45,770 --> 00:10:50,550
+center هتكون just r hat على r hat على r تلقى زى ما
+
+153
+00:10:50,550 --> 00:10:54,110
+انتوا شايفين هى ال volume اللى انا بتحكى عن ال
+
+154
+00:10:54,110 --> 00:10:57,110
+polarization بتاعته ال dialectic اللى هو المحاطب
+
+155
+00:10:57,110 --> 00:11:01,140
+الأزرق هذا هى المخلين اللى يمكن أنه DV primeاللي
+
+156
+00:11:01,140 --> 00:11:03,660
+ماله مش قاعد عند ال origin لو قاعد عند ال origin
+
+157
+00:11:03,660 --> 00:11:07,860
+إيش هتكون x' y' z'؟ Zero، هيكون هنا، لكن هيكون له
+
+158
+00:11:07,860 --> 00:11:13,900
+هنا position ال position هو x' y' z' وانا بدي أيجس
+
+159
+00:11:13,900 --> 00:11:17,960
+ال potential عند النقطة R، اللي هي x, y, z فR
+
+160
+00:11:17,960 --> 00:11:23,860
+كابتن هي الفرق ما بين R minus R'، تمام؟ إذا ال
+
+161
+00:11:23,860 --> 00:11:28,670
+potentialDV الناتج عن ال differential volume DV
+
+162
+00:11:28,670 --> 00:11:33,230
+براين عند النقطة اللي انا بقيثي عندها ال potential
+
+163
+00:11:33,230 --> 00:11:39,130
+ايش هيكون DV بسوة B ال polarization dot R hat DV
+
+164
+00:11:39,130 --> 00:11:43,770
+براين مع 4 بإيسو نوت R تربية R زي ما عرفناها X
+
+165
+00:11:43,770 --> 00:11:47,370
+minus X براين تربية زي Y minus Y براين تربية زي Z
+
+166
+00:11:47,370 --> 00:11:51,370
+minus Z براين تربية لو R تربية بدون تحت الجزر لو
+
+167
+00:11:51,370 --> 00:11:56,550
+كانت R بدو يكون تحت الجزرأحنا عشان بدنا نبسط هذا
+
+168
+00:11:56,550 --> 00:11:59,090
+ال form او بالنهاية انا بدي ال mean ال potential
+
+169
+00:11:59,090 --> 00:12:02,970
+فبتبسط هذا الشكل لشكل اللي قادر اعمله integration
+
+170
+00:12:02,970 --> 00:12:08,610
+يعني بالنهاية بتكامل هذا اول حاجة بدي اربط ال R
+
+171
+00:12:08,610 --> 00:12:12,590
+hat على R تربية ب identity احنا بنعرفها اللي هو ال
+
+172
+00:12:12,590 --> 00:12:16,570
+gradient ل 1 على R دلي prime 1 على R يعني انا بفضل
+
+173
+00:12:16,570 --> 00:12:19,770
+بالنسبة ل ال mean ل X prime Y prime و 6 prime دلي
+
+174
+00:12:19,770 --> 00:12:24,470
+prime 1 على Rهي في الواقع R hat على R تربية بتعمل
+
+175
+00:12:24,470 --> 00:12:28,990
+زي التفاضل العادى R يعني بتصير واحدة على R تربية
+
+176
+00:12:28,990 --> 00:12:31,190
+بس هذا ال vector من وين بيجي ال vector من ال
+
+177
+00:12:31,190 --> 00:12:35,670
+gradient ال gradient D by DX X hat D by DY Y hat D
+
+178
+00:12:35,670 --> 00:12:41,910
+by DZ Z hat هيعطينا ال R hat اللي هو الاتجاه على
+
+179
+00:12:41,910 --> 00:12:48,200
+اللي هو R تربية تفاضلماذا بستفيد من هذا؟ بيصير الـ
+
+180
+00:12:48,200 --> 00:12:52,280
+B Dot R Hat على R تربيه ببساطة بقدر اكتبها على B
+
+181
+00:12:52,280 --> 00:12:56,860
+التي هي Polarization Dot Del Prim 1 على R يعني هذا
+
+182
+00:12:56,860 --> 00:13:03,760
+الشكل اللي هو الـ DV هذا اللي قدامك الـ DV صارت
+
+183
+00:13:03,760 --> 00:13:12,540
+اكتر طبع شكل B Dot Del Prim 1 على R على 4π Epsilon
+
+184
+00:13:12,540 --> 00:13:14,640
+Dot D B Prim
+
+185
+00:13:18,020 --> 00:13:23,420
+بتعرفى ايضا identity احنا برضه اتعلمناها لما اخدنا
+
+186
+00:13:23,420 --> 00:13:30,660
+ال vector الاساس انه diverse scalar مع vector ايش
+
+187
+00:13:30,660 --> 00:13:34,880
+في هالساعة تفاضل الأول و التانى و التانى و التفاضل
+
+188
+00:13:34,880 --> 00:13:38,940
+التانى اذا أخدت ال scalar لغره ايش هيكون تفاضل ال
+
+189
+00:13:38,940 --> 00:13:43,700
+vector زائد لو أخدت ال vector لغره هيكون كل ال
+
+190
+00:13:43,700 --> 00:13:47,950
+product مع تفاضل ال scalar هو ال gradientالشكل
+
+191
+00:13:47,950 --> 00:13:52,110
+اللى أمامنا اللى هو vector dot differential منه
+
+192
+00:13:52,110 --> 00:13:59,050
+إلى scalar هو هذا هذا الشكل بقدر استبدلهمين ال
+
+193
+00:13:59,050 --> 00:14:03,350
+differential لل scalar مع ال vector minus the
+
+194
+00:14:03,350 --> 00:14:07,770
+scalar differential لل vector يعني إيش حيصير اندر
+
+195
+00:14:07,770 --> 00:14:12,430
+دي
+
+196
+00:14:12,430 --> 00:14:18,140
+دي ساويبدل هذا التم 1 على فور بيبسط من هنا و بيبسط
+
+197
+00:14:18,140 --> 00:14:19,020
+من هنا و بيبسط من هنا و بيبسط من هنا و بيبسط من
+
+198
+00:14:19,020 --> 00:14:27,220
+هنا و بيبسط من هنا و بيبسط من هنا و بيبسط من
+
+199
+00:14:27,220 --> 00:14:36,140
+هنا و بيبسط
+
+200
+00:14:36,140 --> 00:14:37,800
+من هنا
+
+201
+00:14:45,260 --> 00:14:49,620
+إذاً V أشبه تساوي التكامل لهذا الحكيم 1 على 4Y سنة
+
+202
+00:14:49,620 --> 00:15:00,820
+التكامل لـ P على R مانوس 1 على R P على R مانوس 1
+
+203
+00:15:00,820 --> 00:15:01,720
+على R P على R مانوس 1 على R مانوس 1 على R مانوس 1
+
+204
+00:15:01,720 --> 00:15:01,960
+على R مانوس 1 على R مانوس 1 على R مانوس 1 على R
+
+205
+00:15:01,960 --> 00:15:03,520
+مانوس 1 على R مانوس 1 على R مانوس 1 على R مانوس 1
+
+206
+00:15:03,520 --> 00:15:03,560
+مانوس 1 على R مانوس 1 على R مانوس 1 على R مانوس 1
+
+207
+00:15:03,560 --> 00:15:08,600
+على R مانوس 1 على R مانوس 1 على R مانوس 1 على R
+
+208
+00:15:08,600 --> 00:15:12,380
+مانوس 1 على R م
+
+209
+00:15:15,820 --> 00:15:19,120
+Diverge الهيكتروه EV من الذاكرينه هذا يعني
+
+210
+00:15:19,120 --> 00:15:25,240
+Diversion Theorem بقدر أقول إن هو دلقلوز Integral
+
+211
+00:15:25,240 --> 00:15:32,040
+على ال surface ل A Dot S صحيح؟ الذاكرينه؟ إذا
+
+212
+00:15:32,040 --> 00:15:35,660
+التكلمه الأولاني بقدر أبسطه ل surface Integral
+
+213
+00:15:35,660 --> 00:15:41,600
+والتاني يدله volume Integral فلنعملها إذا ما ال
+
+214
+00:15:41,600 --> 00:15:44,540
+potential سوا حد على four by epsilon
+
+215
+00:15:56,340 --> 00:16:01,200
+التان والتان هو منصة واحدة على الـ 4 و4 سنة تكمل
+
+216
+00:16:01,200 --> 00:16:01,880
+على الـ volume
+
+217
+00:16:13,580 --> 00:16:16,660
+هاتول الاتنين هم نوع ال charges اللي بالنهاية
+
+218
+00:16:16,660 --> 00:16:21,460
+بيجيبوله potential potential الأولاني و ال
+
+219
+00:16:21,460 --> 00:16:27,120
+potential التاني ندي بي dot ds على r و التاني
+
+220
+00:16:27,120 --> 00:16:32,000
+diverse بي ب dv على r potential تقريبا نايم ده
+
+221
+00:16:32,000 --> 00:16:37,760
+بتبعناه من ال dive الواحد على r صحيح الأولاني ايه
+
+222
+00:16:37,760 --> 00:16:41,810
+اللي احنا عملناه ds كمان بقدر اكتر بهذا الشكلعشان
+
+223
+00:16:41,810 --> 00:16:48,350
+بدأ أحط الشيطنة للشاشة 1 على 4pi epsilon0 plus
+
+224
+00:16:48,350 --> 00:16:52,950
+integral ده v dot اللي هو s hat او يعني ال vector
+
+225
+00:16:52,950 --> 00:16:57,470
+اللي في اتجاه ال surface هو صنعه a n hat a n hat
+
+226
+00:16:57,470 --> 00:17:02,470
+ال prime اللي هو العمودي عمين على ال surface على r
+
+227
+00:17:02,470 --> 00:17:03,830
+d أسمنت سلسلة
+
+228
+00:17:06,930 --> 00:17:11,150
+ب.ds هي s قلنا الـ differential الـ surface
+
+229
+00:17:11,150 --> 00:17:16,790
+واتجاهه عمودي على الـ surface فقول ب.an hat prime
+
+230
+00:17:16,790 --> 00:17:20,670
+اللي هو ميلي العمودي على الـ surface زائد واحد على
+
+231
+00:17:20,670 --> 00:17:26,810
+four by إيصاله منه التكامل minus delta prime ب.b
+
+232
+00:17:26,810 --> 00:17:31,730
+على r دولة
+
+233
+00:17:31,730 --> 00:17:36,080
+شفلينبأعطونى الـ differential الأول اللى حوالين ال
+
+234
+00:17:36,080 --> 00:17:39,380
+surface ناتج عن ال charge surface ال charge
+
+235
+00:17:39,380 --> 00:17:43,380
+مقدارها P dot A أنهى ال differential surface
+
+236
+00:17:43,380 --> 00:17:50,880
+charge density مقدارها كإنى بكامل ρ DS صح total Q
+
+237
+00:17:50,880 --> 00:17:56,160
+فإذا حد بتكون surface charge densityوهنا كأنه raw
+
+238
+00:17:56,160 --> 00:18:01,800
+VdV فهذه volume charge density واضح؟ اذا ال
+
+239
+00:18:01,800 --> 00:18:08,140
+potential الناتج من dielectric اللي فيه diaper
+
+240
+00:18:08,140 --> 00:18:12,480
+moment زي ما احنا بدينا من الأول بيعطيني two parts
+
+241
+00:18:12,480 --> 00:18:16,120
+ال parts الأول كأنه جاي من surface charges قمتها
+
+242
+00:18:16,120 --> 00:18:21,100
+ال density بتاعتها بي dot a n hat prime
+
+243
+00:18:33,420 --> 00:18:36,240
+الشكل الأقل يعني مش ضالر احط الprime يعني بدنا
+
+244
+00:18:36,240 --> 00:18:40,290
+نقول raw bs اللي هي ال surfaceالناتجة من ال
+
+245
+00:18:40,290 --> 00:18:43,830
+surface charge أو ال bound charges بنسميهم bound
+
+246
+00:18:43,830 --> 00:18:46,670
+charges لإن هم مربوطين في 100 في element ال free
+
+247
+00:18:46,670 --> 00:18:50,650
+charges احنا من فترة كنا charge q حرة أو إلكترونات
+
+248
+00:18:50,650 --> 00:18:54,370
+في أي متل اللي بتتحرك بسهولة هاي free charges لكن
+
+249
+00:18:54,370 --> 00:18:57,670
+هذه bounded charges لإن هي مربوطة في atoms سلها
+
+250
+00:19:00,750 --> 00:19:04,350
+بنسميها bound charges أو ال polarization فإذا ال
+
+251
+00:19:04,350 --> 00:19:06,990
+element الأولاني أقول نجان من مين؟ من surface
+
+252
+00:19:06,990 --> 00:19:09,730
+charge يعني بشكل عام هنا عشان احنا مع ال Integra
+
+253
+00:19:09,730 --> 00:19:12,530
+عادي قس ال prime دي في prime حطن ال prime لكن بشكل
+
+254
+00:19:12,530 --> 00:19:15,950
+عام بقدر أقول أن ال surface bound charges density
+
+255
+00:19:15,950 --> 00:19:19,670
+هي ال polarization تقطن norm اللي على ال surfaceو
+
+256
+00:19:19,670 --> 00:19:24,950
+الـ charge density الناتجة من ال bound charges على
+
+257
+00:19:24,950 --> 00:19:27,930
+ال volume المحصولة في ال volume هي minus
+
+258
+00:19:27,930 --> 00:19:32,910
+divergence ال polarization تمام؟ هدولة ال bound
+
+259
+00:19:32,910 --> 00:19:33,370
+charges
+
+260
+00:19:37,370 --> 00:19:40,770
+إذا من ال total charge أشبه تسكون بدأ أول حاجة
+
+261
+00:19:40,770 --> 00:19:44,490
+أجيب ال charge ال total على ال surface ال total
+
+262
+00:19:44,490 --> 00:19:47,390
+charge و ال total charge اللي عمينا على ال volume
+
+263
+00:19:47,390 --> 00:19:51,530
+فبقدر أحسب ال total charge نشوف إيش هي ال total
+
+264
+00:19:51,530 --> 00:19:54,350
+charge إحنا قبل نحكي ع مين إيش متوقع ال total
+
+265
+00:19:54,350 --> 00:19:57,670
+charge بيه تساوي؟ إيش متوقع؟ هنحكي على ال neutral
+
+266
+00:19:57,670 --> 00:20:00,130
+atom صحيح موجودة في ال electrode كتير و صار shift
+
+267
+00:20:00,130 --> 00:20:03,750
+بس في النهاية لو جمعناهم إيش بتعطينا؟ إيش بتعطينا
+
+268
+00:20:03,750 --> 00:20:17,760
+ال neutral atom؟توتر الاتشارج Zero لان
+
+269
+00:20:17,760 --> 00:20:21,000
+انا بحكي على ال neutral dielectric صحيح موجودة في
+
+270
+00:20:21,000 --> 00:20:24,380
+الكريك فيلد وصار shift بس مالها الاتم دلت زي ما هي
+
+271
+00:20:24,380 --> 00:20:29,200
+مجموع الكريك تساوي مجموعالـ booster charges معايا
+
+272
+00:20:29,200 --> 00:20:32,380
+طب نعملها أول حاجة هتبدأش تجيب ال total charge
+
+273
+00:20:32,380 --> 00:20:35,220
+النجرة من الميل من ال surface ال bound surface
+
+274
+00:20:35,220 --> 00:20:38,580
+charges ال bound surface charges لإنها كلها مانع
+
+275
+00:20:38,580 --> 00:20:41,860
+مربوطة في ال atoms يعني مش حرة إيش هتكون هاي
+
+276
+00:20:41,860 --> 00:20:46,420
+التكامل على عشان أجيب Qs إيش هتكون التكامل ل P dot
+
+277
+00:20:46,420 --> 00:20:51,780
+A and half ds وهد عشان أجيب ال total charge هتكامل
+
+278
+00:20:51,780 --> 00:20:55,750
+على ال volume لإن هو دي volume نعمل هذا الحاجةأول
+
+279
+00:20:55,750 --> 00:21:00,310
+حاجة الـ QB اللي هي اللي مالها الـ bounded charges
+
+280
+00:21:00,310 --> 00:21:03,870
+الـ positive اللي مالها على ال surface ال clause
+
+281
+00:21:03,870 --> 00:21:11,890
+integral ل B to DS هي هتسوى ال integral B to DS
+
+282
+00:21:11,890 --> 00:21:15,090
+انا كملت انا لهاي على DS على القول على scalar
+
+283
+00:21:15,090 --> 00:21:22,050
+فبصير A hat في DS بتصير DS vector واضح من أين أجه؟
+
+284
+00:21:22,380 --> 00:21:25,440
+P dot n hat اللي هو في اتجاه ال surface بيبقى
+
+285
+00:21:25,440 --> 00:21:32,080
+كاملها DS فN hat في DS بتصير DS vector واضح؟ او
+
+286
+00:21:32,080 --> 00:21:35,620
+اكترها على اللغة
+
+287
+00:21:35,620 --> 00:21:40,840
+اشري معاكم ال
+
+288
+00:21:40,840 --> 00:21:45,300
+Q اللي هي bond ال surface bond ال charges ايش بيها
+
+289
+00:21:45,300 --> 00:21:50,940
+تساوي التكامل ل raw في DS اللي هي ال surface
+
+290
+00:21:59,510 --> 00:22:05,510
+بتجاه ال S بتساوي ال clause integral ل B dot DS
+
+291
+00:22:05,510 --> 00:22:11,190
+هذا مش تعرف ال charge بس هاي اللي بنعمله احنا في
+
+292
+00:22:11,190 --> 00:22:16,450
+الشركة ايش اختراها؟ رؤس في DS عيها رؤس في DS فإيش
+
+293
+00:22:16,450 --> 00:22:21,400
+بيها تساوي؟ رؤس بدعو بر أنها B dot and hatالنورم
+
+294
+00:22:21,400 --> 00:22:24,580
+على ال surface بتجاه ال surface فهتكون P dot DS
+
+295
+00:22:24,580 --> 00:22:30,160
+فال charges اللي دلت trapped في ال volume مين اللي
+
+296
+00:22:30,160 --> 00:22:33,000
+هي minus QB اللي قلنا إيش بتساوي ال integral على
+
+297
+00:22:33,000 --> 00:22:40,100
+ال volume rho PV في DV تمام؟ حوض عن rho V اللي إيش
+
+298
+00:22:40,100 --> 00:22:46,780
+بتساوي minus minus divergence P فهتكون minus
+
+299
+00:22:46,780 --> 00:22:52,020
+divergence P DV تمام؟مجموعة دولة تاني تاني مش
+
+300
+00:22:52,020 --> 00:22:58,140
+هيعطيني ال raw v dv تكامل على ال surface charge
+
+301
+00:22:58,470 --> 00:23:02,550
+زائد التكامل على ال volume و ال charge بيكون ساوي
+
+302
+00:23:02,550 --> 00:23:07,490
+0 QB minus QB هذه ال QB اللى هي اللى trapped على
+
+303
+00:23:07,490 --> 00:23:10,150
+ال surface و اللى على ال volume اللى هتكون السالب
+
+304
+00:23:10,150 --> 00:23:14,430
+تبعها مجموعة مش لازم ساوي سفر لإن هى زى ما حكينا
+
+305
+00:23:14,430 --> 00:23:17,130
+ال atoms فى حالة ال neutral طبعا صحيح سيبقى
+
+306
+00:23:17,130 --> 00:23:21,430
+بولارزيشن لكن فى النهاية مجموع ال negative charges
+
+307
+00:23:21,430 --> 00:23:25,510
+و مجموع ال positive charges بيكون ساوي 0 واضح؟
+
+308
+00:23:36,350 --> 00:23:38,470
+مجموعة التنش لازم تساوي 0
+
+309
+00:23:44,280 --> 00:23:49,260
+و بتخلفها بالإشارة I بيسوي I I يعني بقدر أرجع
+
+310
+00:23:49,260 --> 00:23:55,400
+أكتبها ال clause integral ل B dot DS ف I مع I هذي
+
+311
+00:23:55,400 --> 00:23:57,920
+السالبة لإن هو أصلا معرفنها أنه ال bounded
+
+312
+00:23:57,920 --> 00:24:01,360
+churches اللي عطلناها فيها سابق فلما أكملها على ال
+
+313
+00:24:01,360 --> 00:24:04,400
+volume هذا التكامل بقدر أكتبه على شكل ال clause
+
+314
+00:24:04,400 --> 00:24:08,940
+integral ل B dot DS مجموعة هذي موجبه هذي السالبة
+
+315
+00:24:08,940 --> 00:24:14,360
+بسوء سفر واضح؟ واضحش اللي بيحكيه؟مش عارفة إيش
+
+316
+00:24:14,360 --> 00:24:18,800
+حاسسة إنها مش واضحة هذي اللي هي من ال surface
+
+317
+00:24:18,800 --> 00:24:22,880
+الباقية اللي هي ال bound اللي على ال volume إيش
+
+318
+00:24:22,880 --> 00:24:26,460
+هتكون هي بتوقعها أنها السلب تبعها؟ اللي هي إيش
+
+319
+00:24:26,460 --> 00:24:35,000
+هتساوي ال integral على VDD اللي بتساوي من minus
+
+320
+00:24:35,000 --> 00:24:40,260
+التكامل ل diverge V ال polarization في DD وهي من
+
+321
+00:24:40,260 --> 00:24:47,290
+divergence theoremب.ds وهي ايضا متساوية هاي فهي
+
+322
+00:24:47,290 --> 00:24:52,370
+ايضا متساوية هاي فهي ايضا متساوية هاي فهي ايضا
+
+323
+00:24:52,370 --> 00:24:53,470
+متساوية هاي فهي ايضا متساوية هاي فهي ايضا متساوية
+
+324
+00:24:53,470 --> 00:24:55,790
+هاي فهي ايضا متساوية هاي فهي ايضا متساوية هاي فهي
+
+325
+00:24:55,790 --> 00:24:56,630
+ايضا متساوية هاي فهي ايضا متساوية هاي فهي ايضا
+
+326
+00:24:56,630 --> 00:24:59,970
+متساوية هاي فهي ايضا متساوية هاي فهي ايضا متساوية
+
+327
+00:24:59,970 --> 00:25:07,570
+هاي فهي ايضا متساوية هاي فهي ايضا متساوية هاي فهي
+
+328
+00:25:07,570 --> 00:25:09,970
+ايضا متساوية
+
+329
+00:25:14,830 --> 00:25:18,690
+نرجع ل raw total ال charge ال total ال charge
+
+330
+00:25:18,690 --> 00:25:23,790
+density هتكون ال raw V ذائد ال raw VV اللي هي ال
+
+331
+00:25:23,790 --> 00:25:27,290
+free charges ذائد ال bonded charges ال total ال
+
+332
+00:25:27,290 --> 00:25:32,710
+free charges ذائد ال bonded charges raw total ايش
+
+333
+00:25:32,710 --> 00:25:36,850
+بتساوي من gauss law diverse D اللي هي مين diverse
+
+334
+00:25:36,850 --> 00:25:41,390
+D؟ YE بشكل عام لو مافيش bond charges لو احنا بنحكي
+
+335
+00:25:41,390 --> 00:25:44,530
+على ال free spaceهيكون ال diverse D بيساومي ال raw
+
+336
+00:25:44,530 --> 00:25:48,450
+free اللي أخدتها في الشبطار السابق لإن انا فيه
+
+337
+00:25:48,450 --> 00:25:50,590
+اندي انا دايا الكترك و فيه اندي point of charges
+
+338
+00:25:50,590 --> 00:25:54,710
+فإيش هيكون عندى ال raw total هي ال raw V زي ال raw
+
+339
+00:25:54,710 --> 00:25:59,890
+point of charges رو V تساومي ال diverse D أو ال
+
+340
+00:25:59,890 --> 00:26:04,510
+diverse E طب ال raw V إيش هتساومي؟ اللي هي ال free
+
+341
+00:26:04,510 --> 00:26:10,670
+chargesDiverge y mod e minus rho bv اللي هي مين
+
+342
+00:26:10,670 --> 00:26:16,810
+rho bv؟ minus rho bv plus diverge b صح هذا gauss
+
+343
+00:26:16,810 --> 00:26:20,170
+law gauss law diverge d بيساوي ال total charge
+
+344
+00:26:20,170 --> 00:26:23,090
+enclosed او charge density هنا لان مابحكيش انتيجة
+
+345
+00:26:23,090 --> 00:26:26,850
+كده ال total charge density فال total charge
+
+346
+00:26:26,850 --> 00:26:29,310
+density في الدايرت بيبقى تكون ال free charges زي
+
+347
+00:26:29,310 --> 00:26:34,320
+ال non charges ال volume charge densityإذا معناه
+
+348
+00:26:34,320 --> 00:26:37,740
+ال free charges رو V بتساوي diverse إبسل نض E
+
+349
+00:26:37,740 --> 00:26:41,880
+minus رو بي V بس رو بي V إيش بتساوي minus diverse
+
+350
+00:26:41,880 --> 00:26:45,900
+B minus diverse polarization بقدر أعوض عن minus رو
+
+351
+00:26:45,900 --> 00:26:49,140
+بي V إنها diverse B بالتالي بقدر أخد ال divergence
+
+352
+00:26:49,140 --> 00:26:54,680
+عن المشترك هيكون إبسل نض E زائد B هذا كله اللي هو
+
+353
+00:26:54,680 --> 00:26:54,960
+ال D
+
+354
+00:27:09,000 --> 00:27:13,100
+Rototal Total Charge Density Rototal Total Charge
+
+355
+00:27:13,100 --> 00:27:13,140
+Density Rototal Total Charge Density Rototal Total
+
+356
+00:27:13,140 --> 00:27:13,920
+Charge Density Rotototal Total Charge Density
+
+357
+00:27:13,920 --> 00:27:15,640
+Rotototal Total Charge Density Rotototal Total
+
+358
+00:27:15,640 --> 00:27:16,500
+Charge Density Rotototal Total Charge Density
+
+359
+00:27:16,500 --> 00:27:18,480
+Rotototal Total Charge Density Rotototal Total
+
+360
+00:27:18,480 --> 00:27:20,060
+Charge Density Rotototal Total Charge Density
+
+361
+00:27:20,060 --> 00:27:23,180
+Rotototal Total Charge Density Rotototal Total
+
+362
+00:27:23,180 --> 00:27:25,160
+Charge Density Rotototal Total Charge Density
+
+363
+00:27:25,160 --> 00:27:28,980
+Rotototal Total Charge Density Rotototal Total
+
+364
+00:27:28,980 --> 00:27:32,540
+Charge Density Rotototal Total Charge Density
+
+365
+00:27:32,540 --> 00:27:36,020
+Rotototal Total Charge Density Rotototal Total
+
+366
+00:27:41,380 --> 00:27:47,740
+أيش بتساوي دايفرج ابسل نوت ايه زائد دايفرج بيه لو
+
+367
+00:27:47,740 --> 00:27:52,620
+أخدت الديفرج ع المشترك هيكون ابسل نوت ايه زائد بيه
+
+368
+00:27:52,620 --> 00:27:57,420
+هذا كله من جاوسله لازم يساوي مين الديه احنا جاوسله
+
+369
+00:27:57,420 --> 00:28:02,940
+نقول ال free charge بتساوي دايفرج ايه اذا عندي
+
+370
+00:28:02,940 --> 00:28:07,960
+ابسلون ايه زائد بيه اللي هو في ال material space
+
+371
+00:28:07,960 --> 00:28:11,880
+بتساوي ديهفي ال free space ال polarization بتكون
+
+372
+00:28:11,880 --> 00:28:16,100
+zero فدى بتساوى بتاع epsilon من ال E زى ما احطته
+
+373
+00:28:16,100 --> 00:28:21,440
+في ال chapter 4 طب فى حاجة تانية كمان احنا بنعرف
+
+374
+00:28:21,440 --> 00:28:25,320
+ان ال polarization بتتناسب تقديا مع E ومعامل
+
+375
+00:28:25,320 --> 00:28:28,980
+التناسب هو عبارة عن susceptibility في epsilon node
+
+376
+00:28:35,600 --> 00:28:38,900
+ال susceptibility اللى بت .. susceptibility او ال
+
+377
+00:28:38,900 --> 00:28:44,680
+susceptible اللى هى ال XCE هادي بتقولى قداش ممكنية
+
+378
+00:28:44,680 --> 00:28:48,220
+ال dielectric انه يسمح بنفاذ ال electric field فى
+
+379
+00:28:48,220 --> 00:28:53,160
+قلبه ال polarization و هذا الاشي اللى بيستغلوه
+
+380
+00:28:53,160 --> 00:28:56,020
+طبعا فى ال .. فى ال microwave انه عندنا احنا بيكون
+
+381
+00:28:56,020 --> 00:28:59,060
+فينا الميه اللى هى dipole material عشان هيك
+
+382
+00:28:59,060 --> 00:29:01,840
+بقولكوا لازم يكون شوية ميه فى المادة اللى بتسخنوها
+
+383
+00:29:01,840 --> 00:29:06,600
+و لا بيصير جامدةبتحط .. لإنها هتستغل الميه اللى
+
+384
+00:29:06,600 --> 00:29:10,180
+موجودة أساسا في الحاجة اللى بدك تسخنيها فال .. ال
+
+385
+00:29:10,180 --> 00:29:16,460
+.. ال microwave إيش بعمل؟ بعمل vibration لل dipole
+
+386
+00:29:16,460 --> 00:29:21,500
+تبع ال .. ال water فموجود ال electric field تبع
+
+387
+00:29:21,500 --> 00:29:24,800
+الميكروفون تمام ال frequency بتاعتهم نفس ال
+
+388
+00:29:24,800 --> 00:29:27,060
+frequency فبيعملها vibration هذا ال vibration
+
+389
+00:29:27,060 --> 00:29:30,020
+المنتج عنه ال heat و هذا ال heat هو اللى بسخن
+
+390
+00:29:30,020 --> 00:29:34,700
+الطعام إذا إحنا وصلنا إنه ال chargeTotal free
+
+391
+00:29:34,700 --> 00:29:37,660
+charges بسوء الـ divergence دي واتفقنا إن ال
+
+392
+00:29:37,660 --> 00:29:41,260
+polarization بتتناسب مع الelectric field ومعامل
+
+393
+00:29:41,260 --> 00:29:44,900
+التناسب هو susceptibility في epsilon0 في E بطولة
+
+394
+00:29:44,900 --> 00:29:48,420
+الاتجاه ال electric field و ال polarization في
+
+395
+00:29:48,420 --> 00:29:50,480
+حالة اللي هناخد اللي هي نوعها ال material
+
+396
+00:29:50,480 --> 00:29:54,040
+homogenous, isotropic إلى أخره يكون نفس الاتجاه
+
+397
+00:29:54,040 --> 00:30:00,250
+إلا إذا كانت unisotropic و not homogenousهذا
+
+398
+00:30:00,250 --> 00:30:02,930
+الاشياش بيسهل علينا لو انا اقعد عن ال B بدلالة ال
+
+399
+00:30:02,930 --> 00:30:07,610
+electric field في المعادلة بتاعتنا اقعدت في ال D
+
+400
+00:30:07,610 --> 00:30:16,210
+عرفنا احنا ال D انها بيتساوى Y not E زائد B فرحة
+
+401
+00:30:16,210 --> 00:30:21,210
+ممكن اللغة اللي بدأت عارفة فرحة يكون Y not E زائد
+
+402
+00:30:21,210 --> 00:30:25,110
+عوض عن polarization هي susceptibility Y not E
+
+403
+00:30:25,110 --> 00:30:30,520
+بلاحظ انه مقدر اخد ال electric field ع المشتركوحتى
+
+404
+00:30:30,520 --> 00:30:33,180
+الـ Epsilon Note مقدر أخدها عامة مشترك هيقنع الـ
+
+405
+00:30:33,180 --> 00:30:40,140
+Epsilon Note في 1 زي ال accessibility في E هذا ال
+
+406
+00:30:40,140 --> 00:30:45,600
+term اللي هو 1 زي ال CE بنسميه relative dielectric
+
+407
+00:30:45,600 --> 00:30:50,720
+لأن هذا كله هسميه Epsilon E Epsilon E هو معامل
+
+408
+00:30:50,720 --> 00:30:55,520
+نفاذية للميديا Epsilon Note معامل نفاذية لمن؟ لل
+
+409
+00:30:55,520 --> 00:31:00,160
+space لل free spaceإبسلون هيكون معاني لفازية لمين
+
+410
+00:31:00,160 --> 00:31:04,040
+ل ال material إحنا في ال material space كل هذا ال
+
+411
+00:31:04,040 --> 00:31:10,080
+chapter فإذا نحكي عندي إبسلون نوت في واحد زائد CE
+
+412
+00:31:10,080 --> 00:31:15,020
+بتساوي إبسلون أو معنى آخر إبسلون على إبسلون نوت
+
+413
+00:31:15,020 --> 00:31:19,200
+بتساوي واحد زائد CE اللي بيسميها إبسلون relative
+
+414
+00:31:19,200 --> 00:31:26,120
+relative dielectric اللي هي مين إبسلون على إبسلون
+
+415
+00:31:26,120 --> 00:31:30,990
+نوتإبسلون هو النفاذية ال permativity بتاعة الـ
+
+416
+00:31:30,990 --> 00:31:33,510
+dielectric، إبسلون نطق اللي هي ال permativity
+
+417
+00:31:33,510 --> 00:31:36,730
+بتاعة ال space، ال ratio بينهم بسميها ال relative
+
+418
+00:31:36,730 --> 00:31:40,570
+permativity، اللي بيساوم واحد زائد ال
+
+419
+00:31:40,570 --> 00:31:41,330
+susceptibility
+
+420
+00:31:43,730 --> 00:31:47,550
+إبسن ر مالهاش unit لأنها عبارة عن إبسن و إبسن نوت
+
+421
+00:31:47,550 --> 00:31:51,450
+و نفس القضية accessibility لأنها ratio واضح؟ إذا
+
+422
+00:31:51,450 --> 00:31:54,630
+أنا لو كنت عارف ال accessibility بتاعة ال media
+
+423
+00:31:54,630 --> 00:31:57,550
+بقدر أجيب مالها ال relative dialectic بتاع ال
+
+424
+00:31:57,550 --> 00:32:00,270
+media لو كنت عارف ال relative dialectic بتاع ال
+
+425
+00:32:00,270 --> 00:32:03,650
+media بقدر أجيب مين accessibility بتاعة ال media
+
+426
+00:32:03,650 --> 00:32:06,590
+لو كنت عارفة برضه ال relative dialectic بتاع ال
+
+427
+00:32:06,590 --> 00:32:09,410
+media بقدر أجيب ال dialectic بتاع ال media لأن
+
+428
+00:32:09,410 --> 00:32:15,500
+إبسن إيش بساوي؟ إبسن ر في إبسن نوتإذا كنت عارفة
+
+429
+00:32:15,500 --> 00:32:18,340
+إبسلون تبع ال media بقدر أجيب إبسلون ال R لأنها
+
+430
+00:32:18,340 --> 00:32:22,540
+هتكون إبسلون على إبسلون نوت واضح؟ إذا إحنا في ال
+
+431
+00:32:22,540 --> 00:32:26,360
+material space فيه هنا بظهر term polarization إنها
+
+432
+00:32:26,360 --> 00:32:32,600
+تجميل ال bound charges بتضيف element زيادة على ال
+
+433
+00:32:32,600 --> 00:32:38,380
+field density D إنها بتساويEpsilon E Epsilon E
+
+434
+00:32:38,380 --> 00:32:39,280
+Epsilon E Epsilon E Epsilon E Epsilon E Epsilon E
+
+435
+00:32:39,280 --> 00:32:39,340
+Epsilon E Epsilon E Epsilon E Epsilon E Epsilon E
+
+436
+00:32:39,340 --> 00:32:42,420
+Epsilon E E E E E E E E E E E E E E E E E E E E E
+
+437
+00:32:42,420 --> 00:32:47,120
+E E E E E E E
+
+438
+00:32:47,120 --> 00:32:50,440
+E E E E E E E E E E E E E E E E E E E E E E E E E
+
+439
+00:32:50,440 --> 00:32:50,740
+E E E E E E E E E E E E E E E E E E E E E E E E E
+
+440
+00:32:50,740 --> 00:32:53,720
+E E E E E E E E E E E E E E E E E E E E E E E E E
+
+441
+00:32:53,720 --> 00:32:55,780
+E E E E E E E E E E E E E E E E E E E E E E E E E
+
+442
+00:32:55,780 --> 00:33:00,500
+E
+
+443
+00:33:01,090 --> 00:33:04,850
+فبنعرف ال dialectic strings قوة ال dialectic هي
+
+444
+00:33:04,850 --> 00:33:08,470
+عبارة عن ال maximum electric field اللي عنده ال
+
+445
+00:33:08,470 --> 00:33:11,250
+dialectic can tolerate or withstand without
+
+446
+00:33:11,250 --> 00:33:14,990
+breakdown يعني ال dialectic strings او قوة احتمال
+
+447
+00:33:14,990 --> 00:33:18,410
+ال dialectic هي ال maximum electric field مقداره
+
+448
+00:33:18,410 --> 00:33:21,820
+بأيس ال dialectic stringsبإن مقدار ال electric
+
+449
+00:33:21,820 --> 00:33:26,380
+field اللي عنده ال dielectric بيضلوا متحمل بدون ما
+
+450
+00:33:26,380 --> 00:33:29,160
+يصلوا break down ال break down بيصير contactor
+
+451
+00:33:29,160 --> 00:33:33,280
+وهدى المشكلة اللى بيصير انه في العوازل تستخدم
+
+452
+00:33:33,280 --> 00:33:38,520
+لحماية عمال كهربا نوع العوازل dielectric تستخدموها
+
+453
+00:33:38,520 --> 00:33:43,380
+عشان يحموهم من ال high potentialفي .. بيقسوهم
+
+454
+00:33:43,380 --> 00:33:46,740
+المفروض في ظروف مخبرية معينة ان يتأكدوا انه بتحمل
+
+455
+00:33:46,740 --> 00:33:50,140
+قداش electric field بدون ما قبل ما يصير ال
+
+456
+00:33:50,140 --> 00:33:54,420
+conductor أحيانا تكون نوعيا مش كافية مش جيدة فبيجي
+
+457
+00:33:54,420 --> 00:33:59,730
+يعمل كهربا هو بيشتغل بيصير electric field بيخترقهي
+
+458
+00:33:59,730 --> 00:34:03,750
+conducting و بوصل الطيار في قلب الإنسان و احنا
+
+459
+00:34:03,750 --> 00:34:07,670
+الطيار قولنا هو الخطر مش ال potential إذا الطيار
+
+460
+00:34:07,670 --> 00:34:11,170
+يخترق جسم الإنسان هو اللي بيعمل مشاكل لما يصير
+
+461
+00:34:11,170 --> 00:34:14,710
+conductor الإنسان لإن العازل اللي قاعد بيعزوه أصلا
+
+462
+00:34:14,710 --> 00:34:19,620
+conductor بس احنا بنعمله عوازلبنحطله كوانتيات و ..
+
+463
+00:34:19,620 --> 00:34:25,400
+او بنلبسه جزم جلد و بنحطله وزع راسه عشان يكون هو
+
+464
+00:34:25,400 --> 00:34:29,020
+dielectric مايصيرش اللي طيار مرفيه إذا هدول ال
+
+465
+00:34:29,020 --> 00:34:32,420
+dielectric اللي هو لبسهم صار لهم break down يعني
+
+466
+00:34:32,420 --> 00:34:35,140
+صار ال conductor على طول الطيار مرفيه في الإنسان
+
+467
+00:34:35,140 --> 00:34:38,760
+لأنه احنا كل المواد اللي لها فيها أملح و مغسل و
+
+468
+00:34:38,760 --> 00:34:43,630
+رباع فصار هذا الحكي كتير من اللي همالعمال اللي
+
+469
+00:34:43,630 --> 00:34:48,070
+بوجه لبسين ال electric .. ال strings تبعه تحمل
+
+470
+00:34:48,070 --> 00:34:51,550
+electric field عالي، إيش ممكن يصلهم؟ يا paralyzed
+
+471
+00:34:51,550 --> 00:34:55,170
+يا وفا يا الاخرين، و غالباً وفا لإن هو مش أعلى
+
+472
+00:34:55,170 --> 00:34:58,450
+أفوه، تجيله السايقة، بوقع، إذا ماتش من الكهرة،
+
+473
+00:34:58,450 --> 00:35:05,810
+بموت من الوقع، تمام؟نحكى دول على السريع و اللقاء
+
+474
+00:35:05,810 --> 00:35:08,770
+القادم بنايدهم أنه linear, isentropic,
+
+475
+00:35:08,890 --> 00:35:12,370
+homogeneous, dielectric كيف بحدد ان هو linear او
+
+476
+00:35:12,370 --> 00:35:15,090
+isentropic او homogeneous بقول عن المادة انها
+
+477
+00:35:15,090 --> 00:35:19,790
+linear اذا كانت D بتتغير linearly مع E يعني مافيش
+
+478
+00:35:19,790 --> 00:35:25,440
+عندي E تربيه او EQLinearly يعني التغيير مع دى زى
+
+479
+00:35:25,440 --> 00:35:29,820
+المثل اللى شوفناه Linear دى بتتناسب مع ايه مش مع
+
+480
+00:35:29,820 --> 00:35:34,700
+ايه تربيه ال material which epsilon or sigma اللى
+
+481
+00:35:34,700 --> 00:35:39,040
+هى ال permittivity و sigma الconductivity لا تعتمد
+
+482
+00:35:39,040 --> 00:35:42,440
+على X Y و Z بنسميها homogenous يعني إذا بتعتمدش
+
+483
+00:35:42,440 --> 00:35:47,170
+على وين اى نقطة فى ال spaceبنسميها homogenous، لكن
+
+484
+00:35:47,170 --> 00:35:50,650
+إذا كانت إبسلون بتعتمد على x, y, z، إيش بنسميها
+
+485
+00:35:50,650 --> 00:35:55,330
+non-homogenous أو inhomogeneous إذا كانت دي بتعتمد
+
+486
+00:35:55,330 --> 00:36:00,810
+على E، إذا كانت إبسلون أو سيجما لا يعتمدوا على x,
+
+487
+00:36:00,890 --> 00:36:03,870
+y, z، بنسميها homogenous، بتعتمد، بنسميها
+
+488
+00:36:03,870 --> 00:36:08,490
+inhomogeneousكمان عندنا ال material اللي عندها D و
+
+489
+00:36:08,490 --> 00:36:11,890
+E are in the same direction بنسميها isotropic يعني
+
+490
+00:36:11,890 --> 00:36:15,790
+E بتكون هك و D بتكون هك مش بينهم زاوية بنسميها
+
+491
+00:36:15,790 --> 00:36:20,430
+isotropic لو كان بينهم مش في نفس الاتجاه بنسميها
+
+492
+00:36:20,430 --> 00:36:24,610
+anisotropic و ساعتها E و C بيصيروا تنصر بيصيروا
+
+493
+00:36:24,610 --> 00:36:29,550
+matrix زي هذا الشكليصير عندى dx و dy و dz، dx ما
+
+494
+00:36:29,550 --> 00:36:33,130
+لها، اللي لها three components مش نفس اتجاه ال E،
+
+495
+00:36:33,130 --> 00:36:36,390
+هيكون تلاتة ال EX والEY والEZ، بيكونوش نفس
+
+496
+00:36:36,390 --> 00:36:40,050
+الاتجاه، بيسميها anisotropic material، anisotropic
+
+497
+00:36:40,050 --> 00:36:42,770
+material، في كتير من ال crystalline material اللي
+
+498
+00:36:42,770 --> 00:36:46,450
+موجودة في الطبيعة اللي بتكون لها طبيعة ال
+
+499
+00:36:46,450 --> 00:36:46,970
+anisotropic
+
+500
+00:36:50,070 --> 00:36:52,990
+طبعا خلّينا الباقى يبقى نفس الحاجة بتتطبق على اللي
+
+501
+00:36:52,990 --> 00:36:56,410
+هو القائل J بيساوي Sigma E اللي هي العلاقة بين J و
+
+502
+00:36:56,410 --> 00:36:59,710
+E إذا Sigma بتعتمدش على X و Y و Z بنقول عنها
+
+503
+00:36:59,710 --> 00:37:03,770
+homogenous J و E بيعتمدوا على linear homogenous
+
+504
+00:37:03,770 --> 00:37:07,930
+بتكون إذا كان E .. J في اتجاه ال E بتكون isotropic
+
+505
+00:37:07,930 --> 00:37:10,950
+إذا مش في اتجاهها بيكون اللي هي Sigma tensor
+
+506
+00:37:10,950 --> 00:37:14,350
+فبتكون unisotropic وبنأكد عليهم اللقاء القادم ان
+
+507
+00:37:14,350 --> 00:37:15,590
+شاء الله يا تقلع
+
diff --git a/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/kG2lS7Q6L98.srt b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/kG2lS7Q6L98.srt
new file mode 100644
index 0000000000000000000000000000000000000000..0b5b1f6b4dbe6f404ae9f9b383c35584680755c5
--- /dev/null
+++ b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/kG2lS7Q6L98.srt
@@ -0,0 +1,2096 @@
+1
+00:00:20,670 --> 00:00:23,490
+بسم الله الرحمن الرحيم السلام عليكم ورحمة الله
+
+2
+00:00:23,490 --> 00:00:26,770
+وبركاته  إحنا اليوم إن شاء الله هنتبع موضوعنا ال
+
+3
+00:00:26,770 --> 00:00:30,470
+boundary value problems أو boundary conditional 
+
+4
+00:00:30,470 --> 00:00:33,610
+problems بكيف نحسب ال potential وقولنا من ال
+
+5
+00:00:33,610 --> 00:00:36,250
+potential حسبنا يقدر نحسب ال electric field
+
+6
+00:00:38,860 --> 00:00:41,780
+المحاضرة الماضية شوفنا أمثلة اللي كان فيها ال
+
+7
+00:00:41,780 --> 00:00:44,460
+potential  specified على one direction one variable
+
+8
+00:00:44,460 --> 00:00:49,000
+وحلناها بال integration اليوم هنشوف مثال اللي لازم
+
+9
+00:00:49,000 --> 00:00:51,800
+إحنا نستخدم ال separation of variables إحنا قولنا
+
+10
+00:00:51,800 --> 00:00:54,420
+فيه طريقتين لحل أسبوع على أسبوع أو بأسبوع equation
+
+11
+00:00:54,420 --> 00:00:56,700
+لإن هي الطريقة الأولى أنه يكون ال potential
+
+12
+00:00:56,700 --> 00:01:00,320
+specified على one variable نعمل integration أو أكثر
+
+13
+00:01:00,320 --> 00:01:02,940
+من variable وساعتها بنعمل separation of variables
+
+14
+00:01:02,940 --> 00:01:08,470
+فخلّينا نشوف مثال على ال separation of variables هنا
+
+15
+00:01:08,470 --> 00:01:13,250
+المثال اللي قدامنا عبارة عن اللي هو متوازي أضلاع
+
+16
+00:01:13,250 --> 00:01:18,750
+waveguide على شكل متوازي أضلاع مبتدئ على طول إنّها
+
+17
+00:01:18,750 --> 00:01:24,390
+key conditions إن عند x equal 0 ال potential y
+
+18
+00:01:24,390 --> 00:01:29,990
+ما بين ال 0 و ال a ال potential بساوي 0 وال wall
+
+19
+00:01:29,990 --> 00:01:36,550
+اللي عند y equal 0 و x من 0 ل b برضه بتساوي 0 وال 
+
+20
+00:01:36,550 --> 00:01:41,710
+wall اللي عند x equal b و y من 0 ل a برضه بتساوي
+
+21
+00:01:41,710 --> 00:01:47,210
+بساوي 0 ال wall اللي عند y بتساوي a و x ما بين ال
+
+22
+00:01:47,210 --> 00:01:51,250
+0 و ال b اللي بتساوي v not وماعطينا قيمة v
+
+23
+00:01:51,250 --> 00:01:55,700
+not إن هو one hundred volt وكمان قولنا إن b هو طول
+
+24
+00:01:55,700 --> 00:02:01,740
+المساطير المساحة المقطع على متوازي الأضلاع إنه إيه
+
+25
+00:02:01,740 --> 00:02:06,560
+بتساوي 2A المطلوب بينقل نقطة potential عند أي
+
+26
+00:02:06,560 --> 00:02:10,840
+نقطة في قلب ال with guide يعني مثلا X بتساوي A على
+
+27
+00:02:10,840 --> 00:02:17,000
+2 هي بالتمام هنا تقريبًا لأن قلنا b 2A فهي A هتكون
+
+28
+00:02:17,000 --> 00:02:21,820
+A على 2 تقريبًا هنا و Y تلاتة A على أربع
+
+29
+00:02:25,010 --> 00:02:28,410
+طالب تربع A يعني somewhere هنا يعني طالب تربع A
+
+30
+00:02:28,410 --> 00:02:32,310
+فاضح؟ إذا هو هاي المطلوب بينا إن أجيب ال potential
+
+31
+00:02:32,310 --> 00:02:38,690
+عند أي نقطة في قلب المتوازي الأضلاع واضح لنا إن ال
+
+32
+00:02:38,690 --> 00:02:41,530
+potential باعتمدنا ده على two variables ال X وال Y
+
+33
+00:02:41,530 --> 00:02:45,390
+لكن في ال Z direction ال Z رايح لل infinity ومفيش
+
+34
+00:02:45,390 --> 00:02:50,950
+اعتمادية على ال Z الاعتمادية فقط على ال X وY مافيش 
+
+35
+00:02:50,950 --> 00:02:58,840
+free chargesفإذا دل تربيع V بيساوي 0 طبعًا
+
+36
+00:02:58,840 --> 00:03:01,560
+إحنا ال coordinate اللي قررنا واضح إنه هناخد
+
+37
+00:03:01,560 --> 00:03:05,840
+Cartesian coordinate ال X و ال Y إذا هتكون الدل
+
+38
+00:03:05,840 --> 00:03:10,140
+تربيع D تربيع V by DX تربيع زي ال DT تربيع by DY
+
+39
+00:03:10,140 --> 00:03:15,460
+تربيع بتساوي 0 لإن مفيش free charges هنستخدم ال
+
+40
+00:03:15,460 --> 00:03:19,590
+last equation بمعنى إن الدل تربيع V بتساوي 0 بنسمع 
+
+41
+00:03:19,590 --> 00:03:21,530
+ال boundary conditions اللي إحنا حكيناها مع بعض
+
+42
+00:03:21,530 --> 00:03:26,850
+إن ال potential عند x equal 0 و y ما بين ال 0 و ال
+
+43
+00:03:26,850 --> 00:03:32,290
+a بساوي 0 ال potential عند x equal b و ال y من 0 ل
+
+44
+00:03:32,290 --> 00:03:37,310
+a بساوي 0 ال potential لل x ما بين ال 0 و ال b و ال
+
+45
+00:03:37,310 --> 00:03:43,370
+y بساوي 0 ال potential عند x ما بين ال 0 و ال b و
+
+46
+00:03:43,370 --> 00:03:46,430
+ال y بساوي a بساوي v ضد هذه هي ال boundary
+
+47
+00:03:46,430 --> 00:03:46,950
+conditions
+
+48
+00:03:49,670 --> 00:03:56,530
+بالنسبة للمشكلة مثل هذه المشكلة نحن لدينا V مالها V
+
+49
+00:03:56,530 --> 00:04:02,710
+مقلد نترميها V مستوى V وقلنا استنتجنا إن V مقلد
+
+50
+00:04:02,710 --> 00:04:11,710
+function of X وY فمعناه استنتجنا إن E تنين V X Y Y
+
+51
+00:04:11,710 --> 00:04:20,650
+D X نترميها زي E تنين Vبايتم دي و بايتم دي و بايتم
+
+52
+00:04:20,650 --> 00:04:21,290
+دي و بايتم دي و بايتم دي و بايتم
+
+53
+00:04:21,290 --> 00:04:29,650
+دي و بايتم دي و بايتم دي و بايتم دي و بايتم
+
+54
+00:04:29,650 --> 00:04:32,330
+دي و بايتم دي و بايتم دي و بايتم دي و بايتم دي و
+
+55
+00:04:32,330 --> 00:04:36,450
+بايتم دي و بايتم دي و بايتم دي و بايتم دي و بايتم
+
+56
+00:04:36,450 --> 00:04:39,430
+دي و بايتم دي
+
+57
+00:04:44,210 --> 00:04:48,730
+في ال X اعتمادية على X لها تعتمد على V لها ال Y
+
+58
+00:04:48,730 --> 00:04:52,070
+عشان نقدر نقول إن هي بقدر أسمها شكل through
+
+59
+00:04:52,070 --> 00:04:57,370
+function XY X هو ال solution اللي بعتمد على X و Y
+
+60
+00:04:57,370 --> 00:05:02,950
+ال solution اللي بعتمد على Y أو بقدر أسمهم VX و VY
+
+61
+00:05:02,950 --> 00:05:05,910
+فهذا ال solution اللي بقدر نضعه عشان نتأكد إنه 
+
+62
+00:05:05,910 --> 00:05:10,600
+اعتمد على X فهذا الاعتمادية على Vهذه الطريقة اللي
+
+63
+00:05:10,600 --> 00:05:14,380
+نسميها طريقة الـ Separation Theory إنّها عرفّتنا إن 
+
+64
+00:05:14,380 --> 00:05:18,540
+ال potential مقدر أفصل اعتماديته على X عن 
+
+65
+00:05:18,540 --> 00:05:23,000
+اعتماديته على Y لو ماقدرش أفصلهم بيظلوا صعب الحل
+
+66
+00:05:23,000 --> 00:05:27,640
+بيظلوا M في الدخل لكن ما إنه أنا الاعتمادية اللي
+
+67
+00:05:27,640 --> 00:05:31,140
+على ال X ده تعتمد على ال Y بقدر أفصل ال two
+
+68
+00:05:31,140 --> 00:05:34,780
+functions في ناس بتلاقوهم بيكسّل X يعني هذا 
+
+69
+00:05:34,780 --> 00:05:38,600
+potential جزء من ال solution وهذا جزء من ال
+
+70
+00:05:38,600 --> 00:05:46,500
+solution مثلًا إحنا في الكتاب بيستخدم X وY فماعود
+
+71
+00:05:46,780 --> 00:05:50,120
+فهذا ال potential في ال problem اللي قدامنا في ال
+
+72
+00:05:50,120 --> 00:05:53,560
+equation اللي معناه هنلاحظ إنه ال term الأولاني
+
+73
+00:05:53,560 --> 00:05:58,060
+بعتمد ع مين؟ ع ال X إذا أنا هذا بس بتفاضل مرتين ال
+
+74
+00:05:58,060 --> 00:06:04,620
+Y بتطلع برة التفاضل فهيكون عندي Y لا تعتمد ع ال X
+
+75
+00:06:04,620 --> 00:06:09,060
+وبيصير عندي exact differential مش partial اتنين ل
+
+76
+00:06:09,060 --> 00:06:14,800
+X أنا متعتمدش اللي ع ال X exactزائر هنا مين ال
+
+77
+00:06:14,800 --> 00:06:18,520
+term التفاظ بالنسبة ل y الجزء اللي على ال x بيطلع
+
+78
+00:06:18,520 --> 00:06:31,080
+بره ال differentiation تمام
+
+79
+00:06:31,080 --> 00:06:36,340
+فهذا هو ال separation theorem التي شهدت جزئية
+
+80
+00:06:36,340 --> 00:06:40,660
+التانية وهي الأهم إن إحنا لو قسمنا على مين؟ على
+
+81
+00:06:40,660 --> 00:06:41,800
+Vxy
+
+82
+00:06:46,670 --> 00:06:53,570
+مين دي ال X و Y؟ X و Y يعني إيش هال بتصير؟ 1 على X
+
+83
+00:06:53,570 --> 00:06:57,370
+V2
+
+84
+00:06:57,370 --> 00:07:06,530
+من X و Y من X تقريبًا زي V2 من Y و Y تقريبًا
+
+85
+00:07:06,530 --> 00:07:14,330
+ما بيبقوا كمين؟ واحد تمام؟
+
+86
+00:07:16,370 --> 00:07:23,990
+أسهل عندي هذا term بيساوي 
+
+87
+00:07:23,990 --> 00:07:30,730
+0 يعني أنا كمان بقول المعلومة التانية بقول إن
+
+88
+00:07:30,730 --> 00:07:37,030
+ال second derivative لل X ل X double prime على X زائد
+
+89
+00:07:37,030 --> 00:07:42,170
+ال second derivative لل Y على Y بتساوي 0 أو بمعنى آخر 
+
+90
+00:07:42,170 --> 00:07:46,700
+X double prime على X بتساوي أو تساوي بتساوي y
+
+91
+00:07:46,700 --> 00:07:53,120
+double prime على y إذا 
+
+92
+00:07:53,120 --> 00:07:56,840
+أسمه x double prime على x بتساوي x double prime
+
+93
+00:07:56,840 --> 00:08:02,800
+على y معناه إن الناتج لا بعتمد على x ولا على y هاي
+
+94
+00:08:02,800 --> 00:08:08,340
+المعنى إذا تفاضل ال x مرتين على x بتساوي تفاضل ال y
+
+95
+00:08:08,340 --> 00:08:11,920
+مرتين على y معناه إن الناتج لا بعتمد على x ولا على
+
+96
+00:08:11,920 --> 00:08:17,110
+y بنسميه دايمًا constant lambda beta إلى أخرى زي ما
+
+97
+00:08:17,110 --> 00:08:21,290
+نشوفين على السطر minus x double prime على x
+
+98
+00:08:21,290 --> 00:08:25,550
+اللي بتساوي y double prime على y لازم كل واحد منهم
+
+99
+00:08:25,550 --> 00:08:29,950
+يكون بساوي some constant كل واحد منهم بساوي some
+
+100
+00:08:29,950 --> 00:08:37,970
+constant إحنا سمّيناه lambda ابتعدي 
+
+101
+00:08:37,970 --> 00:08:42,030
+معادلتين على هيك المعادلة الأولى بتقولي إنه x
+
+102
+00:08:42,030 --> 00:08:42,870
+double prime
+
+103
+00:08:46,700 --> 00:08:51,820
+زائد Lambda X بساوي 0 والتانية بيقولي Y double prime
+
+104
+00:08:51,820 --> 00:08:58,860
+minus Lambda Y بساوي 0 كل واحدة منهم second order
+
+105
+00:08:58,860 --> 00:09:01,700
+differential equation يعني ال second derivative
+
+106
+00:09:01,700 --> 00:09:05,900
+differential equation اللي بقدر أحلهم بسهولة زي ما 
+
+107
+00:09:05,900 --> 00:09:10,420
+استخدمنا هذه ممكن شفتوها أول مرة في الدوائر في ال
+
+108
+00:09:10,420 --> 00:09:14,180
+natural response صح؟ وبعدين أخذهم في الـ
+
+109
+00:09:14,180 --> 00:09:16,620
+differential في هذه المعادلات يعني هذه المعادلات
+
+110
+00:09:16,620 --> 00:09:19,340
+اللي بتوصلوا إنّها معادلات سهلة بالنسبالي أحلوها
+
+111
+00:09:19,340 --> 00:09:23,800
+بدون ما ننسى ال boundary conditions خليني أرجع لل
+
+112
+00:09:23,800 --> 00:09:27,120
+boundary conditions اللي كتبناهم قبل قليل ونعيد
+
+113
+00:09:27,120 --> 00:09:37,940
+كتابتهم لما نفصل ال variables نقول لذي نقطع
+
+114
+00:09:37,940 --> 00:09:42,500
+على جانب لكي نتذكر إنّها هي ال y وهي ال x
+
+115
+00:09:48,720 --> 00:09:52,920
+ال potential هنا بيساوي صفر وهنا بيساوي صفر وهنا 
+
+116
+00:09:52,920 --> 00:09:56,960
+بيساوي صفر هاي الطبيب كونه طبيب هده كون إيه وهده
+
+117
+00:09:56,960 --> 00:10:02,320
+هيكون ال potential طبعًا ال gaps إحنا حكينا عنهم هيك
+
+118
+00:10:02,320 --> 00:10:06,140
+هدولها ال gaps عشان إيش يعمل insulation لأن لو 
+
+119
+00:10:06,140 --> 00:10:10,400
+حاطلناهم جنب بعض إيش بيصير ال potential بتوزع بيصير يا 
+
+120
+00:10:10,400 --> 00:10:15,620
+كله صفر يا كله V node إذا
+
+121
+00:10:15,620 --> 00:10:19,770
+نرجع لل boundary conditions ال Potential عند X equals
+
+122
+00:10:19,770 --> 00:10:24,550
+0 وأي قيمة Y و
+
+123
+00:10:24,550 --> 00:10:31,550
+أي قيمة Y ما بين 0 و B، إيش Potential بتساوي 0؟
+
+124
+00:10:31,550 --> 00:10:43,830
+صح، عند X equals 0،
+
+125
+00:10:43,830 --> 00:10:56,470
+X و 1، X equals 0؟ Y من الـ 0 و الـ A إذا
+
+126
+00:10:56,470 --> 00:10:59,270
+أنا عند X equal 0 و Y من الـ 0 لـ A ال potential
+
+127
+00:10:59,270 --> 00:11:05,070
+بيساوي 0 إنهوض على ال potential دلوقت X و Y X هي 
+
+128
+00:11:05,070 --> 00:11:08,950
+function of X عند قيمة X بتساوي 0 هاي ال boundary
+
+129
+00:11:08,950 --> 00:11:12,510
+عند هاي النقطة بالذات Y as function of Y اللي هي Y
+
+130
+00:11:12,510 --> 00:11:15,330
+قولنا من 0 ل A إيش كمية ال potential عند هذه ال 
+
+131
+00:11:15,330 --> 00:11:20,170
+wall بتساوي 0 عندها الحيطة اللي هي X بتساوي 0 وY 
+
+132
+00:11:20,170 --> 00:11:26,770
+ما بين ال 0 و ال A بتتساوي 0 Y من 0 ل A
+
+133
+00:11:26,770 --> 00:11:32,360
+أتوقعش هتكون 0 قيمة ال potential لكن قد يكون ال
+
+134
+00:11:32,360 --> 00:11:36,420
+potential عند نقطة محددة x at x equal 0 بساوي صفر
+
+135
+00:11:36,420 --> 00:11:42,800
+يعني هذه y as function of y فهذا function بقي بساوي
+
+136
+00:11:42,800 --> 00:11:47,600
+0 إذا اللي أكيد لازم بيساوي 0 قيمة x at 0 إذا ال x
+
+137
+00:11:47,600 --> 00:11:52,420
+at 0 بتساوي صفر كمان مرة ال potential عند x equal b
+
+138
+00:11:52,420 --> 00:11:58,640
+x equal b لها نقطة و y بين ال 0 و ال n برضه بتساوي
+
+139
+00:11:58,640 --> 00:12:04,000
+بساوي 0 أعود عن x equal b و y بيبقى y إنّها بين
+
+140
+00:12:04,000 --> 00:12:10,600
+مجموعة من النقاط من 0 ك a برضه بتساوي 0 y as a
+
+141
+00:12:10,600 --> 00:12:12,720
+function of y قلنا ده ال function ال potential
+
+142
+00:12:12,720 --> 00:12:15,600
+يعني إذا خليتها صفر كل potential تبقى بساوي 0 لو
+
+143
+00:12:15,600 --> 00:12:20,320
+أخذت y ال y بساوي 0 لوش معنى x ال b هي اللي هتساوي 
+
+144
+00:12:20,320 --> 00:12:26,420
+0 إذا استنتجنا إن x عندنا نقطة 0 بساوي 0 هيبقى
+
+145
+00:12:30,420 --> 00:12:36,760
+يجي إنّت اللي هي ال Y equal 0 X أو Zero هتساوي X ال
+
+146
+00:12:36,760 --> 00:12:43,810
+X و Y ال Zero برضه بتساوي صفر x هو بين 0 و b و y
+
+147
+00:12:43,810 --> 00:12:47,610
+بيكون صفر و potential صفر نفس المنطق أنا ماقدرش
+
+148
+00:12:47,610 --> 00:12:50,830
+آخد ال function x of x بيكون صفر لأن إذا حد هو صفر
+
+149
+00:12:50,830 --> 00:12:54,510
+مع إن ال potential صفر لأن y هو صفر لأن y هو صفر
+
+150
+00:12:54,510 --> 00:13:02,810
+لأن y هو صفر لأن y هو صفر لأن y هو صفر لأن y هو
+
+151
+00:13:02,810 --> 00:13:05,670
+صفر لأن y هو صفر لأن y هو صفر لأن y هو صفر لأن y
+
+152
+00:13:05,670 --> 00:13:07,930
+هو صفر لأن y هو صفر لأن y هو صفر لأن y هو صفر لأن
+
+153
+00:13:07,930 --> 00:13:08,690
+y هو صفر لأن y هو صفر لأن y هو صفر لأن y هو صفر
+
+154
+00:13:08,690 --> 00:13:12,870
+لأن y هو صفر لأن y هو صفر لأن y هو صفر لإبتساوي X
+
+155
+00:13:12,870 --> 00:13:22,530
+بتساوي Zero Y و الان X Zero Y الان X ال X عند أي
+
+156
+00:13:22,530 --> 00:13:27,970
+نقطة ل X و Y ال Zero إحنا قولنا X خلّصنا من Zero من 
+
+157
+00:13:27,970 --> 00:13:35,690
+ال B و X equal Zero و X and Y بيساوي B يعني هذا X
+
+158
+00:13:35,690 --> 00:13:36,990
+بتساوي Zero و Y
+
+159
+00:13:54,350 --> 00:13:55,750
+X0YY
+
+160
+00:14:02,940 --> 00:14:07,220
+وبعدين x,b,y اللي هم ال wall هادي وال wall هادي
+
+161
+00:14:07,220 --> 00:14:11,080
+وبعدين أخذنا ال x equal x و y zero اللي هاي ال
+
+162
+00:14:11,080 --> 00:14:18,240
+wall فهد المفروض هد ال y equal zero و ال x equal x
+
+163
+00:14:18,240 --> 00:14:24,880
+وهد ال y بتساوي a و ال x بتساوي x عشان x هادي فهد
+
+164
+00:14:24,880 --> 00:14:27,860
+متأثرة هد x فهي x ال x و y ال a
+
+165
+00:14:30,930 --> 00:14:35,090
+هذه بتساوي V0، إذا عندنا آخر واحدة هي ال X ال
+
+166
+00:14:35,090 --> 00:14:43,010
+function of X و Y هي عند ال R بتساوي V0
+
+167
+00:14:45,750 --> 00:14:49,110
+اللي أنا بقدر أقيم أقول إن ال X of X اللي مستحيل
+
+168
+00:14:49,110 --> 00:14:53,730
+أخليها يعني constant هي variable X ال X و Y ال A
+
+169
+00:14:53,730 --> 00:14:58,410
+مش لحالة هسو ال V0 حاصل ضرب ما هو ال V0 فماش بنقول
+
+170
+00:14:58,410 --> 00:15:01,710
+عنها inseparable مش زي هدولة كان معضح اللي ماقدرش 
+
+171
+00:15:01,710 --> 00:15:05,250
+أقول إن Y ال Y بساوي 0 إذا X ال 0 هي السفر هنا Y
+
+172
+00:15:05,250 --> 00:15:09,160
+ال Y ماقدرش أقول 0 إذا X ال B هي السفرة هنا هو X الـ
+
+173
+00:15:09,160 --> 00:15:13,060
+X في Y الـ A التانية بساوي و V نقطة هذه انسبرة 
+
+174
+00:15:13,060 --> 00:15:17,820
+ماقدرش أفصلهم عن بعض فبظل حاصل الضرب اللي هو X ال
+
+175
+00:15:17,820 --> 00:15:21,940
+X و Y عند ال A طبعًا ال X هنا من 0 ل B اللي هو ال
+
+176
+00:15:21,940 --> 00:15:
+
+201
+00:17:05,600 --> 00:17:12,540
+بتنشط صفر عند x equals 0 بتنشط بساوة زيرو نحط
+
+202
+00:17:21,330 --> 00:17:25,190
+عشان احط عن ال variable X=0 و ال potential بالساوة
+
+203
+00:17:25,190 --> 00:17:30,470
+0 اذا P مالها صفر اذا عند النقطة X بالساوة صفر ال
+
+204
+00:17:30,470 --> 00:17:34,150
+potential X بالساوة 0 اذا P بالساوة 0 اذا هاي
+
+205
+00:17:34,150 --> 00:17:37,250
+المعادلة اتوصلت ل A ايش ل X بالساوة Ax دل على يمين
+
+206
+00:17:37,250 --> 00:17:41,530
+ال A طب احنا كمان عنا كمان boundary condition ان X
+
+207
+00:17:41,530 --> 00:17:49,050
+الـ X عند ال B برضه بتسوى 0 اذا نعود عن هذه
+
+208
+00:17:49,050 --> 00:17:55,350
+المبتدأ X equal B ال potential بيسوى 0 اعود X عند
+
+209
+00:17:55,350 --> 00:18:01,190
+ال B يعني A في B بيسوى 0 صح؟ A في B بيساو صفر بي
+
+210
+00:18:01,190 --> 00:18:03,870
+كونستانت اذا عرفت ان قيمته ممكن تكون عشرة أو كون
+
+211
+00:18:03,870 --> 00:18:07,350
+طول المتوازن اللي اطلع عليه ممكن تكون صفر اذا مين
+
+212
+00:18:07,350 --> 00:18:10,750
+لازم يساو صفر الـA دي طب اذا A صفر وB صفر اذا ال
+
+213
+00:18:10,750 --> 00:18:14,990
+potential X اشمله صفر ال trivial مطبع لما يكون ال
+
+214
+00:18:14,990 --> 00:18:18,490
+potential زيرو هذا هيكون احد الحلول لكن نسميه
+
+215
+00:18:18,490 --> 00:18:21,250
+trivial solution يعني اسهل حلة او دايما الحل لأي
+
+216
+00:18:21,250 --> 00:18:24,370
+معادل differential زيرو احد الحلول هيكون بس مش
+
+217
+00:18:24,370 --> 00:18:30,830
+الحل النهائي اذا نستنتج ان لامدة لا تساوي زيرو أي
+
+218
+00:18:30,830 --> 00:18:35,030
+أكبر من صفر يعني موجبة أو أقل من صفر يعني سالبة
+
+219
+00:18:36,030 --> 00:18:39,370
+ناخد lambda أقل من zero عشان أؤكد لحالي أن lambda
+
+220
+00:18:39,370 --> 00:18:42,890
+أقل من zero باخدها أنها سالب a تربيع حاجة تربيع ال
+
+221
+00:18:42,890 --> 00:18:46,830
+alpha تربيع ال b تربيع لإيش؟ لأن التربيع ملوجة بحط
+
+222
+00:18:46,830 --> 00:18:50,330
+السالب قدامه معناه نأكد أن lambda مالها قيمة سالبة
+
+223
+00:18:50,330 --> 00:18:54,230
+لو أخدتها ده أي حاجة مش مربعة ممكن هيدقول والله
+
+224
+00:18:54,230 --> 00:18:57,910
+ممكن هيدكون سالبة فعشان أعرف الناس أن أنا ماخدة
+
+225
+00:18:57,910 --> 00:19:02,270
+lambda أنها سالبة بقول minus a minus alpha تربيع
+
+226
+00:19:02,270 --> 00:19:07,530
+مثلانعوض عن هذا الحكيم xw' ما نسأل في تربيع x
+
+227
+00:19:07,530 --> 00:19:12,450
+بالساوة 0 ممكن احنا نعملها دلالة d تربيع حيث اعرف
+
+228
+00:19:12,450 --> 00:19:16,950
+دي تربيع هي d by dx بتصير اسهل ليه او ممكن زي ما
+
+229
+00:19:16,950 --> 00:19:20,810
+حكيت انه نحلها انه اعمل اللي هي ال expression
+
+230
+00:19:20,810 --> 00:19:25,230
+variables و احل زي ما استخدمته في دور الواحد او في
+
+231
+00:19:25,230 --> 00:19:28,050
+ال differential d تربيع ما نسأل تربيع x بالساوة 0
+
+232
+00:19:28,050 --> 00:19:34,080
+بستخدم ان هو فرق بمربعيندى plus minus alpha اللى x
+
+233
+00:19:34,080 --> 00:19:37,660
+بتساوي zero فبتعطينا ان ال differential بيه بتساوي
+
+234
+00:19:37,660 --> 00:19:43,720
+plus dx by dx بتساوي alpha x يا dx by dx بتساوي
+
+235
+00:19:43,720 --> 00:19:48,680
+ثالث alpha x اللى هى الحل التانى فده بستكمله
+
+236
+00:19:48,680 --> 00:19:54,980
+للأولى تمام؟ احنا بقى افصل بحط dx على x بتساوي
+
+237
+00:19:54,980 --> 00:20:00,810
+alpha dxو على كامل بيطلع معايا ان x ايش بتساوي a1
+
+238
+00:20:00,810 --> 00:20:05,350
+e to the alpha x لو أخدت السالبة باعد نفس الكلام و
+
+239
+00:20:05,350 --> 00:20:08,290
+بتطلع ل x بتساوي اتنين e to the minus alpha x
+
+240
+00:20:08,290 --> 00:20:13,490
+واضح؟ اذا لو أخدت الموجبة dx by dx بتساوي alpha x
+
+241
+00:20:13,490 --> 00:20:18,190
+واضح يعني ايش اللي انا بحكيه يازم أخطط
+
+242
+00:20:28,040 --> 00:20:41,980
+هذه هي تربية X Y X X X X X X X
+
+243
+00:20:41,980 --> 00:20:42,660
+X X X X X X X X X X X X X X X X X X X X X X X X X
+
+244
+00:20:42,660 --> 00:20:47,440
+X X X
+
+245
+00:20:47,440 --> 00:20:47,980
+X X X X X X X X X X X X X X X X X X X X X X X X X
+
+246
+00:20:47,980 --> 00:20:48,320
+X X X X X X X X X X X X X X X X X X X X X X X X X
+
+247
+00:20:48,320 --> 00:20:50,560
+X X X X X
+
+248
+00:20:57,020 --> 00:21:04,840
+هي أسميها D تربيه مانوس ألف تربيه X تربيه من فضل X
+
+249
+00:21:04,840 --> 00:21:09,200
+تربيه
+
+250
+00:21:09,200 --> 00:21:14,740
+من فضل X تربيه من فضل X تربيه من فضل X تربيه من
+
+251
+00:21:14,740 --> 00:21:16,800
+فضل X تربيه من فضل X تربيه من فضل X تربيه من فضل X
+
+252
+00:21:16,800 --> 00:21:17,000
+تربيه من فضل X تربيه من فضل X تربيه من فضل X تربيه
+
+253
+00:21:17,000 --> 00:21:19,360
+تربيه من فضل X تربيه من فضل X تربيه من فضل X تربيه
+
+254
+00:21:19,360 --> 00:21:23,240
+من فضل
+
+255
+00:21:23,240 --> 00:21:26,460
+X تربيه
+
+256
+00:21:26,460 --> 00:21:26,480
+من
+
+257
+00:21:34,750 --> 00:21:40,530
+بس هنأول لاقينا حل لما Alpha موجبة هي بتعطينا طبعا
+
+258
+00:21:40,530 --> 00:21:48,290
+D بساوي plus minus Alpha X هي عادي تساوي صفر D
+
+259
+00:21:48,290 --> 00:21:51,730
+plus Alpha X بتساوي Zero اذا D بتساوي minus Alpha
+
+260
+00:21:51,730 --> 00:21:56,250
+X او D minus Alpha X بتساوي Zero زمان معناها D بال
+
+261
+00:21:56,250 --> 00:21:59,170
+X بتساوي Alpha X
+
+262
+00:22:26,470 --> 00:22:31,030
+الحل تبعهم زى ما كنتوا شايفين دي ال X على X بتساوي
+
+263
+00:22:31,030 --> 00:22:36,450
+Alpha X أقسم على X و بضرب في DX فهتكون DX على X
+
+264
+00:22:36,450 --> 00:22:41,350
+بتساوي Alpha DX تكامل هي اللي لناوهي هتكون ال X
+
+265
+00:22:41,350 --> 00:22:45,370
+فهتكون لن X زائد Alpha X زائد some constant لتسهيل
+
+266
+00:22:45,370 --> 00:22:50,690
+اللي بناخده لن ال A1 لتسهيل فهتكون عندي لن ال X
+
+267
+00:22:50,690 --> 00:22:55,650
+على A1 بتساوي Alpha X اخد ال exponential هتكون X
+
+268
+00:22:55,650 --> 00:22:59,190
+بتساوي A1 E to the Alpha of X لما ناخد ال Alpha
+
+269
+00:22:59,190 --> 00:23:02,190
+سالبة هيكون ال solution التاني ال complete
+
+270
+00:23:02,190 --> 00:23:06,520
+solution المجموعة التانيةمجموعة لما Alpha قدامها
+
+271
+00:23:06,520 --> 00:23:09,840
+إشارة موجبة و لما تكون قدامها إشارة سابقة حتى إن X
+
+272
+00:23:09,840 --> 00:23:13,500
+بيتساوية A1 E to the Alpha X زي إتنين E to the
+
+273
+00:23:13,500 --> 00:23:18,260
+minus Alpha X تمام هذا ال solution لسه مقاله نقص
+
+274
+00:23:18,260 --> 00:23:21,620
+لأن A1 و A2 مقالهم مش عارفينهم و أين بنتجيبهم ال
+
+275
+00:23:21,620 --> 00:23:27,920
+boundary condition عند X equal 0 و عند X equal A X
+
+276
+00:23:27,920 --> 00:23:32,720
+equal B عند X equal 0 و X equal B و احنا عيلنا
+
+277
+00:23:32,720 --> 00:23:36,380
+قيامهمعند X يبقى نحياتهم أنا حاططهم في الأعلى عشان
+
+278
+00:23:36,380 --> 00:23:41,140
+أستخدمها عند X equals 0 بتساوي 0 وعند X برضه
+
+279
+00:23:41,140 --> 00:23:46,640
+بتساوي D بها تساوي 0 معوض عند X equals 0 ال
+
+280
+00:23:46,640 --> 00:23:53,300
+potential بيساوي 0طبعا انا بقعد اكتب ال E to the X
+
+281
+00:23:53,300 --> 00:23:57,960
+و E to the minus X لكي
+
+282
+00:23:57,960 --> 00:24:00,200
+انا اعرف كيف يتصرف ال sin hyperbolic و ال cos
+
+283
+00:24:00,200 --> 00:24:04,080
+hyperbolic فبقعد اكتب ال solution هذا بها الطريقة
+
+284
+00:24:04,080 --> 00:24:07,920
+B1 cos hyperbolic Alpha X زي B2 sin hyperbolic
+
+285
+00:24:07,920 --> 00:24:11,540
+Alpha X لان دولة مربوطين ال cosine هي أفعل عن E to
+
+286
+00:24:11,540 --> 00:24:15,350
+the Alpha Xزائد e to the minus alpha x على اتنين
+
+287
+00:24:15,350 --> 00:24:18,950
+ال sine hyperbolic e to the alpha x minus e to the
+
+288
+00:24:18,950 --> 00:24:22,250
+minus alpha x على اتنين اذا بعض رعيات ساعدتهم على
+
+289
+00:24:22,250 --> 00:24:23,970
+شكل ال cosine hyperbolic و ال cosine hyperbolic
+
+290
+00:24:23,970 --> 00:24:28,430
+and x equals zero قلنا لو بتنشاش بيساوي zero اعود
+
+291
+00:24:28,430 --> 00:24:37,130
+x zero ال sine ال zero زيرولكن cosh0 هو 1 وcosh0
+
+292
+00:24:37,130 --> 00:24:40,870
+هو 1 وcosh0 هو 0 فما يبقى بيدي بيدي بيدي بيدي واحد
+
+293
+00:24:40,870 --> 00:24:44,210
+في واحد زائد زيرون فبيدي بيدي واحد زائد زائد زيرون
+
+294
+00:24:44,210 --> 00:24:46,030
+واحد في واحد زائد زائد زيرون فبيدي بيدي بيدي واحد
+
+295
+00:24:46,030 --> 00:24:52,950
+في واحد زائد زائد زيرون فبيدي بيدي بيدي واحد في
+
+296
+00:24:52,950 --> 00:24:55,650
+واحد زائد زائد زائد زيرون فبيدي بيدي بيدي واحد في
+
+297
+00:24:55,650 --> 00:25:02,470
+واحد زائد زائد زائد زائد زائد زائد زائد زائ
+
+298
+00:25:02,840 --> 00:25:05,920
+Sin hyperbolic αb بb2
+
+299
+00:25:10,340 --> 00:25:13,920
+عنا Alpha لا تساو Zero احنا اختارناها و قولنا رقم
+
+300
+00:25:13,920 --> 00:25:17,440
+مش قولنا Lambda مش لازمة تساو Zero قولنا Lambda لا
+
+301
+00:25:17,440 --> 00:25:21,420
+تساو Zero minus Alpha تربيع حاجة تربيعية ضربناها
+
+302
+00:25:21,420 --> 00:25:24,700
+تساو عشان نقولها قيمتها سالبة و بيستحيل تكون Zero
+
+303
+00:25:24,700 --> 00:25:29,000
+لان هو طول الضلة تبع ال waveguide بتاعتنا اذا مين
+
+304
+00:25:29,000 --> 00:25:32,820
+لازم يساو صفر؟ B2 اذا هذا مش لازم يساو صفر لا ال
+
+305
+00:25:32,820 --> 00:25:34,220
+Alpha صفر ولا ال B صفر
+
+306
+00:25:42,230 --> 00:25:45,850
+لازم لامدة لا تكون zero ولا تكون سالبة لازم تكون
+
+307
+00:25:45,850 --> 00:25:50,130
+موجبة لذا باخد الحل الصحيح ليه لامدة أكبر من صفر
+
+308
+00:25:50,130 --> 00:25:53,970
+لامدة مثلا ناخدها بي تربيع ليش ناخد بي تربيع كمرة
+
+309
+00:25:53,970 --> 00:25:58,800
+عشان أكد انها موجبةأيش هيكون عندى؟ x double prime
+
+310
+00:25:58,800 --> 00:26:01,940
+زي قدرية تربيع x بالساوية zero نفس الخطوات اللى
+
+311
+00:26:01,940 --> 00:26:04,660
+عملناهم دي تربيع زي قدرية تربيع ال x بالساوية zero
+
+312
+00:26:04,660 --> 00:26:09,860
+معناه دي ال x بتساوية plus minus j beta x فده ايش
+
+313
+00:26:09,860 --> 00:26:14,860
+هتصير؟ هنا
+
+314
+00:26:14,860 --> 00:26:18,620
+كانت الحالة اللي بيقوله minus alpha تربيت اتخيل لو
+
+315
+00:26:18,620 --> 00:26:20,280
+حاطينها بال minus plus
+
+316
+00:26:27,460 --> 00:26:32,900
+يعني هاي x double prime سواء minus beta تربيع x ال
+
+317
+00:26:32,900 --> 00:26:38,200
+minus هي اللي بتجيبنا ال plus minus في ال j واضح؟
+
+318
+00:26:38,200 --> 00:26:41,900
+لأ أسوأ أخدنا يعني طريقة تانية اللي هي الفرق بين
+
+319
+00:26:41,900 --> 00:26:46,620
+المراتبعين second derivative هترسميها ان x prime
+
+320
+00:26:46,620 --> 00:26:51,940
+هتساوي plus minus j beta x
+
+321
+00:26:58,060 --> 00:27:01,860
+هذه حلها بشكل either cos sin او e to the j beta x
+
+322
+00:27:01,860 --> 00:27:06,200
+minus g beta x يعني لو حلنا ال plus هتعطينا اللي
+
+323
+00:27:06,200 --> 00:27:09,340
+هي a to the j beta x ال minus هتعطينا a to the
+
+324
+00:27:09,340 --> 00:27:13,760
+minus j beta x فال total solution مجموع اتنين او
+
+325
+00:27:13,760 --> 00:27:19,200
+اكتبه بشكل cos و sin x في x بيساوي g zero cos beta
+
+326
+00:27:19,200 --> 00:27:23,520
+x زي g واحد sin beta x اذا بتذكرين ال cos مالها e
+
+327
+00:27:23,520 --> 00:27:28,570
+to the j beta xالـ plus e to the minus j beta x
+
+328
+00:27:28,570 --> 00:27:34,150
+على 2 الـ sine لـ beta x e to the j beta x minus e
+
+329
+00:27:34,150 --> 00:27:38,810
+to the minus j beta x على 2j هل تذكرين هذا الحكي؟
+
+330
+00:27:38,810 --> 00:27:42,090
+لنعود إلى الـboundary condition يعني x equal 0
+
+331
+00:27:42,090 --> 00:27:47,650
+بتنشر بسوء 0, j بتعمل 0 ماله؟ 1, sine of 0؟ 0 هذا
+
+332
+00:27:47,650 --> 00:27:50,510
+الصفر ال term تظهر عندي ال j node, لذا ال j node
+
+333
+00:27:50,510 --> 00:27:55,360
+هي الصفرلما اعود هذا مضروف في صفر خلاص Zero هذا
+
+334
+00:27:55,360 --> 00:27:59,680
+الرقم راح يظل عنده صفر ايش بتساوي G0 اذا G0
+
+335
+00:27:59,680 --> 00:28:03,300
+بتساوي صفر اذا هذا ال term كله راح لانه مضروف في
+
+336
+00:28:03,300 --> 00:28:07,460
+Zero يظل عند X ال X ايش بتساوي J1 Sine Beta X ال
+
+337
+00:28:07,460 --> 00:28:09,420
+term التاني و ان ال value of condition تاني عالمين
+
+338
+00:28:09,420 --> 00:28:15,920
+عند X equal B بده يكون potential Zero اذا عند Sine
+
+339
+00:28:15,920 --> 00:28:23,730
+Beta B في J1 هذا لازم يساوي صفر تمامجواحد مش لازم
+
+340
+00:28:23,730 --> 00:28:29,010
+تساوي صفر هذه مش لازم تساوي صفر اذا معناه ال sign
+
+341
+00:28:29,010 --> 00:28:33,030
+بقدر اقول انه بيساوي صفر عند قيم محددة وقت ايش
+
+342
+00:28:33,030 --> 00:28:36,490
+بيكون ال sign بيساوي صفر لما تكون beta b بتساوي
+
+343
+00:28:36,490 --> 00:28:40,810
+مالها multiples of pi يعني لا ال beta تكون zero
+
+344
+00:28:40,810 --> 00:28:44,470
+ولا ال b zero لكن ال multiples تبعهم حصل ضربهم
+
+345
+00:28:44,470 --> 00:28:49,970
+بساويmultiples of B يعني multiply B و Beta في B
+
+346
+00:28:49,970 --> 00:28:54,630
+إذا كانوا multiples of B هيكون صينهم بساوة صفر
+
+347
+00:28:54,630 --> 00:28:57,550
+وبالتالي بتحقق ال boundary condition بتاعي بدون ما
+
+348
+00:28:57,550 --> 00:29:00,690
+أشبر ال Beta تكون صفر أو ال B تكون صفر ال sign
+
+349
+00:29:00,690 --> 00:29:05,630
+تبعهم اللي Zero هذا بيعطينا قيمة مين Beta لأن بيه
+
+350
+00:29:05,630 --> 00:29:09,370
+احنا عارفين هل هو طول المتوازن الأطلع ف Beta ايش
+
+351
+00:29:09,370 --> 00:29:15,650
+هتساور من B على Bهي بس تذكير هذه ال cosine
+
+352
+00:29:15,650 --> 00:29:18,290
+hyperbolic و ال sine hyperbolic ال cosine ال
+
+353
+00:29:18,290 --> 00:29:21,710
+hyperbolic عند ال zero بيساوي واحد ال sine
+
+354
+00:29:21,710 --> 00:29:25,610
+hyperbolic عند ال zero بيساوي zero لكن ال sine و
+
+355
+00:29:25,610 --> 00:29:28,810
+ال cosine هى شكلهم اذا انتوا مش ملاقينهم هى ال
+
+356
+00:29:28,810 --> 00:29:32,010
+sine و ال cosine بس بتكون shift مع ال sine اللى هى
+
+357
+00:29:32,010 --> 00:29:38,050
+بتبدأ من ال zero عند ال واحد، واضح؟ اذا نقول لها
+
+358
+00:29:38,050 --> 00:29:42,470
+ان بيتا ايش هتساوي nb على npi على b و n أرقام من
+
+359
+00:29:42,470 --> 00:29:47,790
+واحد ل infinityإذا X لأنه في X ايش بتساوي جي أن
+
+360
+00:29:47,790 --> 00:29:51,870
+بطلت يعني مجرد constant إحنا عندنا عدد لنهائي من
+
+361
+00:29:51,870 --> 00:29:56,290
+الحلول إحنا قولنا إن X ال X صفت مين جي واحد sign
+
+362
+00:29:56,290 --> 00:30:01,590
+ال beta X ولاقينا إنه beta بقدر تشتبها في دلالة ال
+
+363
+00:30:01,590 --> 00:30:07,050
+N باي على بي فإذا عندي أنا عدد لنهائي من الحلول
+
+364
+00:30:07,050 --> 00:30:12,820
+عند N واحد وانت نين وانت تلاتة فبقول إن ال Xالـ A
+
+365
+00:30:12,820 --> 00:30:19,700
+يعني sub script N بتسوى GN sin N by X على B و Beta
+
+366
+00:30:19,700 --> 00:30:24,860
+تربية بتسوى N تربيع بY تربيع على B تربيع اللي هي
+
+367
+00:30:24,860 --> 00:30:31,060
+Lambda صارت عندنا الحل تبع X بالـ N معروف مافيش
+
+368
+00:30:31,060 --> 00:30:35,340
+ايشي مجهول عندنا الى مين ال GN لسه هنجيب قمةها
+
+369
+00:30:35,340 --> 00:30:41,230
+الحاجة التانية لازم حل مين لل Yالـ y''ما نسبت
+
+370
+00:30:41,230 --> 00:30:45,890
+تربيع y بالساوة zero هتعطينا ان y'' بالساوة beta
+
+371
+00:30:45,890 --> 00:30:53,050
+تربيع y وبالتالي هيكون عندى قيمة ال y عشان ال
+
+372
+00:30:53,050 --> 00:30:57,270
+cosine hyperbola و ال cosine hyperbola بستخدم
+
+373
+00:30:57,270 --> 00
+
+401
+00:33:20,810 --> 00:33:25,630
+واحدة في حياتكم تحلوا السؤال للاخر اللي أنا
+
+402
+00:33:25,630 --> 00:33:26,910
+شرحتلكم يعني
+
+403
+00:33:33,720 --> 00:33:41,020
+طبعا هذه كمان اللي هي لو كنا في .. لو كان أنا عندي
+
+404
+00:33:41,020 --> 00:33:44,580
+ال potential  مالَه في ال cylindrical coordinate نفس
+
+405
+00:33:44,580 --> 00:33:49,760
+الفكرة أو في ال spherical coordinate بيكون عندي ال
+
+406
+00:33:49,760 --> 00:33:50,200
+potential
+
+407
+00:33:53,370 --> 00:33:58,010
+بدأ اعترف أول حاجة أنه أنا بقدر افصل الاعتمادية
+
+408
+00:33:58,010 --> 00:34:00,710
+بتاعة ال raw و ال fi و ال z على بعض يعني بقدر أكتب
+
+409
+00:34:00,710 --> 00:34:04,770
+ال potential ع شكل r في raw في fi في z في هاي
+
+410
+00:34:04,770 --> 00:34:08,950
+الأسئلة اللي ممكن تجيكم يعني برجع بعوض هنا لما
+
+411
+00:34:08,950 --> 00:34:12,230
+أفاض بالنسبة ل raw ال fi و ال z مقالهم constant
+
+412
+00:34:12,230 --> 00:34:16,070
+بالنسبة ل raw فبطلعوا برا تفاضل بيصير اللي fi z
+
+413
+00:34:16,070 --> 00:34:19,190
+على raw d by d raw بيصير exact differential mean
+
+414
+00:34:19,190 --> 00:34:23,800
+لل r ال term التاني باعتمد على الـ phi فبطلع مين
+
+415
+00:34:23,800 --> 00:34:28,120
+عندي ال R و ال Z بتبقى اللي هي الاعتماد هي على ال
+
+416
+00:34:28,120 --> 00:34:31,860
+phi ال term التالت ال R و ال phi constant بالنسبة
+
+417
+00:34:31,860 --> 00:34:36,260
+ل Z فببقى عندي D تنين Z و بعدي Z تربيع لو قسمت على
+
+418
+00:34:36,260 --> 00:34:40,020
+ال potential اللي هي مين R في Phi في Z فهذا ال
+
+419
+00:34:40,020 --> 00:34:43,400
+term بتقل منه S بتروح ل Phi و Z ببقى 1 على R
+
+420
+00:34:47,770 --> 00:34:51,770
+هنا لما أقسم هتظهر ال file وهنا لما أقسم مين هتظهر
+
+421
+00:34:51,770 --> 00:34:57,670
+ال zip نفس الحاجة لو أنا حطيت الاعتمادية على z على
+
+422
+00:34:57,670 --> 00:35:01,870
+الطرف الثاني من المعادلة بقول إنه مجموع الاعتمادية
+
+423
+00:35:01,870 --> 00:35:05,150
+على ال R أو ال R function تفاضله بال second
+
+424
+00:35:05,150 --> 00:35:08,550
+derivative لل R زائد second derivative لل Phi ايش
+
+425
+00:35:08,550 --> 00:35:13,410
+بتساوي ال second derivative لل Z معناه لا يعتمدوا
+
+426
+00:35:13,410 --> 00:35:17,350
+على بعض الناتج لازم يكون constant هناخده معينة
+
+427
+00:35:17,350 --> 00:35:22,380
+أصلًا ده تربيع هيك محل هاي الجزء من المعادلة لو 1 ع
+
+428
+00:35:22,380 --> 00:35:28,480
+Z D 2 Z by D Z تربيع بتساوي لامدا تربيع ها هي الحل
+
+429
+00:35:28,480 --> 00:35:33,380
+ع شكل cosine هبقى بيبقى لجزء الثاني من المعادلة
+
+430
+00:35:33,380 --> 00:35:37,940
+اللي هو ال 10 ما تبقى اللي هو عبارة عن مين 1 ع رو
+
+431
+00:35:37,940 --> 00:35:40,560
+R D by D رو رو D R by D رو
+
+432
+00:35:44,380 --> 00:35:53,920
+و إذا ضربت في مين في R سيصبح واحد على رو D by D رو
+
+433
+00:35:53,920 --> 00:35:59,100
+رو D R by D رو زائد R على رو تربيع على فاي D تنين
+
+434
+00:35:59,100 --> 00:36:06,640
+فاي تربيع فاي تربيع بيصير plus lambda تربيع R أو 
+
+435
+00:36:06,640 --> 00:36:07,280
+حتى ال R
+
+436
+00:36:26,390 --> 00:36:31,730
+ال term الأولاني Z بيصير عشان كوساين هبرب كوساين هبربرك
+
+437
+00:36:31,730 --> 00:36:36,030
+ال term الثاني بيعطينا هذه المعادلة كمان لو أنا
+
+438
+00:36:36,030 --> 00:36:39,310
+حاطيتها دول على طرف اللي بيتمدوا على ال raw و
+
+439
+00:36:39,310 --> 00:36:42,450
+الطرف الثاني نقلته minus 1 على فا دي تنين فا
+
+440
+00:36:42,450 --> 00:36:47,890
+تربيع بقدر أقول إن الاعتمادية على ال raw بتساوي
+
+441
+00:36:47,890 --> 00:36:51,230
+الاعتمادية على ال فا إذا معناه ماله التنين
+
+442
+00:36:51,230 --> 00:36:56,670
+constant بتساوي ميو تربيع إذا نفعد هذا ال term هذا
+
+443
+00:36:56,670 --> 00:37:01,460
+المعادلة اللي دي فا تربيع D2 5 by D5 تربيع تسوي من
+
+444
+00:37:01,460 --> 00:37:05,320
+ميو تربيع 5 تسوي من ميو تربيع 0 هذه حالها برضه
+
+445
+00:37:05,320 --> 00:37:08,820
+معروفة عشان الكوسين والصين بيظل عند المعادلة اللي
+
+446
+00:37:08,820 --> 00:37:12,960
+بتعتمد على مين على ال رو رو تربيع D2 R by D رو
+
+447
+00:37:12,960 --> 00:37:18,120
+تربيع لو ضربنا في ال R زائد رو DR by D رو plus
+
+448
+00:37:18,120 --> 00:37:24,600
+لمدة تربيع Row تربيع minus Mu تربيع كل مضروب R
+
+449
+00:37:24,600 --> 00:37:28,880
+بساوة Zero هذه المعادلة معادلة مشهورة لازم تحفظوا
+
+450
+00:37:28,880 --> 00:37:32,520
+شكلها اسمها Bessel differential equation مرقت
+
+451
+00:37:32,520 --> 00:37:38,420
+عليكم بيسل ال equation؟ أخدتوا communication؟ يعني
+
+452
+00:37:38,420 --> 00:37:40,560
+مسحبكم ولم يمرقتوا عليكم بيسل بال communication
+
+453
+00:37:40,560 --> 00:37:47,490
+لازم تكون مرقت عليكم بيسل المعادلات المشهورةبشكلها
+
+454
+00:37:47,490 --> 00:37:52,590
+موضح ومعروف للرياضيين والمهندسين وغيرهم من اللي هي
+
+455
+00:37:52,590 --> 00:37:55,990
+applied sciences بيستخدموها على طول و بيقولوا إن
+
+456
+00:37:55,990 --> 00:38:00,890
+solution أو حلها معروف موجود في ال tables اللي هو
+
+457
+00:38:00,890 --> 00:38:03,810
+mean Bessel function هذه المعادلة اسمها Bessel
+
+458
+00:38:03,810 --> 00:38:08,390
+equation وحلها اسمه Bessel function هذا هو المطلوب
+
+459
+00:38:08,390 --> 00:38:11,990
+منكم بتتفلق ال cylindrical coordinate ال
+
+460
+00:38:11,990 --> 00:38:16,930
+cylindrical coordinate جربوا هيك تلعبوادلتر بيه V
+
+461
+00:38:16,930 --> 00:38:20,030
+بتساوي Zero كيف بتكون شكلها بالـ spherical
+
+462
+00:38:20,030 --> 00:38:25,250
+coordinate نغلق
+
+463
+00:38:25,250 --> 00:38:28,810
+ال resistance و ال capacitance احنا تعلمنا أشياء
+
+464
+00:38:28,810 --> 00:38:34,750
+كثير خلال المحاضرات الماضية تعلمنا إنه بنكتب ال
+
+465
+00:38:34,750 --> 00:38:38,740
+potential بدلالة ال electric field بتساوي التكامل
+
+466
+00:38:38,740 --> 00:38:42,680
+ل E ضد DL و ال current تعلمنا إنه عبارة عن ال
+
+467
+00:38:42,680 --> 00:38:46,520
+clause integral ل J ضد DS و مين هي J قلنا هي sigma
+
+468
+00:38:46,520 --> 00:38:50,820
+E اللي هي ال point form ل Ohm's law J بتساوي sigma
+
+469
+00:38:50,820 --> 00:38:53,980
+E إذا ال potential اللي هو بيساوي ال integral ل E
+
+470
+00:38:53,980 --> 00:38:57,200
+ضد DL و ال current اللي هو ال clause integral ل J
+
+471
+00:38:57,200 --> 00:39:01,420
+ضد DS أو sigma E ضد DS بقدر أستعين فيهم عشان أحسب
+
+472
+00:39:01,420 --> 00:39:05,280
+المقاومة لل element اللي أنا بدرسه عمري أو ال
+
+473
+00:39:05,280 --> 00:39:09,940
+waveguide اللي أنا بدرسها R بيساوي V على I Ohm's
+
+474
+00:39:09,940 --> 00:39:13,680
+law بيساوي ال integral ل E ضد DL على ال close
+
+475
+00:39:13,680 --> 00:39:19,870
+integral ل sigma E ضد DS أول خطوة أنا دائما هي إن
+
+476
+00:39:19,870 --> 00:39:23,190
+أختار ال coordinate المناسب إذا أنا بحكي على
+
+477
+00:39:23,190 --> 00:39:25,750
+متوازي أطلع إذا كارتيش ال coordinate بحكي على
+
+478
+00:39:25,750 --> 00:39:27,890
+cylindrical و cylindrical coordinate بحكي على سفير
+
+479
+00:39:27,890 --> 00:39:31,890
+و سفير ك coordinate Assume V0 as a potential
+
+480
+00:39:31,890 --> 00:39:35,110
+difference between conductor terminal ال conductor
+
+481
+00:39:35,110 --> 00:39:39,810
+تبعي أسوأ هو cylindrical ولا متوازي أطلع ولا سفير
+
+482
+00:39:39,810 --> 00:39:43,450
+هو بده يكون ال potential difference بين طرفي ال
+
+483
+00:39:43,450 --> 00:39:48,630
+conductor بنحل ال plus equation ل V لأن جيب V احنا
+
+484
+00:39:48,630 --> 00:39:54,770
+بعد إن ال V بقدر أجيب اللي هو E E بتساوي minus دل
+
+485
+00:39:54,770 --> 00:39:59,010
+ال V إذا جيبت ال E بقدر أجيب مين ال current لأن ال
+
+486
+00:39:59,010 --> 00:40:01,170
+current مش بتساوي ال close integral ل Sigma E دول
+
+487
+00:40:01,170 --> 00:40:06,290
+DS جيبنا V جيبنا ال current إذا بجيب المقاومة اللي
+
+488
+00:40:06,290 --> 00:40:10,690
+هتساوى V node على R اللي هو الفرق
+
+489
+00:40:14,880 --> 00:40:20,900
+هو ال current واضح احنا
+
+490
+00:40:20,900 --> 00:40:25,440
+بنعرف الفرق بين طرفي ال conductors لو مثلا هي عندي
+
+491
+00:40:25,440 --> 00:40:30,820
+أنا المكثف مثلا هي plus Q minus Q و عندي بطارية هي
+
+492
+00:40:30,820 --> 00:40:36,040
+الطرف الموجب هو الطرف الثالث هذا الـ conductor واحد
+
+493
+00:40:36,040 --> 00:40:39,460
+اللي هو موصول بي الـ positive charges و أطراف
+
+494
+00:40:39,460 --> 00:40:45,440
+السالبة هي واحد واتنين V هي فرق الجهد بين واحد
+
+495
+00:40:45,440 --> 00:40:50,880
+واتنين V هي فرق الجهد بين واحد واتنين اتجاه ال
+
+496
+00:40:50,880 --> 00:40:54,640
+electric field من موجب للسالب و V اللي هو فرق الجهد
+
+497
+00:40:54,640 --> 00:40:58,600
+بين الأول ومينوس الثاني اللي هو ايش بيساوي سالب ال
+
+498
+00:40:58,600 --> 00:41:06,810
+Integral 2 ل 1 E Dot R الـ notation طبعا، إذا V1-V2
+
+499
+00:41:06,810 --> 00:41:13,610
+يسمى minus ال integral من 2 ل 1 E dot DL واضح؟
+
+500
+00:41:13,610 --> 00:41:18,150
+المكثف،
+
+501
+00:41:18,150 --> 00:41:22,490
+المكثف عبارة عن ميلي Q على V و Q من Gauss Law
+
+502
+00:41:22,490 --> 00:41:27,030
+بيساوي Epsilon ال close integral ل E dot DS و ال
+
+503
+00:41:27,030 --> 00:41:29,650
+potential ما احنا عارفينه ال integral ل E dot DL
+
+504
+00:41:34,750 --> 00:41:42,410
+هم كيف احصل على C؟ أول حاجة بفترض وجود Q و بقرر
+
+505
+00:41:42,410 --> 00:41:50,510
+قد ايش قيمة V in terms of Q إن بحل مين يعصله أو إن
+
+506
+00:41:50,510 --> 00:41:55,670
+أول حاجة بفترض V و بقرر cube دلالة V بحل إن مين
+
+507
+00:41:55,670 --> 00:42:03,000
+لبلاس equation يعني يا ببدأ ب Q و بحل V دلالة Q أو
+
+508
+00:42:03,000 --> 00:42:07,420
+ببدأ فرضية إنه عندي V و بحل ال cube دلالة V
+
+509
+00:42:07,420 --> 00:42:15,680
+باستخدام ال plasic equations طبعا
+
+510
+00:42:15,680 --> 00:42:18,840
+معناه هيك إن دائما لازم أختار ال suitable
+
+511
+00:42:18,840 --> 00:42:21,980
+coordinate system إذا بنحكي على متوازق أطلع و
+
+512
+00:42:21,980 --> 00:42:24,200
+أختار ال Cartesian و ال cylindrical باختار ال
+
+513
+00:42:24,200 --> 00:42:28,470
+cylindrical بختار الـ spherical و بعدين بختار two
+
+514
+00:42:28,470 --> 00:42:31,250
+conducting plates carrying charges plus q و minus
+
+515
+00:42:31,250 --> 00:42:34,630
+q يعني هدول inherited يعني احنا لما نقول كيف احصل
+
+516
+00:42:34,630 --> 00:42:38,630
+على c already أنا بقول لازم أختار coordinate صحيح
+
+517
+00:42:38,630 --> 00:42:41,950
+و عندي هيكون two plates واحد موجب واحد سالب هي
+
+518
+00:42:41,950 --> 00:42:45,990
+معناه إن احصل على c ولا لأ و بعدين يا بفرض q و بحل
+
+519
+00:42:45,990 --> 00:42:53,730
+v بدلالة q يا بفرض ال v و بحل q بدلالة v طيب
+
+520
+00:42:55,550 --> 00:42:58,550
+إذا قلنا بنختار الـ coordinate المناسب to
+
+521
+00:42:58,550 --> 00:43:03,270
+conducting plates بستخدم Gauss law أو Coulombs law
+
+522
+00:43:03,270 --> 00:43:07,350
+عشان أحسب E و منها بحسب V و بعدين بقدر أحسب C
+
+523
+00:43:07,350 --> 00:43:14,210
+بيبسوق U على V هاي مثال، أسهل مثال هو البرر بلاي
+
+524
+00:43:14,210 --> 00:43:18,090
+الكاباستور لأنه أخذنا .. لما أخذنا ال Gauss law
+
+525
+00:43:18,090 --> 00:43:20,830
+جبنا ال electric field تبع البرر بلاي الكاباستور
+
+526
+00:43:21,770 --> 00:43:25,650
+واحد من الـ plates قاعد عند x equal 0 و الـ plate الثاني
+
+527
+00:43:25,650 --> 00:43:30,870
+قاعد عند مين x equal d الموجب عند x equal d و
+
+528
+00:43:30,870 --> 00:43:34,410
+السالب إنه x equal 0 و بين ال two blades في عندنا
+
+529
+00:43:34,410 --> 00:43:38,450
+dielectric media اللي هي y و المساحة بتاعة كل
+
+530
+00:43:38,450 --> 00:43:42,910
+blade يعني هدول زي دفترين دفتر فوق و دفتر تحت
+
+531
+00:43:42,910 --> 00:43:46,650
+المساحة بتاعة كل دفتر هي S هي ال blades
+
+532
+00:43:49,680 --> 00:43:52,960
+Rho S اللي هي charge density على كل surface من
+
+533
+00:43:52,960 --> 00:43:56,700
+هدول ال plates Q على S ال total charge على مساحة
+
+534
+00:43:56,700 --> 00:44:03,260
+بتاعة ال plate اللي هي S و D عبارة عن minus rho S
+
+535
+00:44:03,260 --> 00:44:07,180
+X hat اتجاهها هي اتجاه ال electric field من موجب
+
+536
+00:44:07,180 --> 00:44:10,760
+لسالب و اتجاهه وين يعني معناه في ال minus X
+
+537
+00:44:10,760 --> 00:44:16,200
+direction و هذا ينجزله إنه D إن ال close انتقلة D
+
+538
+00:44:16,200 --> 00:44:20,900
+ضد DS بتساوي من الـ closed الـ Q الـ Q اللي هي مين؟
+
+539
+00:44:20,900 --> 00:44:26,160
+رو أس في أس تروح الأس من الطرفين و تظهر إن D
+
+540
+00:44:26,160 --> 00:44:30,560
+بيساوي minus رو أس except بسبب احنا الاتجاه تبع
+
+541
+00:44:30,560 --> 00:44:34,440
+ال D باتجاه ال minus X E عبارة عن مين؟ D على
+
+542
+00:44:34,440 --> 00:44:39,380
+إبسيلون هي رو أس على إبسيلون في اتجاه الثالث X
+
+543
+00:44:39,380 --> 00:44:45,600
+إبسيلون هي الـ dielectric ما بين ال two plates لو
+
+544
+00:44:45,600 --> 00:44:49,520
+بدي أكتبها دلت الـ Q و الـ S رو S شبه رعمين الـ Q على
+
+545
+00:44:49,520 --> 00:44:54,260
+S فإذا عندي ال electric field بيساوي minus Q على ي
+
+546
+00:44:54,260 --> 00:44:59,300
+S إبسيلون هي جبنا ال electric field بقدر أجيب ال
+
+547
+00:44:59,300 --> 00:45:04,680
+potential أنا لازم عشان أجيب ال C ال potential و Q
+
+548
+00:45:04,680 --> 00:45:07,300
+عرفت إن ال electric field بقدر أجيب ال potential
+
+549
+00:45:07,300 --> 00:45:10,940
+و بالتالي بقدر أجيب ال C ال potential ايش أنا
+
+550
+00:45:10,940 --> 00:45:17,070
+بيساوي minus ال integral من 2 ل 1 D بال DL رحمكم الله
+
+551
+00:45:17,070 --> 00:45:21,330
+احنا قلنا ال electric field بيروح من واحد لاتنين
+
+552
+00:45:21,330 --> 00:45:23,970
+ال notation تبعنا اللي موجب للثالث إذا ما في ايش
+
+553
+00:45:23,970 --> 00:45:29,710
+بيساوي minus ال integral من تنين لواحد E دول DL من
+
+554
+00:45:29,710 --> 00:45:35,290
+وين يعني؟ ايه بقى تنين اللي هي zero و واحد اللي
+
+555
+00:45:35,290 --> 00:45:40,550
+هي دي إذا أنت كامل ال X من وين طبعا DL هي DX هتكون
+
+556
+00:45:40,550 --> 00:45:45,670
+X hat و ال E اللي هو minus Q على Y أس X hat بالتالي
+
+557
+00:45:45,670 --> 00:45:50,430
+هيكون عندي .. بالنسبة لي ال Q و ال إبسيلون S constant
+
+558
+00:45:50,430 --> 00:45:55,830
+بالنسبة لي DX هيكون Q على إبسيلون S و ال DX بكملها من
+
+559
+00:45:55,830 --> 00:46:00,350
+0 ل D يعني قيمتها D إذا V عبارة عن Q على إبسيلون S في
+
+560
+00:46:00,350 --> 00:46:07,210
+D أو ببساطة هي A في D إذا C ايش بنفسه؟ إذا ما عرفين
+
+561
+00:46:07,210 --> 00:46:12,530
+ال potential و عارفين ال Q ال Q على V هي عبارة عن C
+
+562
+00:46:13,100 --> 00:46:17,740
+إذا الـ Q على V بيبقى ثوي Y أس على D بتعرفوا ايه
+
+563
+00:46:17,740 --> 00:46:22,820
+الـ Y على D؟ إن كثافة المكثفة برا الـ Plates
+
+564
+00:46:22,820 --> 00:46:26,680
+بيعتمد على الـ dielectric media اللي بين الـ Two
+
+565
+00:46:26,680 --> 00:46:31,800
+Plates المساحة المقطعية أو مساحة الـ Area تحت الـ
+
+566
+00:46:31,800 --> 00:46:37,950
+Plates و المسافة اللي بينها تمام؟ لو احنا عدنا نفس
+
+567
+00:46:37,950 --> 00:46:41,890
+التجربة و جيبنا C لما يكون ال dialectic عبارة عن
+
+568
+00:46:41,890 --> 00:46:47,690
+مين؟ عن space، هو يعني هيكون C0 بتساوي Y0 S على D
+
+569
+00:46:47,690 --> 00:46:53,470
+بقدر أجيب من ال ratio ال 6 عرفة C قياس قيمتها و
+
+570
+00:46:53,470 --> 00:46:58,410
+C0 بقدر أقول إن C على C0 هي مين؟ YR لأنها هتكون Y
+
+571
+00:46:58,410 --> 00:47:03,640
+على Y0 سي على سي نود هتكون إبسيلون على إبسيلون نود
+
+572
+00:47:03,640 --> 00:47:06,720
+اللي هي إبسيلون R و هاي اللي بيستخدموها الطريقة
+
+573
+00:47:06,720 --> 00:47:11,760
+لحساب ال dialectic constant لأي media أو relative
+
+574
+00:47:11,760 --> 00:47:16,920
+dialectic ل ال media برضه
+
+575
+00:47:16,920 --> 00:47:19,540
+بقدر أحسب ال energy stored لأنها ال energy stored
+
+576
+00
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/kG2lS7Q6L98_postprocess.srt b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/kG2lS7Q6L98_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..2ef5e43e7864f539a48061d2242e65c6af42b18b
--- /dev/null
+++ b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/kG2lS7Q6L98_postprocess.srt
@@ -0,0 +1,2380 @@
+1
+00:00:20,670 --> 00:00:23,490
+بسم الله الرحمن الرحيم السلام عليكم ورحمة الله
+
+2
+00:00:23,490 --> 00:00:26,770
+وبركاته احنا اليوم ان شاء الله هتتبع موضوعنا ال
+
+3
+00:00:26,770 --> 00:00:30,470
+boundary value problems او boundary conditional
+
+4
+00:00:30,470 --> 00:00:33,610
+problems بكيف نحسب ال potential وقولنا من ال
+
+5
+00:00:33,610 --> 00:00:36,250
+potential حسبنا يقدر نحسب ال electric field
+
+6
+00:00:38,860 --> 00:00:41,780
+المحاضرة الماضية شوفنا أمثلة اللي كان فيها ال
+
+7
+00:00:41,780 --> 00:00:44,460
+potential patented على one direction one variable
+
+8
+00:00:44,460 --> 00:00:49,000
+وحلناها بال integration اليوم هشوف مثال اللي لازم
+
+9
+00:00:49,000 --> 00:00:51,800
+احنا نستخدم ال separation of variable احنا قالنا
+
+10
+00:00:51,800 --> 00:00:54,420
+فيه طريقتين لحل أسبوع على أسبوع او بأسبوع equation
+
+11
+00:00:54,420 --> 00:00:56,700
+لإن هي الطريقة الأولى أنه يكون ال potential
+
+12
+00:00:56,700 --> 00:01:00,320
+patented على one variable نعمل integration أو أكثر
+
+13
+00:01:00,320 --> 00:01:02,940
+من variable و ساعتها بنعمل separation of variables
+
+14
+00:01:02,940 --> 00:01:08,470
+فخلنا نشوف مثال على ال separation of variablesهنا
+
+15
+00:01:08,470 --> 00:01:13,250
+المثال اللى قمامنا عبارة عن اللى هو متوازي أطلع
+
+16
+00:01:13,250 --> 00:01:18,750
+waveguide على شكل متوازي أطلع مبتده على طول انها
+
+17
+00:01:18,750 --> 00:01:24,390
+key conditions ان عند x equal 0 ال potential y
+
+18
+00:01:24,390 --> 00:01:29,990
+مابين ال 0 و ال a ال potential بساوة 0و ال wall
+
+19
+00:01:29,990 --> 00:01:36,550
+اللى عند y equal 0 و x من 0 ل b برضه بتنشه 0 و ال
+
+20
+00:01:36,550 --> 00:01:41,710
+wall اللى عند x equal b و y من 0 ل a برضه بتنشه
+
+21
+00:01:41,710 --> 00:01:47,210
+بساوي 0 ال wall اللى عند y بتساوي a و x ما بين ال
+
+22
+00:01:47,210 --> 00:01:51,250
+0 و ال b اللى بتنشه بساوي v not وماعطينا قيمة v
+
+23
+00:01:51,250 --> 00:01:55,700
+not ان هو one hundred voltوكمان قيلنا ان بي هو طول
+
+24
+00:01:55,700 --> 00:02:01,740
+المساطير المساحة المقطع على متوازى الأضلاع انه ايه
+
+25
+00:02:01,740 --> 00:02:06,560
+بتساوي 2A المطلوب بيناقل نقطة potential عند اي
+
+26
+00:02:06,560 --> 00:02:10,840
+نقطة في قلب ال with guide يعني مثلا X بتساوي A على
+
+27
+00:02:10,840 --> 00:02:17,000
+2 هي بالتمام هنا تقريبا لان قلنا بي 2A فهي A هتكون
+
+28
+00:02:17,000 --> 00:02:21,820
+A على 2 تقريبا هنا و Y تلاتة A على أربع
+
+29
+00:02:25,010 --> 00:02:28,410
+طالب ترباع A يعني somewhere هنا يعني طالب ترباع A
+
+30
+00:02:28,410 --> 00:02:32,310
+فاضح؟ اذا هو هاي المطلوب بنا ان اجيب ال potential
+
+31
+00:02:32,310 --> 00:02:38,690
+عند اي نقطة في قلب المتوازي الأطلع واضح لنا ان ال
+
+32
+00:02:38,690 --> 00:02:41,530
+potential باعتنا ده على two variables ال X وال Y
+
+33
+00:02:41,530 --> 00:02:45,390
+لكن في ال Z direction ال Z رايح لل infinity وفيش
+
+34
+00:02:45,390 --> 00:02:50,950
+اعتمادية على ال Z الاعتمادية فقط على ال X وY مافيش
+
+35
+00:02:50,950 --> 00:02:58,840
+free chargesفإذا دل التربيع V بيساوي 0 طبعا
+
+36
+00:02:58,840 --> 00:03:01,560
+احنا ال coordinate اللي قررنا واضح انه هناخد
+
+37
+00:03:01,560 --> 00:03:05,840
+Cartesian coordinate ال X و ال Y إذا هتكون الدل
+
+38
+00:03:05,840 --> 00:03:10,140
+تربيع D تربيع V by DX تربيع زي ال DT تربيع by DY
+
+39
+00:03:10,140 --> 00:03:15,460
+تربيع بتساوي 0 لإن مافيش free charges هنستخدم ال
+
+40
+00:03:15,460 --> 00:03:19,590
+last equation بمعنى أن الدل تربيع V بتساوي 0بنسمع
+
+41
+00:03:19,590 --> 00:03:21,530
+ال boundary conditions اللي احنا حكيناها مع بعض
+
+42
+00:03:21,530 --> 00:03:26,850
+انه ال potential عند x equal 0 و y مابين ال 0 و ال
+
+43
+00:03:26,850 --> 00:03:32,290
+a بساوة 0 ال potential عند x equal b و ال y من 0 ل
+
+44
+00:03:32,290 --> 00:03:37,310
+a بساوة 0 ال potential لل x مابين ال 0 و ال b و ال
+
+45
+00:03:37,310 --> 00:03:43,370
+y بساوة 0 ال potential عند x مابين ال 0 و ال b و
+
+46
+00:03:43,370 --> 00:03:46,430
+ال y بساوة a بساوة v نضد هذه هي ال boundary
+
+47
+00:03:46,430 --> 00:03:46,950
+conditions
+
+48
+00:03:49,670 --> 00:03:56,530
+بالنسبة للمشكلة مثل هذه المشكلة نحن لدينا V ملها V
+
+49
+00:03:56,530 --> 00:04:02,710
+مقلد ترميه V مستوى V وقلنا استنتجنا ان V مقلد
+
+50
+00:04:02,710 --> 00:04:11,710
+function of X وY فمعناه استنتجنا ان E تنين V X Y Y
+
+51
+00:04:11,710 --> 00:04:20,650
+D X ترميه زي E تنين Vبايتم دي و بايتم دي و بايتم
+
+52
+00:04:20,650 --> 00:04:21,290
+دي و بايتم دي و بايتم دي و بايتم دي و بايتم دي و
+
+53
+00:04:21,290 --> 00:04:29,650
+بايتم دي و بايتم دي و بايتم دي و بايتم دي و بايتم
+
+54
+00:04:29,650 --> 00:04:32,330
+دي و بايتم دي و بايتم دي و بايتم دي و بايتم دي و
+
+55
+00:04:32,330 --> 00:04:36,450
+بايتم دي و بايتم دي و بايتم دي و بايتم دي و بايتم
+
+56
+00:04:36,450 --> 00:04:39,430
+دي و بايتم دي
+
+57
+00:04:44,210 --> 00:04:48,730
+فى ال X اعتمادية على X لها تعتمد على V لها ال Y
+
+58
+00:04:48,730 --> 00:04:52,070
+عشان نقدر نقول ان هى بقدر اسمها شكل through
+
+59
+00:04:52,070 --> 00:04:57,370
+function XY X هو ال solution اللى بعتمد على X و Y
+
+60
+00:04:57,370 --> 00:05:02,950
+ال solution اللى بعتمد على Y او بقدر اسمهم VX و VY
+
+61
+00:05:02,950 --> 00:05:05,910
+فهذا ال solution اللى بقدر نضعه عشان نتأكد انه
+
+62
+00:05:05,910 --> 00:05:10,600
+اعتمد على X فهذا الاعتمادية على Vهذه الطريقة اللي
+
+63
+00:05:10,600 --> 00:05:14,380
+نسميها طريقة الـ Separation Theory انها عرفتنا ان
+
+64
+00:05:14,380 --> 00:05:18,540
+ال potential مقدر افصل اعتماديته على X عن
+
+65
+00:05:18,540 --> 00:05:23,000
+اعتماديته على Yلو ماقدرش أفصلهم بيظلوا صعيب الحل
+
+66
+00:05:23,000 --> 00:05:27,640
+بيضالا M في الدخل لكن ما أنه انا الاعتمادية اللي
+
+67
+00:05:27,640 --> 00:05:31,140
+على ال X ده تعتمد على ال Y بقدر افصل ال two
+
+68
+00:05:31,140 --> 00:05:34,780
+functions في ناس بتلاقوهم بيكسل X يعني هذا
+
+69
+00:05:34,780 --> 00:05:38,600
+potential جزء من ال solution وهذا جزء من ال
+
+70
+00:05:38,600 --> 00:05:46,500
+solution مثلا احنا في الكتاب بيستخدم X وY فماعود
+
+71
+00:05:46,780 --> 00:05:50,120
+فهذا ال potential في ال problem اللي قدامنا في ال
+
+72
+00:05:50,120 --> 00:05:53,560
+equation اللي معناه هلاحظ أنه ال term الأولاني
+
+73
+00:05:53,560 --> 00:05:58,060
+بعتمد ع مين؟ ع ال X إذا أنا هذا بس بتفاضل مرتين ال
+
+74
+00:05:58,060 --> 00:06:04,620
+Y بتطلع برا التفاضل فهيكون عندي Y لأ تعتمد ع ال X
+
+75
+00:06:04,620 --> 00:06:09,060
+و بيصير عندي exact differential مش partial اتنين ل
+
+76
+00:06:09,060 --> 00:06:14,800
+X انا متعتمدش اللي ع ال X exactزائر هنا مين ال
+
+77
+00:06:14,800 --> 00:06:18,520
+item التفاظ بالنسبة ل y الجزء اللى على ال x بيطلع
+
+78
+00:06:18,520 --> 00:06:31,080
+برا ال differentiation تمام
+
+79
+00:06:31,080 --> 00:06:36,340
+فهذا هو ال separation theorem التي شهدت جزئية
+
+80
+00:06:36,340 --> 00:06:40,660
+التانية و هي الأهم ان احنا لو قسمنا على مين على
+
+81
+00:06:40,660 --> 00:06:41,800
+Vxy
+
+82
+00:06:46,670 --> 00:06:53,570
+مين دى ال X و Y؟ X و Y يعني إيش هال بتصير؟ 1 على X
+
+83
+00:06:53,570 --> 00:06:57,370
+V2
+
+84
+00:06:57,370 --> 00:07:06,530
+من X و Y من X تقريبا زى V2 من Y و Y تقريبا
+
+85
+00:07:06,530 --> 00:07:14,330
+مابيبقوا كمين؟ واحد تمام؟
+
+86
+00:07:16,370 --> 00:07:23,990
+أسهم عندي هذا تير بساوي
+
+87
+00:07:23,990 --> 00:07:30,730
+0 يعني انا كمان بقول المعلومة التانية بقول ان
+
+88
+00:07:30,730 --> 00:07:37,030
+السفن derivative لل X ل X double prime على X زائد
+
+89
+00:07:37,030 --> 00:07:42,170
+السفن derivative لل Y على Y بتساوي 0 او بمعنى اخر
+
+90
+00:07:42,170 --> 00:07:46,700
+X double prime على X بتساوي او تساويبتساوى y
+
+91
+00:07:46,700 --> 00:07:53,120
+double prime على y إذا
+
+92
+00:07:53,120 --> 00:07:56,840
+أسمة x double prime على x بتساوى x double prime
+
+93
+00:07:56,840 --> 00:08:02,800
+على y معناه إن الناتج لا بعتمد على x ولا على y هاي
+
+94
+00:08:02,800 --> 00:08:08,340
+المعنى إذا تفاض ال x مرتين على x بتساوى تفاض ال y
+
+95
+00:08:08,340 --> 00:08:11,920
+مرتين على y معناه إن الناتج لا بعتمد على x ولا على
+
+96
+00:08:11,920 --> 00:08:17,110
+yبنسميه دايما constant lambda beta إلى أخرى زى ما
+
+97
+00:08:17,110 --> 00:08:21,290
+نشايفين على السطورة minus x double prime على x
+
+98
+00:08:21,290 --> 00:08:25,550
+اللى بتساوي y double prime على y لازم كل واحد منهم
+
+99
+00:08:25,550 --> 00:08:29,950
+يكون بساوي some constant كل واحد منهم بساوي some
+
+100
+00:08:29,950 --> 00:08:37,970
+constant احنا سميناه lambda ابتعدى
+
+101
+00:08:37,970 --> 00:08:42,030
+معادلتين على هيكي المعادلة الأولى بتقولى انه x
+
+102
+00:08:42,030 --> 00:08:42,870
+double prime
+
+103
+00:08:46,700 --> 00:08:51,820
+زائد Lambda X ساوثة والتانية بيقولي Y double prime
+
+104
+00:08:51,820 --> 00:08:58,860
+minus Lambda Y ساوثة كل واحدة منهم second order
+
+105
+00:08:58,860 --> 00:09:01,700
+differential equation يعني ال second derivative
+
+106
+00:09:01,700 --> 00:09:05,900
+differential equation اللي بقدر حلهم بسهولة زي ما
+
+107
+00:09:05,900 --> 00:09:10,420
+استخدمنا هذه ممكن شفتوها أول مرة في الدوائر في ال
+
+108
+00:09:10,420 --> 00:09:14,180
+natural response صح؟و بعدين أخدهم في الـ
+
+109
+00:09:14,180 --> 00:09:16,620
+differential في هذه المعادلات يعني هذه المعادلات
+
+110
+00:09:16,620 --> 00:09:19,340
+اللي بتوصلوا أنها معادلات سهل بالنسبالي تحلوها
+
+111
+00:09:19,340 --> 00:09:23,800
+بدون ما ننسى ال boundary conditions خليني أرجع لل
+
+112
+00:09:23,800 --> 00:09:27,120
+boundary conditions اللي كتبناهم قبل قليل و نعيد
+
+113
+00:09:27,120 --> 00:09:37,940
+كتبتهم لما نفصل ال variables نقول لذى نقطع
+
+114
+00:09:37,940 --> 00:09:42,500
+على جانب لكي نتذكر انه هي ال y وهي ال x
+
+115
+00:09:48,720 --> 00:09:52,920
+الواتنشال هنا بيساوي صفر وهنا بيساوي صفر وهنا
+
+116
+00:09:52,920 --> 00:09:56,960
+بيساوي صفر هاي الطبيب كونه طبيب هده كون ايه وهده
+
+117
+00:09:56,960 --> 00:10:02,320
+هيكون الواتنشال طبعا ال gaps احنا حكينا عنهم هيك
+
+118
+00:10:02,320 --> 00:10:06,140
+هدولها ال gaps عشان ايش يعمل insulation لان لو
+
+119
+00:10:06,140 --> 00:10:10,400
+حاطلناهم جن بعض ايش بيصير الواتنشال بتوزع بيصير يا
+
+120
+00:10:10,400 --> 00:10:15,620
+كله صفر يا كله V node اذا
+
+121
+00:10:15,620 --> 00:10:19,770
+نرجع للvaried conditionsالـ Potential عند X equals
+
+122
+00:10:19,770 --> 00:10:24,550
+0 و أي كيملة Y و
+
+123
+00:10:24,550 --> 00:10:31,550
+أي كيملة Y ما بين 0 و B، إيش Potential بتساوي 0؟
+
+124
+00:10:31,550 --> 00:10:43,830
+صح، عند X equals 0،
+
+125
+00:10:43,830 --> 00:10:56,470
+X و 1، X equals 0؟Y من الـ 0 و الـ A إذا
+
+126
+00:10:56,470 --> 00:10:59,270
+أنا عند X equal 0 و Y من الـ 0 لـ A البوتنشال
+
+127
+00:10:59,270 --> 00:11:05,070
+بيساوي 0 انهوض على البوتنشال دلوقت X و YX اله
+
+128
+00:11:05,070 --> 00:11:08,950
+function of X عند تقيمة X بتساوي 0 هاي ال boundary
+
+129
+00:11:08,950 --> 00:11:12,510
+عند هاي النقطة بالذات Y as function of Y اللي هي Y
+
+130
+00:11:12,510 --> 00:11:15,330
+قولنا من 0 ل A إيش كمية ال potential عند هذه ال
+
+131
+00:11:15,330 --> 00:11:20,170
+wall بتساوي 0 عندها الحيطة اللي هي X بتساوي 0 وY
+
+132
+00:11:20,170 --> 00:11:26,770
+ما بين ال 0 و ال A بتتشتج بساوي 0 Y من 0 ل A
+
+133
+00:11:26,770 --> 00:11:32,360
+أتوقعش مهتكون 0قيمة ال potential لكن قد يكون ال
+
+134
+00:11:32,360 --> 00:11:36,420
+potential عند نقطة محددة x at x equal 0 بسوء سفر
+
+135
+00:11:36,420 --> 00:11:42,800
+يعني هذه y as function of y فهذا function بقي سوء
+
+136
+00:11:42,800 --> 00:11:47,600
+0 اذا اللي اكيد لازم بيسوء 0 قيمة x at 0 اذا ال x
+
+137
+00:11:47,600 --> 00:11:52,420
+at 0 بتسوء سفر كمان مرة ال potential عند x equal b
+
+138
+00:11:52,420 --> 00:11:58,640
+x equal b لها نقطة و y بين ال 0 و ال nبرضه بتنشل
+
+139
+00:11:58,640 --> 00:12:04,000
+بساوة 0 اعود عن x equal b و y بيبقى y انها بين
+
+140
+00:12:04,000 --> 00:12:10,600
+مجموعة من النقاط من 0 ك a برضه بتساوة 0 y as a
+
+141
+00:12:10,600 --> 00:12:12,720
+function of y قلنا ده ال function ال potential
+
+142
+00:12:12,720 --> 00:12:15,600
+يعني اذا خلقتها سفر كل potential تبقى بساوة 0 لو
+
+143
+00:12:15,600 --> 00:12:20,320
+أخدت y ال y بساوة 0 لوش معنى x ال b هي اللي هتساوة
+
+144
+00:12:20,320 --> 00:12:26,420
+0 اذا استنتجنا ان x عندنا نقطة 0 بساوة 0 هيبقى
+
+145
+00:12:30,420 --> 00:12:36,760
+يجي انت اللي هي ال Y equal 0 X أو Zero هتسوى X ال
+
+146
+00:12:36,760 --> 00:12:43,810
+X و Y ال Zero برضه بتسوى صفرx هو بين 0 و b و y
+
+147
+00:12:43,810 --> 00:12:47,610
+بيكون صفر و potential صفر نفس المنطق أنا ماقدرش
+
+148
+00:12:47,610 --> 00:12:50,830
+أخد ال function x of x بيكون صفر لإن إذا حد هو صفر
+
+149
+00:12:50,830 --> 00:12:54,510
+مع أن ال potential صفر لإن y هو صفر لإن y هو صفر
+
+150
+00:12:54,510 --> 00:13:02,810
+لإن y هو صفر لإن y هو صفر لإن y هو صفر لإن y هو
+
+151
+00:13:02,810 --> 00:13:05,670
+صفر لإن y هو صفر لإن y هو صفر لإن y هو صفر لإن y
+
+152
+00:13:05,670 --> 00:13:07,930
+هو صفر لإن y هو صفر لإن y هو صفر لإن y هو صفر لإن
+
+153
+00:13:07,930 --> 00:13:08,690
+y هو صفر لإن y هو صفر لإن y هو صفر لإن y هو صفر
+
+154
+00:13:08,690 --> 00:13:12,870
+لإن y هو صفر لإن y هو صفر لإن y هو صفر لإبتساوي X
+
+155
+00:13:12,870 --> 00:13:22,530
+بتساوي Zero Y and الان X Zero Y الان X ال X عند اي
+
+156
+00:13:22,530 --> 00:13:27,970
+نقطة ل X و Y ال Zero احنا قلنا X خلصها من Zero من
+
+157
+00:13:27,970 --> 00:13:35,690
+ال B و X equal Zero و X and Y بيساوي B يعني هذا X
+
+158
+00:13:35,690 --> 00:13:36,990
+بتساوي Zero و Y
+
+159
+00:13:54,350 --> 00:13:55,750
+X0YY
+
+160
+00:14:02,940 --> 00:14:07,220
+و بعدين x,b,y اللي هم ال wall هادي و ال wall هادي
+
+161
+00:14:07,220 --> 00:14:11,080
+و بعدين أخدنا ال x equal x و y zero اللي هاي ال
+
+162
+00:14:11,080 --> 00:14:18,240
+wall فهد المفروض هد ال y equal zero و ال x equal x
+
+163
+00:14:18,240 --> 00:14:24,880
+و هد ال y بتساوي a و ال x بتساوي x عشان x هادي فهد
+
+164
+00:14:24,880 --> 00:14:27,860
+متأثرة هد x فهي x ال x و y ال a
+
+165
+00:14:30,930 --> 00:14:35,090
+هذه بتساوي V0، اذا عندنا اخر واحدة هي ال X ال
+
+166
+00:14:35,090 --> 00:14:43,010
+function of X و Y هي عند ال R بتساوي V0
+
+167
+00:14:45,750 --> 00:14:49,110
+اللي انا بقدر اقيم اقول ان ال X of X اللي مستحيل
+
+168
+00:14:49,110 --> 00:14:53,730
+اخليها يعني constant هي variable X ال X و Y ال A
+
+169
+00:14:53,730 --> 00:14:58,410
+مش لحالة هسو ال V0 حاصل ضرب ما هو ال V0 فماش بنقول
+
+170
+00:14:58,410 --> 00:15:01,710
+عنها inseparable مش زي هدولة كان معضح اللي بقدرش
+
+171
+00:15:01,710 --> 00:15:05,250
+اقول ان Y ال Y بالسوء 0 اذا X ال 0 هي السفر هنا Y
+
+172
+00:15:05,250 --> 00:15:09,160
+ال Y بقدرش اقول 0 اذا X ال B هي السفرهنا هو X الـ
+
+173
+00:15:09,160 --> 00:15:13,060
+X في Y الـ A التانية بساوة و V نقطة هذه انسبرة
+
+174
+00:15:13,060 --> 00:15:17,820
+ماقدرش أفصلهم عن بعض فبظل حاصل الضرب اللي هو X ال
+
+175
+00:15:17,820 --> 00:15:21,940
+X و Y عند ال A طبعا ال X هنا من 0 ل B اللي هو ال
+
+176
+00:15:21,940 --> 00:15:25,100
+range تبع ال X و Y كمتها A بساوة و V نقطة إذا ما
+
+177
+00:15:25,100 --> 00:15:28,280
+هي الأربعة boundary conditions اللي بدأ أحطهم يعني
+
+178
+00:15:28,280 --> 00:15:33,510
+باعتبار كل الوقتهذه المعادلتين اللي بدي أحلهم عشان
+
+179
+00:15:33,510 --> 00:15:37,470
+أبدأ أحل هدول المعادلتين لازم أعطي تخمينات لقيمة
+
+180
+00:15:37,470 --> 00:15:43,110
+ال Y إذا حلت واحدة تانية ع طول بحلها بغير إشارة ال
+
+181
+00:15:43,110 --> 00:15:46,750
+Lambda أول حاجة عشان أحل واحدة منهم باخد واحدة
+
+182
+00:15:46,750 --> 00:15:50,890
+منهم طبعا ده أحلعشان احلها بدي اخمن ايش قيم اللمدة
+
+183
+00:15:50,890 --> 00:15:56,090
+طبعا احنا بسرعة ممكن نخمن ان اللمدة لازم تكون صفر
+
+184
+00:15:56,090 --> 00:15:58,830
+لازم احط يعني خيارات لها بس لازم نعمل check لهم
+
+185
+00:15:58,830 --> 00:16:02,770
+تلاتة ان احتمالية لمدة تكون zero او موجبة او سلبة
+
+186
+00:16:02,770 --> 00:16:06,930
+موجودين وردين ممكن يكونوا مروا علينا في الدوائر
+
+187
+00:16:06,930 --> 00:16:10,850
+ويعرفنا ايش هو لازم يكون الحل بس لازم نحلهم مرة
+
+188
+00:16:10,850 --> 00:16:15,510
+تانية مع بعض و نتأكد ان الحل صحيحنبدأ في λمدة 0
+
+189
+00:16:15,510 --> 00:16:18,990
+اول حالة ايش معناه ان x double prime مش بالساوة
+
+190
+00:16:18,990 --> 00:16:22,710
+صفر فالمعادلة اللى قدامنا احط لمدة بالساوة صفر اذا
+
+191
+00:16:22,710 --> 00:16:25,250
+x double prime بالساوة صفر صارت مهلها سهل اني
+
+192
+00:16:25,250 --> 00:16:29,390
+اكملها هنا بحلها differential equation separation
+
+193
+00:16:29,390 --> 00:16:36,270
+of variables بحط ال x لحالة ال function x لحالة و
+
+194
+00:16:36,270 --> 00:16:40,730
+ال dx لحالة و بنعمل كمرة تكامل بس بكون شوية أطولة
+
+195
+00:16:40,730 --> 00:16:42,810
+زى ما قلنا ال natural response اللى أخدته في
+
+196
+00:16:42,810 --> 00:16:47,920
+الدوائرهذا أبسط اكس دابل برانز ساوة زيرو هكي اعمل
+
+197
+00:16:47,920 --> 00:16:50,720
+اول مرة او تاني مرة اول مرة هتعطيني some constant
+
+198
+00:16:50,720 --> 00:16:56,580
+ايه المرة التانية هتعطيني ax زائد b تمام بدنا ايش
+
+199
+00:16:56,580 --> 00:16:59,620
+نسويه نستخدم ال boundary conditions فى ان نقولنا
+
+200
+00:16:59,620 --> 00:17:05,600
+عند x equals 0 x equals 0 بيهدف x equals 0 مش كي
+
+201
+00:17:05,600 --> 00:17:12,540
+بتنشط سفر عند x equals 0 بتنشط بساوة زيرو نحط
+
+202
+00:17:21,330 --> 00:17:25,190
+عشان احط عن ال variable X0 و ال potential بالساوة
+
+203
+00:17:25,190 --> 00:17:30,470
+0 اذا P مالها سفر اذا عند النقطة X بالساوة سفر ال
+
+204
+00:17:30,470 --> 00:17:34,150
+potential X بالساوة 0 اذا P بالساوة 0 اذا هاي
+
+205
+00:17:34,150 --> 00:17:37,250
+المعادلة اتوصلت ل A اش ل X بالساوة Ax دل على يمين
+
+206
+00:17:37,250 --> 00:17:41,530
+ال A طب احنا كمان عنا كمان boundary condition ان X
+
+207
+00:17:41,530 --> 00:17:49,050
+ال XX عند ال B برضه بتسوى 0 اذا نعود عن هذه
+
+208
+00:17:49,050 --> 00:17:55,350
+المبتدأ X equal B ال potential بيسوى 0 اعود X عند
+
+209
+00:17:55,350 --> 00:18:01,190
+ال B يعني A في B بيسوى 0 صح؟A بB بيساو سفر بي
+
+210
+00:18:01,190 --> 00:18:03,870
+كونستانت اذا عرفت ان قيمته ممكن تكون عشرة أو كون
+
+211
+00:18:03,870 --> 00:18:07,350
+طول المتوازن اللي اطلع عليه ممكن تكون سفر اذا مين
+
+212
+00:18:07,350 --> 00:18:10,750
+لازم يساو سفر الـA دي طب اذا A سفر وB سفر اذا ال
+
+213
+00:18:10,750 --> 00:18:14,990
+potential X اشمله سفر ال trivia مطبع لما يكون ال
+
+214
+00:18:14,990 --> 00:18:18,490
+potential زيرو هذا هيكون احد الحلول لكن نسميه
+
+215
+00:18:18,490 --> 00:18:21,250
+trivia solution يعني اسهل حلة او دايما الحل لأي
+
+216
+00:18:21,250 --> 00:18:24,370
+معادل differential زيرو احد الحلول هيكون بس مش
+
+217
+00:18:24,370 --> 00:18:30,830
+الحل النهائي اذا نستنتج ان لامدة لا تساوي زيروأي
+
+218
+00:18:30,830 --> 00:18:35,030
+أكبر من صفر يعني موجبة أو أقل من صفر يعني سالبة
+
+219
+00:18:36,030 --> 00:18:39,370
+ناخد lambda أقل من zero عشان أؤكد لحالي أن lambda
+
+220
+00:18:39,370 --> 00:18:42,890
+أقل من zero باخدها أنها سالب a تربيع حاجة تربيع ال
+
+221
+00:18:42,890 --> 00:18:46,830
+alpha تربيع ال b تربيع لإيش؟ لأن التربيع ملوجة بحط
+
+222
+00:18:46,830 --> 00:18:50,330
+السالب قدامه معناه نأكد أن lambda مالها قيمة سالبة
+
+223
+00:18:50,330 --> 00:18:54,230
+لو أخدتها ده أي حاجة مش مربعة ممكن هيدقول والله
+
+224
+00:18:54,230 --> 00:18:57,910
+ممكن هيدكون سالبة فعشان أعرف الناس أن أنا ماخدة
+
+225
+00:18:57,910 --> 00:19:02,270
+lambda أنها سالبة بقول minus a minus alpha تربية
+
+226
+00:19:02,270 --> 00:19:07,530
+مثلانعوض عن هذا الحكيم xw' ما نسأل في تربيع x
+
+227
+00:19:07,530 --> 00:19:12,450
+بالساوة 0 ممكن احنا نعملها دلالة d تربيع حيث اعرف
+
+228
+00:19:12,450 --> 00:19:16,950
+دي تربيع هي d by dx بتصير اسهل ليه او ممكن زي ما
+
+229
+00:19:16,950 --> 00:19:20,810
+حكيت انه نحلها انه اعمل اللي هي ال expression
+
+230
+00:19:20,810 --> 00:19:25,230
+variables و احل زي ما استخدمته في دور الواحد او في
+
+231
+00:19:25,230 --> 00:19:28,050
+ال differential d تربيع ما نسأل تربيع x بالساوة 0
+
+232
+00:19:28,050 --> 00:19:34,080
+بستخدم ان هو فرق بمربعيندى plus minus alpha اللى x
+
+233
+00:19:34,080 --> 00:19:37,660
+بتساوي zero فبتعطينا ان ال differential بيه بتساوي
+
+234
+00:19:37,660 --> 00:19:43,720
+plus dx by dx بتساوي alpha x يا dx by dx بتساوي
+
+235
+00:19:43,720 --> 00:19:48,680
+ثالث alpha x اللى هى الحل التانى فده بستكمله
+
+236
+00:19:48,680 --> 00:19:54,980
+للأولى تمام؟ احنا بقى افصل بحط dx على x بتساوي
+
+237
+00:19:54,980 --> 00:20:00,810
+alpha dxو على كامل بيطلع معايا ان x ايش بتساوي a1
+
+238
+00:20:00,810 --> 00:20:05,350
+e to the alpha x لو أخدت السالبة باعد نفس الكلام و
+
+239
+00:20:05,350 --> 00:20:08,290
+بتطلع ل x بتساوي اتنين e to the minus alpha x
+
+240
+00:20:08,290 --> 00:20:13,490
+واضح؟ اذا لو أخدت الموجبة dx by dx بتساوي alpha x
+
+241
+00:20:13,490 --> 00:20:18,190
+واضح يعني اش اللي انا بحكيه يازم أخطط
+
+242
+00:20:28,040 --> 00:20:41,980
+هذه هي تربية X Y X X X X X X X
+
+243
+00:20:41,980 --> 00:20:42,660
+X X X X X X X X X X X X X X X X X X X X X X X X X
+
+244
+00:20:42,660 --> 00:20:47,440
+X X X
+
+245
+00:20:47,440 --> 00:20:47,980
+X X X X X X X X X X X X X X X X X X X X X X X X X
+
+246
+00:20:47,980 --> 00:20:48,320
+X X X X X X X X X X X X X X X X X X X X X X X X X
+
+247
+00:20:48,320 --> 00:20:50,560
+X X X X X
+
+248
+00:20:57,020 --> 00:21:04,840
+هي أسميها D تربيه مانوس ألف تربيه X تربيه من فضل X
+
+249
+00:21:04,840 --> 00:21:09,200
+تربيه
+
+250
+00:21:09,200 --> 00:21:14,740
+من فضل X تربيه من فضل X تربيه من فضل X تربيه من
+
+251
+00:21:14,740 --> 00:21:16,800
+فضل X تربيه من فضل X تربيه من فضل X تربيه من فضل X
+
+252
+00:21:16,800 --> 00:21:17,000
+تربيه من فضل X تربيه من فضل X تربيه من فضل X تربيه
+
+253
+00:21:17,000 --> 00:21:19,360
+تربيه من فضل X تربيه من فضل X تربيه من فضل X تربيه
+
+254
+00:21:19,360 --> 00:21:23,240
+من فضل
+
+255
+00:21:23,240 --> 00:21:26,460
+X تربيه
+
+256
+00:21:26,460 --> 00:21:26,480
+من
+
+257
+00:21:34,750 --> 00:21:40,530
+بس هنأول لاقينا حل لما Alpha موجبة هي بتعطينا طبعا
+
+258
+00:21:40,530 --> 00:21:48,290
+D بساوي plus minus Alpha X هي عادي تساوي سكر D
+
+259
+00:21:48,290 --> 00:21:51,730
+plus Alpha X بتساوي Zero اذا D بتساوي minus Alpha
+
+260
+00:21:51,730 --> 00:21:56,250
+X او D minus Alpha X بتساوي Zero زمان معناها D بال
+
+261
+00:21:56,250 --> 00:21:59,170
+X بتساوي Alpha X
+
+262
+00:22:26,470 --> 00:22:31,030
+الحل تبعهم زى ما كنتوا شايفين دى ال X على X بتساوي
+
+263
+00:22:31,030 --> 00:22:36,450
+Alpha X أقسم على X و بضرب في DX فهتكون DX على X
+
+264
+00:22:36,450 --> 00:22:41,350
+بتساوي Alpha DX تكامل هى اللى لناوهي هتكون ال X
+
+265
+00:22:41,350 --> 00:22:45,370
+فهتكون لن X زائد Alpha X زائد some constant لتسهيل
+
+266
+00:22:45,370 --> 00:22:50,690
+اللي بناخده لن ال A1 لتسهيل فهتكون عندي لن ال X
+
+267
+00:22:50,690 --> 00:22:55,650
+على A1 بتساوي Alpha X اخد ال exponential هتكون X
+
+268
+00:22:55,650 --> 00:22:59,190
+بتساوي A1 E to the Alpha of X لما ناخد ال Alpha
+
+269
+00:22:59,190 --> 00:23:02,190
+صالبة هيكون ال solution التاني ال complete
+
+270
+00:23:02,190 --> 00:23:06,520
+solution المجموعة التانيةمجموعة لما Alpha قدامها
+
+271
+00:23:06,520 --> 00:23:09,840
+إشارة موجبة و لما تكون قدامها إشارة سابقة حتى إن X
+
+272
+00:23:09,840 --> 00:23:13,500
+بيتساوية A1 E to the Alpha X زي إتنين E to the
+
+273
+00:23:13,500 --> 00:23:18,260
+minus Alpha X تمام هذا ال solution لسه مقاله نقص
+
+274
+00:23:18,260 --> 00:23:21,620
+لأن A1 و A2 مقالهم مش عارفينهم و أين بنتجيبهم ال
+
+275
+00:23:21,620 --> 00:23:27,920
+boundary condition عند X equal 0 و عند X equal A X
+
+276
+00:23:27,920 --> 00:23:32,720
+equal B عند X equal 0 و X equal B و احنا عيلنا
+
+277
+00:23:32,720 --> 00:23:36,380
+قيامهمعند X يبقى نحياتهم أنا حاططهم في الأعلى عشان
+
+278
+00:23:36,380 --> 00:23:41,140
+أستخدمها عند X equals 0 بتساوي 0 وعند X برضه
+
+279
+00:23:41,140 --> 00:23:46,640
+بتساوي D بها تساوي 0 معوض عند X equals 0 ال
+
+280
+00:23:46,640 --> 00:23:53,300
+potential بيساوي 0طبعا انا بقعد اكتب ال E to the X
+
+281
+00:23:53,300 --> 00:23:57,960
+و E to the minus X لكي
+
+282
+00:23:57,960 --> 00:24:00,200
+انا اعرف كيف يتصرف ال sin hyperbolic و ال cos
+
+283
+00:24:00,200 --> 00:24:04,080
+hyperbolic فبقعد اكتب ال solution هذا بها الطريقة
+
+284
+00:24:04,080 --> 00:24:07,920
+B1 cos hyperbolic Alpha X زي B2 sin hyperbolic
+
+285
+00:24:07,920 --> 00:24:11,540
+Alpha X لان دولة مربوطين ال cosine هي أفعل عن E to
+
+286
+00:24:11,540 --> 00:24:15,350
+the Alpha Xزائد e to the minus alpha x على اتنين
+
+287
+00:24:15,350 --> 00:24:18,950
+ال sine hyperbolic e to the alpha x minus e to the
+
+288
+00:24:18,950 --> 00:24:22,250
+minus alpha x على اتنين اذا بعض رعيات ساعدتهم على
+
+289
+00:24:22,250 --> 00:24:23,970
+شكل ال cosine hyperbolic و ال cosine hyperbolic
+
+290
+00:24:23,970 --> 00:24:28,430
+and x equals zero قلنا لو بتنشاش بيساوي zero اعود
+
+291
+00:24:28,430 --> 00:24:37,130
+x zero ال sine ال zero زيرولكن cosh0 هو 1 وcosh0
+
+292
+00:24:37,130 --> 00:24:40,870
+هو 1 وcosh0 هو 0 فما يبقى بيدي بيدي بيدي بيدي واحد
+
+293
+00:24:40,870 --> 00:24:44,210
+في واحد زائد زيرون فبيدي بيدي واحد زائد زائد زيرون
+
+294
+00:24:44,210 --> 00:24:46,030
+واحد في واحد زائد زائد زيرون فبيدي بيدي بيدي واحد
+
+295
+00:24:46,030 --> 00:24:52,950
+في واحد زائد زائد زيرون فبيدي بيدي بيدي واحد في
+
+296
+00:24:52,950 --> 00:24:55,650
+واحد زائد زائد زائد زيرون فبيدي بيدي بيدي واحد في
+
+297
+00:24:55,650 --> 00:25:02,470
+واحد زائد زائد زائد زائد زائد زائد زائد زائ
+
+298
+00:25:02,840 --> 00:25:05,920
+Sin hyperbolic αb بb2
+
+299
+00:25:10,340 --> 00:25:13,920
+عنا Alpha لا تساو Zero احنا اختارناها و قولنا رقم
+
+300
+00:25:13,920 --> 00:25:17,440
+مش قولنا Lambda مش لازمة تساو Zero قولنا Lambda لا
+
+301
+00:25:17,440 --> 00:25:21,420
+تساو Zero minus Alpha تربية حاجة تربيعية ضربناها
+
+302
+00:25:21,420 --> 00:25:24,700
+تساو عشان نقولها قيمتها سالبة و بيستحيل تكون Zero
+
+303
+00:25:24,700 --> 00:25:29,000
+لان هو طول الضلة تبع ال waveguide بتاعتنا اذا مين
+
+304
+00:25:29,000 --> 00:25:32,820
+لازم يساو سفر؟ B2 اذا هذا مش لازم يساو سفر لا ال
+
+305
+00:25:32,820 --> 00:25:34,220
+Alpha سفر ولا ال B سفر
+
+306
+00:25:42,230 --> 00:25:45,850
+لازم لامدة لا تكون zero ولا تكون سالبة لازم تكون
+
+307
+00:25:45,850 --> 00:25:50,130
+موجبة لذا باخد الحل الصحيح ليه لامدة أكبر من سفر
+
+308
+00:25:50,130 --> 00:25:53,970
+لامدة مثلا ناخدها بي تربية ليش ناخد بي تربية كمرة
+
+309
+00:25:53,970 --> 00:25:58,800
+عشان أكد انها موجبةأيش هيكون عندى؟ x double prime
+
+310
+00:25:58,800 --> 00:26:01,940
+زي قدرية تربية x بالساوية zero نفس الخطوات اللى
+
+311
+00:26:01,940 --> 00:26:04,660
+عملناهم دى تربية زي قدرية تربية ال x بالساوية zero
+
+312
+00:26:04,660 --> 00:26:09,860
+معناه دى ال x بتساوية plus minus j beta x فده ايش
+
+313
+00:26:09,860 --> 00:26:14,860
+هتصير؟ هنا
+
+314
+00:26:14,860 --> 00:26:18,620
+كانت الحالة اللى بيقوله minus alpha تربيت اتخيل لو
+
+315
+00:26:18,620 --> 00:26:20,280
+حاطينها بال minus plus
+
+316
+00:26:27,460 --> 00:26:32,900
+يعني هاي x double prime سواء minus beta تردية x ال
+
+317
+00:26:32,900 --> 00:26:38,200
+minus هي اللي بتجيبنا ال plus minus في ال j واضح؟
+
+318
+00:26:38,200 --> 00:26:41,900
+لأ أسوأ أخدنا يعني طريقة تانية اللي هي الفرق بين
+
+319
+00:26:41,900 --> 00:26:46,620
+المراتبعين second derivative هترسميها ان x prime
+
+320
+00:26:46,620 --> 00:26:51,940
+هتساوي plus minus j beta x
+
+321
+00:26:58,060 --> 00:27:01,860
+هذه حلها بشكل either cos sin او e to the j beta x
+
+322
+00:27:01,860 --> 00:27:06,200
+minus g beta x يعني لو حلنا ال plus هتعطينا اللي
+
+323
+00:27:06,200 --> 00:27:09,340
+هي a to the j beta x ال minus هتعطينا a to the
+
+324
+00:27:09,340 --> 00:27:13,760
+minus j beta x فال total solution مجموع اتنين او
+
+325
+00:27:13,760 --> 00:27:19,200
+اكتبه بشكل cos و sin x في x بيساوي g zero cos beta
+
+326
+00:27:19,200 --> 00:27:23,520
+x زي g واحد sin beta x اذا بتذكرين ال cos مالها e
+
+327
+00:27:23,520 --> 00:27:28,570
+to the j beta xالـ plus e to the minus j beta x
+
+328
+00:27:28,570 --> 00:27:34,150
+على 2 الـ sine لـ beta x e to the j beta x minus e
+
+329
+00:27:34,150 --> 00:27:38,810
+to the minus j beta x على 2j هل تذكرين هذا الحكي؟
+
+330
+00:27:38,810 --> 00:27:42,090
+لنعود إلى الـboundary condition يعني x equal 0
+
+331
+00:27:42,090 --> 00:27:47,650
+بتنشر بسوء 0, j بتعمل 0 ماله؟ 1, sine of 0؟ 0 هذا
+
+332
+00:27:47,650 --> 00:27:50,510
+السفر ال term تظهر عندي ال j node, لذا ال j node
+
+333
+00:27:50,510 --> 00:27:55,360
+هي السفرلما اعود هذا مضروف في صفر خلاص Zero هذا
+
+334
+00:27:55,360 --> 00:27:59,680
+الرقم راح يظل عنده Zero ايش بتساوي G0 اذا G0
+
+335
+00:27:59,680 --> 00:28:03,300
+بتساوي صفر اذا هذا ال term كله راح لانه مضروف في
+
+336
+00:28:03,300 --> 00:28:07,460
+Zero يظل عند X ال X ايش بتساوي J1 Sine Beta X ال
+
+337
+00:28:07,460 --> 00:28:09,420
+term التاني و ان ال value of condition تاني عالمين
+
+338
+00:28:09,420 --> 00:28:15,920
+عند X equal B بده يكون potential Zero اذا عند Sine
+
+339
+00:28:15,920 --> 00:28:23,730
+Beta B في J1 هذا لازم يساوي صفر تمامجواحد مش لازم
+
+340
+00:28:23,730 --> 00:28:29,010
+تساوي سفر هذه مش لازم تساوي سفر اذا معناه ال sign
+
+341
+00:28:29,010 --> 00:28:33,030
+بقدر اقول انه بيساوي سفر عند قيم محددة وقت ايش
+
+342
+00:28:33,030 --> 00:28:36,490
+بيكون ال sign بيساوي سفر لما تكون beta b بتساوي
+
+343
+00:28:36,490 --> 00:28:40,810
+مالها multiples of pi يعني لا ال beta تكون zero
+
+344
+00:28:40,810 --> 00:28:44,470
+ولا ال b zero لكن ال multiples تبعهم حصل ضربهم
+
+345
+00:28:44,470 --> 00:28:49,970
+بساويmultiples of B يعني multiply B و Beta في B
+
+346
+00:28:49,970 --> 00:28:54,630
+إذا كانوا multiples of B هيكون صينهم بساوة سفر
+
+347
+00:28:54,630 --> 00:28:57,550
+وبالتالي بتحقق ال boundary condition بتاعي بدون ما
+
+348
+00:28:57,550 --> 00:29:00,690
+أشبر ال Beta تكون سفر أو ال B تكون سفر ال sign
+
+349
+00:29:00,690 --> 00:29:05,630
+تبعهم اللي Zero هذا بيعطينا قيمة مين Beta لأن بيه
+
+350
+00:29:05,630 --> 00:29:09,370
+احنا عارفين هل هو طول المتوازن الأطلع ف Beta اش
+
+351
+00:29:09,370 --> 00:29:15,650
+هتساور من B على Bهي بس تذكير هذه ال cosine
+
+352
+00:29:15,650 --> 00:29:18,290
+hyperbolic و ال sine hyperbolic ال cosine ال
+
+353
+00:29:18,290 --> 00:29:21,710
+hyperbolic عند ال zero بيساوي واحد ال sine
+
+354
+00:29:21,710 --> 00:29:25,610
+hyperbolic عند ال zero بيساوي zero لكن ال sine و
+
+355
+00:29:25,610 --> 00:29:28,810
+ال cosine هى شكلهم اذا انتوا مش ملاقينهم هى ال
+
+356
+00:29:28,810 --> 00:29:32,010
+sine و ال cosine بس بتكون shift مع ال sine اللى هى
+
+357
+00:29:32,010 --> 00:29:38,050
+بتبدأ من ال zero عند ال واحد، واضح؟ اذا نقول لها
+
+358
+00:29:38,050 --> 00:29:42,470
+ان بيتا ايش هتساوي nb على npi على b و n أرقام من
+
+359
+00:29:42,470 --> 00:29:47,790
+واحد ل infinityإذا X لأنه في X إيش بتساوي جي أن
+
+360
+00:29:47,790 --> 00:29:51,870
+بطلت يعني مجرد constant إحنا عندنا عدد لنهائي من
+
+361
+00:29:51,870 --> 00:29:56,290
+الحلول إحنا قولنا إن X ال X صفت مين جي واحد sign
+
+362
+00:29:56,290 --> 00:30:01,590
+ال beta X ولاقينا إنه beta بقدر تشتبها في دلالة ال
+
+363
+00:30:01,590 --> 00:30:07,050
+N باي على بي فإذا عندي أنا عدد لنهائي من الحلول
+
+364
+00:30:07,050 --> 00:30:12,820
+عند N واحد وانت نين وانت تلاتة فبقول إن ال Xالـ A
+
+365
+00:30:12,820 --> 00:30:19,700
+يعني sub script N بتسوى GN sin N by X على B و Beta
+
+366
+00:30:19,700 --> 00:30:24,860
+تربية بتسوى N تربية بY تربية على B تربية اللي هي
+
+367
+00:30:24,860 --> 00:30:31,060
+Lambda صارت عندنا الحل تبع X بالـ N معروف مافيش
+
+368
+00:30:31,060 --> 00:30:35,340
+اشي مجهول عندنا الى مين ال GN لسه هنجيب قمةها
+
+369
+00:30:35,340 --> 00:30:41,230
+الحاجة التانية لازم حل مين لل Yالـ y''ما نسبت
+
+370
+00:30:41,230 --> 00:30:45,890
+تربيع y بالساوة zero هتعطينا ان y'' بالساوة beta
+
+371
+00:30:45,890 --> 00:30:53,050
+تربيع y وبالتالي هيكون عندى قيمة ال y عشان ال
+
+372
+00:30:53,050 --> 00:30:57,270
+cosine hyperbola و ال cosine hyperbola بستخدم
+
+373
+00:30:57,270 --> 00:31:02,330
+boundary conditions بحصل على قيمة ال y وبالتالي
+
+374
+00:31:02,330 --> 00:31:06,310
+بحصل على ال potential الكلي لازل عندى مجهول هو مين
+
+375
+00:31:06,310 --> 00:31:07,250
+ال j و ال h
+
+376
+00:31:14,830 --> 00:31:19,030
+هذا هو ال potential يعني معناه c1v1 زي 6 يعني هى
+
+377
+00:31:19,030 --> 00:31:23,670
+معناه انه انا عندى n منهم ن منهم هى معناه فإذا vxy
+
+378
+00:31:23,670 --> 00:31:28,110
+هيكون مجموع كل الحلول يعني عندى انا معناه v1, v2,
+
+379
+00:31:28,350 --> 00:31:33,590
+v3, v4, v5, v6 الحل الكل مجموعهم كلهم لإنه عندى n
+
+380
+00:31:33,590 --> 00:31:36,410
+قلنا من 1 ل infinity
+
+381
+00:31:39,450 --> 00:31:44,790
+يكون مجموع كلها دولار potentials
+
+382
+00:31:44,790 --> 00:31:50,210
+لتمين ضل عندي برنامج condition and mean و y equal
+
+383
+00:31:50,210 --> 00:31:55,950
+a بسوا V0 هي اللي بستخدمها عشان أكمل الحل تبعي
+
+384
+00:31:55,950 --> 00:32:00,950
+عشان أجيب ال coefficient تبعي عن طريق استخدام free
+
+385
+00:32:00,950 --> 00:32:07,330
+expansion يعني بدي أكامل أضرب في ال sign و أكامل
+
+386
+00:32:08,410 --> 00:32:13,710
+بضرب في الـ sine و بكمل من 0 ل B ال X بطلع معايا
+
+387
+00:32:13,710 --> 00:32:20,290
+قيم اللي هي Cm لما يكون odd و لما يكون even عند
+
+388
+00:32:20,290 --> 00:32:24,710
+الـ N لما يكون odd لا تساوي 0 عند ال even هتعطينا
+
+389
+00:32:24,710 --> 00:32:30,950
+قيم 0 و بحصل على ال potential النهائي ان عند فقط
+
+390
+00:32:30,950 --> 00:32:35,130
+ال N ما لهم odd هاي ال constant تبعي حصلت عليه
+
+391
+00:32:36,010 --> 00:32:41,630
+وبعود و بحصل على ال total potential واضح؟ يعني
+
+392
+00:32:41,630 --> 00:32:47,930
+جزئية المهم لنا في حال زي كده ال separation of
+
+393
+00:32:47,930 --> 00:32:51,430
+variable أن أولا لما أتقن ال deal لproblem زي I
+
+394
+00:32:51,430 --> 00:32:55,510
+متوازن أضلع أبقى أرفع أحدث إيش الاعتمادية تعطي ال
+
+395
+00:32:55,510 --> 00:32:58,470
+potential على أي variable بس بعتمد على ال X و ال Y
+
+396
+00:32:58,470 --> 00:33:02,330
+كيف أقدر أعمل ال separation of variables غالبا
+
+397
+00:33:02,330 --> 00:33:06,330
+سؤال زي هذا مش هأجيبلكم ياه في الامتحانلكن هجيبلكم
+
+398
+00:33:06,330 --> 00:33:10,210
+جزئية منه موجود لكم متوازن قضاء اقولكوا كت بكيف
+
+399
+00:33:10,210 --> 00:33:14,730
+هتكون شكل ال potential على ايش بعتمد حط ال
+
+400
+00:33:14,730 --> 00:33:20,810
+boundary conditions بس لكن مش خطأ انكوا تبقوا مرة
+
+401
+00:33:20,810 --> 00:33:25,630
+واحدة في حياتكوا تحلوا السؤال للاخر اللي انا
+
+402
+00:33:25,630 --> 00:33:26,910
+شرحتلكم يعني
+
+403
+00:33:33,720 --> 00:33:41,020
+طبعا هذه كمان اللي هي لو كنا في .. لو كان انا عندى
+
+404
+00:33:41,020 --> 00:33:44,580
+ال potential ماله فى ال cylindrical coordinate نفس
+
+405
+00:33:44,580 --> 00:33:49,760
+الفكرة او فى ال spherical coordinate بيكون عندى ال
+
+406
+00:33:49,760 --> 00:33:50,200
+potential
+
+407
+00:33:53,370 --> 00:33:58,010
+بدأ اعترف اول حاجة انه انا بقدر افصل الاعتمادية
+
+408
+00:33:58,010 --> 00:34:00,710
+بتاعة ال raw و ال fi و ال z على بعض يعني بقدر اكتب
+
+409
+00:34:00,710 --> 00:34:04,770
+ال potential ع شكل r في raw fi في fi z في z هاي
+
+410
+00:34:04,770 --> 00:34:08,950
+الأسئلة اللي ممكن تجيكم يعني برجع بعوض هنا لما
+
+411
+00:34:08,950 --> 00:34:12,230
+افاض بالنسبة ل raw ال fi و ال z مقالهم constant
+
+412
+00:34:12,230 --> 00:34:16,070
+بالنسبة ل raw فبطلعوا برا تفاضل بيصير اللي fi z
+
+413
+00:34:16,070 --> 00:34:19,190
+على raw d by d raw بيصير exact differential mean
+
+414
+00:34:19,190 --> 00:34:23,800
+لل rالterm التاني باعتمد على الـ phi فبطلع مين
+
+415
+00:34:23,800 --> 00:34:28,120
+عندى ال R و ال Z بتبقى اللى هى الاعتماد هى على ال
+
+416
+00:34:28,120 --> 00:34:31,860
+phi ال term التالت ال R و ال phi constant بالنسبة
+
+417
+00:34:31,860 --> 00:34:36,260
+ل Z فببقى عندى D تنين Z و بعدى Z تربيه لو قسمت على
+
+418
+00:34:36,260 --> 00:34:40,020
+ال potential اللى هى مين R فى Phi فى Z فهذا ال
+
+419
+00:34:40,020 --> 00:34:43,400
+term بتقل منه S بتروح ل Phi و Z ببقى 1 على R
+
+420
+00:34:47,770 --> 00:34:51,770
+هنا لما اقسم هتظهر ال file وهنا لما اقسم مين هتظهر
+
+421
+00:34:51,770 --> 00:34:57,670
+ال zipنفس الحاجة لو انا حطيت الاعتمادية على z على
+
+422
+00:34:57,670 --> 00:35:01,870
+الطرف التاني من المعادلة بقول انه مجموع الاعتمادية
+
+423
+00:35:01,870 --> 00:35:05,150
+على ال R او ال R function تفاضله بال second
+
+424
+00:35:05,150 --> 00:35:08,550
+derivative لل R زاد second derivative لل Phi ايش
+
+425
+00:35:08,550 --> 00:35:13,410
+بتساوي ال second derivative لل Z معناه لا يعتمدوا
+
+426
+00:35:13,410 --> 00:35:17,350
+على بعض الناتج لازم يكون constant هناخده معينة
+
+427
+00:35:17,350 --> 00:35:22,380
+اصلا ده تربيه هيك محلت هاي الجزء من المعادلةلو 1 ع
+
+428
+00:35:22,380 --> 00:35:28,480
+Z D 2 Z by D Z تربية بتساوة لامدة تربية ها هي الحل
+
+429
+00:35:28,480 --> 00:35:33,380
+ع شكل cosine هبقى بيبقى لجزء التاني من المعادلة
+
+430
+00:35:33,380 --> 00:35:37,940
+اللي هو ال 10 ما تبقى اللي هو عبارة عن مين 1 ع رو
+
+431
+00:35:37,940 --> 00:35:40,560
+R D by D رو رو D R by D رو
+
+432
+00:35:44,380 --> 00:35:53,920
+و اذا ضربت في مين في R سيصبح واحد على رو D by D رو
+
+433
+00:35:53,920 --> 00:35:59,100
+رو D R by D رو زائد R على رو تربية على فاي D تنين
+
+434
+00:35:59,100 --> 00:36:06,640
+فاي تربية فاي تربية بيصير plus lambda تربية R او
+
+435
+00:36:06,640 --> 00:36:07,280
+حتى ال R
+
+436
+00:36:26,390 --> 00:36:31,730
+الترم الأولانى Z بيصير عشان كسان هبرب كسان هبربرك
+
+437
+00:36:31,730 --> 00:36:36,030
+الترم التانى بيعطينا هذه المعادلةكمان لو انا
+
+438
+00:36:36,030 --> 00:36:39,310
+حاطيتها دول على طرف اللى بيتمدوا على ال raw و
+
+439
+00:36:39,310 --> 00:36:42,450
+الطرف فالتالى نقلته minus 1 على فا دى تنين فا
+
+440
+00:36:42,450 --> 00:36:47,890
+تربية بقدر اقول ان الاعتمادية على ال raw بتساوي
+
+441
+00:36:47,890 --> 00:36:51,230
+الاعتمادية على ال فا اذا معناه ماله التنين
+
+442
+00:36:51,230 --> 00:36:56,670
+constant بتساوي ميو تربية اذا نفعد هذا ال term هذا
+
+443
+00:36:56,670 --> 00:37:01,460
+المعادلة اللى دى فا تربيةD2 5 by D5 تربية تسوى من
+
+444
+00:37:01,460 --> 00:37:05,320
+ميو تربية 5 تسوى من ميو تربية 0 هذه حالها برضه
+
+445
+00:37:05,320 --> 00:37:08,820
+معروفة عشان الكوسين والصين بيظل عند المعادلة اللى
+
+446
+00:37:08,820 --> 00:37:12,960
+بتعتمد على مين على ال رو رو تربية D2 R by D رو
+
+447
+00:37:12,960 --> 00:37:18,120
+تربية لو ضربنا في ال R زائد رو DR by D رو plus
+
+448
+00:37:18,120 --> 00:37:24,600
+لمدة تربيةRow تربية minus Mu تربية كل مضروف R
+
+449
+00:37:24,600 --> 00:37:28,880
+بساوة Zero هذه المعادلة معادلة مشهورة لازم تحفظوا
+
+450
+00:37:28,880 --> 00:37:32,520
+شكلها اسمها Bessel differential equation مرقت
+
+451
+00:37:32,520 --> 00:37:38,420
+عليكم بيسل ال equation؟ أخدتوا communication؟ يعني
+
+452
+00:37:38,420 --> 00:37:40,560
+مسحبكم ولم يمرقتوا عليكم بيسل بال communication
+
+453
+00:37:40,560 --> 00:37:47,490
+لازم تكون مرقت عليكم بيسل المعادلات المشهورةبشكلها
+
+454
+00:37:47,490 --> 00:37:52,590
+مواضح ومعروف للرياضيين والمهدسين وغيرهم من اللي هي
+
+455
+00:37:52,590 --> 00:37:55,990
+applied sciences بيستخدموها على طول و بيقولوا ان
+
+456
+00:37:55,990 --> 00:38:00,890
+solution أو حلها معروف موجود في ال tables اللي هو
+
+457
+00:38:00,890 --> 00:38:03,810
+mean Bessel function هذه المعادلة اسمها Bessel
+
+458
+00:38:03,810 --> 00:38:08,390
+equation وحلها اسمه Bessel function هذا هو المطلوب
+
+459
+00:38:08,390 --> 00:38:11,990
+منكم بتتفلق ال cylindrical coordinate ال
+
+460
+00:38:11,990 --> 00:38:16,930
+cylindrical coordinate جربوا هيك تلعبوادلتر بيه V
+
+461
+00:38:16,930 --> 00:38:20,030
+بتساوي Zero كيف بتكون شكلها بالـ spherical
+
+462
+00:38:20,030 --> 00:38:25,250
+coordinate نجلاق
+
+463
+00:38:25,250 --> 00:38:28,810
+ال resistance و ال capacitance احنا اتعلمنا اشياء
+
+464
+00:38:28,810 --> 00:38:34,750
+كتير خلال المحاضرات الماضية اتعلمنا انه بنكتب ال
+
+465
+00:38:34,750 --> 00:38:38,740
+potential ابدلالة ال electric fieldبتساوي التكامل
+
+466
+00:38:38,740 --> 00:38:42,680
+ل E ضد DL وال current اتعلمنا انه عبارة عن ال
+
+467
+00:38:42,680 --> 00:38:46,520
+clause integral ل J ضد DS ومين هي J قلنا هي sigma
+
+468
+00:38:46,520 --> 00:38:50,820
+E اللي هي ال point form ل Ohm's law J بتساوي sigma
+
+469
+00:38:50,820 --> 00:38:53,980
+E اذا ال potential اللي هو بساوي ال integral ل E
+
+470
+00:38:53,980 --> 00:38:57,200
+ضد DL وال current اللي هو ال clause integral ل J
+
+471
+00:38:57,200 --> 00:39:01,420
+ضد DS او sigma E ضد DSبقدر استعين فيهم عشان أحسب
+
+472
+00:39:01,420 --> 00:39:05,280
+المقامة لل element اللي أنا بدرسه عمري أو ال
+
+473
+00:39:05,280 --> 00:39:09,940
+waveguide اللي أنا بدرسها R بيسووا V على I Ohm's
+
+474
+00:39:09,940 --> 00:39:13,680
+law بيسووا ال integral ل E ضد DL على ال close
+
+475
+00:39:13,680 --> 00:39:19,870
+integral ل sigma E ضد DSأول خطوة انا دائما هي ان
+
+476
+00:39:19,870 --> 00:39:23,190
+اختار ال coordinate المناسب اذا انا بحكي على
+
+477
+00:39:23,190 --> 00:39:25,750
+متوازي أطلع اذا انكارتيش ال coordinate بحكي على
+
+478
+00:39:25,750 --> 00:39:27,890
+cylindrical و cylindrical coordinate بحكي على سفير
+
+479
+00:39:27,890 --> 00:39:31,890
+و سفير ك coordinate Assume V0 as a potential
+
+480
+00:39:31,890 --> 00:39:35,110
+difference between conductor terminal ال conductor
+
+481
+00:39:35,110 --> 00:39:39,810
+تبعي أسوأ هو cylindrical ولا متوازي أطلع ولا سفير
+
+482
+00:39:39,810 --> 00:39:43,450
+هو بده يكون ال potential difference بين طرفي ال
+
+483
+00:39:43,450 --> 00:39:48,630
+conductorبنحل ال plus equation ل V لان جيب V احنا
+
+484
+00:39:48,630 --> 00:39:54,770
+بعد ان ال V بقدر اجيب اللي هو E E بتسوى minus دل
+
+485
+00:39:54,770 --> 00:39:59,010
+ال V اذا جيبت ال E بقدر اجيب مين ال current لان ال
+
+486
+00:39:59,010 --> 00:40:01,170
+current مش بتسوى ال close integral ل Sigma E دول
+
+487
+00:40:01,170 --> 00:40:06,290
+DS جيبنا V جيبنا ال current اذا بجيب المقامة اللي
+
+488
+00:40:06,290 --> 00:40:10,690
+هتسوى V node على R اللي هو الفرق
+
+489
+00:40:14,880 --> 00:40:20,900
+هو ال current واضح احنا
+
+490
+00:40:20,900 --> 00:40:25,440
+بنعرف الفرق بين طرفي ال conductors لو مثلا هى عندي
+
+491
+00:40:25,440 --> 00:40:30,820
+انا المكسف مثلا هي plus Q minus Q وعندي بطارية هى
+
+492
+00:40:30,820 --> 00:40:36,040
+الطرف الموجب هو الطرف الثالثهذا الـ conductor واحد
+
+493
+00:40:36,040 --> 00:40:39,460
+اللي هو موصول بي الـ positive charges واطراف
+
+494
+00:40:39,460 --> 00:40:45,440
+السالب هي واحد واتنين V هي فرق الجهد بين واحد
+
+495
+00:40:45,440 --> 00:40:50,880
+واتنين V هي فرق الجهد بين واحد واتنين اتجاه ال
+
+496
+00:40:50,880 --> 00:40:54,640
+electric field منوجب للسالب وV اللي هو فرق الجهد
+
+497
+00:40:54,640 --> 00:40:58,600
+بين الأول ومينوس التاني اللي هو ايش بيساوي سالب ال
+
+498
+00:40:58,600 --> 00:41:06,810
+Integral 2 ل 1 E Dot Rالـ notation طبعا، اذا V1-V2
+
+499
+00:41:06,810 --> 00:41:13,610
+يسمى minus ال integral من 2 ل 1 E dot DL واضح؟
+
+500
+00:41:13,610 --> 00:41:18,150
+المكثف،
+
+501
+00:41:18,150 --> 00:41:22,490
+المكثف عبارة عن ميلي Q على V و Q من Gauss Law
+
+502
+00:41:22,490 --> 00:41:27,030
+بيساوي Epsilon ال close integral ل E dot DS و ال
+
+503
+00:41:27,030 --> 00:41:29,650
+potential ما احنا عارفينه ال integral ل E dot DL
+
+504
+00:41:34,750 --> 00:41:42,410
+هم كيف احصل على C؟ اول حاجة بفترض وجود Q و بقرر
+
+505
+00:41:42,410 --> 00:41:50,510
+قدش قيمة V in terms of Q ان بحل مين يعصله او ان
+
+506
+00:41:50,510 --> 00:41:55,670
+اول حاجة بفترض V و بقرر cube دلالة V بحل ان مين
+
+507
+00:41:55,670 --> 00:42:03,000
+لبلاس equation يعني يا ببدأ ب Q و بحل V دلالة Qأو
+
+508
+00:42:03,000 --> 00:42:07,420
+ببدأ فرضية أنه عندي V و بحل ال cube دلالة V
+
+509
+00:42:07,420 --> 00:42:15,680
+باستخدام ال plasic equations طبعا
+
+510
+00:42:15,680 --> 00:42:18,840
+معناه هيك أن دائما لازم أختار ال suitable
+
+511
+00:42:18,840 --> 00:42:21,980
+coordinate system إذا بنحكي على متوازق أطلع و
+
+512
+00:42:21,980 --> 00:42:24,200
+أختار ال Cartesian و الcylindrical باختار ال
+
+513
+00:42:24,200 --> 00:42:28,470
+cylindricalبختار الـ spherical و بعدين بختار two
+
+514
+00:42:28,470 --> 00:42:31,250
+conducting plates carrying charges plus q و minus
+
+515
+00:42:31,250 --> 00:42:34,630
+q يعني هدولة inherited يعني احنا لما نقول كيف احصل
+
+516
+00:42:34,630 --> 00:42:38,630
+على c already انا بقول لازم اختار coordinate صحيح
+
+517
+00:42:38,630 --> 00:42:41,950
+و عندى هيكون two plates واحد موجب واحد سالب هى
+
+518
+00:42:41,950 --> 00:42:45,990
+معناه ان احصل على c ولا لأ و بعدين يا بفرض q و بحل
+
+519
+00:42:45,990 --> 00:42:53,730
+v بدلالة q يا بفرض ال v و بحل q بدلالة v طيب
+
+520
+00:42:55,550 --> 00:42:58,550
+إذا قلنا بنختار الـ coordinate المناسب to
+
+521
+00:42:58,550 --> 00:43:03,270
+conducting plates بستخدم gauss law أو columns law
+
+522
+00:43:03,270 --> 00:43:07,350
+عشان أحسب E ومنها بحسب V و بعدين بقدر أحسب C
+
+523
+00:43:07,350 --> 00:43:14,210
+بيبسوق U على V هاي مثال، أسهل مثال هو البرر بلاي
+
+524
+00:43:14,210 --> 00:43:18,090
+الكاباستور لأنه أخدنا .. لما أخدنا ال gauss law
+
+525
+00:43:18,090 --> 00:43:20,830
+جبنا ال electric field تبع البرر بلاي الكاباستور
+
+526
+00:43:21,770 --> 00:43:25,650
+واحد من البلاد قاعد عند x equal 0 و البلاد التانى
+
+527
+00:43:25,650 --> 00:43:30,870
+قاعد عند مين x equal d الموجب عند x equal d و
+
+528
+00:43:30,870 --> 00:43:34,410
+السلب انه x equal 0 و بين ال two blades فى عندنا
+
+529
+00:43:34,410 --> 00:43:38,450
+dielectric media اللي هي y و المساحة بتاعة كل
+
+530
+00:43:38,450 --> 00:43:42,910
+blade يعني هدول زى دفترين دفتر فى و دفتر تحت
+
+531
+00:43:42,910 --> 00:43:46,650
+المساحة بتاعة كل دفتر هي S هى ال blades
+
+532
+00:43:49,680 --> 00:43:52,960
+Rho S اللي هي charge density على كل surface من
+
+533
+00:43:52,960 --> 00:43:56,700
+هدولة ال plates Q على S ال total charge على مساحة
+
+534
+00:43:56,700 --> 00:44:03,260
+بتاعة ال plate اللي هي S و D عبارة عن minus rho S
+
+535
+00:44:03,260 --> 00:44:07,180
+X hat اتجاهها هي اتجاه ال electric field من موجة
+
+536
+00:44:07,180 --> 00:44:10,760
+بلس سالب و اتجاهه وين يعني معناه في ال minus X
+
+537
+00:44:10,760 --> 00:44:16,200
+direction و هذا ينجزله انه D ان ال clause انتقلة D
+
+538
+00:44:16,200 --> 00:44:20,900
+ضد DS بتساويمن الـ closed الـ Q الـ Q اللي هي مين؟
+
+539
+00:44:20,900 --> 00:44:26,160
+رو أس في أس تروح الأس من الطرفين وتظهر أن D
+
+540
+00:44:26,160 --> 00:44:30,560
+بيتساور minus رو أس except بسبب احنا الاتجاه تبع
+
+541
+00:44:30,560 --> 00:44:34,440
+ال D باتجاه ال minus except E عبارة عن مين؟ D على
+
+542
+00:44:34,440 --> 00:44:39,380
+إبسلون هي رو أس على إبسلون في اتجاه الثالث except
+
+543
+00:44:39,380 --> 00:44:45,600
+إبسلون هي الـ dielectric ما بين ال two platesلو
+
+544
+00:44:45,600 --> 00:44:49,520
+بدى اكتبها دلت الـQ والـS رو S شبه رعمين الـQ على
+
+545
+00:44:49,520 --> 00:44:54,260
+S فإذا عندى ال electric field بيسوا minus Q على ي
+
+546
+00:44:54,260 --> 00:44:59,300
+S except هى جبنا ال electric field بقدر أجيب ال
+
+547
+00:44:59,300 --> 00:45:04,680
+potential انا لازم عشان أجيب ال C ال potential و Q
+
+548
+00:45:04,680 --> 00:45:07,300
+عرفت ان ال electric field بقدر أجيب ال potential
+
+549
+00:45:07,300 --> 00:45:10,940
+وبالتالي بقدر أجيب ال C ال potential ايش انا
+
+550
+00:45:10,940 --> 00:45:17,070
+بيساوي minus ال integral من 2 ل1 D بالDLرحمكم الله
+
+551
+00:45:17,070 --> 00:45:21,330
+احنا قولنا ال electric field بروح من واحد لاتنين
+
+552
+00:45:21,330 --> 00:45:23,970
+ال notation تبعنا اللي موجب للثالث اذا مافيه ايش
+
+553
+00:45:23,970 --> 00:45:29,710
+بيسوى minus ال integral من تنين لواحد E دول DL من
+
+554
+00:45:29,710 --> 00:45:35,290
+وين يعني؟ ايه بقى اتنين اللي هي zero و واحد اللي
+
+555
+00:45:35,290 --> 00:45:40,550
+هي دي اذا انت كامل ال X من وين طبعا DL هي DX هتكون
+
+556
+00:45:40,550 --> 00:45:45,670
+X hat و ال E اللي هو minus Q على Y أس X hatبالتالي
+
+557
+00:45:45,670 --> 00:45:50,430
+هيكون عندى .. بالنسبالى ال Q واليبسون S constant
+
+558
+00:45:50,430 --> 00:45:55,830
+بالنسبالى DX هيكون Q علي يبسون S وال DX بكملها من
+
+559
+00:45:55,830 --> 00:46:00,350
+0 لD يعني قيمتها D إذا V عبارة عن Q علي يبسون S في
+
+560
+00:46:00,350 --> 00:46:07,210
+D أو ببساطة هي A في D إذا C إيش بنفسه؟ إذا ماعرفين
+
+561
+00:46:07,210 --> 00:46:12,530
+ال potential وعارفين ال Q ال Q علي V هي عبارة عن C
+
+562
+00:46:13,100 --> 00:46:17,740
+أذا الـ Q على V بيبقى ثوّي Y أس على D بتعرفوا ايه
+
+563
+00:46:17,740 --> 00:46:22,820
+الـ Y على D؟ إن كسافة المكسفة برا الـ Plates
+
+564
+00:46:22,820 --> 00:46:26,680
+بيعتمد على الـ dielectric media اللي بين الـ Two
+
+565
+00:46:26,680 --> 00:46:31,800
+Plates المساحة المقطعية أو مساحة الـ Area تحت الـ
+
+566
+00:46:31,800 --> 00:46:37,950
+Plates و المسافة اللي بينها تمام؟لو احنا عدنا نفس
+
+567
+00:46:37,950 --> 00:46:41,890
+التجربة و جيبنا C لما يكون ال dialectic عبارة عن
+
+568
+00:46:41,890 --> 00:46:47,690
+مين؟ عن space، هو يعني هيكون C0 بتسوء Y0 S على D
+
+569
+00:46:47,690 --> 00:46:53,470
+بقدر اجيب من ال ratio ال 6 عرفة C قايصة قيمتها و
+
+570
+00:46:53,470 --> 00:46:58,410
+C0 بقدر اقول ان C على C0 هي مين؟ YR لأنها هتكون Y
+
+571
+00:46:58,410 --> 00:47:03,640
+على Y0سي على سي نود هتكون إبسلون على إبسلون نود
+
+572
+00:47:03,640 --> 00:47:06,720
+اللي هي إبسلون R و هاي اللي بيستخدموها الطريقة
+
+573
+00:47:06,720 --> 00:47:11,760
+لحساب ال dialectic constant لأي media أو relative
+
+574
+00:47:11,760 --> 00:47:16,920
+dialectic ل ال media برضه
+
+575
+00:47:16,920 --> 00:47:19,540
+بقدر أحسب ال energy stored لإنها ال energy stored
+
+576
+00:47:19,540 --> 00:47:24,300
+سوى نص CV تربيه اللي عبارة عن نص Q في V لإنه C
+
+577
+00:47:24,300 --> 00:47:28,810
+قلنا إيش بتساويC في V هي عبارة عن Q فبقدر أقول هي
+
+578
+00:47:28,810 --> 00:47:35,530
+برضه نص Q في V أو Q تربيه على اتنين سنة، واضح؟
+
+579
+00:47:35,530 --> 00:47:41,030
+تأسف صار لحد هنا؟ احنا هنكمل المحاضرة القادمة نحسب
+
+580
+00:47:41,030 --> 00:47:48,010
+C للسلمدر و للسفير و بعدين هنحسب ال R لكل نفس
+
+581
+00:47:48,010 --> 00:47:48,510
+الاشي في ال
+
+582
+00:47:51,720 --> 00:47:55,180
+أو سفير و هذا أشي بيهمنا كتير توع القهرة بلانعرف
+
+583
+00:47:55,180 --> 00:47:59,100
+إيش هي مقامة ال coaxial cable مثلا، الكثافة
+
+584
+00:47:59,100 --> 00:48:04,060
+بتاعته، هذه الأشياء اللي احنا ك applied engineers
+
+585
+00:48:04,060 --> 00:48:08,240
+أو ك engineers بتبتهمنا معرفتها و نربطها في وين في
+
+586
+00:48:08,240 --> 00:48:12,290
+الدوارليش احنا قولنا ان الدواء دى حلق حاصة من
+
+587
+00:48:12,290 --> 00:48:14,850
+الكهربا نقصية و احنا كل حاجة أخدناها في الدواء
+
+588
+00:48:14,850 --> 00:48:18,470
+اتنين بنقدر نحلها بالكهربا نقصية لذا هذا ال
+
+589
+00:48:18,470 --> 00:48:23,330
+chapter هنشوف كيف نكمل حساب ال C ل ال cylindrical
+
+590
+00:48:23,330 --> 00:48:27,710
+و ال spherical capacitor و بعدين هنشوف كيف نجيب
+
+591
+00:48:27,710 --> 00:48:34,090
+المقامة لعدد أنواع من ال elements مع بعض و ال
+
+592
+00:48:34,090 --> 00:48:38,450
+contactivityو منكون هذا الغرض من ان هذا ال chapter
+
+593
+00:48:38,450 --> 00:48:42,950
+انتهى لما احصل كل هاي elements يعطيكوا العافية و
+
+594
+00:48:42,950 --> 00:48:46,830
+القادمة نحاول انا أسرع يعني مش هاخد في التفاصيل
+
+595
+00:48:46,830 --> 00:48:50,490
+بتاعة كل ال problem يعني كل هاي تطبيقات
+
diff --git a/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/kG2lS7Q6L98_raw.srt b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/kG2lS7Q6L98_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..c399018b97ae29b56a1483d3a1d126b907d7775c
--- /dev/null
+++ b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/kG2lS7Q6L98_raw.srt
@@ -0,0 +1,2424 @@
+1
+00:00:20,670 --> 00:00:23,490
+بسم الله الرحمن الرحيم السلام عليكم ورحمة الله
+
+2
+00:00:23,490 --> 00:00:26,770
+وبركاته احنا اليوم ان شاء الله هتتبع موضوعنا ال
+
+3
+00:00:26,770 --> 00:00:30,470
+boundary value problems او boundary conditional
+
+4
+00:00:30,470 --> 00:00:33,610
+problems بكيف نحسب ال potential وقولنا من ال
+
+5
+00:00:33,610 --> 00:00:36,250
+potential حسبنا يقدر نحسب ال electric field
+
+6
+00:00:38,860 --> 00:00:41,780
+المحاضرة الماضية شوفنا أمثلة اللي كان فيها ال
+
+7
+00:00:41,780 --> 00:00:44,460
+potential patented على one direction one variable
+
+8
+00:00:44,460 --> 00:00:49,000
+وحلناها بال integration اليوم هشوف مثال اللي لازم
+
+9
+00:00:49,000 --> 00:00:51,800
+احنا نستخدم ال separation of variable احنا قالنا
+
+10
+00:00:51,800 --> 00:00:54,420
+فيه طريقتين لحل أسبوع على أسبوع او بأسبوع equation
+
+11
+00:00:54,420 --> 00:00:56,700
+لإن هي الطريقة الأولى أنه يكون ال potential
+
+12
+00:00:56,700 --> 00:01:00,320
+patented على one variable نعمل integration أو أكثر
+
+13
+00:01:00,320 --> 00:01:02,940
+من variable و ساعتها بنعمل separation of variables
+
+14
+00:01:02,940 --> 00:01:08,470
+فخلنا نشوف مثال على ال separation of variablesهنا
+
+15
+00:01:08,470 --> 00:01:13,250
+المثال اللى قمامنا عبارة عن اللى هو متوازي أطلع
+
+16
+00:01:13,250 --> 00:01:18,750
+waveguide على شكل متوازي أطلع مبتده على طول انها
+
+17
+00:01:18,750 --> 00:01:24,390
+key conditions ان عند x equal 0 ال potential y
+
+18
+00:01:24,390 --> 00:01:29,990
+مابين ال 0 و ال a ال potential بساوة 0و ال wall
+
+19
+00:01:29,990 --> 00:01:36,550
+اللى عند y equal 0 و x من 0 ل b برضه بتنشه 0 و ال
+
+20
+00:01:36,550 --> 00:01:41,710
+wall اللى عند x equal b و y من 0 ل a برضه بتنشه
+
+21
+00:01:41,710 --> 00:01:47,210
+بساوي 0 ال wall اللى عند y بتساوي a و x ما بين ال
+
+22
+00:01:47,210 --> 00:01:51,250
+0 و ال b اللى بتنشه بساوي v not وماعطينا قيمة v
+
+23
+00:01:51,250 --> 00:01:55,700
+not ان هو one hundred voltوكمان قيلنا ان بي هو طول
+
+24
+00:01:55,700 --> 00:02:01,740
+المساطير المساحة المقطع على متوازى الأضلاع انه ايه
+
+25
+00:02:01,740 --> 00:02:06,560
+بتساوي 2A المطلوب بيناقل نقطة potential عند اي
+
+26
+00:02:06,560 --> 00:02:10,840
+نقطة في قلب ال with guide يعني مثلا X بتساوي A على
+
+27
+00:02:10,840 --> 00:02:17,000
+2 هي بالتمام هنا تقريبا لان قلنا بي 2A فهي A هتكون
+
+28
+00:02:17,000 --> 00:02:21,820
+A على 2 تقريبا هنا و Y تلاتة A على أربع
+
+29
+00:02:25,010 --> 00:02:28,410
+طالب ترباع A يعني somewhere هنا يعني طالب ترباع A
+
+30
+00:02:28,410 --> 00:02:32,310
+فاضح؟ اذا هو هاي المطلوب بنا ان اجيب ال potential
+
+31
+00:02:32,310 --> 00:02:38,690
+عند اي نقطة في قلب المتوازي الأطلع واضح لنا ان ال
+
+32
+00:02:38,690 --> 00:02:41,530
+potential باعتنا ده على two variables ال X وال Y
+
+33
+00:02:41,530 --> 00:02:45,390
+لكن في ال Z direction ال Z رايح لل infinity وفيش
+
+34
+00:02:45,390 --> 00:02:50,950
+اعتمادية على ال Z الاعتمادية فقط على ال X وY مافيش
+
+35
+00:02:50,950 --> 00:02:58,840
+free chargesفإذا دل التربيع V بيساوي 0 طبعا
+
+36
+00:02:58,840 --> 00:03:01,560
+احنا ال coordinate اللي قررنا واضح انه هناخد
+
+37
+00:03:01,560 --> 00:03:05,840
+Cartesian coordinate ال X و ال Y إذا هتكون الدل
+
+38
+00:03:05,840 --> 00:03:10,140
+تربيع D تربيع V by DX تربيع زي ال DT تربيع by DY
+
+39
+00:03:10,140 --> 00:03:15,460
+تربيع بتساوي 0 لإن مافيش free charges هنستخدم ال
+
+40
+00:03:15,460 --> 00:03:19,590
+last equation بمعنى أن الدل تربيع V بتساوي 0بنسمع
+
+41
+00:03:19,590 --> 00:03:21,530
+ال boundary conditions اللي احنا حكيناها مع بعض
+
+42
+00:03:21,530 --> 00:03:26,850
+انه ال potential عند x equal 0 و y مابين ال 0 و ال
+
+43
+00:03:26,850 --> 00:03:32,290
+a بساوة 0 ال potential عند x equal b و ال y من 0 ل
+
+44
+00:03:32,290 --> 00:03:37,310
+a بساوة 0 ال potential لل x مابين ال 0 و ال b و ال
+
+45
+00:03:37,310 --> 00:03:43,370
+y بساوة 0 ال potential عند x مابين ال 0 و ال b و
+
+46
+00:03:43,370 --> 00:03:46,430
+ال y بساوة a بساوة v نضد هذه هي ال boundary
+
+47
+00:03:46,430 --> 00:03:46,950
+conditions
+
+48
+00:03:49,670 --> 00:03:56,530
+بالنسبة للمشكلة مثل هذه المشكلة نحن لدينا V ملها V
+
+49
+00:03:56,530 --> 00:04:02,710
+مقلد ترميه V مستوى V وقلنا استنتجنا ان V مقلد
+
+50
+00:04:02,710 --> 00:04:11,710
+function of X وY فمعناه استنتجنا ان E تنين V X Y Y
+
+51
+00:04:11,710 --> 00:04:20,650
+D X ترميه زي E تنين Vبايتم دي و بايتم دي و بايتم
+
+52
+00:04:20,650 --> 00:04:21,290
+دي و بايتم دي و بايتم دي و بايتم دي و بايتم دي و
+
+53
+00:04:21,290 --> 00:04:29,650
+بايتم دي و بايتم دي و بايتم دي و بايتم دي و بايتم
+
+54
+00:04:29,650 --> 00:04:32,330
+دي و بايتم دي و بايتم دي و بايتم دي و بايتم دي و
+
+55
+00:04:32,330 --> 00:04:32,330
+بايتم دي و بايتم دي و بايتم دي و بايتم دي و بايتم
+
+56
+00:04:32,330 --> 00:04:32,330
+دي و بايتم دي و بايتم دي و بايتم دي و بايتم دي و
+
+57
+00:04:32,330 --> 00:04:36,450
+بايتم دي و بايتم دي و بايتم دي و بايتم دي و بايتم
+
+58
+00:04:36,450 --> 00:04:39,430
+دي و بايتم دي
+
+59
+00:04:44,210 --> 00:04:48,730
+فى ال X اعتمادية على X لها تعتمد على V لها ال Y
+
+60
+00:04:48,730 --> 00:04:52,070
+عشان نقدر نقول ان هى بقدر اسمها شكل through
+
+61
+00:04:52,070 --> 00:04:57,370
+function XY X هو ال solution اللى بعتمد على X و Y
+
+62
+00:04:57,370 --> 00:05:02,950
+ال solution اللى بعتمد على Y او بقدر اسمهم VX و VY
+
+63
+00:05:02,950 --> 00:05:05,910
+فهذا ال solution اللى بقدر نضعه عشان نتأكد انه
+
+64
+00:05:05,910 --> 00:05:10,600
+اعتمد على X فهذا الاعتمادية على Vهذه الطريقة اللي
+
+65
+00:05:10,600 --> 00:05:14,380
+نسميها طريقة الـ Separation Theory انها عرفتنا ان
+
+66
+00:05:14,380 --> 00:05:18,540
+ال potential مقدر افصل اعتماديته على X عن
+
+67
+00:05:18,540 --> 00:05:23,000
+اعتماديته على Yلو ماقدرش أفصلهم بيظلوا صعيب الحل
+
+68
+00:05:23,000 --> 00:05:27,640
+بيضالا M في الدخل لكن ما أنه انا الاعتمادية اللي
+
+69
+00:05:27,640 --> 00:05:31,140
+على ال X ده تعتمد على ال Y بقدر افصل ال two
+
+70
+00:05:31,140 --> 00:05:34,780
+functions في ناس بتلاقوهم بيكسل X يعني هذا
+
+71
+00:05:34,780 --> 00:05:38,600
+potential جزء من ال solution وهذا جزء من ال
+
+72
+00:05:38,600 --> 00:05:46,500
+solution مثلا احنا في الكتاب بيستخدم X وY فماعود
+
+73
+00:05:46,780 --> 00:05:50,120
+فهذا ال potential في ال problem اللي قدامنا في ال
+
+74
+00:05:50,120 --> 00:05:53,560
+equation اللي معناه هلاحظ أنه ال term الأولاني
+
+75
+00:05:53,560 --> 00:05:58,060
+بعتمد ع مين؟ ع ال X إذا أنا هذا بس بتفاضل مرتين ال
+
+76
+00:05:58,060 --> 00:06:04,620
+Y بتطلع برا التفاضل فهيكون عندي Y لأ تعتمد ع ال X
+
+77
+00:06:04,620 --> 00:06:09,060
+و بيصير عندي exact differential مش partial اتنين ل
+
+78
+00:06:09,060 --> 00:06:14,800
+X انا متعتمدش اللي ع ال X exactزائر هنا مين ال
+
+79
+00:06:14,800 --> 00:06:18,520
+item التفاظ بالنسبة ل y الجزء اللى على ال x بيطلع
+
+80
+00:06:18,520 --> 00:06:31,080
+برا ال differentiation تمام
+
+81
+00:06:31,080 --> 00:06:36,340
+فهذا هو ال separation theorem التي شهدت جزئية
+
+82
+00:06:36,340 --> 00:06:40,660
+التانية و هي الأهم ان احنا لو قسمنا على مين على
+
+83
+00:06:40,660 --> 00:06:41,800
+Vxy
+
+84
+00:06:46,670 --> 00:06:53,570
+مين دى ال X و Y؟ X و Y يعني إيش هال بتصير؟ 1 على X
+
+85
+00:06:53,570 --> 00:06:57,370
+V2
+
+86
+00:06:57,370 --> 00:07:06,530
+من X و Y من X تقريبا زى V2 من Y و Y تقريبا
+
+87
+00:07:06,530 --> 00:07:14,330
+مابيبقوا كمين؟ واحد تمام؟
+
+88
+00:07:16,370 --> 00:07:23,990
+أسهم عندي هذا تير بساوي
+
+89
+00:07:23,990 --> 00:07:30,730
+0 يعني انا كمان بقول المعلومة التانية بقول ان
+
+90
+00:07:30,730 --> 00:07:37,030
+السفن derivative لل X ل X double prime على X زائد
+
+91
+00:07:37,030 --> 00:07:42,170
+السفن derivative لل Y على Y بتساوي 0 او بمعنى اخر
+
+92
+00:07:42,170 --> 00:07:46,700
+X double prime على X بتساوي او تساويبتساوى y
+
+93
+00:07:46,700 --> 00:07:53,120
+double prime على y إذا
+
+94
+00:07:53,120 --> 00:07:56,840
+أسمة x double prime على x بتساوى x double prime
+
+95
+00:07:56,840 --> 00:08:02,800
+على y معناه إن الناتج لا بعتمد على x ولا على y هاي
+
+96
+00:08:02,800 --> 00:08:08,340
+المعنى إذا تفاض ال x مرتين على x بتساوى تفاض ال y
+
+97
+00:08:08,340 --> 00:08:11,920
+مرتين على y معناه إن الناتج لا بعتمد على x ولا على
+
+98
+00:08:11,920 --> 00:08:17,110
+yبنسميه دايما constant lambda beta إلى أخرى زى ما
+
+99
+00:08:17,110 --> 00:08:21,290
+نشايفين على السطورة minus x double prime على x
+
+100
+00:08:21,290 --> 00:08:25,550
+اللى بتساوي y double prime على y لازم كل واحد منهم
+
+101
+00:08:25,550 --> 00:08:29,950
+يكون بساوي some constant كل واحد منهم بساوي some
+
+102
+00:08:29,950 --> 00:08:37,970
+constant احنا سميناه lambda ابتعدى
+
+103
+00:08:37,970 --> 00:08:42,030
+معادلتين على هيكي المعادلة الأولى بتقولى انه x
+
+104
+00:08:42,030 --> 00:08:42,870
+double prime
+
+105
+00:08:46,700 --> 00:08:51,820
+زائد Lambda X ساوثة والتانية بيقولي Y double prime
+
+106
+00:08:51,820 --> 00:08:58,860
+minus Lambda Y ساوثة كل واحدة منهم second order
+
+107
+00:08:58,860 --> 00:09:01,700
+differential equation يعني ال second derivative
+
+108
+00:09:01,700 --> 00:09:05,900
+differential equation اللي بقدر حلهم بسهولة زي ما
+
+109
+00:09:05,900 --> 00:09:10,420
+استخدمنا هذه ممكن شفتوها أول مرة في الدوائر في ال
+
+110
+00:09:10,420 --> 00:09:14,180
+natural response صح؟و بعدين أخدهم في الـ
+
+111
+00:09:14,180 --> 00:09:16,620
+differential في هذه المعادلات يعني هذه المعادلات
+
+112
+00:09:16,620 --> 00:09:19,340
+اللي بتوصلوا أنها معادلات سهل بالنسبالي تحلوها
+
+113
+00:09:19,340 --> 00:09:23,800
+بدون ما ننسى ال boundary conditions خليني أرجع لل
+
+114
+00:09:23,800 --> 00:09:27,120
+boundary conditions اللي كتبناهم قبل قليل و نعيد
+
+115
+00:09:27,120 --> 00:09:37,940
+كتبتهم لما نفصل ال variables نقول لذى نقطع
+
+116
+00:09:37,940 --> 00:09:42,500
+على جانب لكي نتذكر انه هي ال y وهي ال x
+
+117
+00:09:48,720 --> 00:09:52,920
+الواتنشال هنا بيساوي صفر وهنا بيساوي صفر وهنا
+
+118
+00:09:52,920 --> 00:09:56,960
+بيساوي صفر هاي الطبيب كونه طبيب هده كون ايه وهده
+
+119
+00:09:56,960 --> 00:10:02,320
+هيكون الواتنشال طبعا ال gaps احنا حكينا عنهم هيك
+
+120
+00:10:02,320 --> 00:10:06,140
+هدولها ال gaps عشان ايش يعمل insulation لان لو
+
+121
+00:10:06,140 --> 00:10:10,400
+حاطلناهم جن بعض ايش بيصير الواتنشال بتوزع بيصير يا
+
+122
+00:10:10,400 --> 00:10:15,620
+كله صفر يا كله V node اذا
+
+123
+00:10:15,620 --> 00:10:19,770
+نرجع للvaried conditionsالـ Potential عند X equals
+
+124
+00:10:19,770 --> 00:10:24,550
+0 و أي كيملة Y و
+
+125
+00:10:24,550 --> 00:10:31,550
+أي كيملة Y ما بين 0 و B، إيش Potential بتساوي 0؟
+
+126
+00:10:31,550 --> 00:10:43,830
+صح، عند X equals 0،
+
+127
+00:10:43,830 --> 00:10:56,470
+X و 1، X equals 0؟Y من الـ 0 و الـ A إذا
+
+128
+00:10:56,470 --> 00:10:59,270
+أنا عند X equal 0 و Y من الـ 0 لـ A البوتنشال
+
+129
+00:10:59,270 --> 00:11:05,070
+بيساوي 0 انهوض على البوتنشال دلوقت X و YX اله
+
+130
+00:11:05,070 --> 00:11:08,950
+function of X عند تقيمة X بتساوي 0 هاي ال boundary
+
+131
+00:11:08,950 --> 00:11:12,510
+عند هاي النقطة بالذات Y as function of Y اللي هي Y
+
+132
+00:11:12,510 --> 00:11:15,330
+قولنا من 0 ل A إيش كمية ال potential عند هذه ال
+
+133
+00:11:15,330 --> 00:11:20,170
+wall بتساوي 0 عندها الحيطة اللي هي X بتساوي 0 وY
+
+134
+00:11:20,170 --> 00:11:26,770
+ما بين ال 0 و ال A بتتشتج بساوي 0 Y من 0 ل A
+
+135
+00:11:26,770 --> 00:11:32,360
+أتوقعش مهتكون 0قيمة ال potential لكن قد يكون ال
+
+136
+00:11:32,360 --> 00:11:36,420
+potential عند نقطة محددة x at x equal 0 بسوء سفر
+
+137
+00:11:36,420 --> 00:11:42,800
+يعني هذه y as function of y فهذا function بقي سوء
+
+138
+00:11:42,800 --> 00:11:47,600
+0 اذا اللي اكيد لازم بيسوء 0 قيمة x at 0 اذا ال x
+
+139
+00:11:47,600 --> 00:11:52,420
+at 0 بتسوء سفر كمان مرة ال potential عند x equal b
+
+140
+00:11:52,420 --> 00:11:58,640
+x equal b لها نقطة و y بين ال 0 و ال nبرضه بتنشل
+
+141
+00:11:58,640 --> 00:12:04,000
+بساوة 0 اعود عن x equal b و y بيبقى y انها بين
+
+142
+00:12:04,000 --> 00:12:10,600
+مجموعة من النقاط من 0 ك a برضه بتساوة 0 y as a
+
+143
+00:12:10,600 --> 00:12:12,720
+function of y قلنا ده ال function ال potential
+
+144
+00:12:12,720 --> 00:12:15,600
+يعني اذا خلقتها سفر كل potential تبقى بساوة 0 لو
+
+145
+00:12:15,600 --> 00:12:20,320
+أخدت y ال y بساوة 0 لوش معنى x ال b هي اللي هتساوة
+
+146
+00:12:20,320 --> 00:12:26,420
+0 اذا استنتجنا ان x عندنا نقطة 0 بساوة 0 هيبقى
+
+147
+00:12:30,420 --> 00:12:36,760
+يجي انت اللي هي ال Y equal 0 X أو Zero هتسوى X ال
+
+148
+00:12:36,760 --> 00:12:43,810
+X و Y ال Zero برضه بتسوى صفرx هو بين 0 و b و y
+
+149
+00:12:43,810 --> 00:12:47,610
+بيكون صفر و potential صفر نفس المنطق أنا ماقدرش
+
+150
+00:12:47,610 --> 00:12:50,830
+أخد ال function x of x بيكون صفر لإن إذا حد هو صفر
+
+151
+00:12:50,830 --> 00:12:54,510
+مع أن ال potential صفر لإن y هو صفر لإن y هو صفر
+
+152
+00:12:54,510 --> 00:13:02,810
+لإن y هو صفر لإن y هو صفر لإن y هو صفر لإن y هو
+
+153
+00:13:02,810 --> 00:13:05,670
+صفر لإن y هو صفر لإن y هو صفر لإن y هو صفر لإن y
+
+154
+00:13:05,670 --> 00:13:07,930
+هو صفر لإن y هو صفر لإن y هو صفر لإن y هو صفر لإن
+
+155
+00:13:07,930 --> 00:13:08,690
+y هو صفر لإن y هو صفر لإن y هو صفر لإن y هو صفر
+
+156
+00:13:08,690 --> 00:13:12,870
+لإن y هو صفر لإن y هو صفر لإن y هو صفر لإبتساوي X
+
+157
+00:13:12,870 --> 00:13:22,530
+بتساوي Zero Y and الان X Zero Y الان X ال X عند اي
+
+158
+00:13:22,530 --> 00:13:27,970
+نقطة ل X و Y ال Zero احنا قلنا X خلصها من Zero من
+
+159
+00:13:27,970 --> 00:13:35,690
+ال B و X equal Zero و X and Y بيساوي B يعني هذا X
+
+160
+00:13:35,690 --> 00:13:36,990
+بتساوي Zero و Y
+
+161
+00:13:54,350 --> 00:13:55,750
+X0YY
+
+162
+00:14:02,940 --> 00:14:07,220
+و بعدين x,b,y اللي هم ال wall هادي و ال wall هادي
+
+163
+00:14:07,220 --> 00:14:11,080
+و بعدين أخدنا ال x equal x و y zero اللي هاي ال
+
+164
+00:14:11,080 --> 00:14:18,240
+wall فهد المفروض هد ال y equal zero و ال x equal x
+
+165
+00:14:18,240 --> 00:14:24,880
+و هد ال y بتساوي a و ال x بتساوي x عشان x هادي فهد
+
+166
+00:14:24,880 --> 00:14:27,860
+متأثرة هد x فهي x ال x و y ال a
+
+167
+00:14:30,930 --> 00:14:35,090
+هذه بتساوي V0، اذا عندنا اخر واحدة هي ال X ال
+
+168
+00:14:35,090 --> 00:14:43,010
+function of X و Y هي عند ال R بتساوي V0
+
+169
+00:14:45,750 --> 00:14:49,110
+اللي انا بقدر اقيم اقول ان ال X of X اللي مستحيل
+
+170
+00:14:49,110 --> 00:14:53,730
+اخليها يعني constant هي variable X ال X و Y ال A
+
+171
+00:14:53,730 --> 00:14:58,410
+مش لحالة هسو ال V0 حاصل ضرب ما هو ال V0 فماش بنقول
+
+172
+00:14:58,410 --> 00:15:01,710
+عنها inseparable مش زي هدولة كان معضح اللي بقدرش
+
+173
+00:15:01,710 --> 00:15:05,250
+اقول ان Y ال Y بالسوء 0 اذا X ال 0 هي السفر هنا Y
+
+174
+00:15:05,250 --> 00:15:09,160
+ال Y بقدرش اقول 0 اذا X ال B هي السفرهنا هو X الـ
+
+175
+00:15:09,160 --> 00:15:13,060
+X في Y الـ A التانية بساوة و V نقطة هذه انسبرة
+
+176
+00:15:13,060 --> 00:15:17,820
+ماقدرش أفصلهم عن بعض فبظل حاصل الضرب اللي هو X ال
+
+177
+00:15:17,820 --> 00:15:21,940
+X و Y عند ال A طبعا ال X هنا من 0 ل B اللي هو ال
+
+178
+00:15:21,940 --> 00:15:25,100
+range تبع ال X و Y كمتها A بساوة و V نقطة إذا ما
+
+179
+00:15:25,100 --> 00:15:28,280
+هي الأربعة boundary conditions اللي بدأ أحطهم يعني
+
+180
+00:15:28,280 --> 00:15:33,510
+باعتبار كل الوقتهذه المعادلتين اللي بدي أحلهم عشان
+
+181
+00:15:33,510 --> 00:15:37,470
+أبدأ أحل هدول المعادلتين لازم أعطي تخمينات لقيمة
+
+182
+00:15:37,470 --> 00:15:43,110
+ال Y إذا حلت واحدة تانية ع طول بحلها بغير إشارة ال
+
+183
+00:15:43,110 --> 00:15:46,750
+Lambda أول حاجة عشان أحل واحدة منهم باخد واحدة
+
+184
+00:15:46,750 --> 00:15:50,890
+منهم طبعا ده أحلعشان احلها بدي اخمن ايش قيم اللمدة
+
+185
+00:15:50,890 --> 00:15:56,090
+طبعا احنا بسرعة ممكن نخمن ان اللمدة لازم تكون صفر
+
+186
+00:15:56,090 --> 00:15:58,830
+لازم احط يعني خيارات لها بس لازم نعمل check لهم
+
+187
+00:15:58,830 --> 00:16:02,770
+تلاتة ان احتمالية لمدة تكون zero او موجبة او سلبة
+
+188
+00:16:02,770 --> 00:16:06,930
+موجودين وردين ممكن يكونوا مروا علينا في الدوائر
+
+189
+00:16:06,930 --> 00:16:10,850
+ويعرفنا ايش هو لازم يكون الحل بس لازم نحلهم مرة
+
+190
+00:16:10,850 --> 00:16:15,510
+تانية مع بعض و نتأكد ان الحل صحيحنبدأ في λمدة 0
+
+191
+00:16:15,510 --> 00:16:18,990
+اول حالة ايش معناه ان x double prime مش بالساوة
+
+192
+00:16:18,990 --> 00:16:22,710
+صفر فالمعادلة اللى قدامنا احط لمدة بالساوة صفر اذا
+
+193
+00:16:22,710 --> 00:16:25,250
+x double prime بالساوة صفر صارت مهلها سهل اني
+
+194
+00:16:25,250 --> 00:16:29,390
+اكملها هنا بحلها differential equation separation
+
+195
+00:16:29,390 --> 00:16:36,270
+of variables بحط ال x لحالة ال function x لحالة و
+
+196
+00:16:36,270 --> 00:16:40,730
+ال dx لحالة و بنعمل كمرة تكامل بس بكون شوية أطولة
+
+197
+00:16:40,730 --> 00:16:42,810
+زى ما قلنا ال natural response اللى أخدته في
+
+198
+00:16:42,810 --> 00:16:47,920
+الدوائرهذا أبسط اكس دابل برانز ساوة زيرو هكي اعمل
+
+199
+00:16:47,920 --> 00:16:50,720
+اول مرة او تاني مرة اول مرة هتعطيني some constant
+
+200
+00:16:50,720 --> 00:16:56,580
+ايه المرة التانية هتعطيني ax زائد b تمام بدنا ايش
+
+201
+00:16:56,580 --> 00:16:59,620
+نسويه نستخدم ال boundary conditions فى ان نقولنا
+
+202
+00:16:59,620 --> 00:17:05,600
+عند x equals 0 x equals 0 بيهدف x equals 0 مش كي
+
+203
+00:17:05,600 --> 00:17:12,540
+بتنشط سفر عند x equals 0 بتنشط بساوة زيرو نحط
+
+204
+00:17:21,330 --> 00:17:25,190
+عشان احط عن ال variable X0 و ال potential بالساوة
+
+205
+00:17:25,190 --> 00:17:30,470
+0 اذا P مالها سفر اذا عند النقطة X بالساوة سفر ال
+
+206
+00:17:30,470 --> 00:17:34,150
+potential X بالساوة 0 اذا P بالساوة 0 اذا هاي
+
+207
+00:17:34,150 --> 00:17:37,250
+المعادلة اتوصلت ل A اش ل X بالساوة Ax دل على يمين
+
+208
+00:17:37,250 --> 00:17:41,530
+ال A طب احنا كمان عنا كمان boundary condition ان X
+
+209
+00:17:41,530 --> 00:17:49,050
+ال XX عند ال B برضه بتسوى 0 اذا نعود عن هذه
+
+210
+00:17:49,050 --> 00:17:55,350
+المبتدأ X equal B ال potential بيسوى 0 اعود X عند
+
+211
+00:17:55,350 --> 00:18:01,190
+ال B يعني A في B بيسوى 0 صح؟A بB بيساو سفر بي
+
+212
+00:18:01,190 --> 00:18:03,870
+كونستانت اذا عرفت ان قيمته ممكن تكون عشرة أو كون
+
+213
+00:18:03,870 --> 00:18:07,350
+طول المتوازن اللي اطلع عليه ممكن تكون سفر اذا مين
+
+214
+00:18:07,350 --> 00:18:10,750
+لازم يساو سفر الـA دي طب اذا A سفر وB سفر اذا ال
+
+215
+00:18:10,750 --> 00:18:14,990
+potential X اشمله سفر ال trivia مطبع لما يكون ال
+
+216
+00:18:14,990 --> 00:18:18,490
+potential زيرو هذا هيكون احد الحلول لكن نسميه
+
+217
+00:18:18,490 --> 00:18:21,250
+trivia solution يعني اسهل حلة او دايما الحل لأي
+
+218
+00:18:21,250 --> 00:18:24,370
+معادل differential زيرو احد الحلول هيكون بس مش
+
+219
+00:18:24,370 --> 00:18:30,830
+الحل النهائي اذا نستنتج ان لامدة لا تساوي زيروأي
+
+220
+00:18:30,830 --> 00:18:35,030
+أكبر من صفر يعني موجبة أو أقل من صفر يعني سالبة
+
+221
+00:18:36,030 --> 00:18:39,370
+ناخد lambda أقل من zero عشان أؤكد لحالي أن lambda
+
+222
+00:18:39,370 --> 00:18:42,890
+أقل من zero باخدها أنها سالب a تربيع حاجة تربيع ال
+
+223
+00:18:42,890 --> 00:18:46,830
+alpha تربيع ال b تربيع لإيش؟ لأن التربيع ملوجة بحط
+
+224
+00:18:46,830 --> 00:18:50,330
+السالب قدامه معناه نأكد أن lambda مالها قيمة سالبة
+
+225
+00:18:50,330 --> 00:18:54,230
+لو أخدتها ده أي حاجة مش مربعة ممكن هيدقول والله
+
+226
+00:18:54,230 --> 00:18:57,910
+ممكن هيدكون سالبة فعشان أعرف الناس أن أنا ماخدة
+
+227
+00:18:57,910 --> 00:19:02,270
+lambda أنها سالبة بقول minus a minus alpha تربية
+
+228
+00:19:02,270 --> 00:19:07,530
+مثلانعوض عن هذا الحكيم xw' ما نسأل في تربيع x
+
+229
+00:19:07,530 --> 00:19:12,450
+بالساوة 0 ممكن احنا نعملها دلالة d تربيع حيث اعرف
+
+230
+00:19:12,450 --> 00:19:16,950
+دي تربيع هي d by dx بتصير اسهل ليه او ممكن زي ما
+
+231
+00:19:16,950 --> 00:19:20,810
+حكيت انه نحلها انه اعمل اللي هي ال expression
+
+232
+00:19:20,810 --> 00:19:25,230
+variables و احل زي ما استخدمته في دور الواحد او في
+
+233
+00:19:25,230 --> 00:19:28,050
+ال differential d تربيع ما نسأل تربيع x بالساوة 0
+
+234
+00:19:28,050 --> 00:19:34,080
+بستخدم ان هو فرق بمربعيندى plus minus alpha اللى x
+
+235
+00:19:34,080 --> 00:19:37,660
+بتساوي zero فبتعطينا ان ال differential بيه بتساوي
+
+236
+00:19:37,660 --> 00:19:43,720
+plus dx by dx بتساوي alpha x يا dx by dx بتساوي
+
+237
+00:19:43,720 --> 00:19:48,680
+ثالث alpha x اللى هى الحل التانى فده بستكمله
+
+238
+00:19:48,680 --> 00:19:54,980
+للأولى تمام؟ احنا بقى افصل بحط dx على x بتساوي
+
+239
+00:19:54,980 --> 00:20:00,810
+alpha dxو على كامل بيطلع معايا ان x ايش بتساوي a1
+
+240
+00:20:00,810 --> 00:20:05,350
+e to the alpha x لو أخدت السالبة باعد نفس الكلام و
+
+241
+00:20:05,350 --> 00:20:08,290
+بتطلع ل x بتساوي اتنين e to the minus alpha x
+
+242
+00:20:08,290 --> 00:20:13,490
+واضح؟ اذا لو أخدت الموجبة dx by dx بتساوي alpha x
+
+243
+00:20:13,490 --> 00:20:18,190
+واضح يعني اش اللي انا بحكيه يازم أخطط
+
+244
+00:20:28,040 --> 00:20:41,980
+هذه هي تربية X Y X X X X X X X
+
+245
+00:20:41,980 --> 00:20:42,660
+X X X X X X X X X X X X X X X X X X X X X X X X X
+
+246
+00:20:42,660 --> 00:20:47,440
+X X X
+
+247
+00:20:47,440 --> 00:20:47,980
+X X X X X X X X X X X X X X X X X X X X X X X X X
+
+248
+00:20:47,980 --> 00:20:48,320
+X X X X X X X X X X X X X X X X X X X X X X X X X
+
+249
+00:20:48,320 --> 00:20:48,320
+X X X X X X X X X X X X X X X X X X X X X X X X X
+
+250
+00:20:48,320 --> 00:20:48,320
+X X X X X X X X X X X X X X X X X X X X X X X X X
+
+251
+00:20:48,320 --> 00:20:48,320
+X X X X X X X X X X X X X X X X X X X X X X X X X
+
+252
+00:20:48,320 --> 00:20:48,320
+X X X X X X X X X X X X X X X X X X X X X X X X X
+
+253
+00:20:48,320 --> 00:20:48,320
+X X X X X X X X X X X X X X X X X X X X X X X X X
+
+254
+00:20:48,320 --> 00:20:50,560
+X X X X X
+
+255
+00:20:57,020 --> 00:21:04,840
+هي أسميها D تربيه مانوس ألف تربيه X تربيه من فضل X
+
+256
+00:21:04,840 --> 00:21:09,200
+تربيه
+
+257
+00:21:09,200 --> 00:21:14,740
+من فضل X تربيه من فضل X تربيه من فضل X تربيه من
+
+258
+00:21:14,740 --> 00:21:16,800
+فضل X تربيه من فضل X تربيه من فضل X تربيه من فضل X
+
+259
+00:21:16,800 --> 00:21:17,000
+تربيه من فضل X تربيه من فضل X تربيه من فضل X تربيه
+
+260
+00:21:17,000 --> 00:21:17,000
+من فضل X تربيه من فضل X تربيه من فضل X تربيه من
+
+261
+00:21:17,000 --> 00:21:17,000
+فضل X تربيه من فضل X تربيه من فضل X تربيه من فضل X
+
+262
+00:21:17,000 --> 00:21:19,360
+تربيه من فضل X تربيه من فضل X تربيه من فضل X تربيه
+
+263
+00:21:19,360 --> 00:21:23,240
+من فضل
+
+264
+00:21:23,240 --> 00:21:26,460
+X تربيه
+
+265
+00:21:26,460 --> 00:21:26,480
+من
+
+266
+00:21:34,750 --> 00:21:40,530
+بس هنأول لاقينا حل لما Alpha موجبة هي بتعطينا طبعا
+
+267
+00:21:40,530 --> 00:21:48,290
+D بساوي plus minus Alpha X هي عادي تساوي سكر D
+
+268
+00:21:48,290 --> 00:21:51,730
+plus Alpha X بتساوي Zero اذا D بتساوي minus Alpha
+
+269
+00:21:51,730 --> 00:21:56,250
+X او D minus Alpha X بتساوي Zero زمان معناها D بال
+
+270
+00:21:56,250 --> 00:21:59,170
+X بتساوي Alpha X
+
+271
+00:22:26,470 --> 00:22:31,030
+الحل تبعهم زى ما كنتوا شايفين دى ال X على X بتساوي
+
+272
+00:22:31,030 --> 00:22:36,450
+Alpha X أقسم على X و بضرب في DX فهتكون DX على X
+
+273
+00:22:36,450 --> 00:22:41,350
+بتساوي Alpha DX تكامل هى اللى لناوهي هتكون ال X
+
+274
+00:22:41,350 --> 00:22:45,370
+فهتكون لن X زائد Alpha X زائد some constant لتسهيل
+
+275
+00:22:45,370 --> 00:22:50,690
+اللي بناخده لن ال A1 لتسهيل فهتكون عندي لن ال X
+
+276
+00:22:50,690 --> 00:22:55,650
+على A1 بتساوي Alpha X اخد ال exponential هتكون X
+
+277
+00:22:55,650 --> 00:22:59,190
+بتساوي A1 E to the Alpha of X لما ناخد ال Alpha
+
+278
+00:22:59,190 --> 00:23:02,190
+صالبة هيكون ال solution التاني ال complete
+
+279
+00:23:02,190 --> 00:23:06,520
+solution المجموعة التانيةمجموعة لما Alpha قدامها
+
+280
+00:23:06,520 --> 00:23:09,840
+إشارة موجبة و لما تكون قدامها إشارة سابقة حتى إن X
+
+281
+00:23:09,840 --> 00:23:13,500
+بيتساوية A1 E to the Alpha X زي إتنين E to the
+
+282
+00:23:13,500 --> 00:23:18,260
+minus Alpha X تمام هذا ال solution لسه مقاله نقص
+
+283
+00:23:18,260 --> 00:23:21,620
+لأن A1 و A2 مقالهم مش عارفينهم و أين بنتجيبهم ال
+
+284
+00:23:21,620 --> 00:23:27,920
+boundary condition عند X equal 0 و عند X equal A X
+
+285
+00:23:27,920 --> 00:23:32,720
+equal B عند X equal 0 و X equal B و احنا عيلنا
+
+286
+00:23:32,720 --> 00:23:36,380
+قيامهمعند X يبقى نحياتهم أنا حاططهم في الأعلى عشان
+
+287
+00:23:36,380 --> 00:23:41,140
+أستخدمها عند X equals 0 بتساوي 0 وعند X برضه
+
+288
+00:23:41,140 --> 00:23:46,640
+بتساوي D بها تساوي 0 معوض عند X equals 0 ال
+
+289
+00:23:46,640 --> 00:23:53,300
+potential بيساوي 0طبعا انا بقعد اكتب ال E to the X
+
+290
+00:23:53,300 --> 00:23:57,960
+و E to the minus X لكي
+
+291
+00:23:57,960 --> 00:24:00,200
+انا اعرف كيف يتصرف ال sin hyperbolic و ال cos
+
+292
+00:24:00,200 --> 00:24:04,080
+hyperbolic فبقعد اكتب ال solution هذا بها الطريقة
+
+293
+00:24:04,080 --> 00:24:07,920
+B1 cos hyperbolic Alpha X زي B2 sin hyperbolic
+
+294
+00:24:07,920 --> 00:24:11,540
+Alpha X لان دولة مربوطين ال cosine هي أفعل عن E to
+
+295
+00:24:11,540 --> 00:24:15,350
+the Alpha Xزائد e to the minus alpha x على اتنين
+
+296
+00:24:15,350 --> 00:24:18,950
+ال sine hyperbolic e to the alpha x minus e to the
+
+297
+00:24:18,950 --> 00:24:22,250
+minus alpha x على اتنين اذا بعض رعيات ساعدتهم على
+
+298
+00:24:22,250 --> 00:24:23,970
+شكل ال cosine hyperbolic و ال cosine hyperbolic
+
+299
+00:24:23,970 --> 00:24:28,430
+and x equals zero قلنا لو بتنشاش بيساوي zero اعود
+
+300
+00:24:28,430 --> 00:24:37,130
+x zero ال sine ال zero زيرولكن cosh0 هو 1 وcosh0
+
+301
+00:24:37,130 --> 00:24:40,870
+هو 1 وcosh0 هو 0 فما يبقى بيدي بيدي بيدي بيدي واحد
+
+302
+00:24:40,870 --> 00:24:44,210
+في واحد زائد زيرون فبيدي بيدي واحد زائد زائد زيرون
+
+303
+00:24:44,210 --> 00:24:44,210
+فبيدي بيدي واحد في واحد زائد زائد زيرون فبيدي بيدي
+
+304
+00:24:44,210 --> 00:24:44,210
+بيدي واحد في واحد زائد زائد زيرون فبيدي بيدي بيدي
+
+305
+00:24:44,210 --> 00:24:46,030
+واحد في واحد زائد زائد زيرون فبيدي بيدي بيدي واحد
+
+306
+00:24:46,030 --> 00:24:52,950
+في واحد زائد زائد زيرون فبيدي بيدي بيدي واحد في
+
+307
+00:24:52,950 --> 00:24:55,650
+واحد زائد زائد زائد زيرون فبيدي بيدي بيدي واحد في
+
+308
+00:24:55,650 --> 00:25:02,470
+واحد زائد زائد زائد زائد زائد زائد زائد زائ
+
+309
+00:25:02,840 --> 00:25:05,920
+Sin hyperbolic αb بb2
+
+310
+00:25:10,340 --> 00:25:13,920
+عنا Alpha لا تساو Zero احنا اختارناها و قولنا رقم
+
+311
+00:25:13,920 --> 00:25:17,440
+مش قولنا Lambda مش لازمة تساو Zero قولنا Lambda لا
+
+312
+00:25:17,440 --> 00:25:21,420
+تساو Zero minus Alpha تربية حاجة تربيعية ضربناها
+
+313
+00:25:21,420 --> 00:25:24,700
+تساو عشان نقولها قيمتها سالبة و بيستحيل تكون Zero
+
+314
+00:25:24,700 --> 00:25:29,000
+لان هو طول الضلة تبع ال waveguide بتاعتنا اذا مين
+
+315
+00:25:29,000 --> 00:25:32,820
+لازم يساو سفر؟ B2 اذا هذا مش لازم يساو سفر لا ال
+
+316
+00:25:32,820 --> 00:25:34,220
+Alpha سفر ولا ال B سفر
+
+317
+00:25:42,230 --> 00:25:45,850
+لازم لامدة لا تكون zero ولا تكون سالبة لازم تكون
+
+318
+00:25:45,850 --> 00:25:50,130
+موجبة لذا باخد الحل الصحيح ليه لامدة أكبر من سفر
+
+319
+00:25:50,130 --> 00:25:53,970
+لامدة مثلا ناخدها بي تربية ليش ناخد بي تربية كمرة
+
+320
+00:25:53,970 --> 00:25:58,800
+عشان أكد انها موجبةأيش هيكون عندى؟ x double prime
+
+321
+00:25:58,800 --> 00:26:01,940
+زي قدرية تربية x بالساوية zero نفس الخطوات اللى
+
+322
+00:26:01,940 --> 00:26:04,660
+عملناهم دى تربية زي قدرية تربية ال x بالساوية zero
+
+323
+00:26:04,660 --> 00:26:09,860
+معناه دى ال x بتساوية plus minus j beta x فده ايش
+
+324
+00:26:09,860 --> 00:26:14,860
+هتصير؟ هنا
+
+325
+00:26:14,860 --> 00:26:18,620
+كانت الحالة اللى بيقوله minus alpha تربيت اتخيل لو
+
+326
+00:26:18,620 --> 00:26:20,280
+حاطينها بال minus plus
+
+327
+00:26:27,460 --> 00:26:32,900
+يعني هاي x double prime سواء minus beta تردية x ال
+
+328
+00:26:32,900 --> 00:26:38,200
+minus هي اللي بتجيبنا ال plus minus في ال j واضح؟
+
+329
+00:26:38,200 --> 00:26:41,900
+لأ أسوأ أخدنا يعني طريقة تانية اللي هي الفرق بين
+
+330
+00:26:41,900 --> 00:26:46,620
+المراتبعين second derivative هترسميها ان x prime
+
+331
+00:26:46,620 --> 00:26:51,940
+هتساوي plus minus j beta x
+
+332
+00:26:58,060 --> 00:27:01,860
+هذه حلها بشكل either cos sin او e to the j beta x
+
+333
+00:27:01,860 --> 00:27:06,200
+minus g beta x يعني لو حلنا ال plus هتعطينا اللي
+
+334
+00:27:06,200 --> 00:27:09,340
+هي a to the j beta x ال minus هتعطينا a to the
+
+335
+00:27:09,340 --> 00:27:13,760
+minus j beta x فال total solution مجموع اتنين او
+
+336
+00:27:13,760 --> 00:27:19,200
+اكتبه بشكل cos و sin x في x بيساوي g zero cos beta
+
+337
+00:27:19,200 --> 00:27:23,520
+x زي g واحد sin beta x اذا بتذكرين ال cos مالها e
+
+338
+00:27:23,520 --> 00:27:28,570
+to the j beta xالـ plus e to the minus j beta x
+
+339
+00:27:28,570 --> 00:27:34,150
+على 2 الـ sine لـ beta x e to the j beta x minus e
+
+340
+00:27:34,150 --> 00:27:38,810
+to the minus j beta x على 2j هل تذكرين هذا الحكي؟
+
+341
+00:27:38,810 --> 00:27:42,090
+لنعود إلى الـboundary condition يعني x equal 0
+
+342
+00:27:42,090 --> 00:27:47,650
+بتنشر بسوء 0, j بتعمل 0 ماله؟ 1, sine of 0؟ 0 هذا
+
+343
+00:27:47,650 --> 00:27:50,510
+السفر ال term تظهر عندي ال j node, لذا ال j node
+
+344
+00:27:50,510 --> 00:27:55,360
+هي السفرلما اعود هذا مضروف في صفر خلاص Zero هذا
+
+345
+00:27:55,360 --> 00:27:59,680
+الرقم راح يظل عنده Zero ايش بتساوي G0 اذا G0
+
+346
+00:27:59,680 --> 00:28:03,300
+بتساوي صفر اذا هذا ال term كله راح لانه مضروف في
+
+347
+00:28:03,300 --> 00:28:07,460
+Zero يظل عند X ال X ايش بتساوي J1 Sine Beta X ال
+
+348
+00:28:07,460 --> 00:28:09,420
+term التاني و ان ال value of condition تاني عالمين
+
+349
+00:28:09,420 --> 00:28:15,920
+عند X equal B بده يكون potential Zero اذا عند Sine
+
+350
+00:28:15,920 --> 00:28:23,730
+Beta B في J1 هذا لازم يساوي صفر تمامجواحد مش لازم
+
+351
+00:28:23,730 --> 00:28:29,010
+تساوي سفر هذه مش لازم تساوي سفر اذا معناه ال sign
+
+352
+00:28:29,010 --> 00:28:33,030
+بقدر اقول انه بيساوي سفر عند قيم محددة وقت ايش
+
+353
+00:28:33,030 --> 00:28:36,490
+بيكون ال sign بيساوي سفر لما تكون beta b بتساوي
+
+354
+00:28:36,490 --> 00:28:40,810
+مالها multiples of pi يعني لا ال beta تكون zero
+
+355
+00:28:40,810 --> 00:28:44,470
+ولا ال b zero لكن ال multiples تبعهم حصل ضربهم
+
+356
+00:28:44,470 --> 00:28:49,970
+بساويmultiples of B يعني multiply B و Beta في B
+
+357
+00:28:49,970 --> 00:28:54,630
+إذا كانوا multiples of B هيكون صينهم بساوة سفر
+
+358
+00:28:54,630 --> 00:28:57,550
+وبالتالي بتحقق ال boundary condition بتاعي بدون ما
+
+359
+00:28:57,550 --> 00:29:00,690
+أشبر ال Beta تكون سفر أو ال B تكون سفر ال sign
+
+360
+00:29:00,690 --> 00:29:05,630
+تبعهم اللي Zero هذا بيعطينا قيمة مين Beta لأن بيه
+
+361
+00:29:05,630 --> 00:29:09,370
+احنا عارفين هل هو طول المتوازن الأطلع ف Beta اش
+
+362
+00:29:09,370 --> 00:29:15,650
+هتساور من B على Bهي بس تذكير هذه ال cosine
+
+363
+00:29:15,650 --> 00:29:18,290
+hyperbolic و ال sine hyperbolic ال cosine ال
+
+364
+00:29:18,290 --> 00:29:21,710
+hyperbolic عند ال zero بيساوي واحد ال sine
+
+365
+00:29:21,710 --> 00:29:25,610
+hyperbolic عند ال zero بيساوي zero لكن ال sine و
+
+366
+00:29:25,610 --> 00:29:28,810
+ال cosine هى شكلهم اذا انتوا مش ملاقينهم هى ال
+
+367
+00:29:28,810 --> 00:29:32,010
+sine و ال cosine بس بتكون shift مع ال sine اللى هى
+
+368
+00:29:32,010 --> 00:29:38,050
+بتبدأ من ال zero عند ال واحد، واضح؟ اذا نقول لها
+
+369
+00:29:38,050 --> 00:29:42,470
+ان بيتا ايش هتساوي nb على npi على b و n أرقام من
+
+370
+00:29:42,470 --> 00:29:47,790
+واحد ل infinityإذا X لأنه في X إيش بتساوي جي أن
+
+371
+00:29:47,790 --> 00:29:51,870
+بطلت يعني مجرد constant إحنا عندنا عدد لنهائي من
+
+372
+00:29:51,870 --> 00:29:56,290
+الحلول إحنا قولنا إن X ال X صفت مين جي واحد sign
+
+373
+00:29:56,290 --> 00:30:01,590
+ال beta X ولاقينا إنه beta بقدر تشتبها في دلالة ال
+
+374
+00:30:01,590 --> 00:30:07,050
+N باي على بي فإذا عندي أنا عدد لنهائي من الحلول
+
+375
+00:30:07,050 --> 00:30:12,820
+عند N واحد وانت نين وانت تلاتة فبقول إن ال Xالـ A
+
+376
+00:30:12,820 --> 00:30:19,700
+يعني sub script N بتسوى GN sin N by X على B و Beta
+
+377
+00:30:19,700 --> 00:30:24,860
+تربية بتسوى N تربية بY تربية على B تربية اللي هي
+
+378
+00:30:24,860 --> 00:30:31,060
+Lambda صارت عندنا الحل تبع X بالـ N معروف مافيش
+
+379
+00:30:31,060 --> 00:30:35,340
+اشي مجهول عندنا الى مين ال GN لسه هنجيب قمةها
+
+380
+00:30:35,340 --> 00:30:41,230
+الحاجة التانية لازم حل مين لل Yالـ y''ما نسبت
+
+381
+00:30:41,230 --> 00:30:45,890
+تربيع y بالساوة zero هتعطينا ان y'' بالساوة beta
+
+382
+00:30:45,890 --> 00:30:53,050
+تربيع y وبالتالي هيكون عندى قيمة ال y عشان ال
+
+383
+00:30:53,050 --> 00:30:57,270
+cosine hyperbola و ال cosine hyperbola بستخدم
+
+384
+00:30:57,270 --> 00:31:02,330
+boundary conditions بحصل على قيمة ال y وبالتالي
+
+385
+00:31:02,330 --> 00:31:06,310
+بحصل على ال potential الكلي لازل عندى مجهول هو مين
+
+386
+00:31:06,310 --> 00:31:07,250
+ال j و ال h
+
+387
+00:31:14,830 --> 00:31:19,030
+هذا هو ال potential يعني معناه c1v1 زي 6 يعني هى
+
+388
+00:31:19,030 --> 00:31:23,670
+معناه انه انا عندى n منهم ن منهم هى معناه فإذا vxy
+
+389
+00:31:23,670 --> 00:31:28,110
+هيكون مجموع كل الحلول يعني عندى انا معناه v1, v2,
+
+390
+00:31:28,350 --> 00:31:33,590
+v3, v4, v5, v6 الحل الكل مجموعهم كلهم لإنه عندى n
+
+391
+00:31:33,590 --> 00:31:36,410
+قلنا من 1 ل infinity
+
+392
+00:31:39,450 --> 00:31:44,790
+يكون مجموع كلها دولار potentials
+
+393
+00:31:44,790 --> 00:31:50,210
+لتمين ضل عندي برنامج condition and mean و y equal
+
+394
+00:31:50,210 --> 00:31:55,950
+a بسوا V0 هي اللي بستخدمها عشان أكمل الحل تبعي
+
+395
+00:31:55,950 --> 00:32:00,950
+عشان أجيب ال coefficient تبعي عن طريق استخدام free
+
+396
+00:32:00,950 --> 00:32:07,330
+expansion يعني بدي أكامل أضرب في ال sign و أكامل
+
+397
+00:32:08,410 --> 00:32:13,710
+بضرب في الـ sine و بكمل من 0 ل B ال X بطلع معايا
+
+398
+00:32:13,710 --> 00:32:20,290
+قيم اللي هي Cm لما يكون odd و لما يكون even عند
+
+399
+00:32:20,290 --> 00:32:24,710
+الـ N لما يكون odd لا تساوي 0 عند ال even هتعطينا
+
+400
+00:32:24,710 --> 00:32:30,950
+قيم 0 و بحصل على ال potential النهائي ان عند فقط
+
+401
+00:32:30,950 --> 00:32:35,130
+ال N ما لهم odd هاي ال constant تبعي حصلت عليه
+
+402
+00:32:36,010 --> 00:32:41,630
+وبعود و بحصل على ال total potential واضح؟ يعني
+
+403
+00:32:41,630 --> 00:32:47,930
+جزئية المهم لنا في حال زي كده ال separation of
+
+404
+00:32:47,930 --> 00:32:51,430
+variable أن أولا لما أتقن ال deal لproblem زي I
+
+405
+00:32:51,430 --> 00:32:55,510
+متوازن أضلع أبقى أرفع أحدث إيش الاعتمادية تعطي ال
+
+406
+00:32:55,510 --> 00:32:58,470
+potential على أي variable بس بعتمد على ال X و ال Y
+
+407
+00:32:58,470 --> 00:33:02,330
+كيف أقدر أعمل ال separation of variables غالبا
+
+408
+00:33:02,330 --> 00:33:06,330
+سؤال زي هذا مش هأجيبلكم ياه في الامتحانلكن هجيبلكم
+
+409
+00:33:06,330 --> 00:33:10,210
+جزئية منه موجود لكم متوازن قضاء اقولكوا كت بكيف
+
+410
+00:33:10,210 --> 00:33:14,730
+هتكون شكل ال potential على ايش بعتمد حط ال
+
+411
+00:33:14,730 --> 00:33:20,810
+boundary conditions بس لكن مش خطأ انكوا تبقوا مرة
+
+412
+00:33:20,810 --> 00:33:25,630
+واحدة في حياتكوا تحلوا السؤال للاخر اللي انا
+
+413
+00:33:25,630 --> 00:33:26,910
+شرحتلكم يعني
+
+414
+00:33:33,720 --> 00:33:41,020
+طبعا هذه كمان اللي هي لو كنا في .. لو كان انا عندى
+
+415
+00:33:41,020 --> 00:33:44,580
+ال potential ماله فى ال cylindrical coordinate نفس
+
+416
+00:33:44,580 --> 00:33:49,760
+الفكرة او فى ال spherical coordinate بيكون عندى ال
+
+417
+00:33:49,760 --> 00:33:50,200
+potential
+
+418
+00:33:53,370 --> 00:33:58,010
+بدأ اعترف اول حاجة انه انا بقدر افصل الاعتمادية
+
+419
+00:33:58,010 --> 00:34:00,710
+بتاعة ال raw و ال fi و ال z على بعض يعني بقدر اكتب
+
+420
+00:34:00,710 --> 00:34:04,770
+ال potential ع شكل r في raw fi في fi z في z هاي
+
+421
+00:34:04,770 --> 00:34:08,950
+الأسئلة اللي ممكن تجيكم يعني برجع بعوض هنا لما
+
+422
+00:34:08,950 --> 00:34:12,230
+افاض بالنسبة ل raw ال fi و ال z مقالهم constant
+
+423
+00:34:12,230 --> 00:34:16,070
+بالنسبة ل raw فبطلعوا برا تفاضل بيصير اللي fi z
+
+424
+00:34:16,070 --> 00:34:19,190
+على raw d by d raw بيصير exact differential mean
+
+425
+00:34:19,190 --> 00:34:23,800
+لل rالterm التاني باعتمد على الـ phi فبطلع مين
+
+426
+00:34:23,800 --> 00:34:28,120
+عندى ال R و ال Z بتبقى اللى هى الاعتماد هى على ال
+
+427
+00:34:28,120 --> 00:34:31,860
+phi ال term التالت ال R و ال phi constant بالنسبة
+
+428
+00:34:31,860 --> 00:34:36,260
+ل Z فببقى عندى D تنين Z و بعدى Z تربيه لو قسمت على
+
+429
+00:34:36,260 --> 00:34:40,020
+ال potential اللى هى مين R فى Phi فى Z فهذا ال
+
+430
+00:34:40,020 --> 00:34:43,400
+term بتقل منه S بتروح ل Phi و Z ببقى 1 على R
+
+431
+00:34:47,770 --> 00:34:51,770
+هنا لما اقسم هتظهر ال file وهنا لما اقسم مين هتظهر
+
+432
+00:34:51,770 --> 00:34:57,670
+ال zipنفس الحاجة لو انا حطيت الاعتمادية على z على
+
+433
+00:34:57,670 --> 00:35:01,870
+الطرف التاني من المعادلة بقول انه مجموع الاعتمادية
+
+434
+00:35:01,870 --> 00:35:05,150
+على ال R او ال R function تفاضله بال second
+
+435
+00:35:05,150 --> 00:35:08,550
+derivative لل R زاد second derivative لل Phi ايش
+
+436
+00:35:08,550 --> 00:35:13,410
+بتساوي ال second derivative لل Z معناه لا يعتمدوا
+
+437
+00:35:13,410 --> 00:35:17,350
+على بعض الناتج لازم يكون constant هناخده معينة
+
+438
+00:35:17,350 --> 00:35:22,380
+اصلا ده تربيه هيك محلت هاي الجزء من المعادلةلو 1 ع
+
+439
+00:35:22,380 --> 00:35:28,480
+Z D 2 Z by D Z تربية بتساوة لامدة تربية ها هي الحل
+
+440
+00:35:28,480 --> 00:35:33,380
+ع شكل cosine هبقى بيبقى لجزء التاني من المعادلة
+
+441
+00:35:33,380 --> 00:35:37,940
+اللي هو ال 10 ما تبقى اللي هو عبارة عن مين 1 ع رو
+
+442
+00:35:37,940 --> 00:35:40,560
+R D by D رو رو D R by D رو
+
+443
+00:35:44,380 --> 00:35:53,920
+و اذا ضربت في مين في R سيصبح واحد على رو D by D رو
+
+444
+00:35:53,920 --> 00:35:59,100
+رو D R by D رو زائد R على رو تربية على فاي D تنين
+
+445
+00:35:59,100 --> 00:36:06,640
+فاي تربية فاي تربية بيصير plus lambda تربية R او
+
+446
+00:36:06,640 --> 00:36:07,280
+حتى ال R
+
+447
+00:36:26,390 --> 00:36:31,730
+الترم الأولانى Z بيصير عشان كسان هبرب كسان هبربرك
+
+448
+00:36:31,730 --> 00:36:36,030
+الترم التانى بيعطينا هذه المعادلةكمان لو انا
+
+449
+00:36:36,030 --> 00:36:39,310
+حاطيتها دول على طرف اللى بيتمدوا على ال raw و
+
+450
+00:36:39,310 --> 00:36:42,450
+الطرف فالتالى نقلته minus 1 على فا دى تنين فا
+
+451
+00:36:42,450 --> 00:36:47,890
+تربية بقدر اقول ان الاعتمادية على ال raw بتساوي
+
+452
+00:36:47,890 --> 00:36:51,230
+الاعتمادية على ال فا اذا معناه ماله التنين
+
+453
+00:36:51,230 --> 00:36:56,670
+constant بتساوي ميو تربية اذا نفعد هذا ال term هذا
+
+454
+00:36:56,670 --> 00:37:01,460
+المعادلة اللى دى فا تربيةD2 5 by D5 تربية تسوى من
+
+455
+00:37:01,460 --> 00:37:05,320
+ميو تربية 5 تسوى من ميو تربية 0 هذه حالها برضه
+
+456
+00:37:05,320 --> 00:37:08,820
+معروفة عشان الكوسين والصين بيظل عند المعادلة اللى
+
+457
+00:37:08,820 --> 00:37:12,960
+بتعتمد على مين على ال رو رو تربية D2 R by D رو
+
+458
+00:37:12,960 --> 00:37:18,120
+تربية لو ضربنا في ال R زائد رو DR by D رو plus
+
+459
+00:37:18,120 --> 00:37:24,600
+لمدة تربيةRow تربية minus Mu تربية كل مضروف R
+
+460
+00:37:24,600 --> 00:37:28,880
+بساوة Zero هذه المعادلة معادلة مشهورة لازم تحفظوا
+
+461
+00:37:28,880 --> 00:37:32,520
+شكلها اسمها Bessel differential equation مرقت
+
+462
+00:37:32,520 --> 00:37:38,420
+عليكم بيسل ال equation؟ أخدتوا communication؟ يعني
+
+463
+00:37:38,420 --> 00:37:40,560
+مسحبكم ولم يمرقتوا عليكم بيسل بال communication
+
+464
+00:37:40,560 --> 00:37:47,490
+لازم تكون مرقت عليكم بيسل المعادلات المشهورةبشكلها
+
+465
+00:37:47,490 --> 00:37:52,590
+مواضح ومعروف للرياضيين والمهدسين وغيرهم من اللي هي
+
+466
+00:37:52,590 --> 00:37:55,990
+applied sciences بيستخدموها على طول و بيقولوا ان
+
+467
+00:37:55,990 --> 00:38:00,890
+solution أو حلها معروف موجود في ال tables اللي هو
+
+468
+00:38:00,890 --> 00:38:03,810
+mean Bessel function هذه المعادلة اسمها Bessel
+
+469
+00:38:03,810 --> 00:38:08,390
+equation وحلها اسمه Bessel function هذا هو المطلوب
+
+470
+00:38:08,390 --> 00:38:11,990
+منكم بتتفلق ال cylindrical coordinate ال
+
+471
+00:38:11,990 --> 00:38:16,930
+cylindrical coordinate جربوا هيك تلعبوادلتر بيه V
+
+472
+00:38:16,930 --> 00:38:20,030
+بتساوي Zero كيف بتكون شكلها بالـ spherical
+
+473
+00:38:20,030 --> 00:38:25,250
+coordinate نجلاق
+
+474
+00:38:25,250 --> 00:38:28,810
+ال resistance و ال capacitance احنا اتعلمنا اشياء
+
+475
+00:38:28,810 --> 00:38:34,750
+كتير خلال المحاضرات الماضية اتعلمنا انه بنكتب ال
+
+476
+00:38:34,750 --> 00:38:38,740
+potential ابدلالة ال electric fieldبتساوي التكامل
+
+477
+00:38:38,740 --> 00:38:42,680
+ل E ضد DL وال current اتعلمنا انه عبارة عن ال
+
+478
+00:38:42,680 --> 00:38:46,520
+clause integral ل J ضد DS ومين هي J قلنا هي sigma
+
+479
+00:38:46,520 --> 00:38:50,820
+E اللي هي ال point form ل Ohm's law J بتساوي sigma
+
+480
+00:38:50,820 --> 00:38:53,980
+E اذا ال potential اللي هو بساوي ال integral ل E
+
+481
+00:38:53,980 --> 00:38:57,200
+ضد DL وال current اللي هو ال clause integral ل J
+
+482
+00:38:57,200 --> 00:39:01,420
+ضد DS او sigma E ضد DSبقدر استعين فيهم عشان أحسب
+
+483
+00:39:01,420 --> 00:39:05,280
+المقامة لل element اللي أنا بدرسه عمري أو ال
+
+484
+00:39:05,280 --> 00:39:09,940
+waveguide اللي أنا بدرسها R بيسووا V على I Ohm's
+
+485
+00:39:09,940 --> 00:39:13,680
+law بيسووا ال integral ل E ضد DL على ال close
+
+486
+00:39:13,680 --> 00:39:19,870
+integral ل sigma E ضد DSأول خطوة انا دائما هي ان
+
+487
+00:39:19,870 --> 00:39:23,190
+اختار ال coordinate المناسب اذا انا بحكي على
+
+488
+00:39:23,190 --> 00:39:25,750
+متوازي أطلع اذا انكارتيش ال coordinate بحكي على
+
+489
+00:39:25,750 --> 00:39:27,890
+cylindrical و cylindrical coordinate بحكي على سفير
+
+490
+00:39:27,890 --> 00:39:31,890
+و سفير ك coordinate Assume V0 as a potential
+
+491
+00:39:31,890 --> 00:39:35,110
+difference between conductor terminal ال conductor
+
+492
+00:39:35,110 --> 00:39:39,810
+تبعي أسوأ هو cylindrical ولا متوازي أطلع ولا سفير
+
+493
+00:39:39,810 --> 00:39:43,450
+هو بده يكون ال potential difference بين طرفي ال
+
+494
+00:39:43,450 --> 00:39:48,630
+conductorبنحل ال plus equation ل V لان جيب V احنا
+
+495
+00:39:48,630 --> 00:39:54,770
+بعد ان ال V بقدر اجيب اللي هو E E بتسوى minus دل
+
+496
+00:39:54,770 --> 00:39:59,010
+ال V اذا جيبت ال E بقدر اجيب مين ال current لان ال
+
+497
+00:39:59,010 --> 00:40:01,170
+current مش بتسوى ال close integral ل Sigma E دول
+
+498
+00:40:01,170 --> 00:40:06,290
+DS جيبنا V جيبنا ال current اذا بجيب المقامة اللي
+
+499
+00:40:06,290 --> 00:40:10,690
+هتسوى V node على R اللي هو الفرق
+
+500
+00:40:14,880 --> 00:40:20,900
+هو ال current واضح احنا
+
+501
+00:40:20,900 --> 00:40:25,440
+بنعرف الفرق بين طرفي ال conductors لو مثلا هى عندي
+
+502
+00:40:25,440 --> 00:40:30,820
+انا المكسف مثلا هي plus Q minus Q وعندي بطارية هى
+
+503
+00:40:30,820 --> 00:40:36,040
+الطرف الموجب هو الطرف الثالثهذا الـ conductor واحد
+
+504
+00:40:36,040 --> 00:40:39,460
+اللي هو موصول بي الـ positive charges واطراف
+
+505
+00:40:39,460 --> 00:40:45,440
+السالب هي واحد واتنين V هي فرق الجهد بين واحد
+
+506
+00:40:45,440 --> 00:40:50,880
+واتنين V هي فرق الجهد بين واحد واتنين اتجاه ال
+
+507
+00:40:50,880 --> 00:40:54,640
+electric field منوجب للسالب وV اللي هو فرق الجهد
+
+508
+00:40:54,640 --> 00:40:58,600
+بين الأول ومينوس التاني اللي هو ايش بيساوي سالب ال
+
+509
+00:40:58,600 --> 00:41:06,810
+Integral 2 ل 1 E Dot Rالـ notation طبعا، اذا V1-V2
+
+510
+00:41:06,810 --> 00:41:13,610
+يسمى minus ال integral من 2 ل 1 E dot DL واضح؟
+
+511
+00:41:13,610 --> 00:41:18,150
+المكثف،
+
+512
+00:41:18,150 --> 00:41:22,490
+المكثف عبارة عن ميلي Q على V و Q من Gauss Law
+
+513
+00:41:22,490 --> 00:41:27,030
+بيساوي Epsilon ال close integral ل E dot DS و ال
+
+514
+00:41:27,030 --> 00:41:29,650
+potential ما احنا عارفينه ال integral ل E dot DL
+
+515
+00:41:34,750 --> 00:41:42,410
+هم كيف احصل على C؟ اول حاجة بفترض وجود Q و بقرر
+
+516
+00:41:42,410 --> 00:41:50,510
+قدش قيمة V in terms of Q ان بحل مين يعصله او ان
+
+517
+00:41:50,510 --> 00:41:55,670
+اول حاجة بفترض V و بقرر cube دلالة V بحل ان مين
+
+518
+00:41:55,670 --> 00:42:03,000
+لبلاس equation يعني يا ببدأ ب Q و بحل V دلالة Qأو
+
+519
+00:42:03,000 --> 00:42:07,420
+ببدأ فرضية أنه عندي V و بحل ال cube دلالة V
+
+520
+00:42:07,420 --> 00:42:15,680
+باستخدام ال plasic equations طبعا
+
+521
+00:42:15,680 --> 00:42:18,840
+معناه هيك أن دائما لازم أختار ال suitable
+
+522
+00:42:18,840 --> 00:42:21,980
+coordinate system إذا بنحكي على متوازق أطلع و
+
+523
+00:42:21,980 --> 00:42:24,200
+أختار ال Cartesian و الcylindrical باختار ال
+
+524
+00:42:24,200 --> 00:42:28,470
+cylindricalبختار الـ spherical و بعدين بختار two
+
+525
+00:42:28,470 --> 00:42:31,250
+conducting plates carrying charges plus q و minus
+
+526
+00:42:31,250 --> 00:42:34,630
+q يعني هدولة inherited يعني احنا لما نقول كيف احصل
+
+527
+00:42:34,630 --> 00:42:38,630
+على c already انا بقول لازم اختار coordinate صحيح
+
+528
+00:42:38,630 --> 00:42:41,950
+و عندى هيكون two plates واحد موجب واحد سالب هى
+
+529
+00:42:41,950 --> 00:42:45,990
+معناه ان احصل على c ولا لأ و بعدين يا بفرض q و بحل
+
+530
+00:42:45,990 --> 00:42:53,730
+v بدلالة q يا بفرض ال v و بحل q بدلالة v طيب
+
+531
+00:42:55,550 --> 00:42:58,550
+إذا قلنا بنختار الـ coordinate المناسب to
+
+532
+00:42:58,550 --> 00:43:03,270
+conducting plates بستخدم gauss law أو columns law
+
+533
+00:43:03,270 --> 00:43:07,350
+عشان أحسب E ومنها بحسب V و بعدين بقدر أحسب C
+
+534
+00:43:07,350 --> 00:43:14,210
+بيبسوق U على V هاي مثال، أسهل مثال هو البرر بلاي
+
+535
+00:43:14,210 --> 00:43:18,090
+الكاباستور لأنه أخدنا .. لما أخدنا ال gauss law
+
+536
+00:43:18,090 --> 00:43:20,830
+جبنا ال electric field تبع البرر بلاي الكاباستور
+
+537
+00:43:21,770 --> 00:43:25,650
+واحد من البلاد قاعد عند x equal 0 و البلاد التانى
+
+538
+00:43:25,650 --> 00:43:30,870
+قاعد عند مين x equal d الموجب عند x equal d و
+
+539
+00:43:30,870 --> 00:43:34,410
+السلب انه x equal 0 و بين ال two blades فى عندنا
+
+540
+00:43:34,410 --> 00:43:38,450
+dielectric media اللي هي y و المساحة بتاعة كل
+
+541
+00:43:38,450 --> 00:43:42,910
+blade يعني هدول زى دفترين دفتر فى و دفتر تحت
+
+542
+00:43:42,910 --> 00:43:46,650
+المساحة بتاعة كل دفتر هي S هى ال blades
+
+543
+00:43:49,680 --> 00:43:52,960
+Rho S اللي هي charge density على كل surface من
+
+544
+00:43:52,960 --> 00:43:56,700
+هدولة ال plates Q على S ال total charge على مساحة
+
+545
+00:43:56,700 --> 00:44:03,260
+بتاعة ال plate اللي هي S و D عبارة عن minus rho S
+
+546
+00:44:03,260 --> 00:44:07,180
+X hat اتجاهها هي اتجاه ال electric field من موجة
+
+547
+00:44:07,180 --> 00:44:10,760
+بلس سالب و اتجاهه وين يعني معناه في ال minus X
+
+548
+00:44:10,760 --> 00:44:16,200
+direction و هذا ينجزله انه D ان ال clause انتقلة D
+
+549
+00:44:16,200 --> 00:44:20,900
+ضد DS بتساويمن الـ closed الـ Q الـ Q اللي هي مين؟
+
+550
+00:44:20,900 --> 00:44:26,160
+رو أس في أس تروح الأس من الطرفين وتظهر أن D
+
+551
+00:44:26,160 --> 00:44:30,560
+بيتساور minus رو أس except بسبب احنا الاتجاه تبع
+
+552
+00:44:30,560 --> 00:44:34,440
+ال D باتجاه ال minus except E عبارة عن مين؟ D على
+
+553
+00:44:34,440 --> 00:44:39,380
+إبسلون هي رو أس على إبسلون في اتجاه الثالث except
+
+554
+00:44:39,380 --> 00:44:45,600
+إبسلون هي الـ dielectric ما بين ال two platesلو
+
+555
+00:44:45,600 --> 00:44:49,520
+بدى اكتبها دلت الـQ والـS رو S شبه رعمين الـQ على
+
+556
+00:44:49,520 --> 00:44:54,260
+S فإذا عندى ال electric field بيسوا minus Q على ي
+
+557
+00:44:54,260 --> 00:44:59,300
+S except هى جبنا ال electric field بقدر أجيب ال
+
+558
+00:44:59,300 --> 00:45:04,680
+potential انا لازم عشان أجيب ال C ال potential و Q
+
+559
+00:45:04,680 --> 00:45:07,300
+عرفت ان ال electric field بقدر أجيب ال potential
+
+560
+00:45:07,300 --> 00:45:10,940
+وبالتالي بقدر أجيب ال C ال potential ايش انا
+
+561
+00:45:10,940 --> 00:45:17,070
+بيساوي minus ال integral من 2 ل1 D بالDLرحمكم الله
+
+562
+00:45:17,070 --> 00:45:21,330
+احنا قولنا ال electric field بروح من واحد لاتنين
+
+563
+00:45:21,330 --> 00:45:23,970
+ال notation تبعنا اللي موجب للثالث اذا مافيه ايش
+
+564
+00:45:23,970 --> 00:45:29,710
+بيسوى minus ال integral من تنين لواحد E دول DL من
+
+565
+00:45:29,710 --> 00:45:35,290
+وين يعني؟ ايه بقى اتنين اللي هي zero و واحد اللي
+
+566
+00:45:35,290 --> 00:45:40,550
+هي دي اذا انت كامل ال X من وين طبعا DL هي DX هتكون
+
+567
+00:45:40,550 --> 00:45:45,670
+X hat و ال E اللي هو minus Q على Y أس X hatبالتالي
+
+568
+00:45:45,670 --> 00:45:50,430
+هيكون عندى .. بالنسبالى ال Q واليبسون S constant
+
+569
+00:45:50,430 --> 00:45:55,830
+بالنسبالى DX هيكون Q علي يبسون S وال DX بكملها من
+
+570
+00:45:55,830 --> 00:46:00,350
+0 لD يعني قيمتها D إذا V عبارة عن Q علي يبسون S في
+
+571
+00:46:00,350 --> 00:46:07,210
+D أو ببساطة هي A في D إذا C إيش بنفسه؟ إذا ماعرفين
+
+572
+00:46:07,210 --> 00:46:12,530
+ال potential وعارفين ال Q ال Q علي V هي عبارة عن C
+
+573
+00:46:13,100 --> 00:46:17,740
+أذا الـ Q على V بيبقى ثوّي Y أس على D بتعرفوا ايه
+
+574
+00:46:17,740 --> 00:46:22,820
+الـ Y على D؟ إن كسافة المكسفة برا الـ Plates
+
+575
+00:46:22,820 --> 00:46:26,680
+بيعتمد على الـ dielectric media اللي بين الـ Two
+
+576
+00:46:26,680 --> 00:46:31,800
+Plates المساحة المقطعية أو مساحة الـ Area تحت الـ
+
+577
+00:46:31,800 --> 00:46:37,950
+Plates و المسافة اللي بينها تمام؟لو احنا عدنا نفس
+
+578
+00:46:37,950 --> 00:46:41,890
+التجربة و جيبنا C لما يكون ال dialectic عبارة عن
+
+579
+00:46:41,890 --> 00:46:47,690
+مين؟ عن space، هو يعني هيكون C0 بتسوء Y0 S على D
+
+580
+00:46:47,690 --> 00:46:53,470
+بقدر اجيب من ال ratio ال 6 عرفة C قايصة قيمتها و
+
+581
+00:46:53,470 --> 00:46:58,410
+C0 بقدر اقول ان C على C0 هي مين؟ YR لأنها هتكون Y
+
+582
+00:46:58,410 --> 00:47:03,640
+على Y0سي على سي نود هتكون إبسلون على إبسلون نود
+
+583
+00:47:03,640 --> 00:47:06,720
+اللي هي إبسلون R و هاي اللي بيستخدموها الطريقة
+
+584
+00:47:06,720 --> 00:47:11,760
+لحساب ال dialectic constant لأي media أو relative
+
+585
+00:47:11,760 --> 00:47:16,920
+dialectic ل ال media برضه
+
+586
+00:47:16,920 --> 00:47:19,540
+بقدر أحسب ال energy stored لإنها ال energy stored
+
+587
+00:47:19,540 --> 00:47:24,300
+سوى نص CV تربيه اللي عبارة عن نص Q في V لإنه C
+
+588
+00:47:24,300 --> 00:47:28,810
+قلنا إيش بتساويC في V هي عبارة عن Q فبقدر أقول هي
+
+589
+00:47:28,810 --> 00:47:35,530
+برضه نص Q في V أو Q تربيه على اتنين سنة، واضح؟
+
+590
+00:47:35,530 --> 00:47:41,030
+تأسف صار لحد هنا؟ احنا هنكمل المحاضرة القادمة نحسب
+
+591
+00:47:41,030 --> 00:47:48,010
+C للسلمدر و للسفير و بعدين هنحسب ال R لكل نفس
+
+592
+00:47:48,010 --> 00:47:48,510
+الاشي في ال
+
+593
+00:47:51,720 --> 00:47:55,180
+أو سفير و هذا أشي بيهمنا كتير توع القهرة بلانعرف
+
+594
+00:47:55,180 --> 00:47:59,100
+إيش هي مقامة ال coaxial cable مثلا، الكثافة
+
+595
+00:47:59,100 --> 00:48:04,060
+بتاعته، هذه الأشياء اللي احنا ك applied engineers
+
+596
+00:48:04,060 --> 00:48:08,240
+أو ك engineers بتبتهمنا معرفتها و نربطها في وين في
+
+597
+00:48:08,240 --> 00:48:12,290
+الدوارليش احنا قولنا ان الدواء دى حلق حاصة من
+
+598
+00:48:12,290 --> 00:48:14,850
+الكهربا نقصية و احنا كل حاجة أخدناها في الدواء
+
+599
+00:48:14,850 --> 00:48:18,470
+اتنين بنقدر نحلها بالكهربا نقصية لذا هذا ال
+
+600
+00:48:18,470 --> 00:48:23,330
+chapter هنشوف كيف نكمل حساب ال C ل ال cylindrical
+
+601
+00:48:23,330 --> 00:48:27,710
+و ال spherical capacitor و بعدين هنشوف كيف نجيب
+
+602
+00:48:27,710 --> 00:48:34,090
+المقامة لعدد أنواع من ال elements مع بعض و ال
+
+603
+00:48:34,090 --> 00:48:38,450
+contactivityو منكون هذا الغرض من ان هذا ال chapter
+
+604
+00:48:38,450 --> 00:48:42,950
+انتهى لما احصل كل هاي elements يعطيكوا العافية و
+
+605
+00:48:42,950 --> 00:48:46,830
+القادمة نحاول انا أسرع يعني مش هاخد في التفاصيل
+
+606
+00:48:46,830 --> 00:48:50,490
+بتاعة كل ال problem يعني كل هاي تطبيقات
+
diff --git a/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/mm3J5R-uNUo.srt b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/mm3J5R-uNUo.srt
new file mode 100644
index 0000000000000000000000000000000000000000..6fe2588d6cb3420bad663526a097e300ad8ed210
--- /dev/null
+++ b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/mm3J5R-uNUo.srt
@@ -0,0 +1,1403 @@
+1
+00:00:21,080 --> 00:00:23,760
+باسم الله الرحمن الرحيم السلام عليكم ورحمة الله
+
+2
+00:00:23,760 --> 00:00:27,700
+وبركاته أنا اليوم إن شاء الله هنتابع موضوعنا بمساعدة
+
+3
+00:00:27,700 --> 00:00:32,660
+الكثافة باستخدام أسواق Laplace أو باستخدام Gauss
+
+4
+00:00:32,660 --> 00:00:37,340
+law شفنا من قبل ماضيا الparallel plate capacitor و
+
+5
+00:00:37,340 --> 00:00:39,960
+اليوم هنشوف اللي هو ال coaxial capacitor coaxial
+
+6
+00:00:39,960 --> 00:00:44,260
+capacitor عبارة عن أسطوانات و slender واحدة منهم
+
+7
+00:00:44,260 --> 00:00:46,880
+حاملة شحنة موجبة في ال charges والتانية حاملة شحنة سالبة في ال charges
+
+8
+00:00:48,040 --> 00:00:51,440
+عشان كل الأسطوانات فانا بدي أحسب اللي هو ال
+
+9
+00:00:51,440 --> 00:00:54,520
+electric field أو يعني ال capacitance و بالأحرى
+
+10
+00:00:54,520 --> 00:00:57,320
+اللي احنا بدنا نحسبه اللي هي ال capacitance في ال
+
+11
+00:00:57,320 --> 00:01:00,140
+electric field احنا بنقدر نجيبها بال Gauss law ال
+
+12
+00:01:00,140 --> 00:01:03,840
+Gauss law بين ال two cylinders فعمل ال imaginary
+
+13
+00:01:03,840 --> 00:01:08,080
+surface بقول ان Q تساوي ال closed integral دي دول دي 
+
+14
+00:01:08,080 --> 00:01:12,180
+أسطح اللي هي ال Epsilon E وهنا Epsilon لأن ال
+
+15
+00:01:12,180 --> 00:01:17,180
+media بين ال two cylinders فيها مادة الهواء او 
+
+16
+00:01:17,180 --> 00:01:20,980
+dielectric له permittivity Epsilon لو الهواء بقى
+
+17
+00:01:20,980 --> 00:01:25,430
+ال Epsilon  الناتجة هتكون Epsilon باتجاه ال electric
+
+18
+00:01:25,430 --> 00:01:28,290
+field في اتجاه ال raw فما انتم شايفين من بسطى في
+
+19
+00:01:28,290 --> 00:01:30,470
+ال negative charge هيكون في اتجاه ال raw فشيء
+
+20
+00:01:30,470 --> 00:01:34,190
+إكمالية لا على زد ولا على فاى في اتجاه ال electric
+
+21
+00:01:34,190 --> 00:01:38,470
+field في اتجاه ال raw فهيكون E raw 2pi raw L اللي
+
+22
+00:01:38,470 --> 00:01:42,750
+هي المساحة الجانبية للاسطوانة او مساحة السطح
+
+23
+00:01:42,750 --> 00:01:45,910
+للاسطوانة و الثاني ال electric field باستخدام
+
+24
+00:01:45,910 --> 00:01:49,970
+جاوس لو لل coaxial cable بين ال two cylinders و
+
+25
+00:01:49,970 --> 00:01:55,660
+عبارة عن Q على 2pi epsilon raw L في raw hatواضرب
+
+26
+00:01:55,660 --> 00:02:00,360
+بعدها نجيب ال potential ال potential ما ناقش بساوي
+
+27
+00:02:00,360 --> 00:02:05,920
+ناقص ال integral E من 2 إلى 1 من السالب للموجب E 
+
+28
+00:02:05,920 --> 00:02:12,260
+ضد DL E ضد DL و DL مين هنا في حالة ال raw يعني ان
+
+29
+00:02:12,260 --> 00:02:16,480
+انت من الدائرة الخارجية للدائرة الداخلية هيكون
+
+30
+00:02:16,480 --> 00:02:20,840
+اتجاه ال DL و يعني اتجاه ال raw فDL هي مين دي raw
+
+31
+00:02:20,840 --> 00:02:21,700
+واضرب
+
+32
+00:02:24,160 --> 00:02:28,780
+فإذا ما يكون V بيساوي من 2 ل 1 E دول DL و E اللي
+
+33
+00:02:28,780 --> 00:02:32,500
+هي Q على 2 Pi Epsilon رو L في رو هات و DL قولنا
+
+34
+00:02:32,500 --> 00:02:38,680
+مين D رو رو هات لو كملنا D رو على رو بتعطينا ln ال
+
+35
+00:02:38,680 --> 00:02:44,060
+رو من A ل B بتطلع معنا انه Q على 2 Pi Epsilon ln
+
+36
+00:02:44,060 --> 00:02:50,340
+ال B على A و C ماهي لمين Q على V فبقسم V على Q و
+
+37
+00:02:50,340 --> 00:02:54,420
+بقى اضبط الطرف الثاني فبتكون 2 باي ابسلون L أعلى
+
+38
+00:02:54,420 --> 00:03:01,240
+من ال B على A واضح طب
+
+39
+00:03:01,240 --> 00:03:05,560
+لو كان ال coaxial cable على شكل two spheres طلعوا
+
+40
+00:03:05,560 --> 00:03:09,220
+ورقة وكتبوا أسمائكم عليها وجيبولي ال capacitance
+
+41
+00:03:09,220 --> 00:03:13,780
+ده coaxial cable على شكل سفير spherical coaxial
+
+42
+00:03:13,780 --> 00:03:17,820
+cable ذلكوا بس خمس دقائق هحدد بقى عندهم بالتمام
+
+43
+00:03:21,980 --> 00:03:30,480
+تعال اجمل قدامي يا عزيزي
+
+44
+00:03:30,480 --> 00:03:37,480
+هيبقى
+
+45
+00:03:37,480 --> 00:03:41,500
+أسلمه الورق لو سمحته، ماتنساش تكون كاتب اسمك
+
+46
+00:03:41,500 --> 00:03:41,960
+على الورقة
+
+47
+00:04:07,820 --> 00:04:13,940
+في حد ما سلمش؟ إسراء؟ أسماء؟
+
+48
+00:04:13,940 --> 00:04:19,440
+يلا أسماء هاتي
+
+49
+00:04:19,440 --> 00:04:29,540
+وراء اتركي أسماء هاتي اسراء وراء اتركي
+
+50
+00:04:29,540 --> 00:04:30,960
+عليها معقمة احسن ما تخلص
+
+51
+00:04:34,400 --> 00:04:38,600
+نشوف قد ايه صعب السؤال، السؤال بيقولنا ان ال capacitance
+
+52
+00:04:38,600 --> 00:04:45,210
+لكوكسيا الكابل عشان كان spheres ال radius تبعهم بين
+
+53
+00:04:45,210 --> 00:04:49,090
+ال a و ال b يعني السفير الداخلية ال radius تبعها a
+
+54
+00:04:49,090 --> 00:04:52,470
+و الخارجية b عشان اجيب ال capacitance ان اللي
+
+55
+00:04:52,470 --> 00:04:54,990
+الداخلية عليها شحنة موجبة في ال charge و الخارجية حاملة شحنة سالبة في
+
+56
+00:04:54,990 --> 00:04:58,150
+ال charge بينهم ده electric epsilon عشان اجيب ال
+
+57
+00:04:58,150 --> 00:05:02,870
+electric field جاي ازاي نفترض سفير اللي هو ال
+
+58
+00:05:02,870 --> 00:05:06,470
+imaginary surface بين ال two spheres اللي هو ال
+
+59
+00:05:06,470 --> 00:05:10,210
+radius R فعكسون Q بتساوي ال closed integral دي دول
+
+60
+00:05:10,210 --> 00:05:16,490
+DS ايش تجاهها لما يكون ال sphere هيكون في تجاه
+
+61
+00:05:16,490 --> 00:05:22,510
+ال R هيكون E دوت DS و DS ايش هي عبارة يعني التكامل
+
+62
+00:05:22,510 --> 00:05:29,050
+هيكون في تجاه ال DS النوع بتاعها في تجاه اللي هو
+
+63
+00:05:29,050 --> 00:05:35,750
+ال R برضه R hat ف E دوت DS هتعطينا ER لان برضه ال
+
+64
+00:05:35,750 --> 00:05:40,970
+E هيكون في تجاه ال R hat هيكون ال dot product E في
+
+65
+00:05:40,970 --> 00:05:46,960
+DS والتكامل هي er 4 باي r تربيع اللي هو surface
+
+66
+00:05:46,960 --> 00:05:53,340
+مساحة
+
+67
+00:05:53,340 --> 00:05:57,160
+ال sphere في 4 باي r تربيع وبالتالي E as a
+
+68
+00:05:57,160 --> 00:06:02,040
+vector بتكون Q على 4 باي epsilon r تربيع واتجاه
+
+69
+00:06:02,040 --> 00:06:08,030
+R hat شفتوا قبل كده هذا التكامل القيمة وقلنا انه
+
+70
+00:06:08,030 --> 00:06:12,250
+كانها بالتمام ال field اللي جاي من ال charge في ال
+
+71
+00:06:12,250 --> 00:06:21,730
+center ولا لا هي كمؤثرة جاي بتاع ME 0 0 0 يعني ه
+
+72
+00:06:21,730 --> 00:06:27,770
+شوية خرابيش يعني قريبة مش كتير مش عارفة ايش هذا
+
+73
+00:06:27,770 --> 00:06:34,530
+يعني مش عارفة سفر حاولت
+
+74
+00:06:34,530 --> 00:06:35,650
+مش عارفة الشيء هذه
+
+75
+00:06:48,440 --> 00:06:59,740
+V ناقص integral من 2 ل 1 من السالب للموجب E
+
+76
+00:06:59,740 --> 00:07:05,020
+.DL من DL سيكون في اتجاه ال r hat E هي Q على 4 Y
+
+77
+00:07:05,020 --> 00:07:10,660
+r تربيع في r hat دوت دي r hat الـ Q على 4 باي epsilon
+
+78
+00:07:10,660 --> 00:07:13,420
+تطلع برا ال integration دي اللي عندي تكامل mean دي
+
+79
+00:07:13,420 --> 00:07:17,520
+R على R تربيع تكاملها 1 على R ما هيش انه فيه سالب
+
+80
+00:07:17,520 --> 00:07:21,420
+يروح مع بعض التكامل من A إلى A هيكون 1 على A ناقص
+
+81
+00:07:21,420 --> 00:07:26,420
+1 على B C اللي هي مين ال Q على V فع طول من هذا
+
+82
+00:07:26,420 --> 00:07:29,260
+القانون من قانون ال potential بقدر احصل على C
+
+83
+00:07:29,260 --> 00:07:33,020
+اللي هي Q على V تساوي 4 باي epsilon على 1 على A
+
+84
+00:07:33,020 --> 00:07:34,860
+ناقص 1 على B
+
+85
+00:07:40,280 --> 00:07:44,980
+تلخيص لكل ما حكيناه نستطيع نحسب اذا عرفنا نجيب ال
+
+86
+00:07:44,980 --> 00:07:47,620
+potential او بالأحرى اذا عرفنا ال electric field
+
+87
+00:07:47,620 --> 00:07:51,080
+نجيبه اذا جبنا ال electric field بقدر اجيب 2
+
+88
+00:07:51,080 --> 00:07:56,000
+quantities اللي هي R resistance بتاعة ال
+
+89
+00:07:56,000 --> 00:08:01,060
+transmission line و ال capacitance تاعته وC R هي
+
+90
+00:08:01,060 --> 00:08:06,430
+عبارة عن مين V على I و V هي ال integral E dot DLI
+
+91
+00:08:06,430 --> 00:08:11,730
+الـ closed integral دي ضد دي S دي الـ J ضد دي S J
+
+92
+00:08:11,730 --> 00:08:16,350
+اللي هي current density ومن اللي هو ohm's point Law
+
+93
+00:08:16,350 --> 00:08:20,630
+هتكون J ايش بتساوي سيجما E هذه I اللي هي closed
+
+94
+00:08:20,630 --> 00:08:26,330
+integral جي ضد دي S جي اللي هي سيجما E C هي Q على V
+
+95
+00:08:26,330 --> 00:08:29,670
+وQ اللي هي closed integral دي ضد دي S دي اللي هي
+
+96
+00:08:29,670 --> 00:08:36,150
+الـ Epsilon E و V الintegral E ضد دي L لو اخذنا
+
+97
+00:08:36,150 --> 00:08:40,750
+نوع خاص من ال media homogeneous isotropic السيجما
+
+98
+00:08:40,750 --> 00:08:44,230
+و الابسلون بيطلعوا برا ال integrals أنا بتاعت media
+
+99
+00:08:44,230 --> 00:08:47,930
+اشتغلتها على الكواردينيات و بتكون Linear,
+
+100
+00:08:48,090 --> 00:08:53,230
+Homogenous, Isotropic وضعت ال RFC هلاحظ ان ال RFC
+
+101
+00:08:53,230 --> 00:08:57,290
+ايش بتعطينا ابسلون على سيجما متذكرين ابسلون على 
+
+102
+00:08:57,290 --> 00:09:01,490
+سيجما ورقعت علينا اللي هي relaxation time اللي هو
+
+103
+00:09:01,490 --> 00:09:07,150
+الزمن اللازم ل ال field انه يشوف له relaxation في
+
+104
+00:09:07,150 --> 00:09:10,050
+قلب ال media قلنا في ال conductance كانت قد ايه
+
+105
+00:09:10,050 --> 00:09:14,210
+سريعة جدا في ال dielectric او في ال insulator كانت
+
+106
+00:09:14,210 --> 00:09:18,130
+بتاخذ ايام احدنا مثالين فهذا هو relaxation time
+
+107
+00:09:18,130 --> 00:09:24,560
+بساوي R في C بيساوي epsilon على sigma هذا تلخيص لبعض
+
+108
+00:09:24,560 --> 00:09:27,780
+القيام اللي ممكن نحصل عليها لاسواق الفرر بلاد
+
+109
+00:09:27,780 --> 00:09:33,020
+كبسطور C تاعته هتكون ابسلون S على D او D على سيجما
+
+110
+00:09:33,020 --> 00:09:36,700
+S او زي ما هتكونوا متعودين عليها رو D على S حيث دي
+
+111
+00:09:36,700 --> 00:09:40,380
+هي المسافة بين ال two plates وS اللي هي مساحة ال
+
+112
+00:09:40,380 --> 00:09:43,760
+بلاد و ابسلون هي ال dielectric بين ال two plates
+
+113
+00:09:43,760 --> 00:09:48,580
+و سيجما ال conductivity للبلاد الـ Cylindrical
+
+114
+00:09:48,580 --> 00:09:51,680
+Capacitor اللي حسبناه اليوم مع بعض C بيساوي 2 π
+
+115
+00:09:51,680 --> 00:09:55,580
+ابسلون L على ln ال B على A R بيساوي ln ال B على A
+
+116
+00:09:55,580 --> 00:10:00,940
+على 2 بي سيجما الـ Spherical C بيساوي 4 بي ابسلون
+
+117
+00:10:00,940 --> 00:10:05,200
+على 1 على A ناقص 1 على B R بيساوي 1 على A ناقص 1
+
+118
+00:10:05,200 --> 00:10:09,100
+على B على 4 بي سيجما لل Isolated Spherical
+
+119
+00:10:09,100 --> 00:10:14,040
+Conductor C بيساوي 4 بي ابسلون M يعني الخارجي
+
+120
+00:10:14,040 --> 00:10:20,310
+بيكون grounded فبيكون C بيساوي 4 باي epsilon A و R 1
+
+121
+00:10:20,310 --> 00:10:24,910
+على 4 باي سيجما A كل هدول مطلوب منكم تتعرفوا عليهم
+
+122
+00:10:24,910 --> 00:10:28,650
+تشتقوهم تتأكدوا انكم بتعرفوا تجيبوهم لان اكيد هجيبكم
+
+123
+00:10:28,650 --> 00:10:33,970
+في الامتحان واحد من هذه الاشياء بما انه انا بلحظة
+
+124
+00:10:33,970 --> 00:10:37,450
+انه احل لكم الامثلة و الامثلة هدي عليكم ومطلوبة
+
+125
+00:10:37,450 --> 00:10:40,790
+منكم و اللقاء القادم هتحلوا كل هذه الامثلة و
+
+126
+00:10:40,790 --> 00:10:45,150
+تجيبواهم على ورقة جاهزة احفظوا ايش الامثلة هي لانك
+
+127
+00:10:45,150 --> 00:10:48,210
+اذا ما جبتموهاش هينخصم عليكم 5% من ال
+
+128
+00:10:48,210 --> 00:10:51,570
+term مش هعطيكم علامات من اللي بيجيبوا اللي بتجيبه
+
+129
+00:10:51,570 --> 00:10:55,110
+مش هينخصم منها علامات اللي مش هتجيب هدول الامثلة
+
+130
+00:10:55,110 --> 00:11:02,390
+احفظوا انهي امثلة مثال هذا انت
+
+131
+00:11:02,390 --> 00:11:06,630
+حرة تنسخين نسخ من الكتاب هذه امثلة تفكري وتحلي
+
+132
+00:11:06,630 --> 00:11:10,870
+لحالك اللي مش هتجيبه هتاخد خصم 5% من ال
+
+133
+00:11:10,870 --> 00:11:15,160
+term تقولي لزملائكم اللي غايبين هي كل الامثلة اللي
+
+134
+00:11:15,160 --> 00:11:19,980
+موجودين عليكم
+
+135
+00:11:19,980 --> 00:11:23,920
+احلوا اللي قاعد قادر عشان ما حدش في ال image و كل ما
+
+136
+00:11:23,920 --> 00:11:27,360
+هتعملي هيك هيكون نفس النظام ماهي method of image
+
+137
+00:11:27,360 --> 00:11:30,580
+method of image مهمة جدا انها بتساعد برضه علينا حل
+
+138
+00:11:30,580 --> 00:11:33,500
+بعض ال sophisticated problems يعني لما يكون في عندنا
+
+139
+00:11:33,500 --> 00:11:38,260
+مسألة صعبة كتير لكن لها conditions معينة مش دائما
+
+140
+00:11:38,260 --> 00:11:42,780
+بقدر نساعد من ال image اولا ال image ال problem تم
+
+141
+00:11:42,780 --> 00:11:47,440
+تقنيمها أو طريقة الحل بالإنماج اللي قدمها هو
+
+142
+00:11:47,440 --> 00:11:52,860
+Kelvin اسم مشهور بالنسبة لهم Kelvin Kelvin قال لو
+
+143
+00:11:52,860 --> 00:11:56,840
+أنا كان عندي زي الامثلة اللي قدامكم على ال slide
+
+144
+00:11:56,840 --> 00:12:00,720
+لو كان عندي انا perfect conductor مش عال perfect
+
+145
+00:12:00,720 --> 00:12:04,940
+conductor يعني سيجما اللانهاية perfect
+
+146
+00:12:04,940 --> 00:12:11,910
+conductor و الـ conductor هذا ماله احنا بنعرف انه ال
+
+147
+00:12:11,910 --> 00:12:16,050
+potential له grounded يعني واصلينه بال ground يعني
+
+148
+00:12:16,050 --> 00:12:19,050
+ال potential عنده صفر هو ال potential surface ال
+
+149
+00:12:19,050 --> 00:12:22,510
+conductor وفي هذه الحالة ماله صفر لأننا واصليناه
+
+150
+00:12:22,510 --> 00:12:27,350
+بال ground ال grounded V بيساوي صفر وكان عندي بعض
+
+151
+00:12:27,350 --> 00:12:31,970
+ال sources of charge مثلًا point of charge line of
+
+152
+00:12:31,970 --> 00:12:38,380
+charge او مثلا sphere او cylinder انواع مختلفة من ال
+
+153
+00:12:38,380 --> 00:12:43,520
+sources لل potential لل charges وانطلب مني احسب ال
+
+154
+00:12:43,520 --> 00:12:47,320
+potential في اي نقطة في ال space في اي نقطة في ال
+
+155
+00:12:47,320 --> 00:12:53,300
+space اللي above ال conductor عشان اجيب ال
+
+156
+00:12:53,300 --> 00:12:57,620
+potential على اي نقطة من ال space وجود هذه ال
+
+157
+00:12:57,620 --> 00:13:00,900
+variety من ال sources charges طبعًا انتم تعلمتم
+
+158
+00:13:00,900 --> 00:13:03,980
+خلال ال Gauss law و خلال ال Coulomb's law كيف انكم
+
+159
+00:13:03,980 --> 00:13:07,860
+تجيبوه مش مشكلة لكن هذه الطريقة هتلاقوا انها اسهل
+
+160
+00:13:07,860 --> 00:13:14,080
+بكتير باستخدام ال image لم ينجح احد قال انا عندي
+
+161
+00:13:14,080 --> 00:13:16,520
+هذا امنا perfect conductor potential تبعه صفر
+
+162
+00:13:16,520 --> 00:13:21,670
+وعندي هذه ال sources ال charge وانا بدي ال
+
+163
+00:13:21,670 --> 00:13:24,790
+potential في اي نقطة في ال space المثل بتاعة
+
+164
+00:13:24,790 --> 00:13:28,350
+Kelvin قال ان انا بستبدل ال perfect conductor
+
+165
+00:13:28,350 --> 00:13:32,150
+ب equal potential surface V بيساوي 0 يعني بدل ما ال
+
+166
+00:13:32,150 --> 00:13:36,250
+conductor راح ال space كله ال half زي ما انتم 
+
+167
+00:13:36,250 --> 00:13:40,310
+شايفين النص تحتاني من ال space كله conductor بدله
+
+168
+00:13:40,310 --> 00:13:45,970
+بستبدله surface يعني زي سطح الطاولة surface بدل ما
+
+169
+00:13:45,970 --> 00:13:52,200
+هوملي الفراغ بتاعتي صار مجرد surface وهذا ال
+
+170
+00:13:52,200 --> 00:13:54,520
+surface اللي اللي بتنشل برضه الوصفّر بنسميه
+
+171
+00:13:54,520 --> 00:13:58,900
+equipotential surface انه اي نقطة على هذا ال
+
+172
+00:13:58,900 --> 00:14:01,020
+surface لو هذه الطاولة هي ال surface اللي بحكي
+
+173
+00:14:01,020 --> 00:14:05,140
+عنها اي نقطة حقيقية بتنشل فيها عشان هيكون صفر عشان
+
+174
+00:14:05,140 --> 00:14:09,620
+هيك بنسميه equal equipotential من التساوية فعشان اقول هذا
+
+175
+00:14:09,620 --> 00:14:14,430
+ال equipotential surface هيشتغل شغل المرايا بس
+
+176
+00:14:14,430 --> 00:14:17,210
+المراية ايش بدل ما احنا المراية لو بدأنا نشوف حالة
+
+177
+00:14:17,210 --> 00:14:20,630
+على صورة المراية نشوفها جانبي صح الصورة ال image
+
+178
+00:14:20,630 --> 00:14:25,150
+بس اللي لو احنا بندرسها هي الامتداد، تساكرين؟
+
+179
+00:14:25,150 --> 00:14:29,110
+بتخيلي انا هي
+
+201
+00:16:10,680 --> 00:16:14,280
+في الـ conducting صعيد مش في الاتجاه التاني
+
+202
+00:16:19,090 --> 00:16:23,510
+كمان لازم أكون متأكدة أن الـ potential على الـ eco
+
+203
+00:16:23,510 --> 00:16:26,690
+potential surface بيبقى 0 لأن أصلا هو الـ conductor
+
+204
+00:16:26,690 --> 00:16:31,170
+مصور في الـ ground، grounded، V بتاعه 0 فلازم يكون
+
+205
+00:16:31,170 --> 00:16:35,810
+الـ charges دولة دايما يعطوني potential بساوة 0 على
+
+206
+00:16:35,810 --> 00:16:42,930
+الـ eco potential surface ناخد
+
+207
+00:16:42,930 --> 00:16:46,110
+أبسط مثل هو الـ point of charge، لبداء الـ point of
+
+208
+00:16:46,110 --> 00:16:48,430
+charge، فعندي أنا الـ conductor
+
+209
+00:17:00,730 --> 00:17:05,930
+بنجيب الـ potential عند أي نقطة في الـ space مثلا
+
+210
+00:17:05,930 --> 00:17:09,750
+بدياها عند نقطة بي عند xyz
+
+211
+00:17:13,530 --> 00:17:17,750
+الحل بالإماج فهي جاهزة، يعني واضح إن أنا بقدر
+
+212
+00:17:17,750 --> 00:17:19,890
+استخدام فيها الإماج، بتحقق الـ condition أن عندي
+
+213
+00:17:19,890 --> 00:17:23,310
+conducting plane اللي عنده V بيساوة Zero وعندي
+
+214
+00:17:23,310 --> 00:17:28,790
+point 14 بس تبدل الـ conducting plane الـ surface
+
+215
+00:17:28,790 --> 00:17:35,070
+اللي V بتساوة Zero وإماج، الإماج مالها على امتد Q
+
+216
+00:17:35,070 --> 00:17:41,800
+ويالها سالب Q أنا بدي الـ potential عند النقطة P في
+
+217
+00:17:41,800 --> 00:17:44,280
+الـ space طبعا أعرف بالـ conductor لإن احنا بتعرف
+
+218
+00:17:44,280 --> 00:17:46,300
+إنه في قلب الـ conductor الـ electric و الـ potential
+
+219
+00:17:46,300 --> 00:17:50,940
+معله zero فP
+
+220
+00:17:50,940 --> 00:17:55,140
+الـ XYZ أي نقطة في الـ space اللي هو form بس هتحقق
+
+221
+00:17:55,140 --> 00:18:01,720
+الحالة Z أكبر من 0 أول
+
+222
+00:18:01,720 --> 00:18:04,320
+خطوة بعملها بتجيب الـ electric field إنها تجمد two
+
+223
+00:18:04,320 --> 00:18:08,430
+point charges و هذا مش صعب علينا نحسبهيعني total
+
+224
+00:18:08,430 --> 00:18:13,390
+electric field عن النقطة بـxyz هي عبارة عن E
+
+225
+00:18:13,390 --> 00:18:16,230
+الناتج من positive charge زاد electric field
+
+226
+00:18:16,230 --> 00:18:19,130
+الناتج من negative charge والelectric field من
+
+227
+00:18:19,130 --> 00:18:25,550
+voltage charge يش بيساوي R vector على R magnitude
+
+228
+00:18:25,550 --> 00:18:31,210
+Q R هي المسافة بين الـ source والنقطة الرئيسية
+
+229
+00:18:31,210 --> 00:18:35,920
+عندها الـ potentialعشان أجيبها دايما بتكون عبارة عن
+
+230
+00:18:35,920 --> 00:18:39,900
+mean R بقعد النقطة الدقيقصية فيها الـ electric
+
+231
+00:18:39,900 --> 00:18:43,320
+field minus R prime اللي هي وضع وين الـ position
+
+232
+00:18:43,320 --> 00:18:47,900
+تبع الـ source R احنا اتفقنا من زمان هي عبارة عن R
+
+233
+00:18:47,900 --> 00:19:03,020
+R اللي هي I R I R R واحد هي عبارة عن R minus R
+
+234
+00:19:04,920 --> 00:19:10,740
+بنسميها 1 الـ prime الـ 1 الـ prime هو الأعضاء فلو
+
+235
+00:19:10,740 --> 00:19:16,460
+أخدنا هذا الطول هو h اللي يوضع مكان الـ cube عبارة
+
+236
+00:19:16,460 --> 00:19:22,840
+عن h هذي يقدر يكون 00h وهذه النقطة اللي هي xyz فال
+
+237
+00:19:22,840 --> 00:19:29,420
+difference بينهم r-r prime هو عبارة عن xyz-00h
+
+238
+00:19:29,420 --> 00:19:37,520
+بالتالي هتكون xY ومن هيتغير هي Z component Z-H R2
+
+239
+00:19:37,520 --> 00:19:40,900
+نفس الشيء الـ E ناتج من negative charge الفرقية انه
+
+240
+00:19:40,900 --> 00:19:44,380
+بس هيكون بدل positive negative minus Q ع 4 epsilon
+
+241
+00:19:44,380 --> 00:19:49,240
+not R2 vector ع R2 magnitude of Q مين هى R2 اللى
+
+242
+00:19:49,240 --> 00:19:52,700
+هى نفس الحاجة الفرق بين R
+
+243
+00:20:00,080 --> 00:20:08,860
+هتكون R-RB' وR هي XYZ وR' يعني 00-H بوقع الـ image
+
+244
+00:20:08,860 --> 00:20:14,000
+win على minus H إذا Q قعدة على H, minus Q هتكون
+
+245
+00:20:14,000 --> 00:20:17,760
+على نفس البعد لإنها الـ image بتاعتها وإلها ما لها
+
+246
+00:20:17,760 --> 00:20:24,160
+إشارة مخالفة جيبنا R1 وR2 بعود عنهم في الـ electric
+
+247
+00:20:24,160 --> 00:20:27,580
+field إذا الـ Q إيش هيساوي four by epsilon not؟
+
+248
+00:20:27,580 --> 00:20:37,130
+فين؟R1 هي XYZ يعني Z-H Z-H
+
+249
+00:20:37,130 --> 00:20:44,950
+Z-H Z-H Z-H Z-H Z-H Z-H Z-H Z-H Z-H Z-H Z-H Z-H Z
+
+250
+00:20:44,950 --> 00:20:45,170
+-H Z-H Z-H Z-H Z-H Z-H Z-H Z-H Z-H Z-H Z-H Z-H Z-H
+
+251
+00:20:45,170 --> 00:20:55,210
+Z-H Z-H Z-H Z-H Z-H Z-H Z-H Z-H
+
+252
+00:20:55,210 --> 00:20:59,230
+Z-H Z-H Z-H Z-H Z-H Z-H Z-H Z-H Z-H Z-H Z-H Z-Hزي
+
+253
+00:20:59,230 --> 00:21:05,310
+من اين؟ من ان عندي Q سالبة R2 X X hat زي Y Y hat
+
+254
+00:21:05,310 --> 00:21:10,910
+زي Z plus H زي Z minus minus H بيصير plus H Z hat
+
+255
+00:21:10,910 --> 00:21:14,670
+على نفس القضية X تربيه زي Y تربيه زي Z plus H كل
+
+256
+00:21:14,670 --> 00:21:21,030
+تربيه تحت الجزر كل Q فبصير قوة 3 على 2 هذا اللي
+
+257
+00:21:21,030 --> 00:21:24,670
+اترك فيه في اي صعوبة ايجا دلوقتي اترك فيها؟ في اش
+
+258
+00:21:24,670 --> 00:21:29,360
+جديدتعلم انك تجيب الـ electric field بين two و
+
+259
+00:21:29,360 --> 00:21:35,320
+three و five و مليون charge صح؟ vector بجمعهم بجمع
+
+260
+00:21:35,320 --> 00:21:41,490
+الـ vectors مع بعض V minus الintegral ل E dot DLأو
+
+261
+00:21:41,490 --> 00:21:45,190
+بعنى آخر هي عبارة عن positive potential زي ال
+
+262
+00:21:45,190 --> 00:21:47,010
+negative potential، و positive potential جاي من ال
+
+263
+00:21:47,010 --> 00:21:50,150
+positive charge و ال negative الجاي من مين؟ من ال
+
+264
+00:21:50,150 --> 00:21:53,290
+negative charge، لو أنا كملت الـ electric field
+
+265
+00:21:53,290 --> 00:21:56,010
+اللي هو ناتج من الـ positive charge، برضه بعطيني ال
+
+266
+00:21:56,010 --> 00:21:59,530
+potential، لو كملت هاي، و لو كملت هاي بتعطيني ال
+
+267
+00:21:59,530 --> 00:22:02,190
+potential ناتج من الـ negative chargeوأحنا أصلا
+
+268
+00:22:02,190 --> 00:22:06,330
+عارفين الـ potential body charge وبار عالي Q على 4
+
+269
+00:22:06,330 --> 00:22:12,230
+أبسل نوت R1 زائد minus Q على 4 أبسل نوت R2 على طول
+
+270
+00:22:12,230 --> 00:22:15,770
+بحساب الـ potential الـ total potential جاء من two
+
+271
+00:22:15,770 --> 00:22:16,750
+charges
+
+272
+00:22:19,640 --> 00:22:24,480
+هذا الـ potential إذا اللي ناتج من الـ two charges
+
+273
+00:22:24,480 --> 00:22:27,880
+اللي واحدة منهم الحقيقية والتانية الـ image عند أي
+
+274
+00:22:27,880 --> 00:22:31,780
+نقطة بالـ space for z مايلها أكبر من أوت ساوسفر ال
+
+275
+00:22:31,780 --> 00:22:34,860
+space اللي فوق الـ conductor فقلب الـ conductor إيش
+
+276
+00:22:34,860 --> 00:22:37,800
+بدو يكون الـ potential؟ لازم يكون بساوسفر ال
+
+277
+00:22:37,800 --> 00:22:41,670
+potential فقلب الـ conductorلازم بيساوي 0 ال
+
+278
+00:22:41,670 --> 00:22:45,310
+potential هنا 0 for z أقل من او بيساوي 0 لازم يكون
+
+279
+00:22:45,310 --> 00:22:49,570
+v بيساوي 0 و بيساوي potential عند z equal 0 لو
+
+280
+00:22:49,570 --> 00:22:54,030
+اقضع z equal 0 ماش بيصير عندى aq على four by
+
+281
+00:22:54,030 --> 00:22:57,510
+epsilon naught في واحد على x تربية زي ادوية تربية
+
+282
+00:22:57,510 --> 00:23:01,910
+زي h تربية تحت الجزر minus واحد على x تربية زي
+
+283
+00:23:01,910 --> 00:23:06,410
+ادوية تربية زي h تربية تحت الجزر مروحوا مع بعض اذا
+
+284
+00:23:06,410 --> 00:23:13,910
+عند z equal 0و تحت الـ Z أقل من Zero بيظل ال
+
+285
+00:23:13,910 --> 00:23:16,730
+potential of السفر سافر لأن هو هذا الـ Ecological
+
+286
+00:23:16,730 --> 00:23:17,810
+Potential Surface
+
+287
+00:23:21,210 --> 00:23:24,730
+لو أنا بتأكد قداش قيمة الـ Q انترنزك او أنا بتأكد
+
+288
+00:23:24,730 --> 00:23:28,290
+قداش الـ image الـ Q بتاعتها انها لازم تكون minus ال
+
+289
+00:23:28,290 --> 00:23:32,110
+Q نروح لمين لـ boundary conditions الـ boundary
+
+290
+00:23:32,110 --> 00:23:35,830
+conditions ايش بتقولنا أن الـ surface تشجعش بالساوي
+
+291
+00:23:35,830 --> 00:23:38,610
+الـ normal component لـ D من الـ boundary conditions
+
+292
+00:23:38,610 --> 00:23:43,150
+و D تشبه الساوي ي نو دقيقة ان هدم يلوم ماقلتش ان
+
+293
+00:23:43,150 --> 00:23:46,310
+في عندي دايلكتريك فده هوة موجودة في الـ هوة مش في
+
+294
+00:23:46,310 --> 00:23:51,750
+قلب دايلكتريكهذا boundary بين contactor و ال
+
+295
+00:23:51,750 --> 00:23:56,050
+vacuum فإذا الـ normal component لـ DN إيش بيحت سوى
+
+296
+00:23:56,050 --> 00:24:03,290
+الـ recharge رؤس و DN هتسوى إبسل نوض EM عند مين؟
+
+297
+00:24:03,290 --> 00:24:09,210
+عند z equals 0 هو عند الـ boundary أعوض عن الـ EM
+
+298
+00:24:09,210 --> 00:24:13,510
+اللي هو الـ electric field عن z equals 0 تطلع معاه
+
+299
+00:24:13,510 --> 00:24:17,300
+هذا المنطقر بس بتعود عن z equals 0 في الـ Eهي عندى
+
+300
+00:24:17,300 --> 00:24:22,280
+الكتابة هى اقعد على z equals 0 z equals 0 بعدين
+
+301
+00:24:22,280 --> 00:24:26,040
+minus h فى البصد و أنا عندى minus h فى البصد بنجمه
+
+302
+00:24:26,040 --> 00:24:29,980
+بيصيروا minus 2 الـ X بتروح مع الـ X الـ Y بتروح مع
+
+303
+00:24:29,980 --> 00:24:36,660
+الـ Y معين مافيش دورة تبلح لو احط z equals 0 هد
+
+304
+00:24:36,660 --> 00:24:40,120
+بيصير المقال نفس الاشي لأن هى X تربيع زي Y تربيع
+
+305
+00:24:40,120 --> 00:24:43,360
+زي H تربيع نفس الاشي هنا X تربيع زي Y تربيع زي H
+
+306
+00:24:43,360 --> 00:24:49,430
+تربيع البصد اش بيصير X minus X بتروحY-Y بتروح زد
+
+307
+00:24:49,430 --> 00:24:53,250
+صفر عندي minus H وهنا كمان minus H هسي minus ثانية
+
+308
+00:24:53,250 --> 00:24:57,870
+H زدها على X تربيه زاد Y تربيه زاد X تربيه القوة
+
+309
+00:24:57,870 --> 00:25:00,410
+تلاتة على اتنين هي الـ electric field and Z equals
+
+310
+00:25:00,410 --> 00:25:08,270
+zero معود عنها بحصل على مين على الـ row S and Z
+
+311
+00:25:08,270 --> 00:25:13,170
+equals zero الـ QI اللي هي لماشية سوية تكامل رو S
+
+312
+00:25:13,170 --> 00:25:16,370
+DS و DS زي ما انتوا شايفين في الـ XY
+
+313
+00:25:19,140 --> 00:25:23,420
+الـ surface تبعي في الـ x,y لأنها يستد عمودي عليها
+
+314
+00:25:23,420 --> 00:25:26,280
+فالـ surface هيكون في الـ x,y فهيكون التكامل ل x
+
+315
+00:25:26,280 --> 00:25:29,400
+minus infinity ل plus infinity و ال y minus
+
+316
+00:25:29,400 --> 00:25:35,940
+infinity ل plus infinity ρو s ds إذا هتكون اللي هي
+
+317
+00:25:35,940 --> 00:25:39,640
+رو أس اللي حسبناها مع بعض minus qh على 2pi x ترجع
+
+318
+00:25:39,640 --> 00:25:43,360
+إلى y ترجع إلى h فيها القوة 3 ع 2 في اللي هو
+
+319
+00:25:43,360 --> 00:25:46,940
+التكامل للـ surface اللي هو dx dy minus infinity ل
+
+320
+00:25:46,940 --> 00:25:51,060
+plus infinityطبعا لو احنا ساخدنا الـ change of
+
+321
+00:25:51,060 --> 00:25:54,700
+variables اخدنا الـ X تربية زي الـ Y تربية سمناها رو
+
+322
+00:25:54,700 --> 00:25:58,740
+تربية يعني اخدنا من الـ Cartesian و روحنا لل بولر ل
+
+323
+00:25:58,740 --> 00:26:01,860
+رو تربية اذا انا هبدل دي X دي Y اش هيكون عندى رو
+
+324
+00:26:01,860 --> 00:26:05,180
+دي رو دي فاي هيتبسط عندى الـ integration هي مجرد ال
+
+325
+00:26:05,180 --> 00:26:08,520
+trick أخدتها اكيد في التكاملات عشان انه يصير
+
+326
+00:26:08,520 --> 00:26:10,760
+التكامل سهل جدا فاي بتروح
+
+327
+00:26:33,270 --> 00:26:40,010
+نفس الكلام نقدر نغيره أو نضيفه
+
+328
+00:26:40,010 --> 00:26:47,810
+للي هتعملوه في البيتهنجيب الـ electric field و ال
+
+329
+00:26:47,810 --> 00:26:52,810
+potential عند أي نقطة النادجة من الـ line of charge
+
+330
+00:26:52,810 --> 00:26:58,930
+اللي عليه charge density رؤال و
+
+331
+00:26:58,930 --> 00:27:03,030
+نفس
+
+332
+00:27:03,030 --> 00:27:09,270
+الحاجة لو كان عندى charge واحدة طبعا الحاجة المهمة
+
+333
+00:27:09,270 --> 00:27:14,510
+انه لازم نلاحظ أن عدد الـ charges بختلفحسب اللى هو
+
+334
+00:27:14,510 --> 00:27:18,270
+الزاوية اللى بين الـ conductor و اللى هو الموضع
+
+335
+00:27:18,270 --> 00:27:22,830
+اللى هو الـ charge يعني عند الـ conducting plane
+
+336
+00:27:22,830 --> 00:27:27,950
+هلقيتها بهذا الشكل شكيله واقع
+
+337
+00:27:27,950 --> 00:27:30,890
+على زاوية قائمة مع الـ charge لو رجعنا احنا للسؤال
+
+338
+00:27:30,890 --> 00:27:31,490
+الأولانى
+
+339
+00:27:39,270 --> 00:27:44,030
+لما أخدنا الـ one image كان الـ conducting الـ plan و
+
+340
+00:27:44,030 --> 00:27:47,770
+موضوع الـ charge بهذا الشكل يعني الـ plan عامل زاوية
+
+341
+00:27:47,770 --> 00:27:52,930
+قداش مية و تمانين كيلو مية و تمانين لو أنا اجيت
+
+342
+00:27:52,930 --> 00:27:56,210
+على المثال اللي أنا بدأ افرجكوا معاه الـ plan عامل
+
+343
+00:27:56,210 --> 00:28:00,710
+تسعين درجة الـ plan عامل تسعين درجة اكم image
+
+344
+00:28:00,710 --> 00:28:06,470
+تتوقعه هيكون معناه اكم اتنين اكم واحدة تتوقعه
+
+345
+00:28:06,470 --> 00:28:11,290
+اتنين زي ما بتقولبس تنتين يعني واحدة هنا و واحدة
+
+346
+00:28:11,290 --> 00:28:17,130
+هنا طبعا في الشيشة بتتوقع يكون سوريه هيكون عند
+
+347
+00:28:17,130 --> 00:28:23,470
+تلاتة images واحدة طبعا لازم هنا أنا الانماج اللى
+
+348
+00:28:23,470 --> 00:28:27,510
+هنا هتكون سالبة و الانماج اللى عندها هتكون موجبة و
+
+349
+00:28:27,510 --> 00:28:30,330
+بعدين الانماج اللى هنا هتكون سالبة فزان هيكون اللى
+
+350
+00:28:30,330 --> 00:28:34,590
+تلاتة images لما يكون الزاوية 90 درجة و نفس الحاجة
+
+351
+00:28:34,590 --> 00:28:36,950
+لو مابيجي بتحسب الـ potential عند أي نقطة في ال
+
+352
+00:28:36,950 --> 00:28:40,350
+space بتأجيب الـ potential لكل واحدة من هدول النقاط
+
+353
+00:28:40,350 --> 00:28:43,850
+و طبعا قانون ستة و مفروض حافظينه زي اسمكم بس
+
+354
+00:28:43,850 --> 00:28:46,010
+الحاجة اللى هتبقى لكوا ترعوها هي تجيبوا ال
+
+355
+00:28:46,010 --> 00:28:51,320
+position اللى هي الفرق ما بين موضعالنقطة من ال
+
+356
+00:28:51,320 --> 00:28:55,920
+origin ناقص وضع الـ source r minus r prime و برضه
+
+357
+00:28:55,920 --> 00:29:00,140
+ماعقدتش أنها مشكلة هنا في الحالة طالب الـ force
+
+358
+00:29:00,140 --> 00:29:04,840
+اللي على النقطة الحقيقية من الـ images و طبعا سهولة
+
+359
+00:29:04,840 --> 00:29:09,400
+بتنحسن فيه نقانون لقداش الزاوية اللي بيعملها ال
+
+360
+00:29:09,400 --> 00:29:13,560
+conductor لو الـ conductor مثلا عالي 60 درجة قداش
+
+361
+00:29:13,560 --> 00:29:18,070
+أكم image بدأ أحط عشان أعرف عدد الـ imagesبستخدم
+
+362
+00:29:18,070 --> 00:29:21,710
+هذا القانون n بتساوي تلات مية و سبتين على five
+
+363
+00:29:21,710 --> 00:29:27,870
+minus واحد نيجي ناخد اللي هي five مية و تمانين اول
+
+364
+00:29:27,870 --> 00:29:33,560
+مثال360 على 180 يعني اتنين مقاس واحد واحد اي واحدة
+
+365
+00:29:33,560 --> 00:29:38,040
+المثال التاني قداش تسعين 360 على تسعين قداش تعطينا
+
+366
+00:29:38,040 --> 00:29:43,820
+اربعة مقاس واحد تلاتة ستين مقاش تكون ستة مقاس واحد
+
+367
+00:29:43,820 --> 00:29:46,840
+خمسة اذا المقاس اللي انتوا شايفينه عندي خمسة
+
+368
+00:29:46,840 --> 00:29:53,160
+هيكونه plus q هيكون هنا minus q plus q minus q
+
+369
+00:29:53,160 --> 00:29:56,820
+plus q minus q تمام
+
+370
+00:29:59,080 --> 00:30:02,020
+الـ principle المفروض أنه واضح كيف نحسب الـ charges
+
+371
+00:30:02,020 --> 00:30:04,580
+الـ potential عند أي نقطة في الـ space ودولة كلهم
+
+372
+00:30:04,580 --> 00:30:08,180
+pointed charges وحتى لو كان الـ line a charge لازم
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/mm3J5R-uNUo_postprocess.srt b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/mm3J5R-uNUo_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..d9503139ad304d6a5865064cd54c3ffa16f27549
--- /dev/null
+++ b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/mm3J5R-uNUo_postprocess.srt
@@ -0,0 +1,1512 @@
+1
+00:00:21,080 --> 00:00:23,760
+باسم الله الرحمن الرحيم السلام عليكم ورحمة الله
+
+2
+00:00:23,760 --> 00:00:27,700
+وبركاته انا اليوم ان شاء الله هنتبع موضوعنا بساعد
+
+3
+00:00:27,700 --> 00:00:32,660
+الكثافة باستخدام أسواق Laplace او باستخدام Gauss
+
+4
+00:00:32,660 --> 00:00:37,340
+law شفنا من حدرا ماضيا الbarrel blade capacitor و
+
+5
+00:00:37,340 --> 00:00:39,960
+اليوم هنشوف اللي هو ال coaxial capacitor coaxial
+
+6
+00:00:39,960 --> 00:00:44,260
+capacitor عبارة عن استوشات و slenders واحدة منهم
+
+7
+00:00:44,260 --> 00:00:46,880
+حامل اغسط في ال charges والتانية نجت في ال charges
+
+8
+00:00:48,040 --> 00:00:51,440
+عشان كل الاستوانات فانا بده احسب اللي هو ال
+
+9
+00:00:51,440 --> 00:00:54,520
+electric field او يعني ال capacitance و فالاحر
+
+10
+00:00:54,520 --> 00:00:57,320
+اللي احنا بدنا نحسبه اللي هي ال capacitance ف ال
+
+11
+00:00:57,320 --> 00:01:00,140
+electric field احنا بنقدر نجيهه بال gauss law ال
+
+12
+00:01:00,140 --> 00:01:03,840
+gauss law بين ال two cylinders فعمل ال imaginary
+
+13
+00:01:03,840 --> 00:01:08,080
+surface بقول ان Q سوى ال closed integral دي دول دي
+
+14
+00:01:08,080 --> 00:01:12,180
+اسدى اللى هى ال Epsilon E وهنا Epsilon لإن ال
+
+15
+00:01:12,180 --> 00:01:17,180
+media بين ال two cylinders فيها مادة الها او
+
+16
+00:01:17,180 --> 00:01:20,980
+dielectric له permittivity Epsilon لو الهوى بقوا
+
+17
+00:01:20,980 --> 00:01:25,430
+ال Epsilon نضت هتكون Epsilonباتجاه ال electric
+
+18
+00:01:25,430 --> 00:01:28,290
+field فى اتجاه ال raw فما انتوا شايفين من بسطى فى
+
+19
+00:01:28,290 --> 00:01:30,470
+ال negative charge هيكون فى اتجاه ال raw فشية
+
+20
+00:01:30,470 --> 00:01:34,190
+اكمالية لا على زد ولا على فاى فى اتجاه ال electric
+
+21
+00:01:34,190 --> 00:01:38,470
+field فى اتجاه ال raw فهيكون E raw 2pi raw L اللى
+
+22
+00:01:38,470 --> 00:01:42,750
+هى المساحة الجانبية للإستوانة أو مساحة السطح
+
+23
+00:01:42,750 --> 00:01:45,910
+للإستوانة و التانى ال electric field باستخدام
+
+24
+00:01:45,910 --> 00:01:49,970
+جاوسلو للكيكسيا الكيبل بين ال two cylinders و
+
+25
+00:01:49,970 --> 00:01:55,660
+عبارة عن Q على 2pi epsilon raw L فى raw headواضر
+
+26
+00:01:55,660 --> 00:02:00,360
+بعدها نجيب ال potential ال potential مانقش بساوي
+
+27
+00:02:00,360 --> 00:02:05,920
+minus ال integral E من 2 إلى 1 من السلب للموجة E
+
+28
+00:02:05,920 --> 00:02:12,260
+ضد DL E ضد DL و DL مين هنا في حالة ال raw يعني ان
+
+29
+00:02:12,260 --> 00:02:16,480
+انت من الدائرة الخارجية للدائرة الداخلية هيكون
+
+30
+00:02:16,480 --> 00:02:20,840
+اتجاه ال DL و يعني اتجاه ال raw فDL هي مين دي raw
+
+31
+00:02:20,840 --> 00:02:21,700
+واضر
+
+32
+00:02:24,160 --> 00:02:28,780
+فاذا ماحيكون V بيساوية من 2 ل 1 E دول DL و E اللي
+
+33
+00:02:28,780 --> 00:02:32,500
+هي Q على 2 Pi Epsilon رو L في رو هات و DL قولنا
+
+34
+00:02:32,500 --> 00:02:38,680
+مين D رو رو هات لو كملنا D رو على رو بتعطينا لن ال
+
+35
+00:02:38,680 --> 00:02:44,060
+رو من A ل B بتطلع معنا انه Q على 2 Pi Epsilon لن
+
+36
+00:02:44,060 --> 00:02:50,340
+ال B على A و C ماهي لمين Q على Vفبقسم V على Q و
+
+37
+00:02:50,340 --> 00:02:54,420
+بقى أضبط الطرف التاني فبتكون two by epsilon L أعلى
+
+38
+00:02:54,420 --> 00:03:01,240
+من ال B على L واضح طب
+
+39
+00:03:01,240 --> 00:03:05,560
+لو كان ال coaxial cable ع شكل two spheres طلوا
+
+40
+00:03:05,560 --> 00:03:09,220
+ورقة و كتبوا أسميكوا عليها و جيبولي ال capacitance
+
+41
+00:03:09,220 --> 00:03:13,780
+ده coaxial cable ع شكل سفير spherical coaxial
+
+42
+00:03:13,780 --> 00:03:17,820
+cable دالكوا بس خمس دقايق هحد بقى عندهم بالتمام
+
+43
+00:03:21,980 --> 00:03:30,480
+تعال أجمل قدامي يا عزيزي
+
+44
+00:03:30,480 --> 00:03:37,480
+هبقى
+
+45
+00:03:37,480 --> 00:03:41,500
+أسلمه الورق لو سمحته، ماتنسيش تكون الكاتبة اسمك
+
+46
+00:03:41,500 --> 00:03:41,960
+على الورقة
+
+47
+00:04:07,820 --> 00:04:13,940
+في حد ما سلمش؟ إسراء؟ أسماء؟
+
+48
+00:04:13,940 --> 00:04:19,440
+يلّا أسماء هاتي
+
+49
+00:04:19,440 --> 00:04:29,540
+ورا أتركي أسماء هاتي أسرائي ورا أتركي
+
+50
+00:04:29,540 --> 00:04:30,960
+عليها معقن أحسن ما تخلص
+
+51
+00:04:34,400 --> 00:04:38,600
+نشوف قداش صعب السؤال، السؤال بقولنا ان التبستاس
+
+52
+00:04:38,600 --> 00:04:45,210
+لكوكسيا الكابل عشان كان سفيرز ال radius تبعهمابين
+
+53
+00:04:45,210 --> 00:04:49,090
+ال a و ال b يعني السفير الداخلية ال radius تبعها a
+
+54
+00:04:49,090 --> 00:04:52,470
+و الخارجية b عشان اجيب ال capacitance ان اللي
+
+55
+00:04:52,470 --> 00:04:54,990
+الداخلية عليها واسط في ال charge و الخارجية نكت في
+
+56
+00:04:54,990 --> 00:04:58,150
+ال charge بينهم ده electric epsilon عشان اجيب ال
+
+57
+00:04:58,150 --> 00:05:02,870
+electric field جه أصله نفترض سفير اللي هو ال
+
+58
+00:05:02,870 --> 00:05:06,470
+imaginary surface بين ال two spheres اللي هو ال
+
+59
+00:05:06,470 --> 00:05:10,210
+radius R فعكسون Q بتسوى ال closed integral دي دول
+
+60
+00:05:10,210 --> 00:05:16,490
+DSدى إيش تجاهها لما يكون ال sphere هيكون في تجاه
+
+61
+00:05:16,490 --> 00:05:22,510
+ال R هيكون E دوت DS و DS إيش هي عبارة يعني التكامل
+
+62
+00:05:22,510 --> 00:05:29,050
+هيكون في تجاه ال DS النوع بتبعها في تجاه اللي هو
+
+63
+00:05:29,050 --> 00:05:35,750
+ال R برضه R hat ف E دوت DS هتعطينا ER لإن برضه ال
+
+64
+00:05:35,750 --> 00:05:40,970
+E هيكون في تجاه ال R hat هيكون ال dot product E في
+
+65
+00:05:40,970 --> 00:05:46,960
+DSوالتكامل هى er four by r تربيع اللى هو surface
+
+66
+00:05:46,960 --> 00:05:53,340
+مساحة
+
+67
+00:05:53,340 --> 00:05:57,160
+ال sphere فى four by r تربيع وبالتالى E as a
+
+68
+00:05:57,160 --> 00:06:02,040
+vector بتكون Q على four by epsilon r تربيع واتجاه
+
+69
+00:06:02,040 --> 00:06:08,030
+R hat شفتوا قبل هيك هذا التكامل القيمة وقولناإنه
+
+70
+00:06:08,030 --> 00:06:12,250
+كإنها بالتمام ال field اللى جاي من ال charge في ال
+
+71
+00:06:12,250 --> 00:06:21,730
+center و لا لأ هى كموحلة جاي بتاع ME 0 0 0 يعني ه
+
+72
+00:06:21,730 --> 00:06:27,770
+شوية خرابيش يعني قريبة مش كتير مش عارفة إيش هذا
+
+73
+00:06:27,770 --> 00:06:34,530
+يعني مش عارفة سفر حاولت
+
+74
+00:06:34,530 --> 00:06:35,650
+مش عارفة الشىء هذه
+
+75
+00:06:48,440 --> 00:06:59,740
+V-integral من 2 ل1 من السالب للموجب E
+
+76
+00:06:59,740 --> 00:07:05,020
+.DL من DL سيكون في اتجاه الارهات E هي Q على 4 Y
+
+77
+00:07:05,020 --> 00:07:10,660
+أرثر بي ارهات دوت دي ارهاتالـ Q على 4 by epsilon
+
+78
+00:07:10,660 --> 00:07:13,420
+تطلع برا ال integration دي اللي عندي تكمل mean دي
+
+79
+00:07:13,420 --> 00:07:17,520
+R على R تربية تكملها 1 على R ماهيساش أنه فيه سلب
+
+80
+00:07:17,520 --> 00:07:21,420
+يروح مع بعض التكمل من A إلى A هيكون 1 على A minus
+
+81
+00:07:21,420 --> 00:07:26,420
+1 على B C اللي هي مين ال Q على V فعطول من هذا
+
+82
+00:07:26,420 --> 00:07:29,260
+القانون من القانون ال potential بقدر أحصل على C
+
+83
+00:07:29,260 --> 00:07:33,020
+اللي هي Q على V تساوي 4 by epsilon على 1 على A
+
+84
+00:07:33,020 --> 00:07:34,860
+minus 1 على B
+
+85
+00:07:40,280 --> 00:07:44,980
+طالخيص لكل ما حكيناه نستطيع نحسب إذا عرفنا نجيب ال
+
+86
+00:07:44,980 --> 00:07:47,620
+potential أو بالأحرى إذا عرفنا ال electric field
+
+87
+00:07:47,620 --> 00:07:51,080
+نجيبه إذا جيبنا ال electric field بقدر أجيب two
+
+88
+00:07:51,080 --> 00:07:56,000
+quantities اللي هي R resistance بتاعة ال
+
+89
+00:07:56,000 --> 00:08:01,060
+transmission line وال capacitance تاعته وC R هي
+
+90
+00:08:01,060 --> 00:08:06,430
+عبارة عن مين V على I و V هي ال integral E dot DLI
+
+91
+00:08:06,430 --> 00:08:11,730
+الـ closed integral دي ضد دي S دي الـ J ضد دي S J
+
+92
+00:08:11,730 --> 00:08:16,350
+اللي هي current density ومن اللي هو arms point Law
+
+93
+00:08:16,350 --> 00:08:20,630
+هتكون J إيش بتساوي سجن E هذه I اللي هي closed
+
+94
+00:08:20,630 --> 00:08:26,330
+integral جي ضد دي S جي اللي هي سجن E C هي Q على V
+
+95
+00:08:26,330 --> 00:08:29,670
+وQ اللي هي closed integral دي ضد دي S دي اللي هي
+
+96
+00:08:29,670 --> 00:08:36,150
+الـ Epsilon E و V الintegral ايه ضد دي Lلو أخدنا
+
+97
+00:08:36,150 --> 00:08:40,750
+نوع خاص من ال media يوموجينوس أستروبيك السيجما
+
+98
+00:08:40,750 --> 00:08:44,230
+والإبسلون بيطلعوا برا ال integrals أنا بتاعت ميديا
+
+99
+00:08:44,230 --> 00:08:47,930
+اشتغلتها على الكواردينيات و بتكون Linear,
+
+100
+00:08:48,090 --> 00:08:53,230
+Homogenous, Astrobic وضعت ال RFC هلاحظ ان ال RFC
+
+101
+00:08:53,230 --> 00:08:57,290
+إيش بتعطينا إبسلون على سيجما متذكرى إبسلون على
+
+102
+00:08:57,290 --> 00:09:01,490
+سيجما ورقعت علينا اللي هي relaxation timeاللي هو
+
+103
+00:09:01,490 --> 00:09:07,150
+الزمن اللازم ل ال field انه يشتر له relaxation في
+
+104
+00:09:07,150 --> 00:09:10,050
+قلب ال media قولنا في ال conductance كانت قداش
+
+105
+00:09:10,050 --> 00:09:14,210
+سريع جدا في ال dielectric او في ال insulator كانت
+
+106
+00:09:14,210 --> 00:09:18,130
+بتاخد أيام احدنا مثالين فهذا هو relaxation time
+
+107
+00:09:18,130 --> 00:09:24,560
+بسوء R في C بسوء epsilon على sigmaهذا تلخيص لبعض
+
+108
+00:09:24,560 --> 00:09:27,780
+القيام اللي ممكن نحصل عليها لأسواق الفرر بلاد
+
+109
+00:09:27,780 --> 00:09:33,020
+كبسطور C تاعته هتكون يبسلون S على D او D على سيجما
+
+110
+00:09:33,020 --> 00:09:36,700
+S او زي ما هتكون متعودين عليها رو D على S حيث دي
+
+111
+00:09:36,700 --> 00:09:40,380
+هي المسافة بين ال two plates وS اللي هي مساحة ال
+
+112
+00:09:40,380 --> 00:09:43,760
+بلاد ويبسلون هي ال dielectric بين ال two plates
+
+113
+00:09:43,760 --> 00:09:48,580
+وسيجما ال conductivity للبلادلـ Cylindrical
+
+114
+00:09:48,580 --> 00:09:51,680
+Capacitor اللى حسبناه اليوم مع بعض C بيساوى 2 π
+
+115
+00:09:51,680 --> 00:09:55,580
+إبسلون L على لن ال B على A R بيساوى لن ال B على A
+
+116
+00:09:55,580 --> 00:10:00,940
+على 2 بي سجنه أقل Spherical C بيساوى 4 بي إبسلون
+
+117
+00:10:00,940 --> 00:10:05,200
+على 1 على A مانص 1 على B R بيساوى 1 على A مانص 1
+
+118
+00:10:05,200 --> 00:10:09,100
+على B على 4 بي سجنه لل Isolated Spherical
+
+119
+00:10:09,100 --> 00:10:14,040
+Conductor C بيساوى 4 بي إبسلون M يعني الخارجى
+
+120
+00:10:14,040 --> 00:10:20,310
+بيكونgrounded فبكون C بيسوي 4 by epsilon A و R 1
+
+121
+00:10:20,310 --> 00:10:24,910
+على 4 by sigma A كل هدول مطلوب منكم تتعرفوا عليهم
+
+122
+00:10:24,910 --> 00:10:28,650
+تشتقوهم تتأكد انكم بتعرفوا جيبيهم لإن أكيد هجيكوا
+
+123
+00:10:28,650 --> 00:10:33,970
+في الامتحان واحد من هذه الأشياء بما انه انا بلحظة
+
+124
+00:10:33,970 --> 00:10:37,450
+انه حللكوا الأمثلة و الأمثلة هدي عليكم و مطلوبة
+
+125
+00:10:37,450 --> 00:10:40,790
+منكم و اللقاء القادم هتحلوا كل هذه الأمثلة و
+
+126
+00:10:40,790 --> 00:10:45,150
+تجيبهم على ورقة جاهزةاحفظوا إيش الأمثلة هاي لأنك
+
+127
+00:10:45,150 --> 00:10:48,210
+إذا ما جيبتهوهاش هينخصم عليكم خمسة في المية من ال
+
+128
+00:10:48,210 --> 00:10:51,570
+term مش هعطيكم علامات من اللي بيجيبوه اللي بتجيبه
+
+129
+00:10:51,570 --> 00:10:55,110
+مش هينخصم منها علامات اللي مش هتجيب هدولة الأمثلة
+
+130
+00:10:55,110 --> 00:11:02,390
+احفظوا أنهي أمثلة مثال هذا أنت
+
+131
+00:11:02,390 --> 00:11:06,630
+حرة تنسخي نسخ من الكتاب هذه أمثلة تفكري و تحلي
+
+132
+00:11:06,630 --> 00:11:10,870
+لحالك اللي مش هتجيبه هتاخد خصم خمسة في المية من ال
+
+133
+00:11:10,870 --> 00:11:15,160
+termتقول لزمالكم اللي غايبين هي كل الأمثلة اللي
+
+134
+00:11:15,160 --> 00:11:19,980
+موجودين عليكم
+
+135
+00:11:19,980 --> 00:11:23,920
+حلهم اللي قاعد قادر عشان ما حد في ال image و كل ما
+
+136
+00:11:23,920 --> 00:11:27,360
+هتعمله هيك هيكون نفس النظام ماهي method of image
+
+137
+00:11:27,360 --> 00:11:30,580
+method of image مهم جدا انها بتسحل برضه علينا حل
+
+138
+00:11:30,580 --> 00:11:33,500
+بعض ال sophisticated problems يعني لما يكون في عنا
+
+139
+00:11:33,500 --> 00:11:38,260
+مسألة صعبة كتير لكن لها conditions معينة مش دائما
+
+140
+00:11:38,260 --> 00:11:42,780
+بقدر نسحل من ال image أولا ال image ال problemتم
+
+141
+00:11:42,780 --> 00:11:47,440
+تقنيمها أو الطريقة الحل بالإنماج اللى قدمها هو
+
+142
+00:11:47,440 --> 00:11:52,860
+Kelvin اسم مشهور بالنسبالهم Kelvin Kelvin قال لو
+
+143
+00:11:52,860 --> 00:11:56,840
+أنا كان عندي زى الأمثلة اللى قدامكم على ال slide
+
+144
+00:11:56,840 --> 00:12:00,720
+لو كان عندي أنا perfect conductor مش عال perfect
+
+145
+00:12:00,720 --> 00:12:04,940
+conductor يعني sigma اله infinity perfect
+
+146
+00:12:04,940 --> 00:12:11,910
+conductorوالـ conductor هذا ماله احنا بنعرف انه ال
+
+147
+00:12:11,910 --> 00:12:16,050
+potential له grounded يعني واصلينه بال ground يعني
+
+148
+00:12:16,050 --> 00:12:19,050
+ال potential عنده zero هو ال potential surface ال
+
+149
+00:12:19,050 --> 00:12:22,510
+conductor وفي هذه الحالة مالها zero لأننا واصلاها
+
+150
+00:12:22,510 --> 00:12:27,350
+بال ground ال grounded V بيساوة Zero وكان يندي بعض
+
+151
+00:12:27,350 --> 00:12:31,970
+ال sources of charge مثلا point of charge line of
+
+152
+00:12:31,970 --> 00:12:38,380
+charge او مثلا أسفيرأو سيلندر، أنواع مختلفة من ال
+
+153
+00:12:38,380 --> 00:12:43,520
+sources لل potential لل charges وانطلب مني أحسن ال
+
+154
+00:12:43,520 --> 00:12:47,320
+potential في أي نقطة في ال space في أي نقطة في ال
+
+155
+00:12:47,320 --> 00:12:53,300
+space اللي above ال conductorعشان اجيب ال
+
+156
+00:12:53,300 --> 00:12:57,620
+potential على اي نقطة من ال space وجود هذه ال
+
+157
+00:12:57,620 --> 00:13:00,900
+variety من ال sources charges طبعا انتوا اتعلمتوا
+
+158
+00:13:00,900 --> 00:13:03,980
+خلال ال gauss law و خلال ال columns law كيف انكوا
+
+159
+00:13:03,980 --> 00:13:07,860
+تجيبوه مش مشكلة لكن هذه الطريقة هتلاقوا انها اسهل
+
+160
+00:13:07,860 --> 00:13:14,080
+بكتير باستخدام ال image لم ينجش اهل قال انا عندي
+
+161
+00:13:14,080 --> 00:13:16,520
+هذا امنا perfect conductor potential تبعه zero
+
+162
+00:13:16,520 --> 00:13:21,670
+وعندي هذه ال sourcesالـ charge وانا بدي ال
+
+163
+00:13:21,670 --> 00:13:24,790
+potential في اي نقطة في ال space المثل بتاعة
+
+164
+00:13:24,790 --> 00:13:28,350
+Kelvin قال ان انا بستبدل ال perfect conductor
+
+165
+00:13:28,350 --> 00:13:32,150
+بequal potential surface V بساوة 0 يعني بدل ما ال
+
+166
+00:13:32,150 --> 00:13:36,250
+conductor راح ال space كله ال half زي ما انتوا
+
+167
+00:13:36,250 --> 00:13:40,310
+شايفين النص تحتاني من ال space كله conductor بدله
+
+168
+00:13:40,310 --> 00:13:45,970
+بستبدله surface يعني زي سطح الطوا surface بدل ما
+
+169
+00:13:45,970 --> 00:13:52,200
+هوملي الفراغ بتاعتانى صار مجرد surface وهذا ال
+
+170
+00:13:52,200 --> 00:13:54,520
+surface الى اللى بتنشل برضه الوصفر بنسميه
+
+171
+00:13:54,520 --> 00:13:58,900
+equipotential surface انه اى نقطة عليا لهذا ال
+
+172
+00:13:58,900 --> 00:14:01,020
+surface لو هذه الطاولة هي ال surface اللى بحكى
+
+173
+00:14:01,020 --> 00:14:05,140
+عنها اى نقطة حقيقة بتنشل فيها عشان هيكون zero عشان
+
+174
+00:14:05,140 --> 00:14:09,620
+هيك بنسميه equal ايقوى من التساوية فعشان أقول هذا
+
+175
+00:14:09,620 --> 00:14:14,430
+ال equipotential surface هيشتغل شغل المرايابس
+
+176
+00:14:14,430 --> 00:14:17,210
+المراية ايش بدل ما احنا المراية لو بدأ اشوف حالة
+
+177
+00:14:17,210 --> 00:14:20,630
+على صورة المراية اشوفها جانبي صح الصورة ال image
+
+178
+00:14:20,630 --> 00:14:25,150
+بس اللي لو احنا بتدرسها هي الامتداد، تساكرين؟
+
+179
+00:14:25,150 --> 00:14:29,110
+بتهيألي انا هي اللي لو احنا طلعنا درسنا physics او
+
+180
+00:14:29,110 --> 00:14:32,790
+يعني optics الإشعة بتيجي وبتناكس فيا و في الواقع
+
+181
+00:14:32,790 --> 00:14:34,590
+الصورة بتاعتنا بس هنا بشوفها بشوفها في قلب
+
+182
+00:14:34,590 --> 00:14:39,450
+المراية، امتداد الشعة تبعكنفس الاشياء على الأقل
+
+183
+00:14:39,450 --> 00:14:43,370
+خلّيني أتطلع أنا عندي هتلعب لعب image إذا كل
+
+184
+00:14:43,370 --> 00:14:48,050
+charge هيكون فيها صورة في قلب الـ equipotential
+
+185
+00:14:48,050 --> 00:14:51,630
+surface أو خلف الـ equipotential surface خلفه لأن
+
+186
+00:14:51,630 --> 00:14:55,570
+هو مجرد surface بسمعها إذا كانت عند positive
+
+187
+00:14:55,570 --> 00:15:00,210
+charge هتصير ال image بتاعتها سلبت ال charge يعني
+
+188
+00:15:00,210 --> 00:15:02,750
+أنا مثلا point of charge Q هيكون ال image بتاعتها
+
+189
+00:15:02,750 --> 00:15:06,350
+minus Q ال line رؤال
+
+190
+00:15:22,880 --> 00:15:26,160
+بعدين بحسب ال potential عند أي نقطة في ال space
+
+191
+00:15:26,160 --> 00:15:28,540
+الناتج منها دول ال elements كلها
+
+192
+00:15:33,490 --> 00:15:39,170
+تسكير أو تلخيص لأن حكاته عشان أستخدم ال image لازم
+
+193
+00:15:39,170 --> 00:15:44,270
+يكون عنده two conditions أول حاجة لازم تكون ال
+
+194
+00:15:44,270 --> 00:15:48,090
+charge image لازم تكون في ال conducting region
+
+195
+00:15:48,090 --> 00:15:51,410
+يعني و أنا حطيت ال images الصور في ال conducting
+
+196
+00:15:51,410 --> 00:15:54,670
+region في الواقع هذه كلها رالية على conductor بس
+
+197
+00:15:54,670 --> 00:15:57,350
+استبدأت ال conductor بإيه؟ بإيه ال confidential
+
+198
+00:15:57,350 --> 00:16:03,860
+surface والصورمش سوينا استبدلنا ال conducting او
+
+199
+00:16:03,860 --> 00:16:07,180
+ال perfectly conducting plan ايه بقاش ايه كنتش ال
+
+200
+00:16:07,180 --> 00:16:10,680
+surface وعندي ال images يعني وان بتكون ال images
+
+201
+00:16:10,680 --> 00:16:14,280
+في ال conducting صعيد مش في الاتجاه التاني
+
+202
+00:16:19,090 --> 00:16:23,510
+كمان لازم اكون متأكدة ان ال potential على ال eco
+
+203
+00:16:23,510 --> 00:16:26,690
+potential surface بيبقى 0 لأن اصلا هو ال conductor
+
+204
+00:16:26,690 --> 00:16:31,170
+مصور في ال ground، grounded، V بتاعه 0 فلازم يكون
+
+205
+00:16:31,170 --> 00:16:35,810
+ال charges دولة دايما يعطوني potential بساوة 0 على
+
+206
+00:16:35,810 --> 00:16:42,930
+ال eco potential surface ناخد
+
+207
+00:16:42,930 --> 00:16:46,110
+أبسط مثل هو ال point of charge، لبداء ال point of
+
+208
+00:16:46,110 --> 00:16:48,430
+charge، فعندي انا ال conductor
+
+209
+00:17:00,730 --> 00:17:05,930
+بنجيب ال potential عند اي نقطة في ال space مثلا
+
+210
+00:17:05,930 --> 00:17:09,750
+بدياها عند نقطة بي عند xyz
+
+211
+00:17:13,530 --> 00:17:17,750
+الحل بالإماج فهي جاهزة، يعني واضح إن أنا بقدر
+
+212
+00:17:17,750 --> 00:17:19,890
+استخدام فيها الإماج، بتحقق ال condition أن عندي
+
+213
+00:17:19,890 --> 00:17:23,310
+conducting plane اللي عنده V بيساوة Zero وعندي
+
+214
+00:17:23,310 --> 00:17:28,790
+point 14 بس تبدل ال conducting plane ال surface
+
+215
+00:17:28,790 --> 00:17:35,070
+اللي V بتساوة Zero وإماج، الإماج مالها على امتد Q
+
+216
+00:17:35,070 --> 00:17:41,800
+ويالها سالب Qأنا بدي ال potential عند النقطة P في
+
+217
+00:17:41,800 --> 00:17:44,280
+ال space طبعا أعرف بال conductor لإن احنا بتعرف
+
+218
+00:17:44,280 --> 00:17:46,300
+إنه في قلب ال conductor ال electric و ال potential
+
+219
+00:17:46,300 --> 00:17:50,940
+معله zero فP
+
+220
+00:17:50,940 --> 00:17:55,140
+ال XYZ أي نقطة في ال space اللي هو form بس هتحقق
+
+221
+00:17:55,140 --> 00:18:01,720
+الحالة Z أكبر من 0 أول
+
+222
+00:18:01,720 --> 00:18:04,320
+خطوة بعملها بتجيب ال electric field إنها تجمد two
+
+223
+00:18:04,320 --> 00:18:08,430
+point charges و هذا مش صعب علينا نحسبهيعني total
+
+224
+00:18:08,430 --> 00:18:13,390
+electric field عن النقطة بـxyz هي عبارة عن E
+
+225
+00:18:13,390 --> 00:18:16,230
+الناتج من positive charge زاد electric field
+
+226
+00:18:16,230 --> 00:18:19,130
+الناتج من negative charge والelectric field من
+
+227
+00:18:19,130 --> 00:18:25,550
+voltage charge يش بيساوي R vector على R magnitude
+
+228
+00:18:25,550 --> 00:18:31,210
+Q R هي المسافة بين ال source والنقطة الرئيسية
+
+229
+00:18:31,210 --> 00:18:35,920
+عندها ال potentialعشان أجيبها دايما بتكون عبارة عن
+
+230
+00:18:35,920 --> 00:18:39,900
+mean R بقعد النقطة الدقيقصية فيها ال electric
+
+231
+00:18:39,900 --> 00:18:43,320
+field minus R prime اللي هي وضع وين ال position
+
+232
+00:18:43,320 --> 00:18:47,900
+تبع ال source R احنا اتفقنا من زمان هي عبارة عن R
+
+233
+00:18:47,900 --> 00:19:03,020
+R اللي هي I R I R R واحد هي عبارة عن R minus R
+
+234
+00:19:04,920 --> 00:19:10,740
+بنسميها 1 الـ prime الـ 1 الـ prime هو الأعضاء فلو
+
+235
+00:19:10,740 --> 00:19:16,460
+أخدنا هذا الطول هو h اللي يوضع مكان الـ cube عبارة
+
+236
+00:19:16,460 --> 00:19:22,840
+عن h هذي يقدر يكون 00h وهذه النقطة اللي هي xyz فال
+
+237
+00:19:22,840 --> 00:19:29,420
+difference بينهم r-r prime هو عبارة عن xyz-00h
+
+238
+00:19:29,420 --> 00:19:37,520
+بالتالي هتكون xY ومن هيتغير هي Z component Z-H R2
+
+239
+00:19:37,520 --> 00:19:40,900
+نفس الشيء ال E ناتج من negative charge الفرقية انه
+
+240
+00:19:40,900 --> 00:19:44,380
+بس هيكون بدل positive negative minus Q ع 4 epsilon
+
+241
+00:19:44,380 --> 00:19:49,240
+not R2 vector ع R2 magnitude of Q مين هى R2 اللى
+
+242
+00:19:49,240 --> 00:19:52,700
+هى نفس الحاجة الفرق بين R
+
+243
+00:20:00,080 --> 00:20:08,860
+هتكون R-RB' وR هي XYZ وR' يعني 00-H بوقع ال image
+
+244
+00:20:08,860 --> 00:20:14,000
+win على minus H إذا Q قعدة على H, minus Q هتكون
+
+245
+00:20:14,000 --> 00:20:17,760
+على نفس البعد لإنها ال image بتاعتها وإلها ما لها
+
+246
+00:20:17,760 --> 00:20:24,160
+إشارة مخالفة جيبنا R1 وR2 بعود عنهم في ال electric
+
+247
+00:20:24,160 --> 00:20:27,580
+field إذا ال Q إيش هيساوي four by epsilon not؟
+
+248
+00:20:27,580 --> 00:20:37,130
+فين؟R1 هي XYZ يعني Z-H Z-H
+
+249
+00:20:37,130 --> 00:20:44,950
+Z-H Z-H Z-H Z-H Z-H Z-H Z-H Z-H Z-H Z-H Z-H Z-H Z
+
+250
+00:20:44,950 --> 00:20:45,170
+-H Z-H Z-H Z-H Z-H Z-H Z-H Z-H Z-H Z-H Z-H Z-H Z-H
+
+251
+00:20:45,170 --> 00:20:55,210
+Z-H Z-H Z-H Z-H Z-H Z-H Z-H Z-H
+
+252
+00:20:55,210 --> 00:20:59,230
+Z-H Z-H Z-H Z-H Z-H Z-H Z-H Z-H Z-H Z-H Z-H Z-Hزي
+
+253
+00:20:59,230 --> 00:21:05,310
+من اين؟ من ان عندي Q سالبة R2 X X hat زي Y Y hat
+
+254
+00:21:05,310 --> 00:21:10,910
+زي Z plus H زي Z minus minus H بيصير plus H Z hat
+
+255
+00:21:10,910 --> 00:21:14,670
+على نفس القضية X تربيه زي Y تربيه زي Z plus H كل
+
+256
+00:21:14,670 --> 00:21:21,030
+تربيه تحت الجزر كل Q فبصير قوة 3 على 2 هذا اللي
+
+257
+00:21:21,030 --> 00:21:24,670
+اترك فيه في اي صعوبة ايجا دلوقتي اترك فيها؟ في اش
+
+258
+00:21:24,670 --> 00:21:29,360
+جديدتعلم انك تجيب ال electric field بين two و
+
+259
+00:21:29,360 --> 00:21:35,320
+three و five و مليون charge صح؟ vector بجمعهم بجمع
+
+260
+00:21:35,320 --> 00:21:41,490
+ال vectors مع بعض V minus الintegral ل E dot DLأو
+
+261
+00:21:41,490 --> 00:21:45,190
+بعنى آخر هي عبارة عن positive potential زي ال
+
+262
+00:21:45,190 --> 00:21:47,010
+negative potential، و positive potential جاي من ال
+
+263
+00:21:47,010 --> 00:21:50,150
+positive charge و ال negative الجاي من مين؟ من ال
+
+264
+00:21:50,150 --> 00:21:53,290
+negative charge، لو أنا كملت ال electric field
+
+265
+00:21:53,290 --> 00:21:56,010
+اللي هو ناتج من ال positive charge، برضه بعطيني ال
+
+266
+00:21:56,010 --> 00:21:59,530
+potential، لو كملت هاي، و لو كملت هاي بتعطيني ال
+
+267
+00:21:59,530 --> 00:22:02,190
+potential ناتج من ال negative chargeوأحنا أصلا
+
+268
+00:22:02,190 --> 00:22:06,330
+عارفين ال potential body charge وبار عالي Q على 4
+
+269
+00:22:06,330 --> 00:22:12,230
+أبسل نوت R1 زائد minus Q على 4 أبسل نوت R2 على طول
+
+270
+00:22:12,230 --> 00:22:15,770
+بحساب ال potential ال total potential جاء من two
+
+271
+00:22:15,770 --> 00:22:16,750
+charges
+
+272
+00:22:19,640 --> 00:22:24,480
+هذا ال potential إذا اللي ناتج من ال two charges
+
+273
+00:22:24,480 --> 00:22:27,880
+اللي واحدة منهم الحقيقية والتانية ال image عند أي
+
+274
+00:22:27,880 --> 00:22:31,780
+نقطة بال space for z مايلها أكبر من أوت ساوسفر ال
+
+275
+00:22:31,780 --> 00:22:34,860
+space اللي فوق ال conductor فقلب ال conductor إيش
+
+276
+00:22:34,860 --> 00:22:37,800
+بدو يكون ال potential؟ لازم يكون بساوسفر ال
+
+277
+00:22:37,800 --> 00:22:41,670
+potential فقلب ال conductorلازم بيساوي 0 ال
+
+278
+00:22:41,670 --> 00:22:45,310
+potential هنا 0 for z أقل من او بيساوي 0 لازم يكون
+
+279
+00:22:45,310 --> 00:22:49,570
+v بيساوي 0 و بيساوي potential عند z equal 0 لو
+
+280
+00:22:49,570 --> 00:22:54,030
+اقضع z equal 0 ماش بيصير عندى aq على four by
+
+281
+00:22:54,030 --> 00:22:57,510
+epsilon naught في واحد على x تربية زي ادوية تربية
+
+282
+00:22:57,510 --> 00:23:01,910
+زي h تربية تحت الجزر minus واحد على x تربية زي
+
+283
+00:23:01,910 --> 00:23:06,410
+ادوية تربية زي h تربية تحت الجزر مروحوا مع بعض اذا
+
+284
+00:23:06,410 --> 00:23:13,910
+عند z equal 0و تحت الـ Z أقل من Zero بيظل ال
+
+285
+00:23:13,910 --> 00:23:16,730
+potential of السفر سافر لأن هو هذا الـ Ecological
+
+286
+00:23:16,730 --> 00:23:17,810
+Potential Surface
+
+287
+00:23:21,210 --> 00:23:24,730
+لو انا بتأكد قداش قيمة ال Q انترنزك او انا بتأكد
+
+288
+00:23:24,730 --> 00:23:28,290
+قداش ال image ال Q بتاعتها انها لازم تكون minus ال
+
+289
+00:23:28,290 --> 00:23:32,110
+Q نروح لمين لـ boundary conditions ال boundary
+
+290
+00:23:32,110 --> 00:23:35,830
+conditions ايش بتقولنا ان ال surface تشجعش بالساوي
+
+291
+00:23:35,830 --> 00:23:38,610
+ال normal component ل D من ال boundary conditions
+
+292
+00:23:38,610 --> 00:23:43,150
+و D تشبه الساوي ي نو دقيقة ان هدم يلوم ماقلتش ان
+
+293
+00:23:43,150 --> 00:23:46,310
+في عندي دايلكتريك فده هوة موجودة في ال هوة مش في
+
+294
+00:23:46,310 --> 00:23:51,750
+قلب دايلكتريكهذا boundary بين contactor و ال
+
+295
+00:23:51,750 --> 00:23:56,050
+vacuum فإذا ال normal component ل DN إيش بيحت سوى
+
+296
+00:23:56,050 --> 00:24:03,290
+ال recharge رؤس و DN هتسوى إبسل نوض EM عند مين؟
+
+297
+00:24:03,290 --> 00:24:09,210
+عند z equals 0 هو عند ال boundary أعوض عن ال EM
+
+298
+00:24:09,210 --> 00:24:13,510
+اللي هو ال electric field عن z equals 0 تطلع معاه
+
+299
+00:24:13,510 --> 00:24:17,300
+هذا المنطقر بس بتعود عن z equals 0 في ال Eهي عندى
+
+300
+00:24:17,300 --> 00:24:22,280
+الكتابة هى اقعد على z equals 0 z equals 0 بعدين
+
+301
+00:24:22,280 --> 00:24:26,040
+minus h فى البصد و انا عندى minus h فى البصد بنجمه
+
+302
+00:24:26,040 --> 00:24:29,980
+بيصيروا minus 2 ال X بتروح مع ال X ال Y بتروح مع
+
+303
+00:24:29,980 --> 00:24:36,660
+ال Y معين مافيش دورة تبلح لو احط z equals 0 هد
+
+304
+00:24:36,660 --> 00:24:40,120
+بيصير المقال نفس الاشي لأن هى X تربيع زي Y تربيع
+
+305
+00:24:40,120 --> 00:24:43,360
+زي H تربيع نفس الاشي هنا X تربيع زي Y تربيع زي H
+
+306
+00:24:43,360 --> 00:24:49,430
+تربيع البصد اش بيصير X minus X بتروحY-Y بتروح زد
+
+307
+00:24:49,430 --> 00:24:53,250
+صفر عندي minus H وهنا كمان minus H هسي minus ثانية
+
+308
+00:24:53,250 --> 00:24:57,870
+H زدها على X تربيه زاد Y تربيه زاد X تربيه القوة
+
+309
+00:24:57,870 --> 00:25:00,410
+تلاتة على اتنين هي ال electric field and Z equals
+
+310
+00:25:00,410 --> 00:25:08,270
+zero معود عنها بحصل على مين على ال row S and Z
+
+311
+00:25:08,270 --> 00:25:13,170
+equals zero ال QI اللي هي لماشية سوية تكامل رو S
+
+312
+00:25:13,170 --> 00:25:16,370
+DS و DS زي ما انتوا شايفين في ال XY
+
+313
+00:25:19,140 --> 00:25:23,420
+الـ surface تبعي في الـ x,y لأنها يستد عمودي عليها
+
+314
+00:25:23,420 --> 00:25:26,280
+فالـ surface هيكون في الـ x,y فهيكون التكامل ل x
+
+315
+00:25:26,280 --> 00:25:29,400
+minus infinity ل plus infinity و ال y minus
+
+316
+00:25:29,400 --> 00:25:35,940
+infinity ل plus infinity ρو s ds إذا هتكون اللي هي
+
+317
+00:25:35,940 --> 00:25:39,640
+رو أس اللي حسبناها مع بعض minus qh على 2pi x ترجع
+
+318
+00:25:39,640 --> 00:25:43,360
+إلى y ترجع إلى h فيها القوة 3 ع 2 في اللي هو
+
+319
+00:25:43,360 --> 00:25:46,940
+التكامل لل surface اللي هو dx dy minus infinity ل
+
+320
+00:25:46,940 --> 00:25:51,060
+plus infinityطبعا لو احنا ساخدنا ال change of
+
+321
+00:25:51,060 --> 00:25:54,700
+variables اخدنا ال X تربية زي ال Y تربية سمناها رو
+
+322
+00:25:54,700 --> 00:25:58,740
+تربية يعني اخدنا من ال Cartesian و روحنا لل بولر ل
+
+323
+00:25:58,740 --> 00:26:01,860
+رو تربية اذا انا هبدل دي X دي Y اش هيكون عندى رو
+
+324
+00:26:01,860 --> 00:26:05,180
+دي رو دي فاي هيتبسط عندى ال integration هي مجرد ال
+
+325
+00:26:05,180 --> 00:26:08,520
+trick أخدتها اكيد في التكاملات عشان انه يصير
+
+326
+00:26:08,520 --> 00:26:10,760
+التكامل سهل جدا فاي بتروح
+
+327
+00:26:33,270 --> 00:26:40,010
+نفس الكلام نقدر نغيره أو نضيفه
+
+328
+00:26:40,010 --> 00:26:47,810
+للي هتعملوه في البيتهنجيب ال electric field و ال
+
+329
+00:26:47,810 --> 00:26:52,810
+potential عند أي نقطة النادجة من ال line of charge
+
+330
+00:26:52,810 --> 00:26:58,930
+اللي عليه charge density رؤال و
+
+331
+00:26:58,930 --> 00:27:03,030
+نفس
+
+332
+00:27:03,030 --> 00:27:09,270
+الحاجة لو كان عندى charge واحدة طبعا الحاجة المهمة
+
+333
+00:27:09,270 --> 00:27:14,510
+انه لازم نلاحظ ان عدد ال charges بختلفحسب اللى هو
+
+334
+00:27:14,510 --> 00:27:18,270
+الزاوية اللى بين ال conductor و اللى هو الموضع
+
+335
+00:27:18,270 --> 00:27:22,830
+اللى هو ال charge يعني عند ال conducting plane
+
+336
+00:27:22,830 --> 00:27:27,950
+هلقيتها بهذا الشكل شكيله واقع
+
+337
+00:27:27,950 --> 00:27:30,890
+على زاوية قائمة مع ال charge لو رجعنا احنا للسؤال
+
+338
+00:27:30,890 --> 00:27:31,490
+الأولانى
+
+339
+00:27:39,270 --> 00:27:44,030
+لما أخدنا ال one image كان ال conducting ال plan و
+
+340
+00:27:44,030 --> 00:27:47,770
+موضوع ال charge بهذا الشكل يعني ال plan عامل زاوية
+
+341
+00:27:47,770 --> 00:27:52,930
+قداش مية و تمانين كيلو مية و تمانين لو انا اجيت
+
+342
+00:27:52,930 --> 00:27:56,210
+على المثال اللي انا بدأ افرجكوا معاه ال plan عامل
+
+343
+00:27:56,210 --> 00:28:00,710
+تسعين درجة ال plan عامل تسعين درجة اكم image
+
+344
+00:28:00,710 --> 00:28:06,470
+تتوقعه هيكون معناه اكم اتنين اكم واحدة تتوقعه
+
+345
+00:28:06,470 --> 00:28:11,290
+اتنين زي ما بتقولبس تنتين يعني واحدة هنا و واحدة
+
+346
+00:28:11,290 --> 00:28:17,130
+هنا طبعا في الشيشة بتتوقع يكون سوريه هيكون عند
+
+347
+00:28:17,130 --> 00:28:23,470
+تلاتة images واحدة طبعا لازم هنا اناالانماج اللى
+
+348
+00:28:23,470 --> 00:28:27,510
+هنا هتكون سالبة و الانماج اللى عندها هتكون موجبة و
+
+349
+00:28:27,510 --> 00:28:30,330
+بعدين الانماج اللى هنا هتكون سالبة فزان هيكون اللى
+
+350
+00:28:30,330 --> 00:28:34,590
+تلاتة images لما يكون الزاوية 90 درجة و نفس الحاجة
+
+351
+00:28:34,590 --> 00:28:36,950
+لو مابيجي بتحسب ال potential عند أي نقطة في ال
+
+352
+00:28:36,950 --> 00:28:40,350
+space بتأجيب ال potential لكل واحدة من هدول النقاط
+
+353
+00:28:40,350 --> 00:28:43,850
+و طبعا قانون ستة و مفروض حافظينه زى اسمكم بس
+
+354
+00:28:43,850 --> 00:28:46,010
+الحاجة اللى هتبقى لكوا ترعوها هي تجيبوا ال
+
+355
+00:28:46,010 --> 00:28:51,320
+position اللى هي الفرق ما بين موضعالنقطة من ال
+
+356
+00:28:51,320 --> 00:28:55,920
+origin ناقص وضع ال source r minus r prime و برضه
+
+357
+00:28:55,920 --> 00:29:00,140
+ماعقدتش أنها مشكلة هنا في الحالة طالب ال force
+
+358
+00:29:00,140 --> 00:29:04,840
+اللي على النقطة الحقيقية من ال images و طبعا سهولة
+
+359
+00:29:04,840 --> 00:29:09,400
+بتنحسن فيه نقانون لقداش الزاوية اللي بيعملها ال
+
+360
+00:29:09,400 --> 00:29:13,560
+conductor لو ال conductor مثلا عالي 60 درجة قداش
+
+361
+00:29:13,560 --> 00:29:18,070
+أكم image بدأ أحط عشان أعرف عدد ال imagesبستخدم
+
+362
+00:29:18,070 --> 00:29:21,710
+هذا القانون n بتساوي تلات مية و سبتين على five
+
+363
+00:29:21,710 --> 00:29:27,870
+minus واحد نيجي ناخد اللي هي five مية و تمانين اول
+
+364
+00:29:27,870 --> 00:29:33,560
+مثال360 على 180 يعني اتنين مقاس واحد واحد اي واحدة
+
+365
+00:29:33,560 --> 00:29:38,040
+المثال التاني قداش تسعين 360 على تسعين قداش تعطينا
+
+366
+00:29:38,040 --> 00:29:43,820
+اربعة مقاس واحد تلاتة ستين مقاش تكون ستة مقاس واحد
+
+367
+00:29:43,820 --> 00:29:46,840
+خمسة اذا المقاس اللي انتوا شايفينه عندي خمسة
+
+368
+00:29:46,840 --> 00:29:53,160
+هيكونه plus q هيكون هنا minus q plus q minus q
+
+369
+00:29:53,160 --> 00:29:56,820
+plus q minus q تمام
+
+370
+00:29:59,080 --> 00:30:02,020
+ال principle المفروض أنه واضح كيف نحسب ال charges
+
+371
+00:30:02,020 --> 00:30:04,580
+ال potential عند أي نقطة في ال space ودولة كلهم
+
+372
+00:30:04,580 --> 00:30:08,180
+pointed charges وحتى لو كان ال line a charge لازم
+
+373
+00:30:08,180 --> 00:30:12,840
+تكونوا قادرين كيف تحسبوه وهيك أنا بكون خلصت الشكتة
+
+374
+00:30:12,840 --> 00:30:17,240
+النقاء القادم الأمثلة اللي أنا مريت عليهم لازم
+
+375
+00:30:17,240 --> 00:30:22,220
+تكون معاكم وجايبينهم هي ورقة عليها اسمكم مرتب
+
+376
+00:30:22,220 --> 00:30:27,640
+بالكلام وواضحواللي غابوا بيكفيهم ان هم غايبين و
+
+377
+00:30:27,640 --> 00:30:33,060
+هيحفظوا غصب مع غياب يحفظوا و يجيبوا معهم اللي هم
+
+378
+00:30:33,060 --> 00:30:34,600
+مركبت بسؤالية
+
diff --git a/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/mm3J5R-uNUo_raw.srt b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/mm3J5R-uNUo_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..d9503139ad304d6a5865064cd54c3ffa16f27549
--- /dev/null
+++ b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/mm3J5R-uNUo_raw.srt
@@ -0,0 +1,1512 @@
+1
+00:00:21,080 --> 00:00:23,760
+باسم الله الرحمن الرحيم السلام عليكم ورحمة الله
+
+2
+00:00:23,760 --> 00:00:27,700
+وبركاته انا اليوم ان شاء الله هنتبع موضوعنا بساعد
+
+3
+00:00:27,700 --> 00:00:32,660
+الكثافة باستخدام أسواق Laplace او باستخدام Gauss
+
+4
+00:00:32,660 --> 00:00:37,340
+law شفنا من حدرا ماضيا الbarrel blade capacitor و
+
+5
+00:00:37,340 --> 00:00:39,960
+اليوم هنشوف اللي هو ال coaxial capacitor coaxial
+
+6
+00:00:39,960 --> 00:00:44,260
+capacitor عبارة عن استوشات و slenders واحدة منهم
+
+7
+00:00:44,260 --> 00:00:46,880
+حامل اغسط في ال charges والتانية نجت في ال charges
+
+8
+00:00:48,040 --> 00:00:51,440
+عشان كل الاستوانات فانا بده احسب اللي هو ال
+
+9
+00:00:51,440 --> 00:00:54,520
+electric field او يعني ال capacitance و فالاحر
+
+10
+00:00:54,520 --> 00:00:57,320
+اللي احنا بدنا نحسبه اللي هي ال capacitance ف ال
+
+11
+00:00:57,320 --> 00:01:00,140
+electric field احنا بنقدر نجيهه بال gauss law ال
+
+12
+00:01:00,140 --> 00:01:03,840
+gauss law بين ال two cylinders فعمل ال imaginary
+
+13
+00:01:03,840 --> 00:01:08,080
+surface بقول ان Q سوى ال closed integral دي دول دي
+
+14
+00:01:08,080 --> 00:01:12,180
+اسدى اللى هى ال Epsilon E وهنا Epsilon لإن ال
+
+15
+00:01:12,180 --> 00:01:17,180
+media بين ال two cylinders فيها مادة الها او
+
+16
+00:01:17,180 --> 00:01:20,980
+dielectric له permittivity Epsilon لو الهوى بقوا
+
+17
+00:01:20,980 --> 00:01:25,430
+ال Epsilon نضت هتكون Epsilonباتجاه ال electric
+
+18
+00:01:25,430 --> 00:01:28,290
+field فى اتجاه ال raw فما انتوا شايفين من بسطى فى
+
+19
+00:01:28,290 --> 00:01:30,470
+ال negative charge هيكون فى اتجاه ال raw فشية
+
+20
+00:01:30,470 --> 00:01:34,190
+اكمالية لا على زد ولا على فاى فى اتجاه ال electric
+
+21
+00:01:34,190 --> 00:01:38,470
+field فى اتجاه ال raw فهيكون E raw 2pi raw L اللى
+
+22
+00:01:38,470 --> 00:01:42,750
+هى المساحة الجانبية للإستوانة أو مساحة السطح
+
+23
+00:01:42,750 --> 00:01:45,910
+للإستوانة و التانى ال electric field باستخدام
+
+24
+00:01:45,910 --> 00:01:49,970
+جاوسلو للكيكسيا الكيبل بين ال two cylinders و
+
+25
+00:01:49,970 --> 00:01:55,660
+عبارة عن Q على 2pi epsilon raw L فى raw headواضر
+
+26
+00:01:55,660 --> 00:02:00,360
+بعدها نجيب ال potential ال potential مانقش بساوي
+
+27
+00:02:00,360 --> 00:02:05,920
+minus ال integral E من 2 إلى 1 من السلب للموجة E
+
+28
+00:02:05,920 --> 00:02:12,260
+ضد DL E ضد DL و DL مين هنا في حالة ال raw يعني ان
+
+29
+00:02:12,260 --> 00:02:16,480
+انت من الدائرة الخارجية للدائرة الداخلية هيكون
+
+30
+00:02:16,480 --> 00:02:20,840
+اتجاه ال DL و يعني اتجاه ال raw فDL هي مين دي raw
+
+31
+00:02:20,840 --> 00:02:21,700
+واضر
+
+32
+00:02:24,160 --> 00:02:28,780
+فاذا ماحيكون V بيساوية من 2 ل 1 E دول DL و E اللي
+
+33
+00:02:28,780 --> 00:02:32,500
+هي Q على 2 Pi Epsilon رو L في رو هات و DL قولنا
+
+34
+00:02:32,500 --> 00:02:38,680
+مين D رو رو هات لو كملنا D رو على رو بتعطينا لن ال
+
+35
+00:02:38,680 --> 00:02:44,060
+رو من A ل B بتطلع معنا انه Q على 2 Pi Epsilon لن
+
+36
+00:02:44,060 --> 00:02:50,340
+ال B على A و C ماهي لمين Q على Vفبقسم V على Q و
+
+37
+00:02:50,340 --> 00:02:54,420
+بقى أضبط الطرف التاني فبتكون two by epsilon L أعلى
+
+38
+00:02:54,420 --> 00:03:01,240
+من ال B على L واضح طب
+
+39
+00:03:01,240 --> 00:03:05,560
+لو كان ال coaxial cable ع شكل two spheres طلوا
+
+40
+00:03:05,560 --> 00:03:09,220
+ورقة و كتبوا أسميكوا عليها و جيبولي ال capacitance
+
+41
+00:03:09,220 --> 00:03:13,780
+ده coaxial cable ع شكل سفير spherical coaxial
+
+42
+00:03:13,780 --> 00:03:17,820
+cable دالكوا بس خمس دقايق هحد بقى عندهم بالتمام
+
+43
+00:03:21,980 --> 00:03:30,480
+تعال أجمل قدامي يا عزيزي
+
+44
+00:03:30,480 --> 00:03:37,480
+هبقى
+
+45
+00:03:37,480 --> 00:03:41,500
+أسلمه الورق لو سمحته، ماتنسيش تكون الكاتبة اسمك
+
+46
+00:03:41,500 --> 00:03:41,960
+على الورقة
+
+47
+00:04:07,820 --> 00:04:13,940
+في حد ما سلمش؟ إسراء؟ أسماء؟
+
+48
+00:04:13,940 --> 00:04:19,440
+يلّا أسماء هاتي
+
+49
+00:04:19,440 --> 00:04:29,540
+ورا أتركي أسماء هاتي أسرائي ورا أتركي
+
+50
+00:04:29,540 --> 00:04:30,960
+عليها معقن أحسن ما تخلص
+
+51
+00:04:34,400 --> 00:04:38,600
+نشوف قداش صعب السؤال، السؤال بقولنا ان التبستاس
+
+52
+00:04:38,600 --> 00:04:45,210
+لكوكسيا الكابل عشان كان سفيرز ال radius تبعهمابين
+
+53
+00:04:45,210 --> 00:04:49,090
+ال a و ال b يعني السفير الداخلية ال radius تبعها a
+
+54
+00:04:49,090 --> 00:04:52,470
+و الخارجية b عشان اجيب ال capacitance ان اللي
+
+55
+00:04:52,470 --> 00:04:54,990
+الداخلية عليها واسط في ال charge و الخارجية نكت في
+
+56
+00:04:54,990 --> 00:04:58,150
+ال charge بينهم ده electric epsilon عشان اجيب ال
+
+57
+00:04:58,150 --> 00:05:02,870
+electric field جه أصله نفترض سفير اللي هو ال
+
+58
+00:05:02,870 --> 00:05:06,470
+imaginary surface بين ال two spheres اللي هو ال
+
+59
+00:05:06,470 --> 00:05:10,210
+radius R فعكسون Q بتسوى ال closed integral دي دول
+
+60
+00:05:10,210 --> 00:05:16,490
+DSدى إيش تجاهها لما يكون ال sphere هيكون في تجاه
+
+61
+00:05:16,490 --> 00:05:22,510
+ال R هيكون E دوت DS و DS إيش هي عبارة يعني التكامل
+
+62
+00:05:22,510 --> 00:05:29,050
+هيكون في تجاه ال DS النوع بتبعها في تجاه اللي هو
+
+63
+00:05:29,050 --> 00:05:35,750
+ال R برضه R hat ف E دوت DS هتعطينا ER لإن برضه ال
+
+64
+00:05:35,750 --> 00:05:40,970
+E هيكون في تجاه ال R hat هيكون ال dot product E في
+
+65
+00:05:40,970 --> 00:05:46,960
+DSوالتكامل هى er four by r تربيع اللى هو surface
+
+66
+00:05:46,960 --> 00:05:53,340
+مساحة
+
+67
+00:05:53,340 --> 00:05:57,160
+ال sphere فى four by r تربيع وبالتالى E as a
+
+68
+00:05:57,160 --> 00:06:02,040
+vector بتكون Q على four by epsilon r تربيع واتجاه
+
+69
+00:06:02,040 --> 00:06:08,030
+R hat شفتوا قبل هيك هذا التكامل القيمة وقولناإنه
+
+70
+00:06:08,030 --> 00:06:12,250
+كإنها بالتمام ال field اللى جاي من ال charge في ال
+
+71
+00:06:12,250 --> 00:06:21,730
+center و لا لأ هى كموحلة جاي بتاع ME 0 0 0 يعني ه
+
+72
+00:06:21,730 --> 00:06:27,770
+شوية خرابيش يعني قريبة مش كتير مش عارفة إيش هذا
+
+73
+00:06:27,770 --> 00:06:34,530
+يعني مش عارفة سفر حاولت
+
+74
+00:06:34,530 --> 00:06:35,650
+مش عارفة الشىء هذه
+
+75
+00:06:48,440 --> 00:06:59,740
+V-integral من 2 ل1 من السالب للموجب E
+
+76
+00:06:59,740 --> 00:07:05,020
+.DL من DL سيكون في اتجاه الارهات E هي Q على 4 Y
+
+77
+00:07:05,020 --> 00:07:10,660
+أرثر بي ارهات دوت دي ارهاتالـ Q على 4 by epsilon
+
+78
+00:07:10,660 --> 00:07:13,420
+تطلع برا ال integration دي اللي عندي تكمل mean دي
+
+79
+00:07:13,420 --> 00:07:17,520
+R على R تربية تكملها 1 على R ماهيساش أنه فيه سلب
+
+80
+00:07:17,520 --> 00:07:21,420
+يروح مع بعض التكمل من A إلى A هيكون 1 على A minus
+
+81
+00:07:21,420 --> 00:07:26,420
+1 على B C اللي هي مين ال Q على V فعطول من هذا
+
+82
+00:07:26,420 --> 00:07:29,260
+القانون من القانون ال potential بقدر أحصل على C
+
+83
+00:07:29,260 --> 00:07:33,020
+اللي هي Q على V تساوي 4 by epsilon على 1 على A
+
+84
+00:07:33,020 --> 00:07:34,860
+minus 1 على B
+
+85
+00:07:40,280 --> 00:07:44,980
+طالخيص لكل ما حكيناه نستطيع نحسب إذا عرفنا نجيب ال
+
+86
+00:07:44,980 --> 00:07:47,620
+potential أو بالأحرى إذا عرفنا ال electric field
+
+87
+00:07:47,620 --> 00:07:51,080
+نجيبه إذا جيبنا ال electric field بقدر أجيب two
+
+88
+00:07:51,080 --> 00:07:56,000
+quantities اللي هي R resistance بتاعة ال
+
+89
+00:07:56,000 --> 00:08:01,060
+transmission line وال capacitance تاعته وC R هي
+
+90
+00:08:01,060 --> 00:08:06,430
+عبارة عن مين V على I و V هي ال integral E dot DLI
+
+91
+00:08:06,430 --> 00:08:11,730
+الـ closed integral دي ضد دي S دي الـ J ضد دي S J
+
+92
+00:08:11,730 --> 00:08:16,350
+اللي هي current density ومن اللي هو arms point Law
+
+93
+00:08:16,350 --> 00:08:20,630
+هتكون J إيش بتساوي سجن E هذه I اللي هي closed
+
+94
+00:08:20,630 --> 00:08:26,330
+integral جي ضد دي S جي اللي هي سجن E C هي Q على V
+
+95
+00:08:26,330 --> 00:08:29,670
+وQ اللي هي closed integral دي ضد دي S دي اللي هي
+
+96
+00:08:29,670 --> 00:08:36,150
+الـ Epsilon E و V الintegral ايه ضد دي Lلو أخدنا
+
+97
+00:08:36,150 --> 00:08:40,750
+نوع خاص من ال media يوموجينوس أستروبيك السيجما
+
+98
+00:08:40,750 --> 00:08:44,230
+والإبسلون بيطلعوا برا ال integrals أنا بتاعت ميديا
+
+99
+00:08:44,230 --> 00:08:47,930
+اشتغلتها على الكواردينيات و بتكون Linear,
+
+100
+00:08:48,090 --> 00:08:53,230
+Homogenous, Astrobic وضعت ال RFC هلاحظ ان ال RFC
+
+101
+00:08:53,230 --> 00:08:57,290
+إيش بتعطينا إبسلون على سيجما متذكرى إبسلون على
+
+102
+00:08:57,290 --> 00:09:01,490
+سيجما ورقعت علينا اللي هي relaxation timeاللي هو
+
+103
+00:09:01,490 --> 00:09:07,150
+الزمن اللازم ل ال field انه يشتر له relaxation في
+
+104
+00:09:07,150 --> 00:09:10,050
+قلب ال media قولنا في ال conductance كانت قداش
+
+105
+00:09:10,050 --> 00:09:14,210
+سريع جدا في ال dielectric او في ال insulator كانت
+
+106
+00:09:14,210 --> 00:09:18,130
+بتاخد أيام احدنا مثالين فهذا هو relaxation time
+
+107
+00:09:18,130 --> 00:09:24,560
+بسوء R في C بسوء epsilon على sigmaهذا تلخيص لبعض
+
+108
+00:09:24,560 --> 00:09:27,780
+القيام اللي ممكن نحصل عليها لأسواق الفرر بلاد
+
+109
+00:09:27,780 --> 00:09:33,020
+كبسطور C تاعته هتكون يبسلون S على D او D على سيجما
+
+110
+00:09:33,020 --> 00:09:36,700
+S او زي ما هتكون متعودين عليها رو D على S حيث دي
+
+111
+00:09:36,700 --> 00:09:40,380
+هي المسافة بين ال two plates وS اللي هي مساحة ال
+
+112
+00:09:40,380 --> 00:09:43,760
+بلاد ويبسلون هي ال dielectric بين ال two plates
+
+113
+00:09:43,760 --> 00:09:48,580
+وسيجما ال conductivity للبلادلـ Cylindrical
+
+114
+00:09:48,580 --> 00:09:51,680
+Capacitor اللى حسبناه اليوم مع بعض C بيساوى 2 π
+
+115
+00:09:51,680 --> 00:09:55,580
+إبسلون L على لن ال B على A R بيساوى لن ال B على A
+
+116
+00:09:55,580 --> 00:10:00,940
+على 2 بي سجنه أقل Spherical C بيساوى 4 بي إبسلون
+
+117
+00:10:00,940 --> 00:10:05,200
+على 1 على A مانص 1 على B R بيساوى 1 على A مانص 1
+
+118
+00:10:05,200 --> 00:10:09,100
+على B على 4 بي سجنه لل Isolated Spherical
+
+119
+00:10:09,100 --> 00:10:14,040
+Conductor C بيساوى 4 بي إبسلون M يعني الخارجى
+
+120
+00:10:14,040 --> 00:10:20,310
+بيكونgrounded فبكون C بيسوي 4 by epsilon A و R 1
+
+121
+00:10:20,310 --> 00:10:24,910
+على 4 by sigma A كل هدول مطلوب منكم تتعرفوا عليهم
+
+122
+00:10:24,910 --> 00:10:28,650
+تشتقوهم تتأكد انكم بتعرفوا جيبيهم لإن أكيد هجيكوا
+
+123
+00:10:28,650 --> 00:10:33,970
+في الامتحان واحد من هذه الأشياء بما انه انا بلحظة
+
+124
+00:10:33,970 --> 00:10:37,450
+انه حللكوا الأمثلة و الأمثلة هدي عليكم و مطلوبة
+
+125
+00:10:37,450 --> 00:10:40,790
+منكم و اللقاء القادم هتحلوا كل هذه الأمثلة و
+
+126
+00:10:40,790 --> 00:10:45,150
+تجيبهم على ورقة جاهزةاحفظوا إيش الأمثلة هاي لأنك
+
+127
+00:10:45,150 --> 00:10:48,210
+إذا ما جيبتهوهاش هينخصم عليكم خمسة في المية من ال
+
+128
+00:10:48,210 --> 00:10:51,570
+term مش هعطيكم علامات من اللي بيجيبوه اللي بتجيبه
+
+129
+00:10:51,570 --> 00:10:55,110
+مش هينخصم منها علامات اللي مش هتجيب هدولة الأمثلة
+
+130
+00:10:55,110 --> 00:11:02,390
+احفظوا أنهي أمثلة مثال هذا أنت
+
+131
+00:11:02,390 --> 00:11:06,630
+حرة تنسخي نسخ من الكتاب هذه أمثلة تفكري و تحلي
+
+132
+00:11:06,630 --> 00:11:10,870
+لحالك اللي مش هتجيبه هتاخد خصم خمسة في المية من ال
+
+133
+00:11:10,870 --> 00:11:15,160
+termتقول لزمالكم اللي غايبين هي كل الأمثلة اللي
+
+134
+00:11:15,160 --> 00:11:19,980
+موجودين عليكم
+
+135
+00:11:19,980 --> 00:11:23,920
+حلهم اللي قاعد قادر عشان ما حد في ال image و كل ما
+
+136
+00:11:23,920 --> 00:11:27,360
+هتعمله هيك هيكون نفس النظام ماهي method of image
+
+137
+00:11:27,360 --> 00:11:30,580
+method of image مهم جدا انها بتسحل برضه علينا حل
+
+138
+00:11:30,580 --> 00:11:33,500
+بعض ال sophisticated problems يعني لما يكون في عنا
+
+139
+00:11:33,500 --> 00:11:38,260
+مسألة صعبة كتير لكن لها conditions معينة مش دائما
+
+140
+00:11:38,260 --> 00:11:42,780
+بقدر نسحل من ال image أولا ال image ال problemتم
+
+141
+00:11:42,780 --> 00:11:47,440
+تقنيمها أو الطريقة الحل بالإنماج اللى قدمها هو
+
+142
+00:11:47,440 --> 00:11:52,860
+Kelvin اسم مشهور بالنسبالهم Kelvin Kelvin قال لو
+
+143
+00:11:52,860 --> 00:11:56,840
+أنا كان عندي زى الأمثلة اللى قدامكم على ال slide
+
+144
+00:11:56,840 --> 00:12:00,720
+لو كان عندي أنا perfect conductor مش عال perfect
+
+145
+00:12:00,720 --> 00:12:04,940
+conductor يعني sigma اله infinity perfect
+
+146
+00:12:04,940 --> 00:12:11,910
+conductorوالـ conductor هذا ماله احنا بنعرف انه ال
+
+147
+00:12:11,910 --> 00:12:16,050
+potential له grounded يعني واصلينه بال ground يعني
+
+148
+00:12:16,050 --> 00:12:19,050
+ال potential عنده zero هو ال potential surface ال
+
+149
+00:12:19,050 --> 00:12:22,510
+conductor وفي هذه الحالة مالها zero لأننا واصلاها
+
+150
+00:12:22,510 --> 00:12:27,350
+بال ground ال grounded V بيساوة Zero وكان يندي بعض
+
+151
+00:12:27,350 --> 00:12:31,970
+ال sources of charge مثلا point of charge line of
+
+152
+00:12:31,970 --> 00:12:38,380
+charge او مثلا أسفيرأو سيلندر، أنواع مختلفة من ال
+
+153
+00:12:38,380 --> 00:12:43,520
+sources لل potential لل charges وانطلب مني أحسن ال
+
+154
+00:12:43,520 --> 00:12:47,320
+potential في أي نقطة في ال space في أي نقطة في ال
+
+155
+00:12:47,320 --> 00:12:53,300
+space اللي above ال conductorعشان اجيب ال
+
+156
+00:12:53,300 --> 00:12:57,620
+potential على اي نقطة من ال space وجود هذه ال
+
+157
+00:12:57,620 --> 00:13:00,900
+variety من ال sources charges طبعا انتوا اتعلمتوا
+
+158
+00:13:00,900 --> 00:13:03,980
+خلال ال gauss law و خلال ال columns law كيف انكوا
+
+159
+00:13:03,980 --> 00:13:07,860
+تجيبوه مش مشكلة لكن هذه الطريقة هتلاقوا انها اسهل
+
+160
+00:13:07,860 --> 00:13:14,080
+بكتير باستخدام ال image لم ينجش اهل قال انا عندي
+
+161
+00:13:14,080 --> 00:13:16,520
+هذا امنا perfect conductor potential تبعه zero
+
+162
+00:13:16,520 --> 00:13:21,670
+وعندي هذه ال sourcesالـ charge وانا بدي ال
+
+163
+00:13:21,670 --> 00:13:24,790
+potential في اي نقطة في ال space المثل بتاعة
+
+164
+00:13:24,790 --> 00:13:28,350
+Kelvin قال ان انا بستبدل ال perfect conductor
+
+165
+00:13:28,350 --> 00:13:32,150
+بequal potential surface V بساوة 0 يعني بدل ما ال
+
+166
+00:13:32,150 --> 00:13:36,250
+conductor راح ال space كله ال half زي ما انتوا
+
+167
+00:13:36,250 --> 00:13:40,310
+شايفين النص تحتاني من ال space كله conductor بدله
+
+168
+00:13:40,310 --> 00:13:45,970
+بستبدله surface يعني زي سطح الطوا surface بدل ما
+
+169
+00:13:45,970 --> 00:13:52,200
+هوملي الفراغ بتاعتانى صار مجرد surface وهذا ال
+
+170
+00:13:52,200 --> 00:13:54,520
+surface الى اللى بتنشل برضه الوصفر بنسميه
+
+171
+00:13:54,520 --> 00:13:58,900
+equipotential surface انه اى نقطة عليا لهذا ال
+
+172
+00:13:58,900 --> 00:14:01,020
+surface لو هذه الطاولة هي ال surface اللى بحكى
+
+173
+00:14:01,020 --> 00:14:05,140
+عنها اى نقطة حقيقة بتنشل فيها عشان هيكون zero عشان
+
+174
+00:14:05,140 --> 00:14:09,620
+هيك بنسميه equal ايقوى من التساوية فعشان أقول هذا
+
+175
+00:14:09,620 --> 00:14:14,430
+ال equipotential surface هيشتغل شغل المرايابس
+
+176
+00:14:14,430 --> 00:14:17,210
+المراية ايش بدل ما احنا المراية لو بدأ اشوف حالة
+
+177
+00:14:17,210 --> 00:14:20,630
+على صورة المراية اشوفها جانبي صح الصورة ال image
+
+178
+00:14:20,630 --> 00:14:25,150
+بس اللي لو احنا بتدرسها هي الامتداد، تساكرين؟
+
+179
+00:14:25,150 --> 00:14:29,110
+بتهيألي انا هي اللي لو احنا طلعنا درسنا physics او
+
+180
+00:14:29,110 --> 00:14:32,790
+يعني optics الإشعة بتيجي وبتناكس فيا و في الواقع
+
+181
+00:14:32,790 --> 00:14:34,590
+الصورة بتاعتنا بس هنا بشوفها بشوفها في قلب
+
+182
+00:14:34,590 --> 00:14:39,450
+المراية، امتداد الشعة تبعكنفس الاشياء على الأقل
+
+183
+00:14:39,450 --> 00:14:43,370
+خلّيني أتطلع أنا عندي هتلعب لعب image إذا كل
+
+184
+00:14:43,370 --> 00:14:48,050
+charge هيكون فيها صورة في قلب الـ equipotential
+
+185
+00:14:48,050 --> 00:14:51,630
+surface أو خلف الـ equipotential surface خلفه لأن
+
+186
+00:14:51,630 --> 00:14:55,570
+هو مجرد surface بسمعها إذا كانت عند positive
+
+187
+00:14:55,570 --> 00:15:00,210
+charge هتصير ال image بتاعتها سلبت ال charge يعني
+
+188
+00:15:00,210 --> 00:15:02,750
+أنا مثلا point of charge Q هيكون ال image بتاعتها
+
+189
+00:15:02,750 --> 00:15:06,350
+minus Q ال line رؤال
+
+190
+00:15:22,880 --> 00:15:26,160
+بعدين بحسب ال potential عند أي نقطة في ال space
+
+191
+00:15:26,160 --> 00:15:28,540
+الناتج منها دول ال elements كلها
+
+192
+00:15:33,490 --> 00:15:39,170
+تسكير أو تلخيص لأن حكاته عشان أستخدم ال image لازم
+
+193
+00:15:39,170 --> 00:15:44,270
+يكون عنده two conditions أول حاجة لازم تكون ال
+
+194
+00:15:44,270 --> 00:15:48,090
+charge image لازم تكون في ال conducting region
+
+195
+00:15:48,090 --> 00:15:51,410
+يعني و أنا حطيت ال images الصور في ال conducting
+
+196
+00:15:51,410 --> 00:15:54,670
+region في الواقع هذه كلها رالية على conductor بس
+
+197
+00:15:54,670 --> 00:15:57,350
+استبدأت ال conductor بإيه؟ بإيه ال confidential
+
+198
+00:15:57,350 --> 00:16:03,860
+surface والصورمش سوينا استبدلنا ال conducting او
+
+199
+00:16:03,860 --> 00:16:07,180
+ال perfectly conducting plan ايه بقاش ايه كنتش ال
+
+200
+00:16:07,180 --> 00:16:10,680
+surface وعندي ال images يعني وان بتكون ال images
+
+201
+00:16:10,680 --> 00:16:14,280
+في ال conducting صعيد مش في الاتجاه التاني
+
+202
+00:16:19,090 --> 00:16:23,510
+كمان لازم اكون متأكدة ان ال potential على ال eco
+
+203
+00:16:23,510 --> 00:16:26,690
+potential surface بيبقى 0 لأن اصلا هو ال conductor
+
+204
+00:16:26,690 --> 00:16:31,170
+مصور في ال ground، grounded، V بتاعه 0 فلازم يكون
+
+205
+00:16:31,170 --> 00:16:35,810
+ال charges دولة دايما يعطوني potential بساوة 0 على
+
+206
+00:16:35,810 --> 00:16:42,930
+ال eco potential surface ناخد
+
+207
+00:16:42,930 --> 00:16:46,110
+أبسط مثل هو ال point of charge، لبداء ال point of
+
+208
+00:16:46,110 --> 00:16:48,430
+charge، فعندي انا ال conductor
+
+209
+00:17:00,730 --> 00:17:05,930
+بنجيب ال potential عند اي نقطة في ال space مثلا
+
+210
+00:17:05,930 --> 00:17:09,750
+بدياها عند نقطة بي عند xyz
+
+211
+00:17:13,530 --> 00:17:17,750
+الحل بالإماج فهي جاهزة، يعني واضح إن أنا بقدر
+
+212
+00:17:17,750 --> 00:17:19,890
+استخدام فيها الإماج، بتحقق ال condition أن عندي
+
+213
+00:17:19,890 --> 00:17:23,310
+conducting plane اللي عنده V بيساوة Zero وعندي
+
+214
+00:17:23,310 --> 00:17:28,790
+point 14 بس تبدل ال conducting plane ال surface
+
+215
+00:17:28,790 --> 00:17:35,070
+اللي V بتساوة Zero وإماج، الإماج مالها على امتد Q
+
+216
+00:17:35,070 --> 00:17:41,800
+ويالها سالب Qأنا بدي ال potential عند النقطة P في
+
+217
+00:17:41,800 --> 00:17:44,280
+ال space طبعا أعرف بال conductor لإن احنا بتعرف
+
+218
+00:17:44,280 --> 00:17:46,300
+إنه في قلب ال conductor ال electric و ال potential
+
+219
+00:17:46,300 --> 00:17:50,940
+معله zero فP
+
+220
+00:17:50,940 --> 00:17:55,140
+ال XYZ أي نقطة في ال space اللي هو form بس هتحقق
+
+221
+00:17:55,140 --> 00:18:01,720
+الحالة Z أكبر من 0 أول
+
+222
+00:18:01,720 --> 00:18:04,320
+خطوة بعملها بتجيب ال electric field إنها تجمد two
+
+223
+00:18:04,320 --> 00:18:08,430
+point charges و هذا مش صعب علينا نحسبهيعني total
+
+224
+00:18:08,430 --> 00:18:13,390
+electric field عن النقطة بـxyz هي عبارة عن E
+
+225
+00:18:13,390 --> 00:18:16,230
+الناتج من positive charge زاد electric field
+
+226
+00:18:16,230 --> 00:18:19,130
+الناتج من negative charge والelectric field من
+
+227
+00:18:19,130 --> 00:18:25,550
+voltage charge يش بيساوي R vector على R magnitude
+
+228
+00:18:25,550 --> 00:18:31,210
+Q R هي المسافة بين ال source والنقطة الرئيسية
+
+229
+00:18:31,210 --> 00:18:35,920
+عندها ال potentialعشان أجيبها دايما بتكون عبارة عن
+
+230
+00:18:35,920 --> 00:18:39,900
+mean R بقعد النقطة الدقيقصية فيها ال electric
+
+231
+00:18:39,900 --> 00:18:43,320
+field minus R prime اللي هي وضع وين ال position
+
+232
+00:18:43,320 --> 00:18:47,900
+تبع ال source R احنا اتفقنا من زمان هي عبارة عن R
+
+233
+00:18:47,900 --> 00:19:03,020
+R اللي هي I R I R R واحد هي عبارة عن R minus R
+
+234
+00:19:04,920 --> 00:19:10,740
+بنسميها 1 الـ prime الـ 1 الـ prime هو الأعضاء فلو
+
+235
+00:19:10,740 --> 00:19:16,460
+أخدنا هذا الطول هو h اللي يوضع مكان الـ cube عبارة
+
+236
+00:19:16,460 --> 00:19:22,840
+عن h هذي يقدر يكون 00h وهذه النقطة اللي هي xyz فال
+
+237
+00:19:22,840 --> 00:19:29,420
+difference بينهم r-r prime هو عبارة عن xyz-00h
+
+238
+00:19:29,420 --> 00:19:37,520
+بالتالي هتكون xY ومن هيتغير هي Z component Z-H R2
+
+239
+00:19:37,520 --> 00:19:40,900
+نفس الشيء ال E ناتج من negative charge الفرقية انه
+
+240
+00:19:40,900 --> 00:19:44,380
+بس هيكون بدل positive negative minus Q ع 4 epsilon
+
+241
+00:19:44,380 --> 00:19:49,240
+not R2 vector ع R2 magnitude of Q مين هى R2 اللى
+
+242
+00:19:49,240 --> 00:19:52,700
+هى نفس الحاجة الفرق بين R
+
+243
+00:20:00,080 --> 00:20:08,860
+هتكون R-RB' وR هي XYZ وR' يعني 00-H بوقع ال image
+
+244
+00:20:08,860 --> 00:20:14,000
+win على minus H إذا Q قعدة على H, minus Q هتكون
+
+245
+00:20:14,000 --> 00:20:17,760
+على نفس البعد لإنها ال image بتاعتها وإلها ما لها
+
+246
+00:20:17,760 --> 00:20:24,160
+إشارة مخالفة جيبنا R1 وR2 بعود عنهم في ال electric
+
+247
+00:20:24,160 --> 00:20:27,580
+field إذا ال Q إيش هيساوي four by epsilon not؟
+
+248
+00:20:27,580 --> 00:20:37,130
+فين؟R1 هي XYZ يعني Z-H Z-H
+
+249
+00:20:37,130 --> 00:20:44,950
+Z-H Z-H Z-H Z-H Z-H Z-H Z-H Z-H Z-H Z-H Z-H Z-H Z
+
+250
+00:20:44,950 --> 00:20:45,170
+-H Z-H Z-H Z-H Z-H Z-H Z-H Z-H Z-H Z-H Z-H Z-H Z-H
+
+251
+00:20:45,170 --> 00:20:55,210
+Z-H Z-H Z-H Z-H Z-H Z-H Z-H Z-H
+
+252
+00:20:55,210 --> 00:20:59,230
+Z-H Z-H Z-H Z-H Z-H Z-H Z-H Z-H Z-H Z-H Z-H Z-Hزي
+
+253
+00:20:59,230 --> 00:21:05,310
+من اين؟ من ان عندي Q سالبة R2 X X hat زي Y Y hat
+
+254
+00:21:05,310 --> 00:21:10,910
+زي Z plus H زي Z minus minus H بيصير plus H Z hat
+
+255
+00:21:10,910 --> 00:21:14,670
+على نفس القضية X تربيه زي Y تربيه زي Z plus H كل
+
+256
+00:21:14,670 --> 00:21:21,030
+تربيه تحت الجزر كل Q فبصير قوة 3 على 2 هذا اللي
+
+257
+00:21:21,030 --> 00:21:24,670
+اترك فيه في اي صعوبة ايجا دلوقتي اترك فيها؟ في اش
+
+258
+00:21:24,670 --> 00:21:29,360
+جديدتعلم انك تجيب ال electric field بين two و
+
+259
+00:21:29,360 --> 00:21:35,320
+three و five و مليون charge صح؟ vector بجمعهم بجمع
+
+260
+00:21:35,320 --> 00:21:41,490
+ال vectors مع بعض V minus الintegral ل E dot DLأو
+
+261
+00:21:41,490 --> 00:21:45,190
+بعنى آخر هي عبارة عن positive potential زي ال
+
+262
+00:21:45,190 --> 00:21:47,010
+negative potential، و positive potential جاي من ال
+
+263
+00:21:47,010 --> 00:21:50,150
+positive charge و ال negative الجاي من مين؟ من ال
+
+264
+00:21:50,150 --> 00:21:53,290
+negative charge، لو أنا كملت ال electric field
+
+265
+00:21:53,290 --> 00:21:56,010
+اللي هو ناتج من ال positive charge، برضه بعطيني ال
+
+266
+00:21:56,010 --> 00:21:59,530
+potential، لو كملت هاي، و لو كملت هاي بتعطيني ال
+
+267
+00:21:59,530 --> 00:22:02,190
+potential ناتج من ال negative chargeوأحنا أصلا
+
+268
+00:22:02,190 --> 00:22:06,330
+عارفين ال potential body charge وبار عالي Q على 4
+
+269
+00:22:06,330 --> 00:22:12,230
+أبسل نوت R1 زائد minus Q على 4 أبسل نوت R2 على طول
+
+270
+00:22:12,230 --> 00:22:15,770
+بحساب ال potential ال total potential جاء من two
+
+271
+00:22:15,770 --> 00:22:16,750
+charges
+
+272
+00:22:19,640 --> 00:22:24,480
+هذا ال potential إذا اللي ناتج من ال two charges
+
+273
+00:22:24,480 --> 00:22:27,880
+اللي واحدة منهم الحقيقية والتانية ال image عند أي
+
+274
+00:22:27,880 --> 00:22:31,780
+نقطة بال space for z مايلها أكبر من أوت ساوسفر ال
+
+275
+00:22:31,780 --> 00:22:34,860
+space اللي فوق ال conductor فقلب ال conductor إيش
+
+276
+00:22:34,860 --> 00:22:37,800
+بدو يكون ال potential؟ لازم يكون بساوسفر ال
+
+277
+00:22:37,800 --> 00:22:41,670
+potential فقلب ال conductorلازم بيساوي 0 ال
+
+278
+00:22:41,670 --> 00:22:45,310
+potential هنا 0 for z أقل من او بيساوي 0 لازم يكون
+
+279
+00:22:45,310 --> 00:22:49,570
+v بيساوي 0 و بيساوي potential عند z equal 0 لو
+
+280
+00:22:49,570 --> 00:22:54,030
+اقضع z equal 0 ماش بيصير عندى aq على four by
+
+281
+00:22:54,030 --> 00:22:57,510
+epsilon naught في واحد على x تربية زي ادوية تربية
+
+282
+00:22:57,510 --> 00:23:01,910
+زي h تربية تحت الجزر minus واحد على x تربية زي
+
+283
+00:23:01,910 --> 00:23:06,410
+ادوية تربية زي h تربية تحت الجزر مروحوا مع بعض اذا
+
+284
+00:23:06,410 --> 00:23:13,910
+عند z equal 0و تحت الـ Z أقل من Zero بيظل ال
+
+285
+00:23:13,910 --> 00:23:16,730
+potential of السفر سافر لأن هو هذا الـ Ecological
+
+286
+00:23:16,730 --> 00:23:17,810
+Potential Surface
+
+287
+00:23:21,210 --> 00:23:24,730
+لو انا بتأكد قداش قيمة ال Q انترنزك او انا بتأكد
+
+288
+00:23:24,730 --> 00:23:28,290
+قداش ال image ال Q بتاعتها انها لازم تكون minus ال
+
+289
+00:23:28,290 --> 00:23:32,110
+Q نروح لمين لـ boundary conditions ال boundary
+
+290
+00:23:32,110 --> 00:23:35,830
+conditions ايش بتقولنا ان ال surface تشجعش بالساوي
+
+291
+00:23:35,830 --> 00:23:38,610
+ال normal component ل D من ال boundary conditions
+
+292
+00:23:38,610 --> 00:23:43,150
+و D تشبه الساوي ي نو دقيقة ان هدم يلوم ماقلتش ان
+
+293
+00:23:43,150 --> 00:23:46,310
+في عندي دايلكتريك فده هوة موجودة في ال هوة مش في
+
+294
+00:23:46,310 --> 00:23:51,750
+قلب دايلكتريكهذا boundary بين contactor و ال
+
+295
+00:23:51,750 --> 00:23:56,050
+vacuum فإذا ال normal component ل DN إيش بيحت سوى
+
+296
+00:23:56,050 --> 00:24:03,290
+ال recharge رؤس و DN هتسوى إبسل نوض EM عند مين؟
+
+297
+00:24:03,290 --> 00:24:09,210
+عند z equals 0 هو عند ال boundary أعوض عن ال EM
+
+298
+00:24:09,210 --> 00:24:13,510
+اللي هو ال electric field عن z equals 0 تطلع معاه
+
+299
+00:24:13,510 --> 00:24:17,300
+هذا المنطقر بس بتعود عن z equals 0 في ال Eهي عندى
+
+300
+00:24:17,300 --> 00:24:22,280
+الكتابة هى اقعد على z equals 0 z equals 0 بعدين
+
+301
+00:24:22,280 --> 00:24:26,040
+minus h فى البصد و انا عندى minus h فى البصد بنجمه
+
+302
+00:24:26,040 --> 00:24:29,980
+بيصيروا minus 2 ال X بتروح مع ال X ال Y بتروح مع
+
+303
+00:24:29,980 --> 00:24:36,660
+ال Y معين مافيش دورة تبلح لو احط z equals 0 هد
+
+304
+00:24:36,660 --> 00:24:40,120
+بيصير المقال نفس الاشي لأن هى X تربيع زي Y تربيع
+
+305
+00:24:40,120 --> 00:24:43,360
+زي H تربيع نفس الاشي هنا X تربيع زي Y تربيع زي H
+
+306
+00:24:43,360 --> 00:24:49,430
+تربيع البصد اش بيصير X minus X بتروحY-Y بتروح زد
+
+307
+00:24:49,430 --> 00:24:53,250
+صفر عندي minus H وهنا كمان minus H هسي minus ثانية
+
+308
+00:24:53,250 --> 00:24:57,870
+H زدها على X تربيه زاد Y تربيه زاد X تربيه القوة
+
+309
+00:24:57,870 --> 00:25:00,410
+تلاتة على اتنين هي ال electric field and Z equals
+
+310
+00:25:00,410 --> 00:25:08,270
+zero معود عنها بحصل على مين على ال row S and Z
+
+311
+00:25:08,270 --> 00:25:13,170
+equals zero ال QI اللي هي لماشية سوية تكامل رو S
+
+312
+00:25:13,170 --> 00:25:16,370
+DS و DS زي ما انتوا شايفين في ال XY
+
+313
+00:25:19,140 --> 00:25:23,420
+الـ surface تبعي في الـ x,y لأنها يستد عمودي عليها
+
+314
+00:25:23,420 --> 00:25:26,280
+فالـ surface هيكون في الـ x,y فهيكون التكامل ل x
+
+315
+00:25:26,280 --> 00:25:29,400
+minus infinity ل plus infinity و ال y minus
+
+316
+00:25:29,400 --> 00:25:35,940
+infinity ل plus infinity ρو s ds إذا هتكون اللي هي
+
+317
+00:25:35,940 --> 00:25:39,640
+رو أس اللي حسبناها مع بعض minus qh على 2pi x ترجع
+
+318
+00:25:39,640 --> 00:25:43,360
+إلى y ترجع إلى h فيها القوة 3 ع 2 في اللي هو
+
+319
+00:25:43,360 --> 00:25:46,940
+التكامل لل surface اللي هو dx dy minus infinity ل
+
+320
+00:25:46,940 --> 00:25:51,060
+plus infinityطبعا لو احنا ساخدنا ال change of
+
+321
+00:25:51,060 --> 00:25:54,700
+variables اخدنا ال X تربية زي ال Y تربية سمناها رو
+
+322
+00:25:54,700 --> 00:25:58,740
+تربية يعني اخدنا من ال Cartesian و روحنا لل بولر ل
+
+323
+00:25:58,740 --> 00:26:01,860
+رو تربية اذا انا هبدل دي X دي Y اش هيكون عندى رو
+
+324
+00:26:01,860 --> 00:26:05,180
+دي رو دي فاي هيتبسط عندى ال integration هي مجرد ال
+
+325
+00:26:05,180 --> 00:26:08,520
+trick أخدتها اكيد في التكاملات عشان انه يصير
+
+326
+00:26:08,520 --> 00:26:10,760
+التكامل سهل جدا فاي بتروح
+
+327
+00:26:33,270 --> 00:26:40,010
+نفس الكلام نقدر نغيره أو نضيفه
+
+328
+00:26:40,010 --> 00:26:47,810
+للي هتعملوه في البيتهنجيب ال electric field و ال
+
+329
+00:26:47,810 --> 00:26:52,810
+potential عند أي نقطة النادجة من ال line of charge
+
+330
+00:26:52,810 --> 00:26:58,930
+اللي عليه charge density رؤال و
+
+331
+00:26:58,930 --> 00:27:03,030
+نفس
+
+332
+00:27:03,030 --> 00:27:09,270
+الحاجة لو كان عندى charge واحدة طبعا الحاجة المهمة
+
+333
+00:27:09,270 --> 00:27:14,510
+انه لازم نلاحظ ان عدد ال charges بختلفحسب اللى هو
+
+334
+00:27:14,510 --> 00:27:18,270
+الزاوية اللى بين ال conductor و اللى هو الموضع
+
+335
+00:27:18,270 --> 00:27:22,830
+اللى هو ال charge يعني عند ال conducting plane
+
+336
+00:27:22,830 --> 00:27:27,950
+هلقيتها بهذا الشكل شكيله واقع
+
+337
+00:27:27,950 --> 00:27:30,890
+على زاوية قائمة مع ال charge لو رجعنا احنا للسؤال
+
+338
+00:27:30,890 --> 00:27:31,490
+الأولانى
+
+339
+00:27:39,270 --> 00:27:44,030
+لما أخدنا ال one image كان ال conducting ال plan و
+
+340
+00:27:44,030 --> 00:27:47,770
+موضوع ال charge بهذا الشكل يعني ال plan عامل زاوية
+
+341
+00:27:47,770 --> 00:27:52,930
+قداش مية و تمانين كيلو مية و تمانين لو انا اجيت
+
+342
+00:27:52,930 --> 00:27:56,210
+على المثال اللي انا بدأ افرجكوا معاه ال plan عامل
+
+343
+00:27:56,210 --> 00:28:00,710
+تسعين درجة ال plan عامل تسعين درجة اكم image
+
+344
+00:28:00,710 --> 00:28:06,470
+تتوقعه هيكون معناه اكم اتنين اكم واحدة تتوقعه
+
+345
+00:28:06,470 --> 00:28:11,290
+اتنين زي ما بتقولبس تنتين يعني واحدة هنا و واحدة
+
+346
+00:28:11,290 --> 00:28:17,130
+هنا طبعا في الشيشة بتتوقع يكون سوريه هيكون عند
+
+347
+00:28:17,130 --> 00:28:23,470
+تلاتة images واحدة طبعا لازم هنا اناالانماج اللى
+
+348
+00:28:23,470 --> 00:28:27,510
+هنا هتكون سالبة و الانماج اللى عندها هتكون موجبة و
+
+349
+00:28:27,510 --> 00:28:30,330
+بعدين الانماج اللى هنا هتكون سالبة فزان هيكون اللى
+
+350
+00:28:30,330 --> 00:28:34,590
+تلاتة images لما يكون الزاوية 90 درجة و نفس الحاجة
+
+351
+00:28:34,590 --> 00:28:36,950
+لو مابيجي بتحسب ال potential عند أي نقطة في ال
+
+352
+00:28:36,950 --> 00:28:40,350
+space بتأجيب ال potential لكل واحدة من هدول النقاط
+
+353
+00:28:40,350 --> 00:28:43,850
+و طبعا قانون ستة و مفروض حافظينه زى اسمكم بس
+
+354
+00:28:43,850 --> 00:28:46,010
+الحاجة اللى هتبقى لكوا ترعوها هي تجيبوا ال
+
+355
+00:28:46,010 --> 00:28:51,320
+position اللى هي الفرق ما بين موضعالنقطة من ال
+
+356
+00:28:51,320 --> 00:28:55,920
+origin ناقص وضع ال source r minus r prime و برضه
+
+357
+00:28:55,920 --> 00:29:00,140
+ماعقدتش أنها مشكلة هنا في الحالة طالب ال force
+
+358
+00:29:00,140 --> 00:29:04,840
+اللي على النقطة الحقيقية من ال images و طبعا سهولة
+
+359
+00:29:04,840 --> 00:29:09,400
+بتنحسن فيه نقانون لقداش الزاوية اللي بيعملها ال
+
+360
+00:29:09,400 --> 00:29:13,560
+conductor لو ال conductor مثلا عالي 60 درجة قداش
+
+361
+00:29:13,560 --> 00:29:18,070
+أكم image بدأ أحط عشان أعرف عدد ال imagesبستخدم
+
+362
+00:29:18,070 --> 00:29:21,710
+هذا القانون n بتساوي تلات مية و سبتين على five
+
+363
+00:29:21,710 --> 00:29:27,870
+minus واحد نيجي ناخد اللي هي five مية و تمانين اول
+
+364
+00:29:27,870 --> 00:29:33,560
+مثال360 على 180 يعني اتنين مقاس واحد واحد اي واحدة
+
+365
+00:29:33,560 --> 00:29:38,040
+المثال التاني قداش تسعين 360 على تسعين قداش تعطينا
+
+366
+00:29:38,040 --> 00:29:43,820
+اربعة مقاس واحد تلاتة ستين مقاش تكون ستة مقاس واحد
+
+367
+00:29:43,820 --> 00:29:46,840
+خمسة اذا المقاس اللي انتوا شايفينه عندي خمسة
+
+368
+00:29:46,840 --> 00:29:53,160
+هيكونه plus q هيكون هنا minus q plus q minus q
+
+369
+00:29:53,160 --> 00:29:56,820
+plus q minus q تمام
+
+370
+00:29:59,080 --> 00:30:02,020
+ال principle المفروض أنه واضح كيف نحسب ال charges
+
+371
+00:30:02,020 --> 00:30:04,580
+ال potential عند أي نقطة في ال space ودولة كلهم
+
+372
+00:30:04,580 --> 00:30:08,180
+pointed charges وحتى لو كان ال line a charge لازم
+
+373
+00:30:08,180 --> 00:30:12,840
+تكونوا قادرين كيف تحسبوه وهيك أنا بكون خلصت الشكتة
+
+374
+00:30:12,840 --> 00:30:17,240
+النقاء القادم الأمثلة اللي أنا مريت عليهم لازم
+
+375
+00:30:17,240 --> 00:30:22,220
+تكون معاكم وجايبينهم هي ورقة عليها اسمكم مرتب
+
+376
+00:30:22,220 --> 00:30:27,640
+بالكلام وواضحواللي غابوا بيكفيهم ان هم غايبين و
+
+377
+00:30:27,640 --> 00:30:33,060
+هيحفظوا غصب مع غياب يحفظوا و يجيبوا معهم اللي هم
+
+378
+00:30:33,060 --> 00:30:34,600
+مركبت بسؤالية
+
diff --git a/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/oTaDolk77vQ.srt b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/oTaDolk77vQ.srt
new file mode 100644
index 0000000000000000000000000000000000000000..8f8f9183e0b635559d5e4c7aa199a32ae12890cf
--- /dev/null
+++ b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/oTaDolk77vQ.srt
@@ -0,0 +1,2105 @@
+1
+00:00:20,940 --> 00:00:23,260
+بسم الله الرحمن الرحيم السلام عليكم و رحمة الله و 
+
+2
+00:00:23,260 --> 00:00:25,100
+بركاته و نحن اليوم سنتبع إن شاء الله ال vector
+
+3
+00:00:25,100 --> 00:00:28,580
+analysis ونحن في المحاضرة الماضية ميزنا بين scalar و
+
+4
+00:00:28,580 --> 00:00:33,260
+vector وميزنا بين ال position و ال distance و
+
+5
+00:00:33,260 --> 00:00:36,620
+vectors و parameters ميزنا بين كيف أنه أعمل الجميع
+
+6
+00:00:36,620 --> 00:00:40,120
+وبنعمل الطرح والأخرين اليوم نحن  واخدمها
+
+7
+00:00:40,120 --> 00:00:43,580
+نحن سيرنا الدرب نحن بس شفنا الجميع والطرح أن
+
+8
+00:00:43,580 --> 00:00:46,480
+الدرّب في ال vector مختلف كليًا عن الدرب في ال
+
+9
+00:00:46,480 --> 00:00:50,180
+scalarالدرجة من ال vector أنه طرف ثاني حتى دلتاني 
+
+10
+00:00:50,180 --> 00:00:53,880
+واحدة نسميها scalar أو ال dot product والثاني 
+
+11
+00:00:53,880 --> 00:00:57,200
+اسمه vector or cross product الأسماء جاية من
+
+12
+00:00:57,200 --> 00:01:00,880
+الناتج المنتج تبعهم ال dot product الناتج تبعه
+
+13
+00:01:00,880 --> 00:01:04,500
+scalar عشان هيك اسمه scalar الناتج تبع ال cross 
+
+14
+00:01:04,500 --> 00:01:09,480
+product vector عشان هيك هو اسمه vectorتتوقف هنا ال
+
+15
+00:01:09,480 --> 00:01:12,800
+multiplication لأكثر من 2 vectors يعني لو كان عندي
+
+16
+00:01:12,800 --> 00:01:17,200
+بس 2 vectors سيكون يا عندي dot أو scalar يا عندي 
+
+17
+00:01:17,200 --> 00:01:20,180
+vector ال product لو كان عندي مثلًا ثلاثة vectors
+
+18
+00:01:20,180 --> 00:01:23,720
+يكون عندي برضه أنموعة ثانية من ال product سيكون
+
+19
+00:01:23,720 --> 00:01:26,160
+في عندي مثلًا scalar whichever product برضه نفس 
+
+20
+00:01:26,160 --> 00:01:30,160
+القضية ال scalar جاي من الناتج الناتج تبع a dot b 
+
+21
+00:01:30,160 --> 00:01:33,220
+cross c scalar لأنه b cross c قلنا إيش الناتج
+
+22
+00:01:33,220 --> 00:01:36,080
+تبعها vector a dot vector
+
+23
+00:01:38,530 --> 00:01:42,410
+والنوع الثالث أو الرابع سيكون هو vector a triple
+
+24
+00:01:42,410 --> 00:01:46,990
+product اللي هو a cross b cross c وهذا أنه يشتبع
+
+25
+00:01:46,990 --> 00:01:55,790
+عرض ال vector نجي 
+
+26
+00:01:55,790 --> 00:01:58,930
+لل vector product لو أنا عندي two vectors نحن 
+
+27
+00:01:58,930 --> 00:02:05,030
+قلنا لهم أن أنا a cross b يعطينا cمعناه أنه لازم
+
+28
+00:02:05,030 --> 00:02:07,890
+ال vector الثالث له اتجاه عشان أحدد اتجاه ال 
+
+29
+00:02:07,890 --> 00:02:10,770
+vector الثالث نستخدم ال right hand rule ال right
+
+30
+00:02:10,770 --> 00:02:13,490
+hand rule بتقوله بحط أيدي على ال vector الأول هو ال
+
+31
+00:02:13,490 --> 00:02:17,290
+A وبلف في اتجاه B وين بي موجودة بلف أيدي عليه
+
+32
+00:02:17,290 --> 00:02:22,670
+فتصبح A cross B تقرين اتجاه C يعني لو أنا كانوا 
+
+33
+00:02:22,670 --> 00:02:24,830
+عاملة ال vector استعيني بهذا الشكل هم اللي بيدعملهم
+
+34
+00:02:24,830 --> 00:02:30,150
+cross product A وB أروح من A لB أو كان هناك هقول
+
+35
+00:02:30,150 --> 00:02:34,630
+من A لB هي معناه أني بلفبلغوف من اتجاه ال vector
+
+36
+00:02:34,630 --> 00:02:37,290
+الأول للثاني أما بتعمل cross ما بين ال a و ال b 
+
+37
+00:02:37,290 --> 00:02:41,630
+فبقول a cross b بطني c لو كان ال b هنا إيش اعمل 
+
+38
+00:02:41,630 --> 00:02:46,790
+cross ايه؟ a cross b بطلع ال c لتحت كمان ممكن نحن
+
+39
+00:02:46,790 --> 00:02:48,850
+بدل ما نستخدم ال right hand rule هذا اسم ال right
+
+40
+00:02:48,850 --> 00:02:52,490
+hand rule اللي بعمل a cross b بطني c ممكن استخدم 
+
+41
+00:02:52,490 --> 00:02:55,070
+أن هي فكرة ال fact في ناس بيحبوا البراغي بالذات و
+
+42
+00:02:55,070 --> 00:02:57,350
+أنا بحب فكرة البراغي أكثر من ال right hand rule
+
+43
+00:02:58,130 --> 00:03:00,470
+عارف زمان واحنا ببرسات قلنا راحت هغلو وتعمل
+
+44
+00:03:00,470 --> 00:03:02,790
+مشاكل، بيجي الولد على ال .. لازم يدرس على
+
+45
+00:03:02,790 --> 00:03:05,110
+البراندة، بقعد يعمل هيك، يعمل هيك، بيجي الجار وي
+
+46
+00:03:05,110 --> 00:03:10,670
+ضربه على الأرض، قعد أشهر لابنته، فبقولك أحسن حاجة
+
+47
+00:03:10,670 --> 00:03:15,010
+هي مين ال .. البرغة بالنسبة للشباب، المرئيش بيطلع، 
+
+48
+00:03:15,010 --> 00:03:18,230
+بقول أنا بدي ألف البرغة من تجار A لB، إذا هيك A 
+
+49
+00:03:18,230 --> 00:03:23,040
+وB، بلفه هكفلما تلف البرغة اللي هيتحرك هي على فوق
+
+50
+00:03:23,040 --> 00:03:26,520
+A لتحت فأنا هاي البرغة تبعي وبدأت ألف من A ل B 
+
+51
+00:03:26,520 --> 00:03:30,440
+اتجاه هاي A وهاي B هنا فبلف البرغة وأنا بطلع و
+
+52
+00:03:30,440 --> 00:03:33,860
+أنا بطلع على فوق فهذا اتجاه ال vector الثالث واضح؟
+
+53
+00:03:33,860 --> 00:03:36,760
+لو كان العكس لو أنا عندي A ل B هاي هذا ال vector
+
+54
+00:03:36,760 --> 00:03:40,120
+الثالث اللي فاك تبعي وبدي ألف من A ل B هي هنا A و
+
+55
+00:03:40,120 --> 00:03:44,040
+هاي B بدي ألف اتجاه ال B بنزل البرغة لتحت فهذا
+
+56
+00:03:44,040 --> 00:03:47,560
+بيكون اتجاه ال set يعني إيه ال right hand rule؟
+
+57
+00:03:47,560 --> 00:03:50,830
+إيه إيه الشركات البرغة؟ بلفه هك إذا أنا رايحة من A
+
+58
+00:03:50,830 --> 00:03:54,830
+ل B أو بلفه هك إذا رايحة من A ل B إذا كانت B تلات
+
+59
+00:03:54,830 --> 00:03:59,770
+اتجاه إذا هذا هو اللي بيحدد لي اتجاه ال vector 
+
+60
+00:03:59,770 --> 00:04:04,750
+across ال product نجي ندرس واحد منهم بالواحد يعني 
+
+61
+00:04:04,750 --> 00:04:07,870
+ناخد كيف بتعمل هذا ال product أسوأ ال dot product
+
+62
+00:04:07,870 --> 00:04:10,710
+ولا ال vector product نبدأ بال dot product نحن
+
+63
+00:04:10,710 --> 00:04:15,030
+قلنا A dot B لازم يعطيني scalar مقدار هذا ال scalar
+
+64
+00:04:15,030 --> 00:04:20,450
+يساوي المجلد تبع A بالمجلد تبع Bالزاوية اللي
+
+65
+00:04:20,450 --> 00:04:26,750
+بينها يعني لو كان عندي هاي ال vector A وهي ال
+
+66
+00:04:26,750 --> 00:04:31,510
+vector B وهي الزاوية اللي بينهم أنا هسميها theta
+
+67
+00:04:31,510 --> 00:04:37,990
+AB سيكون عندي ال product هو magnitude تبع A وال
+
+68
+00:04:37,990 --> 00:04:43,310
+magnitude تبع B فهو جبت برامج الزاوية اللي بينهم
+
+69
+00:04:45,270 --> 00:04:48,610
+يعني مثلًا لو كنت عندي a اللي هو ال vector a، اللي
+
+70
+00:04:48,610 --> 00:04:50,950
+هو ال components، نحن قلنا هذا تمثيل تبع ال 
+
+71
+00:04:50,950 --> 00:04:56,210
+vectors، يا مصدر الأقراص وهذه ال X component وY
+
+72
+00:04:56,210 --> 00:05:01,890
+component وZ component، يا أكتبه بشكل اللي هو ax x
+
+73
+00:05:01,890 --> 00:05:07,870
+hat زي ay y hat زي az z hat، كنت فاقناه يكتبها x
+
+74
+00:05:07,870 --> 00:05:12,410
+hat y hat z hat، يا زي ما الكتاب يعملها ax hat ay
+
+75
+00:05:12,410 --> 00:05:18,410
+hat ez hat، أه؟ نفس الشيء لل V هذا vector وهاي ال
+
+76
+00:05:18,410 --> 00:05:21,950
+components بتاعتها في X و Y و Z  أنددنا product
+
+77
+00:05:21,950 --> 00:05:26,510
+بقولوا التالي أندي ال component X مع ال component
+
+78
+00:05:26,510 --> 00:05:31,150
+X doted بشكل أهم هو اللي بقدر اعمل product لكل ال
+
+79
+00:05:31,150 --> 00:05:36,690
+components يعني إذا بدأنا بتفصيل R
+
+80
+00:05:36,690 --> 00:05:50,460
+dot V هي عبارة عن Ax Ayisn doted مع bx by bz ستكون
+
+81
+00:05:50,460 --> 00:05:57,640
+ال component الأولى مع الأولى بax x hat doted مع 
+
+82
+00:05:57,640 --> 00:06:05,960
+bx x hat الثانية الأولى مع الثانية زائد ax x hat
+
+83
+00:06:05,960 --> 00:06:17,900
+doted مع by y hat زائد ax x hatاكس اكسها دتت مع بي
+
+84
+00:06:17,900 --> 00:06:24,980
+زد زدها وهكذا نبدأ بالاي و ايها دتت مع بي اكس
+
+85
+00:06:24,980 --> 00:06:31,300
+اكسها وهكذا معين؟ لكن في حاجة مهمة جدًا في ال dot 
+
+86
+00:06:31,300 --> 00:06:34,440
+product قلنا ال dot product تبع أي two components
+
+87
+00:06:34,440 --> 00:06:37,940
+بيعطينا قيمة الأول وقيمة الثانية في جيب الزاوية 
+
+88
+00:06:37,940 --> 00:06:42,340
+اللي بينهم نحن ال XYZ معلة فده Cartesian
+
+89
+00:06:42,340 --> 00:06:56,670
+CoordinateX Y و Z أسوأ طالع ولا داخل هي X هي Y X Y
+
+90
+00:06:56,670 --> 00:07:01,870
+Z بأخذ ال right hand rule هنا عند X hat عند Y hat
+
+91
+00:07:01,870 --> 00:07:09,010
+وعند Z hat هدولة بتسميهم unit vectors X hat و Y
+
+92
+00:07:09,010 --> 00:07:15,470
+hat و Z hatماذا يعني أن المجموعة تبقى واحدة يعني
+
+93
+00:07:15,470 --> 00:07:22,050
+إذا أجيب X hat مجموعة يتحكم واحدة لأن المجموعة
+
+94
+00:07:22,050 --> 00:07:26,950
+ستعرف عليه جزر التربية ل X hat dot X hat إذا كنت
+
+95
+00:07:26,950 --> 00:07:30,530
+تسعى معنا dot product إيش معناه رابع عن جزر 
+
+96
+00:07:30,530 --> 00:07:33,550
+التربية المجموعة تبقى الها أول ومجموعة تبقى الثاني
+
+97
+00:07:33,550 --> 00:07:37,770
+تجيب سواء بينهم اللي يبقى رابع عن كسين اللي يتسين
+
+98
+00:07:37,770 --> 00:07:45,490
+تجيب تسين اداش واحدجيب تمام إذا وغير بينهم Zero X
+
+99
+00:07:45,490 --> 00:07:49,470
+hat 
+
+100
+00:07:49,470 --> 00:07:54,470
+مجنته تبعها واحد ال Y hat مجنته تبعها واحد ال Z
+
+101
+00:07:54,470 --> 00:07:58,670
+hat مجنته تبعها واحد فإذا X hat dot X hat واحد
+
+102
+00:07:58,670 --> 00:08:03,990
+بينما X hat dot Y hat ماتساوش اللي حطيتلكميها في
+
+103
+00:08:03,990 --> 00:08:07,800
+ال group لأنه عادي مجنته تبع X hat هو واحدفي
+
+104
+00:08:07,800 --> 00:08:11,020
+مجموعة y hat واحد في جيب التوية الزاوية بينه مقدر 
+
+105
+00:08:11,020 --> 00:08:16,200
+كتان درجة جيب تان تسعين زيرو إذا أنا عندها ده اللي
+
+106
+00:08:16,200 --> 00:08:20,260
+بيحقق هو الشرط اللي هي unit vectors إذا كانوا
+
+107
+00:08:20,260 --> 00:08:22,780
+اثنين متعامدين مع بعض x hat و y hat الشيء اللي
+
+108
+00:08:22,780 --> 00:08:26,020
+بيكون ال total product تبعهم زيرو x hat و z hat ال
+
+109
+00:08:26,020 --> 00:08:30,700
+total product تبعهم زيرو x hat و x hat واحد y hat
+
+110
+00:08:30,700 --> 00:08:37,330
+و y hat واحد z hat و z hat واحد إذا بنقول هدولة ال
+
+111
+00:08:37,330 --> 00:08:41,770
+components أي حاجة فيها x hat و y hat أي حاجة فيها 
+
+112
+00:08:41,770 --> 00:08:48,710
+0 y hat و x hat 0 x hat و z hat 0 سيظل عند مين 
+
+113
+00:08:48,710 --> 00:08:54,090
+اللي هي مثلًا ال a
+
+114
+00:08:54,090 --> 00:09:02,310
+y hat a y y hat dot by y hat سيظل عند مين a z z 
+
+115
+00:09:02,310 --> 00:09:04,750
+hat dot 
+
+116
+00:09:17,660 --> 00:09:20,640
+عشان هيك بيطلعوا معناه كهذه formula
+
+117
+00:09:25,900 --> 00:09:30,520
+زي ال AYBY زي ال AZBZ فإن أي حاجة اي dot ثاني ما
+
+118
+00:09:30,520 --> 00:09:32,980
+بين ال components الباقين يعني لو أنا عملت ال dot
+
+119
+00:09:32,980 --> 00:09:37,720
+ما بين ال AX والBY ستكون zero، ما ضر؟ إذا البساطة
+
+120
+00:09:37,720 --> 00:09:40,580
+ال dot ال product هو عبارة عن حاصل ال similar
+
+121
+00:09:40,580 --> 00:09:43,200
+components يعني ال X components مع بعض زي ال Y
+
+122
+00:09:43,200 --> 00:09:47,800
+components مع بعض زي ال Z components مع بعض كمان
+
+123
+00:09:47,800 --> 00:09:51,940
+ال dot ال product نحن مش معرفينه بA بB بقصين
+
+124
+00:09:51,940 --> 00:09:54,600
+الزاوية إذا أنا بقدر أعمل ال dot ال product بهذه
+
+125
+00:09:54,600 --> 00:09:59,700
+الطريقة أجيب المجلد تبع A والمجلد تبع B وأدرسه في 
+
+126
+00:09:59,700 --> 00:10:02,320
+ال case file يزور بينهم أو إذا كنت عارفة ال
+
+127
+00:10:02,320 --> 00:10:06,180
+components اعمل الهاي الطريقة كما الهاي كما
+
+128
+00:10:06,180 --> 00:10:09,620
+بتساعدني لو أنا كنت عارفة قيم A وB وال 
+
+129
+00:10:09,620 --> 00:10:22,780
+components عامهم أجيب يتزور بينهم معايا؟ طيب إيش
+
+130
+00:10:22,780 --> 00:10:29,940
+فيه من خصائص ال productخصائصه أنه ال commutative
+
+131
+00:10:29,940 --> 00:10:34,760
+law إيش يعني ال commutative law أنه سواء ضابط a
+
+132
+00:10:34,760 --> 00:10:38,540
+dot b أو b dot a لازم يبقى نفس الحاجة ومن هنا ده
+
+133
+00:10:38,540 --> 00:10:44,620
+الحقيقة لو أنا حضرت هنا b dot a حضرت هنا bx ex هل 
+
+134
+00:10:44,620 --> 00:10:48,820
+حد فرقها إيه ولا by ay ماهد أخذناها في المخدرات 
+
+135
+00:10:48,820 --> 00:10:50,200
+الماضية مش هيك 
+
+136
+00:10:54,090 --> 00:10:57,010
+في ال not distributive يعني التوزيع لو أنا أول
+
+137
+00:10:57,010 --> 00:11:01,350
+جمعة أندي طلعتها vector A وB وC لو جمعت أول ال B
+
+138
+00:11:01,350 --> 00:11:05,590
+مع ال C عملتلهم dot ال product مع ال A لازم يساوي
+
+139
+00:11:05,590 --> 00:11:08,950
+لو أنا عملت أول dot ال product ما بين ال A وB و
+
+140
+00:11:08,950 --> 00:11:13,510
+dot ال product مع ال A وC وجمعت ال نواتي مع بعض
+
+141
+00:11:13,510 --> 00:11:19,410
+يعني زي ما أنتم شايفين أسوأ في البداية جمعت ال B 
+
+142
+00:11:19,410 --> 00:11:24,490
+مع ال Cوالناتج أو أول عملت dot product ما بين ال 
+
+143
+00:11:24,490 --> 00:11:27,410
+a و ال b و ال dot product ما بين ال a و ال c و
+
+144
+00:11:27,410 --> 00:11:30,350
+بعدين جمعتهم مع بعض نفس الناتج طبعًا هذا ال
+
+145
+00:11:30,350 --> 00:11:33,350
+magnitude اللي هو a dot a ناتج من اللي اللي هي 
+
+146
+00:11:33,350 --> 00:11:36,210
+العلاقة اللي هنا
+
+147
+00:11:41,780 --> 00:11:45,360
+أو من هنا تعني مثل حاجة ستعطينا a في a اللي هو ال
+
+148
+00:11:45,360 --> 00:11:48,220
+magneto في magneto فجبتهم يزول بينهم، قداشر تعمل
+
+149
+00:11:48,220 --> 00:11:51,620
+تمام يزول بين ال a و ال a، zero، جبتهم zero واحد،
+
+150
+00:11:51,620 --> 00:11:55,560
+إذا ال dot product ل a مع dot m هتسوي إيه تنبيه؟ 
+
+151
+00:11:55,560 --> 00:11:58,740
+إذا a هي ال magneto، مش بتسوي الجزر التنبيهي ل a
+
+152
+00:11:58,740 --> 00:12:01,300
+dot a، واضح؟
+
+153
+00:12:04,530 --> 00:12:07,370
+وهذا أنا حكيتلكم يا ال unit vectors لازم إذا كان 
+
+154
+00:12:07,370 --> 00:12:10,530
+ال unit vector معروف أنه ال magnitude تبعه ال unit
+
+155
+00:12:10,530 --> 00:12:13,710
+vector تعريفه هو ال unit vector ال magnitude تبعه
+
+156
+00:12:13,710 --> 00:12:16,710
+واحد ف ال dot product مع ال unit vector نفسه 
+
+157
+00:12:16,710 --> 00:12:19,610
+بعطيني واحد unit vector و vector وأن unit vector
+
+158
+00:12:19,610 --> 00:12:24,150
+عمودي عليها بيكون zero كي اسف صار لحد هنا؟ هيك
+
+159
+00:12:24,150 --> 00:12:27,690
+نحن خلصنا ال dot product ديش ال cross product ال 
+
+160
+00:12:27,690 --> 00:12:29,970
+cross product اللي هو ال vector product كمان
+
+161
+00:12:29,970 --> 00:12:32,250
+سميناه لأنه ال نميش تبعه vector 
+
+162
+00:12:35,490 --> 00:12:38,090
+ال magnitude تبع ال cross product هذا ال 
+
+163
+00:12:38,090 --> 00:12:42,910
+magnitude تبعه هو عبارة عن a في b ب sign الزاوية 
+
+164
+00:12:42,910 --> 00:12:48,830
+اللي بينهم هذا ال magnitude عشان
+
+165
+00:12:48,830 --> 00:12:53,050
+هذا vector فإيش سيكون فيه الاتجاه تبع ال vector
+
+166
+00:12:53,050 --> 00:12:56,090
+الجديد am يمثل اتجاه ال vector الناتج من ال cross 
+
+167
+00:12:56,090 --> 00:13:00,370
+product تبع a مع b إذا a cross b سيعطينا ال vector
+
+168
+00:13:00,370 --> 00:13:03,930
+اللي مقداره a في b ب sign الزاوية اللي بينهم
+
+169
+00:13:03,930 --> 00:13:09,980
+واتجاهه اللي هوأيه هذا؟ أنا ممكن كمان أعرف ال 
+
+170
+00:13:09,980 --> 00:13:12,100
+cross product عن طريق ال determinant بتاع ال 
+
+171
+00:13:12,100 --> 00:13:16,640
+matrix A cross B فهو ال determinant بوزر ال unit 
+
+172
+00:13:16,640 --> 00:13:18,980
+vectors اللي هي ال partition مثلًا في حالتنا نحن
+
+173
+00:13:18,980 --> 00:13:21,940
+مثلًا بنعمل ال partition X hat وY hat وZ hat ال
+
+174
+00:13:21,940 --> 00:13:24,360
+component بتاعة ال vector الأول وال component
+
+175
+00:13:24,360 --> 00:13:26,600
+بتاعة ال vector الثاني بتعرفوا تعملوا ال
+
+176
+00:13:26,600 --> 00:13:30,480
+determinant تحسوها ولا في داعي راجعوا مع بعض كله 
+
+177
+00:13:30,480 --> 00:13:31,880
+عارف في حد مش عارف
+
+178
+00:13:41,470 --> 00:13:46,390
+هذا اللي هي ال permutative يعني أنا عندي أي unit 
+
+179
+00:13:46,390 --> 00:13:50,
+
+201
+00:15:16,700 --> 00:15:21,000
+بتطلع لفوق و  a × b بتطلع تحت نفس المقضيب فهي
+
+202
+00:15:21,000 --> 00:15:24,180
+anticommutative يعني معناه أنه في إشارة سالبة 
+
+203
+00:15:24,180 --> 00:15:28,660
+a × b بيكون تجاه مثلا ال z hat لكن ال b 
+
+204
+00:15:28,660 --> 00:15:33,800
+× a بيكون تجاه هوفر سالب it is not associative
+
+205
+00:15:33,800 --> 00:15:37,300
+يعني أنا ما بقدرش أوزعها ما بقدرش أقول أن a × b
+
+206
+00:15:37,300 --> 00:15:40,400
+× c أنه associative يعني مثلا أول أعمل ×
+
+207
+00:15:40,400 --> 00:15:44,160
+product بين ال a و ال b وبعدين أعمل × مع c لا 
+
+208
+00:15:44,160 --> 00:15:47,920
+تساوي اللي لو عملت × product b مع c وعملتلها 
+
+209
+00:15:47,920 --> 00:15:50,860
+× product مع a ما بيساويوش معك بسبب أن هذا 
+
+210
+00:15:50,860 --> 00:15:55,520
+vector product لكن هي distributive يعني أسوأ عملت 
+
+211
+00:15:55,520 --> 00:15:58,940
+أول جمعت ال P مع ال C وعملت ال × product مع
+
+212
+00:15:58,940 --> 00:16:02,840
+A أو أول عملت × A × P بعدين A × C نفس 
+
+213
+00:16:02,840 --> 00:16:05,840
+النتيجة وقولنا ال vector × مع نفسه بيعطينا
+
+214
+00:16:05,840 --> 00:16:06,360
+Zero
+
+215
+00:16:10,360 --> 00:16:13,680
+الـtriple product scalar الـtriple product وهذا
+
+216
+00:16:13,680 --> 00:16:16,600
+شفناه قلنا ليش هو scalar triple لأن قلنا في عملية ضرب 
+
+217
+00:16:16,600 --> 00:16:19,640
+أول × product ال بيعطينا vector دُتت معايا
+
+218
+00:16:19,640 --> 00:16:22,400
+scalar بيعطينا scalar ببساطة ال triple product
+
+219
+00:16:22,400 --> 00:16:25,720
+اللي عبّر عنه برضه ال determinant الناتج تبع ال
+
+220
+00:16:25,720 --> 00:16:29,200
+determinant بيعطينا القيمة اللي هو ال triple product 
+
+221
+00:16:29,200 --> 00:16:33,620
+برتب ال vector الأول اللي هو ال A السطر الأول ال 
+
+222
+00:16:33,620 --> 00:16:37,460
+الـ V السطر الثاني و ال C السطر الثالث
+
+223
+00:16:55,490 --> 00:17:05,050
+عشان الناس تحفظها بيقولوا back cap يعني مجرد
+
+224
+00:17:05,050 --> 00:17:10,410
+تذكير بس لازم تكون حاصل أنه a × b × c يعني 
+
+225
+00:17:10,410 --> 00:17:13,070
+لو وجدت كرموز ثانية حطها على جانب a × b ×
+
+226
+00:17:13,070 --> 00:17:16,450
+c وقول back cap back cap إيش معناه أن الترتيب 
+
+227
+00:17:16,450 --> 00:17:21,050
+الأولاني هو back والترتيب الثاني cap back هيكون ال
+
+228
+00:17:21,050 --> 00:17:26,870
+b مضروب في a · c والترتيب minus c a · b يعني
+
+229
+00:17:26,870 --> 00:17:30,750
+أنها لازم تعرف حاجة بس عشان تتذكر الترتيب اللي هي
+
+230
+00:17:30,750 --> 00:17:32,650
+back cap واضح؟
+
+231
+00:17:37,420 --> 00:17:42,640
+أن a · b مضروبة في c vector لها تساوي a مضروبة
+
+232
+00:17:42,640 --> 00:17:46,000
+بي · c لأنه طبعا زي ما قولنا هدول كلهم vector
+
+233
+00:17:46,000 --> 00:17:52,040
+فبيكون أنها مش مساوية أي تشكيل لكن عند a · b هذا
+
+234
+00:17:52,040 --> 00:17:56,840
+إيش طلع عليه vector مع c بسبب c a · b هذا مافيش 
+
+235
+00:17:56,840 --> 00:18:00,280
+فيها أي مشكلة الترتيب بسبب أحطيت ال a · b هنا
+
+236
+00:18:00,280 --> 00:18:04,090
+اللي هو صار scalar عفوا أن هادي scalar لأنه ضرب بس 
+
+237
+00:18:04,090 --> 00:18:06,950
+هو أحضرتها دي تبقى الناتج مثلا خمسة أو خمسة عشر أو
+
+238
+00:18:06,950 --> 00:18:09,210
+خمسة عشر أو خمسة عشر أو خمسة عشر أو خمسة عشر أو خمسة
+
+239
+00:18:09,210 --> 00:18:11,310
+عشر أو خمسة عشر أو خمسة عشر أو خمسة عشر أو خمسة عشر أو
+
+240
+00:18:11,310 --> 00:18:11,890
+خمسة عشر أو خمسة عشر أو خمسة عشر أو خمسة عشر أو خمسة
+
+241
+00:18:11,890 --> 00:18:14,590
+عشر أو خمسة عشر أو خمسة عشر أو خمسة عشر أو خمسة عشر أو
+
+242
+00:18:14,590 --> 00:18:14,610
+خمسة عشر أو خمسة عشر أو خمسة عشر أو خمسة عشر أو خمسة
+
+243
+00:18:14,610 --> 00:18:22,850
+عشر أو خمسة عشر أو خمسة عشر أو
+
+244
+00:18:22,850 --> 00:18:29,870
+خمسة عشر أو خمسة عشر أو
+
+245
+00:18:29,870 --> 00:18:33,690
+خمسة وببدأ أعرف ال component بتاعته في اتجاه ال B
+
+246
+00:18:33,690 --> 00:18:37,530
+عشان أعرف ال component بتاعت ال vector A تجاه ال
+
+247
+00:18:37,530 --> 00:18:42,050
+B هتكون عبارة عن قيمة A كما أنتم أخذتم في ال ..
+
+248
+00:18:42,050 --> 00:18:45,730
+أي مصطلحات ال component بتاعته في اتجاه ال X hat 
+
+249
+00:18:45,730 --> 00:18:48,570
+أو ال Y hat بس إحنا بدنا نقول ال X اتجاه ال B يعني
+
+250
+00:18:48,570 --> 00:18:52,010
+ال vector A و ال vector B ال component بتاعت A
+
+251
+00:18:52,010 --> 00:18:55,230
+تجاه ال B اللي هي عبارة عن مقدار A بكساين الزاوية
+
+252
+00:18:55,230 --> 00:19:03,260
+لل B A كوساين الزاوية تمام؟إذاً هاي ال component هي
+
+253
+00:19:03,260 --> 00:19:06,540
+عبارة يعني مثلا أنتم تتذكروا إننا نحن نتحلل أي
+
+254
+00:19:06,540 --> 00:19:10,720
+vector مثلا هاي ال F وكنا نقول هاي ال component في
+
+255
+00:19:10,720 --> 00:19:14,860
+هذا الاتجاه هي θ هي F cos θ في اتجاه مثلا ال X hat
+
+256
+00:19:14,860 --> 00:19:19,180
+وهي ال component هتكون F cos θ في اتجاه ال Y hat
+
+257
+00:19:19,180 --> 00:19:23,280
+فإذا ال component في اتجاه ال B عبارة عن مقدار
+
+258
+00:19:23,280 --> 00:19:27,660
+مقدار A cos θ AB هاي ال component اللي في
+
+259
+00:19:27,660 --> 00:19:32,880
+هذا الاتجاه هذا إيش معناه؟معناه هي المقدار تبع A في
+
+260
+00:19:32,880 --> 00:19:37,620
+ال magnitude تبع ال B hat ال unit vector اتجاه ال
+
+261
+00:19:37,620 --> 00:19:41,620
+B اللي هو واحد، ده واحد يعني مقدر أضيفه وإيه صح 
+
+262
+00:19:41,620 --> 00:19:46,300
+فجبته من الزاوية اللي هي θتا بين ال A و ال B أو 
+
+263
+00:19:46,300 --> 00:19:48,380
+هذا إيش قلنا بيساوي، اللي هو المقدار تبع ال vector 
+
+264
+00:19:48,380 --> 00:19:50,460
+الأول في المقدار تبع ال vector الثاني في الزاوية
+
+265
+00:19:50,460 --> 00:19:53,200
+اللي بينهم وضربت ال product between هدول two 
+
+266
+00:19:53,200 --> 00:19:57,540
+vectors يعني ال component بتاعة A اتجاه ال B هي
+
+267
+00:19:57,540 --> 00:20:00,160
+عبارة عن مقدار ال product ما بين ال Aو ال unit 
+
+268
+00:20:00,160 --> 00:20:04,520
+vector في اتجاه ال B أنا هتعطيني المقدار تبع ال A
+
+269
+00:20:04,520 --> 00:20:09,080
+اللي هو A مضروب المقدار تبع ال unit vector B hat
+
+270
+00:20:09,080 --> 00:20:11,600
+اللي هو واحد تجيب الزاوية اللي بينهم اللي هي تيتا
+
+271
+00:20:11,600 --> 00:20:15,660
+واضح؟إذا أنا بأجيب component لأي vector في اتجاه 
+
+272
+00:20:15,660 --> 00:20:20,740
+معين بضربه في ال unit vector في هذا الاتجاه كمان
+
+273
+00:20:20,740 --> 00:20:21,620
+مرة ولا واضح؟
+
+274
+00:20:27,760 --> 00:20:30,820
+طب إذا بدي أعبّر عنه بشكل vector ما بديش أعبّر عنه ب
+
+275
+00:20:30,820 --> 00:20:36,440
+component يعني عرفنا إن هذا الطول هو عبارة عن A 
+
+276
+00:20:36,440 --> 00:20:42,520
+· B hat طب أنا بدي اتجاهه، بدي كل مرة أقول إن
+
+277
+00:20:42,520 --> 00:20:45,000
+هو في اتجاه الـB، لأ أقوم بقول هو اتجاه اللي هو 
+
+278
+00:20:45,000 --> 00:20:48,520
+الـB hat زي ما هنا أنا بدي أقول هذه ال component 
+
+279
+00:20:48,520 --> 00:20:57,550
+هي في X، vector، هتسوّأ ف و سعي و ستة، X hat عشان
+
+280
+00:20:57,550 --> 00:21:00,390
+أعرف ال component بتاعة أي vector في اتجاه معين 
+
+281
+00:21:00,390 --> 00:21:03,050
+بعملها dot product مع unit vector في هذا الاتجاه 
+
+282
+00:21:03,050 --> 00:21:13,530
+والاتجاه هيكون هو هذا ال unit vector تشوف
+
+283
+00:21:13,530 --> 00:21:16,810
+أمثلة على المعلومات اللي أخذناها لو كان عندي two 
+
+284
+00:21:16,810 --> 00:21:22,590
+vectors A وB وبدي الزاوية اللي بين A وB دي أحد
+
+285
+00:21:22,590 --> 00:21:24,350
+بيقدر يحللنا يلا تفضل 
+
+286
+00:21:51,800 --> 00:21:55,420
+عشان تجيب الزاوية اللي بينهم بتجيب ال dot product
+
+287
+00:21:55,420 --> 00:21:59,020
+يعني a · b بتساوي a magnitude في b magnitude في
+
+288
+00:21:59,020 --> 00:22:02,660
+cosine الزاوية اللي بينهم فبتعمل ال magnitude تبع 
+
+289
+00:22:02,660 --> 00:22:06,880
+a وطبعا كمان بدها جيب اللي هي a · b اللي هي ال
+
+290
+00:22:06,880 --> 00:22:11,100
+component الأولى في الثانية ال a x في b x زائد ال
+
+291
+00:22:11,100 --> 00:22:16,440
+a y في b y تمام
+
+292
+00:22:16,440 --> 00:22:19,840
+إن ال b x zero فعطول طلعت الناتج 
+
+293
+00:22:43,920 --> 00:23:07,840
+في أي استفسار لحد هنا؟
+
+294
+00:23:10,400 --> 00:23:14,380
+أول حاجة ممكن أجيبها بالـ dot product زي ما عملت
+
+295
+00:23:14,380 --> 00:23:18,720
+زملائي لكن كمان برضه أقدر أجيبها بطريقة ثانية اللي 
+
+296
+00:23:18,720 --> 00:23:22,900
+هي برضه ال cross product cross product حاولنا
+
+297
+00:23:22,900 --> 00:23:27,460
+نعرف أن ال magnitude تبع a × b إيش بيساوي الأول
+
+298
+00:23:27,460 --> 00:23:30,200
+a في ال magnitude تبع b في sin الزاوية اللي بينهم 
+
+299
+00:23:30,200 --> 00:23:33,260
+فبجيب ال a × b اللي هي باستخدام ال determinant
+
+300
+00:23:33,260 --> 00:23:36,640
+هي جبت ال vector الناتج بجيب ال magnitude تبع a
+
+301
+00:23:36,640 --> 00:23:40,080
+× b وبعدين إيش بقول هذا المقدار ما بيساوي
+
+302
+00:23:40,080 --> 00:23:43,120
+المقدار تبع ال A في المقدار تبع ال B في sign 
+
+303
+00:23:43,120 --> 00:23:47,900
+الزاوية فإذا نتساوي إيش هتكون sign ال inverse اللي 
+
+304
+00:23:47,900 --> 00:23:51,060
+هو المقدار تبع ال A × B على المقدار تبع ال 
+
+305
+00:23:51,060 --> 00:23:53,560
+A في المقدار تبع ال .. هنا في بس طيب و sign
+
+306
+00:23:53,560 --> 00:23:58,840
+inverse فلقيت
+
+307
+00:23:58,840 --> 00:24:04,600
+كمان بدي أعمل derivation ده مثال ثاني اللي هو أنا
+
+308
+00:24:04,600 --> 00:24:07,780
+لو بدي أجيب هدول الأمثلة اللي كنا خذناها في
+
+309
+00:24:07,780 --> 00:24:11,700
+الجيبرة في المدرسة اللي هو القانون الأول اللي بقول 
+
+310
+00:24:11,700 --> 00:24:19,180
+ليه لو كان عندي مثلث زي هيكي أطلعوا A وB وC هدول 
+
+311
+00:24:19,180 --> 00:24:24,580
+أطلعوا أن ال A تربيع بيساوي ال C تربيع زائد ال B 
+
+312
+00:24:24,580 --> 00:24:29,040
+تربيع ناقص اثنين B في C في جيب تمام الزاوية اللي
+
+313
+00:24:29,040 --> 00:24:33,780
+بعدهم كنا اخذناها ده القانون وكمان عندنا اللي هي sin
+
+314
+00:24:33,780 --> 00:24:36,180
+formula اللي هي مشهورة sin formula اللي هي sin
+
+315
+00:24:36,180 --> 00:24:40,340
+الزاوية على ضلع قبالها sin ال a على a بيساوي sin 
+
+316
+00:24:40,340 --> 00:24:45,370
+ال b على ال b قبالها بتساوي sin ال C اللي هي 
+
+317
+00:24:45,370 --> 00:24:48,530
+زاوية على الضلع اللي قبالها بدنا نثبت هدول ال
+
+318
+00:24:48,530 --> 00:24:52,370
+two formulas طبعا واضح أنه أكيد هنحتاج ال total
+
+319
+00:24:52,370 --> 00:24:55,930
+product فعشان أحتاج ال total product بدي أحدد مين
+
+320
+00:24:55,930 --> 00:24:58,050
+اللي بدي أحط بينهم ال total product واضح أنه في 
+
+321
+00:24:58,050 --> 00:25:01,470
+عندي A تربيع و B تربيع و C تربيع بين ال B و ال C
+
+322
+00:25:01,470 --> 00:25:05,470
+إذا أنا بدي أحدد ثلاثة مش واحد منهم بدي اخذ مجموع
+
+323
+00:25:05,470 --> 00:25:07,770
+هدول ال vectors إيش مجموع هدول ال vectors بتبدأ 
+
+324
+00:25:07,770 --> 00:25:12,250
+من هنا عند ال A زي ال B زي ال C إيش بيساوي؟ Zero
+
+325
+00:25:13,820 --> 00:25:18,720
+لأن هي ال component بتاعته للمجموع A زي B زي C بها 
+
+326
+00:25:18,720 --> 00:25:22,260
+ساوي وصفر طب هي واضح بين ال dot product من مين و
+
+327
+00:25:22,260 --> 00:25:25,980
+B و C فإذا أنا قلت A vector زي B vector زي C
+
+328
+00:25:25,980 --> 00:25:28,980
+vector مش بساوي وصفر بقى نقول الثانية اللي أنتم 
+
+329
+00:25:28,980 --> 00:25:31,320
+شاطرين وقولتم هو ال dot product بين ال B و ال C
+
+330
+00:25:31,320 --> 00:25:35,060
+على طرف وبضل طرف الثاني مين ال A وبأخذ دوتاتها
+
+331
+00:25:35,060 --> 00:25:40,180
+اللي هي ال dot product تبع هدول ال vectors أول حاجة
+
+332
+00:25:40,180 --> 00:25:42,580
+بجيب المجموع بتاعهم هدول ال vectors اللي هم
+
+333
+00:25:42,580 --> 00:25:45,260
+موجودين في ال formula اللي هي ال A و ال B و ال C
+
+334
+00:25:45,260 --> 00:25:48,780
+بعدين بنقول ال two vectors اللي هو ال A و ال C في
+
+335
+00:25:48,780 --> 00:25:53,140
+جهة و ال A في جهة فهيكون B زائد C بيساوي ناقص A بعدين
+
+336
+00:25:53,140 --> 00:25:56,520
+بعمل ال dot product ل ال vectors في نفسهم يعني أنا
+
+337
+00:25:56,520 --> 00:26:00,320
+هأخذ ال A · A بقي التربيع هتساوي B زائد C · B
+
+338
+00:26:00,320 --> 00:26:04,570
+زائد C معايا؟ زي ما أنتم شايفين على السبورة إذا
+
+339
+00:26:04,570 --> 00:26:08,350
+نعدي الطرف هذا هيكون a · a اللي هو حاطينا a
+
+340
+00:26:08,350 --> 00:26:12,310
+تربيع والطرف هذا b زائد c dotted مع b زائد c
+
+341
+00:26:12,310 --> 00:26:16,010
+اتفقنا هدول هيكون ال component الأولى أو يعني 
+
+342
+00:26:16,010 --> 00:26:20,190
+هنا vectors عنهم هيكون b · b و c · c اللي هو 
+
+343
+00:26:20,190 --> 00:26:23,410
+اللي بالنص اللي هو هيكون ناقص 2 c · b لأن
+
+344
+00:26:23,410 --> 00:26:29,440
+اتفقنا c · b بيساوي c b · c إذاً a تربيع 
+
+345
+00:26:29,440 --> 00:26:34,280
+هتساوي P · P اللي هي P تربيع C · C، C تربيع وP
+
+346
+00:26:34,280 --> 00:26:37,260
+· C اللي هي عبارة عن المقدار تبع الأول في 
+
+347
+00:26:37,260 --> 00:26:39,160
+المقدار تبع الثاني في جيب تمام الزاوية بينهم، مين
+
+348
+00:26:39,160 --> 00:26:47,740
+جيب تمام الزاوية بينهم، اللي هي الزاوية هاي اللي 
+
+349
+00:26:47,740 --> 00:26:51,220
+هي عبارة عن 180 ناقص F عشان تطلعوا هنا إشارة سالبة 
+
+350
+00:26:51,220 --> 00:26:52,260
+على سنة
+
+351
+00:26:58,770 --> 00:27:03,810
+إذا الزاوية اللي بين P و C هي 180 نقص ف بطلع هنا 
+
+352
+00:27:03,810 --> 00:27:09,510
+الإشارة السالفة واضح هذا بالنسبة لل formula الأولى 
+
+353
+00:27:09,510 --> 00:27:15,430
+نيجي لل formula الثانية إحنا 
+
+354
+00:27:15,430 --> 00:27:21,650
+بنعرف أن ال area مساحة المثلث هو نصف القاعدة في
+
+355
+00:27:21,650 --> 00:27:25,840
+الارتفاع إذا أشهر من نصف القاعدة في الارتفاع a × b
+
+356
+00:27:25,840 --> 00:27:33,560
+نصف a × b اللي هي نصف القاعدة في الارتفاع نصف b 
+
+357
+00:27:33,560 --> 00:27:38,400
+× c نصف c × a هذا هتقول اللي هي ال area
+
+358
+00:27:38,400 --> 00:27:45,060
+بتاعة ال triangle لو 
+
+359
+00:27:45,060 --> 00:27:47,940
+عوّضنا عن كل واحدة هتعطينا a في b sin الزاوية اللي
+
+360
+00:27:47,940 --> 00:27:49,900
+بينها دول magnitude طبعا لأن ال area مالها
+
+361
+00:27:49,900 --> 00:27:54,500
+magnitude مقدار مقدار مقدار مقدار مقدار مقدار 
+
+362
+00:27:54,500 --> 00:27:55,120
+مقدار مقدار مقدار مقدار مقدار مقدار مقدار
+
+363
+00:27:55,120 --> 00:28:01,500
+مقدار مقدار مقدار مقدار مقدار مقدار مقدار
+
+364
+00:28:01,500 --> 00:28:06,160
+مقدار مقدار مقدار مقدار مقدار مقدار مقدار
+
+365
+00:28:06,160 --> 00:28:06,400
+مقدار مقدار مقدار مقدار مقدار مقدار مقدار
+
+366
+00:28:06,400 --> 00:28:06,460
+مقدار مقدار مقدار مقدار مقدار مقدار مقدار
+
+367
+00:28:06,460 --> 00:28:13,360
+مقدار مقدار مقدار
+
+368
+00:28:13,360 --> 00:28:18,940
+مقدار
+
+369
+00:28:22,940 --> 00:28:27,560
+هذه الأمثلة كلها موجودة عندكم في الكتاب كويس أنكم 
+
+370
+00:28:27,560 --> 00:28:31,440
+ترجعوا لها المثال هذا إيش بقول لي عندك أنت ثلاث نقاط 
+
+371
+00:28:31,440 --> 00:28:37,360
+B1 وB2 وB3 كلها تقع على خط واحد يعني زي ما أنتم 
+
+372
+00:28:37,360 --> 00:28:43,260
+شايفين مثل هذا المثلث هتفترض من B1 وB2 B1
+
+373
+00:28:43,260 --> 00:28:47,900
+وB2 وB3 وعينها نفس الخط بقول لي
+
+374
+00:28:49,080 --> 00:28:52,460
+to determine the shortest distance between طبعا 
+
+375
+00:28:52,460 --> 00:28:55,040
+أول حاجة بقول لنا أث
+
+401
+00:31:09,110 --> 00:31:11,690
+هجيب الـ cross product إذا طلع الـ cross product له
+
+402
+00:31:11,690 --> 00:31:15,510
+يساوي zero إذا هم مش قاعدين على نفس الخط لكن لو الـ
+
+403
+00:31:15,510 --> 00:31:19,250
+cross product تبعهم صفر هيكون بيساوي صفر بيكونوا في
+
+404
+00:31:19,250 --> 00:31:23,450
+نفس الخط لأنه احنا شرحنا cross product A cross B
+
+405
+00:31:23,450 --> 00:31:28,250
+نفس المتجه هيعبر عن A × B  فسه بيساوي صفرين
+
+406
+00:31:29,850 --> 00:31:33,270
+إذا كانت الزاوية 0 ثاني الـ 180 فالـ cross product
+
+407
+00:31:33,270 --> 00:31:36,310
+صفر، لو ماكانتش بالصفر و صفر مش هيكون الـ cross
+
+408
+00:31:36,310 --> 00:31:38,490
+product بالصفر و صفر، احنا بنحاول تكون الزاوية بينهم
+
+409
+00:31:38,490 --> 00:31:41,370
+صفر عشان يقعوا نفس الخط، الخط، إذا الـ cross product
+
+410
+00:31:41,370 --> 00:31:46,340
+طلع صفر معناه أنه قاعدين نفس الخط، معايا؟ لما نجي
+
+411
+00:31:46,340 --> 00:31:49,960
+نعمل cross product بالفعل بيطلع صفر إذا هم الـ B1
+
+412
+00:31:49,960 --> 00:31:54,320
+وB2 وB3 واقعين على نفس الخط إذا الخطوة الأولى أثبتنا
+
+413
+00:31:54,320 --> 00:31:57,380
+كيف بيقعوا على نفس الخط أنه جبت المسافة بين كل نقطة
+
+414
+00:31:57,380 --> 00:32:00,660
+و التانية و بعدين جبت cross product بين هدول
+
+415
+00:32:00,660 --> 00:32:04,540
+المسافات طلع صفر معناه أنهم بالفعل قاعدين على نفس
+
+416
+00:32:04,540 --> 00:32:08,440
+الخط ما طلع الصفر معناه لأ في بينهم زاوية يعني مش
+
+417
+00:32:08,440 --> 00:32:12,000
+واقعين على نفس الخط الجزء الثاني هو نبي نطلع أقصر
+
+418
+00:32:12,000 --> 00:32:18,640
+مسافة ما بين النقطة P4 و الخط اللي هم واقعين عليه 
+
+419
+00:32:18,640 --> 00:32:22,200
+النقطة يعني ما بين الخط اللي وقع عليه النقطة P1 و
+
+420
+00:32:22,200 --> 00:32:28,160
+P2 و P3 و بين الخط اللي وقع عليه النقطة P4 النقطة
+
+421
+00:32:28,160 --> 00:32:31,520
+P4 هذا هو الخط اللي هم واقعين عليه فبندي فيه نقطة
+
+422
+00:32:31,520 --> 00:32:34,940
+P4 عرف الـ axis بتاعي
+
+423
+00:32:37,860 --> 00:32:45,310
+أقصر مسافة بين الـ P4 وهذا بحط أقصر مسافة بينهم اللي
+
+424
+00:32:45,310 --> 00:32:48,490
+هي هتكون المسافة العمودية و لا لأ أقصر مسافة هي
+
+425
+00:32:48,490 --> 00:32:52,290
+المسافة العمودية هي الخط اللي بين الـ P1 و P2 و P3
+
+426
+00:32:52,290 --> 00:32:55,490
+أي هذا الخط اللي أسفلنا هم واقعين كلهم عليه وهي
+
+427
+00:32:55,490 --> 00:33:00,570
+النقطة P4 بدي أقول هي هي المسافة أقصر مسافة بين P4 و
+
+428
+00:33:00,570 --> 00:33:03,890
+الخط طبعا واضح أنه لازم نحتاج في هي الحالة
+
+429
+00:33:03,890 --> 00:33:07,630
+cross product لأنه بدي أنا مسافة عمودية هتكون الـ
+
+430
+00:33:07,630 --> 00:33:10,730
+cross product بين الخط اللي هو P1 و P4 اللي هو
+
+431
+00:33:10,730 --> 00:33:13,290
+احنا حسبناه  تبقى و أنا بديّه على الجزء الثاني اللي
+
+432
+00:33:13,290 --> 00:33:14,450
+هو بين P1 و P4
+
+433
+00:33:17,220 --> 00:33:20,400
+لأنه لازمني أعرف هي المسافة عشان أقدر أحدد الـ D
+
+434
+00:33:20,400 --> 00:33:23,900
+لأن الـ D إيش هتكون هذا اللي هو الـ .. الـ .. الـ
+
+435
+00:33:23,900 --> 00:33:26,700
+vector و هي الزاوية الثالثة فبقدر أجيبه من ما
+
+436
+00:33:26,700 --> 00:33:28,980
+عرفت اللي هو الـ vector و الزاوية اللي هو بالمعنى
+
+437
+00:33:28,980 --> 00:33:33,580
+الأخر اللي هو الـ  perpendicular part هتكون المسافة D هي
+
+438
+00:33:33,580 --> 00:33:37,380
+هي المسافة R بي واحد بي أربعة اللي هو الـ vector في
+
+439
+00:33:37,380 --> 00:33:42,000
+ساين الزاوية معايا؟ اه انتوا تعرفوا هي الأشياء
+
+440
+00:33:42,800 --> 00:33:46,060
+اللي عبارة عن مين؟ R في ساين الزاوية هي عبارة عن
+
+441
+00:33:46,060 --> 00:33:50,780
+هوقع الـ cross product بين R بي واحد بي أربعة مع
+
+442
+00:33:50,780 --> 00:33:54,660
+مين؟ مع unit vector في اتجاه هذا الاتجاه نفس
+
+443
+00:33:54,660 --> 00:34:00,100
+الفكرة اللي احنا عملناها بالهيكل هذه عبارة عن R بي
+
+444
+00:34:00,100 --> 00:34:05,960
+واحد بي أربعة في الـ unit vector اللي في اتجاه الـ بي
+
+445
+00:34:05,960 --> 00:34:12,360
+واحد بي اتنين بيجوز في ساين ثيتا 
+
+446
+00:34:16,370 --> 00:34:20,490
+ماذا يعني هذا؟ هذا واضح أن مجموع الـ cross product
+
+447
+00:34:20,490 --> 00:34:23,490
+بين هذين المتجهين مجموع الـ cross product بين
+
+448
+00:34:23,490 --> 00:34:26,290
+هذين المتجهين المجموعة الأولى في المجموعة الثانية
+
+449
+00:34:26,290 --> 00:34:30,450
+في ساين زي ولي بينهم فلما أضعها ر بي واحد بي أربعة
+
+450
+00:34:30,450 --> 00:34:35,590
+ساين ستة وأضيف unit vector هو في اتجاه ب1 ب2 هتكون
+
+451
+00:34:35,590 --> 00:34:39,790
+في الواقع الـ magnitude لـ cross product بين r ب1
+
+452
+00:34:39,790 --> 00:34:42,970
+ب4 cross product مع اللي هو الـ unit vector في
+
+453
+00:34:42,970 --> 00:34:47,730
+اتجاه b1 b2 عشان أجيب الـ unit vector في اتجاه الـ
+
+454
+00:34:47,730 --> 00:34:51,950
+b1 b2 إيش هيكون الـ vector على الـ magnitude تبعه
+
+455
+00:34:51,950 --> 00:34:56,550
+احنا شفنا إيش تعريف الـ unit vector لأي
+
+456
+00:34:56,550 --> 00:35:02,730
+vector الـ unit vector في اتجاه الـ a لو سميته a
+
+457
+00:35:03,400 --> 00:35:06,100
+عبارة عن الـ vector A أخدناه في المادة الهندسية
+
+458
+00:35:06,100 --> 00:35:11,460
+الموجودة بـ A عشان أجيب unit vector احنا وصلنا
+
+459
+00:35:11,460 --> 00:35:16,620
+المهدي shortest distance بيعبر عن الـ cross product
+
+460
+00:35:16,620 --> 00:35:22,380
+ما بين المسافة R ب 1 ب 4 المجموعات تبعها الـ
+
+461
+00:35:22,380 --> 00:35:26,400
+crossed مع مين مع اللي هو الـ unit vector في اتجاه P1
+
+462
+00:35:26,400 --> 00:35:31,160
+P2 اللي هو إيش هيساوي الـ vector  P1P2 الـ
+
+463
+00:35:31,160 --> 00:35:36,820
+magnitude تبع  P1P2 هنعوض عنه و هيطلع معي اللي
+
+464
+00:35:36,820 --> 00:35:40,920
+هو الناتج D اللي هي shortest distance بين الخط اللي
+
+465
+00:35:40,920 --> 00:35:46,800
+وقع عليه النقطة P1 P2 و P3 و النقطة P4 واضح؟
+
+466
+00:35:51,560 --> 00:35:54,800
+فهذا المثال احنا تعلمنا أنه فيه right hand rule
+
+467
+00:35:54,800 --> 00:36:01,500
+يعني عند cross product بين two vectors بيعطينا الـ
+
+468
+00:36:01,500 --> 00:36:06,410
+vector الثالث في الـ rectangular coordinate لازم
+
+469
+00:36:06,410 --> 00:36:08,850
+يكون عندي الـ right hand rule rectangular
+
+470
+00:36:08,850 --> 00:36:12,030
+coordinate بتطبق لي الـ right hand rule يعني x cross
+
+471
+00:36:12,030 --> 00:36:20,030
+y هتعطينا z y cross z هتعطيني x z cross x هتعطينا y z 
+
+472
+00:36:20,030 --> 00:36:24,870
+cross x هتعطينا y تمام؟  مي من هدول بتحققش فيها الـ
+
+473
+00:36:24,870 --> 00:36:27,690
+rectangular coordinate يعني مي من فيها إن الـ x
+
+474
+00:36:27,690 --> 00:36:33,110
+cross y بتعطينا شيء  positive z يعني لو استخدمت الـ
+
+475
+00:36:33,110 --> 00:36:37,740
+right hand rule خلّيني أبدأ في الأولى x cross y
+
+476
+00:36:37,740 --> 00:36:43,040
+واضحة z اتجاه صحيح نيجي للتانية x cross y اتجاه
+
+477
+00:36:43,040 --> 00:36:50,380
+اضحك هي ريحتنا الثانية الخاطئة بتحققش في المشكلة
+
+478
+00:36:50,380 --> 00:36:58,540
+c x cross y z اللي تحت لنيجي لـ x cross y اتجاه
+
+479
+00:36:58,540 --> 00:37:03,950
+x تحت درفعها لـ y اتجاه z  فادة اللي بعدها x cross
+
+480
+00:37:03,950 --> 00:37:08,110
+مع y هذا
+
+481
+00:37:08,110 --> 00:37:11,750
+الشكل هتعطينا z عشان هيك أنا بحب البرمجة أكتر
+
+482
+00:37:11,750 --> 00:37:16,050
+بعدين الأخيرة اللي هي x برضه across y هتعطينا اللي
+
+483
+00:37:16,050 --> 00:37:26,050
+هي اتجاه z قبل
+
+484
+00:37:26,050 --> 00:37:35,790
+الأخر L الأخيرة E X X cross Y هتكون الـ Z لجوه صح
+
+485
+00:37:35,790 --> 00:37:40,430
+كلامكم X cross Y هتعطينا اتجاه Z لو برضه الـ E غلط
+
+486
+00:37:40,430 --> 00:37:45,330
+لأن X cross Y هتكون في هذا الاتجاه الـ Z صح كلامكم
+
+487
+00:37:45,330 --> 00:37:50,050
+هي X cross Y هي X لفوق سكرتها على الـ Y هيكون تجاه
+
+488
+00:37:50,050 --> 00:37:54,250
+الـ Z لبرا فـ B و E التنتين فيهم مشكلة مش
+
+489
+00:37:54,250 --> 00:37:55,710
+rectangular coordinate
+
+490
+00:37:59,150 --> 00:38:03,350
+هذا السؤال كل هذا طبعًا تطبيقات للـ vector analysis
+
+491
+00:38:03,350 --> 00:38:08,850
+عندنا جسم بيلف عمال و هذا جسم عند النقطة بيه و قاعد
+
+492
+00:38:08,850 --> 00:38:12,470
+بيلف طبعًا الـ rigid body يعني زي حجر حجر و قاعد
+
+493
+00:38:12,470 --> 00:38:16,770
+بيلف حوالين اللي هو المحور اللي انتوا شايفينه ب
+
+494
+00:38:16,770 --> 00:38:20,310
+angular velocity مقدرها omega radian per second
+
+495
+00:38:20,310 --> 00:38:25,890
+بيلف
+
+496
+00:38:25,890 --> 00:38:30,300
+حول هذا الـ axis اللي بيقرقر في الـ origin zero زي
+
+497
+00:38:30,300 --> 00:38:34,040
+ما هو مضطح قدامنا في الـ figure قولنا خلّينا نقول R
+
+498
+00:38:34,040 --> 00:38:38,060
+هي المسافة اللي هي distance vector من zero لـ P
+
+499
+00:38:42,250 --> 00:38:46,050
+الواقع تبع اللي هو وضع الـ particle يعني هذا الـ
+
+500
+00:38:46,050 --> 00:38:48,350
+position vector الـ position تبع الـ P ماحنا عرفناش
+
+501
+00:38:48,350 --> 00:38:50,390
+معانا الـ position vector أنه أنا لو عندي object
+
+502
+00:38:50,390 --> 00:38:53,630
+بتحدد مكانه بالنسبة للـ origin الـ distance between
+
+503
+00:38:53,630 --> 00:38:58,130
+two objects فالـ distance او الـ position تبع الـ P
+
+504
+00:38:58,130 --> 00:39:01,250
+بالنسبة للـ origin هذا هو الـ R هي عند الـ origin
+
+505
+00:39:01,250 --> 00:39:06,030
+و هذا هو الـ axis اللي بتلف الحجر او الـ object وR اللي
+
+506
+00:39:06,030 --> 00:39:08,330
+هي position vector تبع النقطة P
+
+507
+00:39:12,610 --> 00:39:15,310
+the velocity v of the body at B، الـ velocity
+
+508
+00:39:15,310 --> 00:39:18,330
+تعرفها، يمكن أخدتها بالفيزياء، هي الـ magnitude
+
+509
+00:39:18,330 --> 00:39:23,110
+تبعها D في Omega، اللي هي هذه المسافة D في قيمة
+
+510
+00:39:23,110 --> 00:39:28,590
+Omega او عبارة عن R، magnitude، اللي هي D من هي R
+
+511
+00:39:28,590 --> 00:39:34,050
+في sin θ، صح؟ Rsinθ في Omega اللي عبارة عن مين
+
+512
+00:39:34,050 --> 00:39:37,650
+Rsinθ Omega اللي هي المجنتود في الـ magnitude لو
+
+513
+00:39:37,650 --> 00:39:41,290
+بتستعمل مجنتود تبع U هي المجنتود لـ Omega cross R
+
+514
+00:39:41,290 --> 00:39:46,610
+بشكل عن الـ velocity V او U هي عبارة عن Omega cross
+
+515
+00:39:46,610 --> 00:39:50,390
+R إذا ما كنتوا عارفينها يعني في الـ physics فده هي
+
+516
+00:39:50,390 --> 00:39:55,200
+يعني U magnitude هي عبارة عن قيمة الـ velocity هي D
+
+517
+00:39:55,200 --> 00:39:58,420
+في R في Omega وطبعًا الـ units كمان بتأكدكم إن هذا
+
+518
+00:39:58,420 --> 00:40:01,060
+الحاجة صحيحة اللي هو العلاقة بين الـ angular
+
+519
+00:40:01,060 --> 00:40:04,780
+velocity و الـ linear velocity الـ linear velocity U
+
+520
+00:40:04,780 --> 00:40:08,940
+اللي هي اللي عندكم نقطة بعضها بحسبها علاقتها بالـ
+
+521
+00:40:08,940 --> 00:40:12,880
+angular velocity اللي V بتساوي الـ distance ما بين
+
+522
+00:40:12,880 --> 00:40:16,660
+الـ object و الـ axis اللي بيلف حواليها مضروبة في
+
+523
+00:40:16,660 --> 00:40:19,580
+قيمة اللي هي الـ angular velocity الـ distance دي
+
+524
+00:40:19,580 --> 00:40:23,230
+إيش اللي مستعدة؟ متر في omega radian per second
+
+525
+00:40:23,230 --> 00:40:26,190
+فإيش هتكون unit meter per second اللي هي الـ linear
+
+526
+00:40:26,190 --> 00:40:29,550
+velocity إذا V بتساوي هذه اللي هي الـ linear
+
+527
+00:40:29,550 --> 00:40:32,550
+velocity للـ object بتاعة كل نقطة و الـ omega اللي
+
+528
+00:40:32,550 --> 00:40:36,810
+هي الـ radian velocity إذا بشكل عام اللي هي الـ
+
+529
+00:40:36,810 --> 00:40:39,510
+linear velocity عبارة عن omega اللي هي الـ angular
+
+530
+00:40:39,510 --> 00:40:42,210
+velocity crossed مع R ليه هي الـ R؟
+
+531
+00:40:46,280 --> 00:40:49,000
+بقول إذا كان الجسم بيلف تلاتة radian per second
+
+532
+00:40:49,000 --> 00:40:52,880
+عطانا الـ magnitude تبع الـ Omega هو about an axis
+
+533
+00:40:52,880 --> 00:40:58,120
+parallel to يعني عطاني أنه بيلف بأومجا مقدارها تلاتة
+
+534
+00:40:58,120 --> 00:41:03,860
+حول axis موازي الـ axis او موازي لخط او يعني ل ..
+
+535
+00:41:03,860 --> 00:41:09,560
+ل .. لـ vector قيمته a x hat minus 2 a y hat زائد 2 z
+
+536
+00:41:09,560 --> 00:41:13,320
+hat أنا اللي مهمي بيعني الاتجاه الـ Y يعني بتجيب الـ
+
+537
+00:41:13,320 --> 00:41:16,240
+Y .. ال .. الاتجاه الـ ω الـ vector تبع الـ ω
+
+538
+00:41:16,240 --> 00:41:20,120
+المجموعة تبعها و اتجاهها المجموعة التبعها عطانيها
+
+539
+00:41:20,120 --> 00:41:23,460
+3 radian per second اتجاهها هيكون موازية لاتجاه
+
+540
+00:41:23,460 --> 00:41:27,530
+الخط اللي عطانيها يعني بقدر أقول إن اتجاه الـ
+
+541
+00:41:27,530 --> 00:41:31,390
+angular velocity هو الـ vector هذا مقسوم على الـ
+
+542
+00:41:31,390 --> 00:41:37,030
+magnitude تبعه فبجيب الـ omega vector صح؟ معايا هو
+
+543
+00:41:37,030 --> 00:41:40,890
+عطاني الـ unit القيمة تاعت omega قيمتها تلاتة
+
+544
+00:41:40,890 --> 00:41:44,590
+radian per second و اتجاهها موازن اتجاه الـ axis
+
+545
+00:41:44,590 --> 00:41:47,990
+موازٍ هذا الاتجاه إذا اتجاهه هو هيك فهذا اتجاه الـ
+
+546
+00:41:47,990 --> 00:41:51,510
+axis لو بقول موازٍ الـ x hat مشهور اتجاهها الـ x hat
+
+547
+00:41:51,510 --> 00:41:56,070
+فهو موازي هذا الـ vector هو ax hat minus 2ay hat زائد
+
+548
+00:41:56,070 --> 00:42:00,450
+2az hat موازي اتجاه الـ omega عشان أجيب الاتجاه
+
+549
+00:42:00,450 --> 00:42:03,270
+ماقدرش أستخدم vector بدي unit vector هيكون الـ
+
+550
+00:42:03,270 --> 00:42:05,850
+vector على مجنتوده بتبعه بتن اتجاه الـ omega إذا الـ
+
+551
+00:42:05,850 --> 00:42:09,250
+omega s بتاعها في كل بياناتها مقدارها تلاتة و
+
+552
+00:42:09,250 --> 00:42:12,330
+اتجاهها اللي هو هذا الـ unit vector على مجنتوده ..
+
+553
+00:42:12,330 --> 00:42:15,170
+هذا السواق متعفن آسفة هذا الـ vector على ال .. على
+
+554
+00:42:15,170 --> 00:42:18,110
+المجنتود بتبعه اللي هو الـ unit vector في اتجاه هذا
+
+555
+00:42:18,110 --> 00:42:23,410
+الـ axis عرفنا كل المعلومات على omega إذا الـ object
+
+556
+00:42:23,410 --> 00:42:27,390
+هذا بيلف على نقطة تلاتة radian per second موازق
+
+557
+00:42:27,390 --> 00:42:31,410
+لهذا الـ access and passing through a point الـ
+
+558
+00:42:31,410 --> 00:42:35,470
+object .. ال .. ال .. الـ access هذا passing الـ
+
+559
+00:42:35,470 --> 00:42:38,950
+access اللي هو يعطينا موازق له passing through هذه
+
+560
+00:42:38,950 --> 00:42:42,670
+النقطة اللي هي اتنين ومانثلثة وواحد determine الـ
+
+561
+00:42:42,670 --> 00:42:46,350
+velocity عند هذه النقطة إيش لازمني أنا عشان أجيب
+
+562
+00:42:46,350 --> 00:42:49,510
+الـ velocity قلنا omega cross r omega و عرفنا كل
+
+563
+00:42:49,510 --> 00:42:54,210
+بياناتها بضل عليّ اليمين R بدي أجيب الـ R R هي عبارة
+
+564
+00:42:54,210 --> 00:42:58,210
+عن مين الـ position ما بين النقطة B و الـ zero فإذا
+
+565
+00:42:58,210 --> 00:43:03,890
+R إيش هتكون B minus O بي احنا عارفينها و عارفين الـ O
+
+566
+00:43:03,890 --> 00:43:07,310
+فبجيب الـ R و أقعد طول بعمل الـ cross product بجيب الـ
+
+567
+00:43:07,310 --> 00:43:10,590
+velocity واضح؟ إذا أنا هيدا تطبيق مباشرة برضه وين
+
+568
+00:43:10,590 --> 00:43:14,400
+أنا بستخدم الـ cross product احنا شفنا كذا مثال لحد
+
+569
+00:43:14,400 --> 00:43:17,120
+اللي هي طويل فبنحتاج الـ vector analysis و كيف
+
+570
+00:43:17,120 --> 00:43:20,140
+ممكن أستعين في تطبيق له استخدمناه في الجبر
+
+571
+00:43:20,140 --> 00:43:24,760
+واستخدمناه هنا في الـ rigid body rotation إذا خلّينا
+
+572
+00:43:24,760 --> 00:43:28,620
+نشوف اللي حكيناه حكيته شفاهي أول حاجة بتاع المعطى
+
+573
+00:43:28,620 --> 00:43:31,
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/oTaDolk77vQ_raw.json b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/oTaDolk77vQ_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..655c3b290bc5ee2aafa7aeb4a46a1deee36f31c7
--- /dev/null
+++ b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/oTaDolk77vQ_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 4682, "start": 20.94, "end": 46.82, "text": "بسم الله الرحمن الرحيم السلام عليكم و رحمة الله و بركاته و احنا اليوم هنتبع ان شاء الله ال vector analysis و احنا المحاضر الماضي ميزنا بين scalar و vector وميزنا بين ال position و ال distance و vectors و parameters ميزنا بين كيف انه اعمل الجميع و بنعمل الطريح و الا اخرين اليوم احنا و اخدمها احنا سيرت الدرب احنا بس شوفنا الجميع و الطريح ان الدرب في ال vector مختلف كليا عن الدرب في ال scalar", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 21136, 37440, 25894, 24793, 4032, 12602, 35571, 3660, 21984, 4032, 4724, 31747, 9307, 3224, 4032, 1975, 5016, 8315, 45595, 20498, 8032, 29399, 3555, 3615, 16472, 13412, 16606, 21984, 2423, 8062, 5215, 4032, 1975, 5016, 8315, 9673, 5016, 46958, 2288, 9673, 46958, 1829, 3714, 1829, 11622, 8315, 49374, 39684, 4032, 8062, 4032, 2304, 1829, 11622, 8315, 49374, 2423, 2535, 4032, 2423, 4560, 4032, 18875, 4032, 9834, 3714, 1829, 11622, 8315, 49374, 9122, 33911, 16472, 3224, 1975, 25957, 1211, 25724, 2304, 40228, 4032, 44945, 25957, 1211, 41950, 16572, 5016, 4032, 42963, 1975, 34740, 9957, 45595, 20498, 1975, 5016, 8315, 4032, 1975, 9778, 40448, 11296, 1975, 5016, 8315, 8608, 13546, 2655, 32748, 25513, 1975, 5016, 8315, 4724, 3794, 13412, 38688, 8315, 25724, 2304, 40228, 4032, 41950, 16572, 5016, 16472, 32748, 25513, 8978, 2423, 8062, 3714, 46456, 46538, 9122, 20292, 995, 18871, 32748, 25513, 8978, 2423, 39684], "avg_logprob": -0.23304738484176934, "compression_ratio": 2.2006920415224913, "no_speech_prob": 4.172325134277344e-07, "words": [{"start": 20.94, "end": 21.24, "word": "بسم", "probability": 0.8935546875}, {"start": 21.24, "end": 21.4, "word": " الله", "probability": 0.95263671875}, {"start": 21.4, "end": 21.74, "word": " الرحمن", "probability": 0.9466145833333334}, {"start": 21.74, "end": 22.12, "word": " الرحيم", "probability": 0.9855143229166666}, {"start": 22.12, "end": 22.46, "word": " السلام", "probability": 0.8486328125}, 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المنتج تبعهم ال dot product الناتج تبعه scalar عشان هيك اسمه scalar الناتج تبع ال cross product vector عشان هيك هو اسمه vector", "tokens": [6027, 3215, 47341, 3660, 9154, 2423, 8062, 16472, 3224, 23032, 28480, 6055, 7649, 1829, 11331, 49975, 11778, 1211, 2655, 7649, 1829, 36764, 24401, 3660, 8717, 38251, 1829, 11296, 39684, 34051, 2423, 5893, 1674, 16070, 2655, 7649, 1829, 24525, 2304, 11296, 8062, 420, 3278, 1674, 16247, 38251, 16606, 10874, 995, 10632, 9154, 28239, 9307, 7435, 9673, 29399, 7435, 6055, 3555, 3615, 16095, 2423, 5893, 1674, 28239, 9307, 7435, 6055, 3555, 3615, 3224, 39684, 6225, 8592, 7649, 39896, 4117, 24525, 2304, 3224, 39684, 28239, 9307, 7435, 6055, 3555, 3615, 2423, 3278, 1674, 8062, 6225, 8592, 7649, 39896, 4117, 31439, 24525, 2304, 3224, 8062], "avg_logprob": -0.2571997511036256, "compression_ratio": 2.0721649484536084, "no_speech_prob": 4.76837158203125e-07, "words": [{"start": 47.3, "end": 47.88, "word": "الدرجة", "probability": 0.6361083984375}, {"start": 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magnitude عشان هذا vector فإيش هيكون فيه الاتجاه تبع ال vector الجديد am يمثل اتجاه ال vector النتج من ال cross product تبع a مع b إذا a cross b هيعطينا ال vector اللي مقداره a في b ب sign الزاوية اللي بينهم واتجاهه اللي هو", "tokens": [6027, 39184, 15668, 6055, 3555, 3615, 2423, 3278, 1674, 23758, 2423, 15668, 6055, 3555, 3615, 3224, 31439, 6225, 3555, 9640, 3660, 18871, 257, 8978, 272, 4724, 1465, 6024, 110, 995, 2407, 10632, 13672, 1829, 49374, 16095, 23758, 2423, 15668, 6225, 8592, 7649, 23758, 8062, 6156, 28814, 1829, 8592, 39896, 30544, 8978, 3224, 2423, 9307, 7435, 40294, 6055, 3555, 3615, 2423, 8062, 25724, 16254, 3215, 669, 7251, 2304, 12984, 1211, 1975, 2655, 7435, 40294, 2423, 8062, 28239, 2655, 7435, 9154, 2423, 3278, 1674, 6055, 3555, 3615, 257, 20449, 272, 11933, 15730, 257, 3278, 272, 39896, 3615, 9566, 1829, 8315, 2423, 8062, 13672, 1829, 3714, 28543, 9640, 3224, 257, 8978, 272, 4724, 1465, 6024, 110, 995, 2407, 10632, 13672, 1829, 49374, 16095, 4032, 9307, 7435, 40294, 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في اتجاه ال B انا هتعطيني المجلد تبع ال A اللي هو A مضروف المجلد تبع ال unit vector B hat اللي هو واحد تجيب الزاوية اللي بينهم اللي هي تاتر واضح؟ اذا انا باجيب component لأي vector في اتجاه معين بضربه في ال unit vector في هذا الاتجاه كمان مرة ولا واضح؟", "tokens": [2407, 2423, 4985, 8062, 8978, 1975, 2655, 7435, 40294, 2423, 363, 1975, 8315, 8032, 2655, 3615, 9566, 1829, 22653, 9673, 7435, 1211, 3215, 6055, 3555, 3615, 2423, 316, 13672, 1829, 31439, 316, 3714, 11242, 32887, 5172, 9673, 7435, 1211, 3215, 6055, 3555, 3615, 2423, 4985, 8062, 363, 2385, 13672, 1829, 31439, 36764, 24401, 6055, 7435, 1829, 3555, 6024, 110, 995, 2407, 10632, 13672, 1829, 49374, 16095, 13672, 1829, 39896, 6055, 9307, 2288, 4032, 46958, 5016, 22807, 1975, 15730, 1975, 8315, 4724, 26108, 1829, 3555, 6542, 5296, 10721, 1829, 8062, 8978, 1975, 2655, 7435, 40294, 20449, 9957, 4724, 11242, 25513, 3224, 8978, 2423, 4985, 8062, 8978, 23758, 2423, 9307, 7435, 40294, 9122, 2304, 7649, 3714, 25720, 49429, 4032, 46958, 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{"start": 1249.08, "end": 1249.82, "word": " X،", "probability": 0.526123046875}, {"start": 1249.82, "end": 1250.78, "word": " vector،", "probability": 0.5191650390625}, {"start": 1250.78, "end": 1251.22, "word": " هتسوّأ", "probability": 0.5207112630208334}, {"start": 1251.22, "end": 1251.56, "word": " ف", "probability": 0.3916015625}, {"start": 1251.56, "end": 1251.92, "word": " و", "probability": 0.469970703125}, {"start": 1251.92, "end": 1252.36, "word": " سعي", "probability": 0.4519856770833333}, {"start": 1252.36, "end": 1252.54, "word": " و", "probability": 0.93408203125}, {"start": 1252.54, "end": 1253.58, "word": " ستة،", "probability": 0.669189453125}, {"start": 1253.58, "end": 1253.86, "word": " X", "probability": 0.7060546875}, {"start": 1253.86, "end": 1254.24, "word": " hat", "probability": 0.9453125}], "temperature": 1.0}, {"id": 47, "seek": 128434, "start": 1256.83, "end": 1284.35, "text": "عشان اعرف ال component بتاعة اي vector في اتجاه معين بعملها dot product مع unit vector في هذا الاتجاه والاتجاه هيكون هو هذا ال unit vector تشوف أمثلة على المعلومات اللي أخدناها لو كان عندي two vectors A وB وبدى الزاوية اللي بين A وB دي حد بيقدر يحللنا يلا تفضل", "tokens": [3615, 8592, 7649, 1975, 3615, 28480, 2423, 6542, 39894, 995, 27884, 1975, 1829, 8062, 8978, 1975, 2655, 7435, 40294, 20449, 9957, 4724, 25957, 1211, 11296, 5893, 1674, 20449, 4985, 8062, 8978, 23758, 2423, 9307, 7435, 40294, 16070, 9307, 7435, 40294, 39896, 30544, 31439, 23758, 2423, 4985, 8062, 6055, 8592, 38688, 5551, 2304, 12984, 37977, 15844, 9673, 30241, 20498, 9307, 13672, 1829, 5551, 9778, 3215, 8315, 11296, 45164, 25961, 18871, 16254, 732, 18875, 316, 4032, 33, 4032, 44510, 7578, 6024, 110, 995, 2407, 10632, 13672, 1829, 49374, 316, 4032, 33, 11778, 1829, 11331, 3215, 4724, 1829, 28543, 2288, 7251, 5016, 1211, 1211, 8315, 7251, 15040, 6055, 5172, 11242, 1211], "avg_logprob": -0.2601777490125884, "compression_ratio": 1.7415254237288136, "no_speech_prob": 0.0, "words": [{"start": 1256.83, 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" sign", "probability": 0.81103515625}, {"start": 1476.18, "end": 1476.84, "word": " الزاوية", "probability": 0.9583984375}, {"start": 1476.84, "end": 1477.06, "word": " على", "probability": 0.806640625}, {"start": 1477.06, "end": 1477.34, "word": " ضلع", "probability": 0.67919921875}, {"start": 1477.34, "end": 1477.88, "word": " لقبالها", "probability": 0.79365234375}, {"start": 1477.88, "end": 1478.22, "word": " sign", "probability": 0.56005859375}, {"start": 1478.22, "end": 1478.36, "word": " ال", "probability": 0.75830078125}, {"start": 1478.36, "end": 1478.6, "word": " a", "probability": 0.427001953125}, {"start": 1478.6, "end": 1478.8, "word": " على", "probability": 0.85107421875}, {"start": 1478.8, "end": 1479.2, "word": " a", "probability": 0.96728515625}, {"start": 1479.2, "end": 1479.98, "word": " بسوى", "probability": 0.700927734375}, {"start": 1479.98, "end": 1480.34, "word": " sign", "probability": 0.91015625}, {"start": 1480.34, "end": 1480.58, "word": " ال", 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"text": "لأن هى ال component بتاعته للمجموع A زي B زي C بها ساوة و سفر طب هى واضح بين ال dot product من مين و B و C فإذا أنا قولت A vector زي B vector زي C vector مش بساوة و سفر بقى نقول التانية اللى انتوا شاطرين و قولتوا هو ال dot product بين ال B و ال C على طرف و بضل طرف التاني مين ال A و باخد دقساتها اللى هى ال dot product تبع هدول ال vectors", "tokens": [1211, 33456, 8032, 7578, 2423, 6542, 39894, 995, 34268, 3224, 5296, 19528, 7435, 2304, 45367, 316, 30767, 1829, 363, 30767, 1829, 383, 4724, 11296, 8608, 995, 2407, 3660, 4032, 8608, 5172, 2288, 23032, 3555, 8032, 7578, 4032, 46958, 5016, 49374, 2423, 5893, 1674, 9154, 3714, 9957, 4032, 363, 4032, 383, 6156, 28814, 15730, 41850, 12174, 12610, 2655, 316, 8062, 30767, 1829, 363, 8062, 30767, 1829, 383, 8062, 37893, 4724, 3794, 995, 2407, 3660, 4032, 8608, 5172, 2288, 4724, 4587, 7578, 8717, 39648, 16712, 7649, 10632, 13672, 7578, 16472, 2655, 14407, 13412, 41193, 2288, 9957, 4032, 12174, 12610, 2655, 14407, 31439, 2423, 5893, 1674, 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"temperature": 1.0}, {"id": 60, "seek": 164229, "start": 1618.77, "end": 1642.29, "text": "Ic الزاوية اللى بين P و C هي 180 نقص فبطلع هنا الإشارة السالفة واضح هذا بالنسبة لل formula الأولى نيجي لل formula التانية احنا بنعرف ان ال area مساحة المثلث هو نص الدلعب الارتفاع", "tokens": [40, 66, 2423, 11622, 995, 2407, 10632, 13672, 7578, 49374, 430, 4032, 383, 39896, 11971, 8717, 4587, 9381, 6156, 3555, 9566, 1211, 3615, 34105, 33688, 8592, 9640, 3660, 21136, 6027, 5172, 3660, 4032, 46958, 5016, 23758, 20666, 1863, 35457, 3660, 24976, 8513, 16247, 12610, 7578, 8717, 1829, 7435, 1829, 24976, 8513, 16712, 7649, 10632, 1975, 5016, 8315, 44945, 3615, 28480, 16472, 2423, 1859, 47524, 39319, 3660, 9673, 12984, 1211, 12984, 31439, 8717, 9381, 32748, 1211, 3615, 3555, 2423, 9640, 2655, 5172, 45761], "avg_logprob": -0.3782003012048193, "compression_ratio": 1.5549738219895288, "no_speech_prob": 2.384185791015625e-07, "words": [{"start": 1618.77, "end": 1619.41, "word": "Ic", "probability": 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مواطن هذا ال vector هو ax hat minus 2ay hat زي 2az hat موازن اتجاه ال omega", "tokens": [2304, 3615, 995, 25528, 31439, 1975, 3615, 9566, 7649, 7578, 2423, 4985, 25062, 32640, 3660, 6055, 995, 34268, 10498, 12174, 32640, 2655, 11296, 6055, 1211, 9307, 3660, 2843, 952, 680, 1150, 4032, 9307, 7435, 40294, 11296, 3714, 2407, 31377, 1863, 1975, 2655, 7435, 40294, 2423, 10298, 3714, 2407, 31377, 1863, 23758, 2423, 9307, 7435, 40294, 1975, 15730, 16472, 2655, 7435, 40294, 31439, 39896, 4117, 6156, 3224, 15730, 1975, 2655, 7435, 40294, 2423, 10298, 45164, 4724, 39648, 3714, 2407, 31377, 1863, 2423, 2031, 2385, 37893, 3224, 13063, 6055, 7435, 40294, 11296, 2423, 2031, 2385, 6156, 3224, 2407, 3714, 2407, 41193, 1863, 23758, 2423, 8062, 31439, 6360, 2385, 3175, 568, 320, 2385, 30767, 1829, 568, 921, 2385, 3714, 2407, 31377, 1863, 1975, 2655, 7435, 40294, 2423, 10498], "avg_logprob": -0.2591765766579007, "compression_ratio": 2.0093023255813955, "no_speech_prob": 2.384185791015625e-07, "words": 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2643.55, "word": " استفسار", "probability": 0.7607421875}, {"start": 2643.55, "end": 2646.33, "word": " بس", "probability": 0.86572265625}, {"start": 2646.33, "end": 2646.53, "word": " احنا", "probability": 0.9752604166666666}, {"start": 2646.53, "end": 2646.81, "word": " بدنا", "probability": 0.938720703125}, {"start": 2646.81, "end": 2647.21, "word": " ياكوا", "probability": 0.6983235677083334}, {"start": 2647.21, "end": 2647.93, "word": " ترجعولنا", "probability": 0.8037109375}, {"start": 2647.93, "end": 2649.07, "word": " المعلومات", "probability": 0.966552734375}, {"start": 2649.07, "end": 2649.19, "word": " اللى", "probability": 0.975830078125}, {"start": 2649.19, "end": 2649.61, "word": " أخدناها", "probability": 0.792431640625}, {"start": 2649.61, "end": 2649.77, "word": " زى", "probability": 0.957275390625}, {"start": 2649.77, "end": 2649.83, "word": " ما", "probability": 0.9482421875}, {"start": 2649.83, "end": 2650.13, "word": " شفنا", "probability": 0.8623046875}, {"start": 2650.13, "end": 2650.37, "word": " احنا", "probability": 0.939453125}, {"start": 2650.37, "end": 2650.63, "word": " شفنا", "probability": 0.9822591145833334}, {"start": 2650.63, "end": 2651.29, "word": " مفتقاطه", "probability": 0.7072347005208334}, {"start": 2651.29, "end": 2651.39, "word": " فى", "probability": 0.809326171875}, {"start": 2651.39, "end": 2651.45, "word": " ال", "probability": 0.90234375}, {"start": 2651.45, "end": 2651.73, "word": " vector", "probability": 0.96044921875}, {"start": 2651.73, "end": 2652.25, "word": " analysis", "probability": 0.78271484375}, {"start": 2652.25, "end": 2653.27, "word": " شفنا", "probability": 0.9278971354166666}, {"start": 2653.27, "end": 2653.67, "word": " كمان", "probability": 0.9920247395833334}, {"start": 2653.67, "end": 2654.01, "word": " فى", "probability": 0.8486328125}, {"start": 2654.01, "end": 2654.39, "word": " rigid", "probability": 0.8515625}, {"start": 2654.39, "end": 2654.77, "word": " body", "probability": 0.84375}, {"start": 2654.77, "end": 2655.51, "word": " rotation", "probability": 0.966796875}, {"start": 2655.51, "end": 2656.03, "word": " وقبل", "probability": 0.9189453125}, {"start": 2656.03, "end": 2656.25, "word": " هيك", "probability": 0.6966552734375}, {"start": 2656.25, "end": 2656.69, "word": " شفنا", "probability": 0.9944661458333334}, {"start": 2656.69, "end": 2657.37, "word": " relative", "probability": 0.630859375}, {"start": 2657.37, "end": 2657.93, "word": " velocity", "probability": 0.86962890625}, {"start": 2657.93, "end": 2659.05, "word": " في", "probability": 0.360107421875}, {"start": 2659.05, "end": 2659.45, "word": " المحاضرة", "probability": 0.983642578125}, {"start": 2659.45, "end": 2659.95, "word": " الماضية", "probability": 0.9895833333333334}, {"start": 2659.95, "end": 2660.59, "word": " شفنا", "probability": 0.9768880208333334}, {"start": 2660.59, "end": 2661.19, "word": " مثال", "probability": 0.9599609375}, {"start": 2661.19, "end": 2661.35, "word": " اللى", "probability": 0.965576171875}, {"start": 2661.35, "end": 2661.47, "word": " هو", "probability": 0.91845703125}, {"start": 2661.47, "end": 2661.65, "word": " كيف", "probability": 0.942138671875}, {"start": 2661.65, "end": 2662.11, "word": " حساب", "probability": 0.8250325520833334}, {"start": 2662.11, "end": 2662.55, "word": " relative", "probability": 0.87548828125}, {"start": 2662.55, "end": 2662.93, "word": " velocity", "probability": 0.91943359375}, {"start": 2662.93, "end": 2663.67, "word": " باستعانة", "probability": 0.8134765625}, {"start": 2663.67, "end": 2664.13, "word": " فى", "probability": 0.69482421875}, {"start": 2664.13, "end": 2664.33, "word": " اللى", "probability": 0.96337890625}, {"start": 2664.33, "end": 2664.53, "word": " هو", "probability": 0.90673828125}, {"start": 2664.53, "end": 2664.69, "word": " ال", "probability": 0.91845703125}, {"start": 2664.69, "end": 2664.89, "word": " vectors", "probability": 0.54150390625}], "temperature": 1.0}, {"id": 105, "seek": 268932, "start": 2678.82, "end": 2689.32, "text": "الشبطر التاني هيميزنا بين ال coordinates احنا لحد دلوقت هبنحكي عن ال Cartesian coordinates اذا انتم متبهين هبنحكي عن X Y Z اللي قال قادم هنشوف برضه ال", "tokens": [6027, 8592, 3555, 9566, 2288, 16712, 7649, 1829, 8032, 32640, 1829, 11622, 8315, 49374, 2423, 21056, 1975, 5016, 8315, 5296, 24401, 11778, 1211, 30543, 2655, 8032, 3555, 1863, 5016, 4117, 1829, 18871, 2423, 22478, 42434, 21056, 1975, 15730, 16472, 39237, 44650, 3555, 3224, 9957, 8032, 3555, 1863, 5016, 4117, 1829, 18871, 1783, 398, 1176, 13672, 1829, 50239, 12174, 18513, 2304, 8032, 1863, 8592, 38688, 4724, 43042, 3224, 2423], "avg_logprob": -0.4773550724637681, "compression_ratio": 1.5031446540880504, "no_speech_prob": 7.748603820800781e-07, "words": [{"start": 2678.82, "end": 2679.48, "word": "الشبطر", "probability": 0.463720703125}, {"start": 2679.48, "end": 2680.14, "word": " التاني", "probability": 0.681640625}, {"start": 2680.14, "end": 2681.28, "word": " هيميزنا", "probability": 0.73443603515625}, {"start": 2681.28, "end": 2681.48, "word": " بين", "probability": 0.8994140625}, {"start": 2681.48, "end": 2681.6, "word": " ال", "probability": 0.7548828125}, {"start": 2681.6, "end": 2682.16, "word": " coordinates", "probability": 0.433349609375}, {"start": 2682.16, "end": 2682.82, "word": " احنا", "probability": 0.664794921875}, {"start": 2682.82, "end": 2683.04, "word": " لحد", "probability": 0.771728515625}, {"start": 2683.04, "end": 2683.3, "word": " دلوقت", "probability": 0.6368408203125}, {"start": 2683.3, "end": 2683.72, "word": " هبنحكي", "probability": 0.8245442708333334}, {"start": 2683.72, "end": 2683.8, "word": " عن", "probability": 0.416748046875}, {"start": 2683.8, "end": 2683.88, "word": " ال", "probability": 0.43603515625}, {"start": 2683.88, "end": 2684.22, "word": " Cartesian", "probability": 0.69287109375}, {"start": 2684.22, "end": 2684.72, "word": " coordinates", "probability": 0.37255859375}, {"start": 2684.72, "end": 2684.86, "word": " اذا", "probability": 0.6148681640625}, {"start": 2684.86, "end": 2685.06, "word": " انتم", "probability": 0.701416015625}, {"start": 2685.06, "end": 2685.66, "word": " متبهين", "probability": 0.79693603515625}, {"start": 2685.66, "end": 2686.16, "word": " هبنحكي", "probability": 0.7750651041666666}, {"start": 2686.16, "end": 2686.28, "word": " عن", "probability": 0.73095703125}, {"start": 2686.28, "end": 2686.58, "word": " X", "probability": 0.420654296875}, {"start": 2686.58, "end": 2686.98, "word": " Y", "probability": 0.53857421875}, {"start": 2686.98, "end": 2687.4, "word": " Z", "probability": 0.89599609375}, {"start": 2687.4, "end": 2687.98, "word": " اللي", "probability": 0.770263671875}, {"start": 2687.98, "end": 2688.12, "word": " قال", "probability": 0.83447265625}, {"start": 2688.12, "end": 2688.42, "word": " قادم", "probability": 0.857421875}, {"start": 2688.42, "end": 2688.82, "word": " هنشوف", "probability": 0.9232177734375}, {"start": 2688.82, "end": 2689.14, "word": " برضه", "probability": 0.8675130208333334}, {"start": 2689.14, "end": 2689.32, "word": " ال", "probability": 0.521484375}], "temperature": 1.0}, {"id": 106, "seek": 270839, "start": 2691.85, "end": 2708.39, "text": "الـ cylindrical coordinate يعني هنتعرف على ال coordinates البقية و كيف انا انقل من ال Cartesian coordinate ل ال spherical coordinate و لعكس و كيف انقل برضه من ال Cartesian ل ال cylindrical و لعكس او من spherical ل cylindrical و cylindrical ل spherical ان شاء الله", "tokens": [6027, 39184, 28044, 15888, 15670, 37495, 22653, 8032, 29399, 3615, 28480, 15844, 2423, 21056, 29739, 4587, 10632, 4032, 9122, 33911, 1975, 8315, 16472, 4587, 1211, 9154, 2423, 22478, 42434, 15670, 5296, 2423, 37300, 15670, 4032, 5296, 3615, 4117, 3794, 4032, 9122, 33911, 16472, 4587, 1211, 4724, 43042, 3224, 9154, 2423, 22478, 42434, 5296, 2423, 28044, 15888, 4032, 5296, 3615, 4117, 3794, 1975, 2407, 9154, 37300, 5296, 28044, 15888, 4032, 28044, 15888, 5296, 37300, 16472, 13412, 16606, 21984], "avg_logprob": -0.2870592964001191, "compression_ratio": 2.0, "no_speech_prob": 3.1828880310058594e-05, "words": [{"start": 2691.8500000000004, "end": 2692.4500000000003, "word": "الـ", "probability": 0.1668701171875}, {"start": 2692.4500000000003, "end": 2693.05, "word": " cylindrical", "probability": 0.794677734375}, {"start": 2693.05, "end": 2693.55, "word": " coordinate", "probability": 0.416259765625}, {"start": 2693.55, "end": 2693.79, "word": " يعني", "probability": 0.60302734375}, {"start": 2693.79, "end": 2694.31, "word": " هنتعرف", "probability": 0.8951416015625}, {"start": 2694.31, "end": 2694.53, "word": " على", "probability": 0.72021484375}, {"start": 2694.53, "end": 2694.71, "word": " ال", "probability": 0.81201171875}, {"start": 2694.71, "end": 2695.09, "word": " coordinates", "probability": 0.77734375}, {"start": 2695.09, "end": 2695.71, "word": " البقية", "probability": 0.8138020833333334}, {"start": 2695.71, "end": 2696.13, "word": " و", "probability": 0.90625}, {"start": 2696.13, "end": 2696.35, "word": " كيف", "probability": 0.8671875}, {"start": 2696.35, "end": 2696.51, "word": " انا", "probability": 0.6488037109375}, {"start": 2696.51, "end": 2696.95, "word": " انقل", "probability": 0.8487955729166666}, {"start": 2696.95, "end": 2697.15, "word": " من", "probability": 0.98095703125}, {"start": 2697.15, "end": 2697.45, "word": " ال", "probability": 0.8720703125}, {"start": 2697.45, "end": 2697.89, "word": " Cartesian", "probability": 0.6318359375}, {"start": 2697.89, "end": 2698.37, "word": " coordinate", "probability": 0.79248046875}, {"start": 2698.37, "end": 2699.01, "word": " ل", "probability": 0.65673828125}, {"start": 2699.01, "end": 2699.25, "word": " ال", "probability": 0.5810546875}, {"start": 2699.25, "end": 2699.49, "word": " spherical", "probability": 0.306396484375}, {"start": 2699.49, "end": 2700.19, "word": " coordinate", "probability": 0.81005859375}, {"start": 2700.19, "end": 2700.61, "word": " و", "probability": 0.8251953125}, {"start": 2700.61, "end": 2701.13, "word": " لعكس", "probability": 0.80780029296875}, {"start": 2701.13, "end": 2701.31, "word": " و", "probability": 0.9560546875}, {"start": 2701.31, "end": 2701.51, "word": " كيف", "probability": 0.945068359375}, {"start": 2701.51, "end": 2701.79, "word": " انقل", "probability": 0.87548828125}, {"start": 2701.79, "end": 2702.07, "word": " برضه", "probability": 0.8707682291666666}, {"start": 2702.07, "end": 2702.17, "word": " من", "probability": 0.9658203125}, {"start": 2702.17, "end": 2702.25, "word": " ال", "probability": 0.82958984375}, {"start": 2702.25, "end": 2702.65, "word": " Cartesian", "probability": 0.86767578125}, {"start": 2702.65, "end": 2702.77, "word": " ل", "probability": 0.45849609375}, {"start": 2702.77, "end": 2702.87, "word": " ال", "probability": 0.72509765625}, {"start": 2702.87, "end": 2703.31, "word": " cylindrical", "probability": 0.937255859375}, {"start": 2703.31, "end": 2703.47, "word": " و", "probability": 0.63916015625}, {"start": 2703.47, "end": 2703.83, "word": " لعكس", "probability": 0.9215087890625}, {"start": 2703.83, "end": 2704.03, "word": " او", "probability": 0.85498046875}, {"start": 2704.03, "end": 2704.15, "word": " من", "probability": 0.9755859375}, {"start": 2704.15, "end": 2704.47, "word": " spherical", "probability": 0.36572265625}, {"start": 2704.47, "end": 2704.69, "word": " ل", "probability": 0.95458984375}, {"start": 2704.69, "end": 2705.31, "word": " cylindrical", "probability": 0.9140625}, {"start": 2705.31, "end": 2705.71, "word": " و", "probability": 0.90185546875}, {"start": 2705.71, "end": 2706.23, "word": " cylindrical", "probability": 0.93017578125}, {"start": 2706.23, "end": 2706.53, "word": " ل", "probability": 0.90869140625}, {"start": 2706.53, "end": 2706.87, "word": " spherical", "probability": 0.80224609375}, {"start": 2706.87, "end": 2708.03, "word": " ان", "probability": 0.78857421875}, {"start": 2708.03, "end": 2708.27, "word": " شاء", "probability": 0.96142578125}, {"start": 2708.27, "end": 2708.39, "word": " الله", "probability": 0.9521484375}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2709.2115, "duration_after_vad": 2546.1831249999905}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/oTaDolk77vQ_raw.srt b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/oTaDolk77vQ_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..6f9b9740e32cb5ce901af3d53d2cb48222d3d61a
--- /dev/null
+++ b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/oTaDolk77vQ_raw.srt
@@ -0,0 +1,2388 @@
+1
+00:00:20,940 --> 00:00:23,260
+بسم الله الرحمن الرحيم السلام عليكم و رحمة الله و
+
+2
+00:00:23,260 --> 00:00:25,100
+بركاته و احنا اليوم هنتبع ان شاء الله ال vector
+
+3
+00:00:25,100 --> 00:00:28,580
+analysis و احنا المحاضر الماضي ميزنا بين scalar و
+
+4
+00:00:28,580 --> 00:00:33,260
+vector وميزنا بين ال position و ال distance و
+
+5
+00:00:33,260 --> 00:00:36,620
+vectors و parameters ميزنا بين كيف انه اعمل الجميع
+
+6
+00:00:36,620 --> 00:00:40,120
+و بنعمل الطريح و الا اخرين اليوم احنا و اخدمها
+
+7
+00:00:40,120 --> 00:00:43,580
+احنا سيرت الدرب احنا بس شوفنا الجميع و الطريح ان
+
+8
+00:00:43,580 --> 00:00:46,480
+الدرب في ال vector مختلف كليا عن الدرب في ال
+
+9
+00:00:46,480 --> 00:00:50,180
+scalarالدرجة من ال vector انه طرف تاني حتى دلتاني
+
+10
+00:00:50,180 --> 00:00:53,880
+واحدة نسميها scalar أو ال dot product والتاني
+
+11
+00:00:53,880 --> 00:00:57,200
+اسمها vector or cross product الأسماء جاية من
+
+12
+00:00:57,200 --> 00:01:00,880
+الناتج المنتج تبعهم ال dot product الناتج تبعه
+
+13
+00:01:00,880 --> 00:01:04,500
+scalar عشان هيك اسمه scalar الناتج تبع ال cross
+
+14
+00:01:04,500 --> 00:01:09,480
+product vector عشان هيك هو اسمه vectorبتجمد هنا ال
+
+15
+00:01:09,480 --> 00:01:12,800
+multiplication لأكتر من 2 vectors يعني لو كان عندي
+
+16
+00:01:12,800 --> 00:01:17,200
+بس 2 vectors هيكون يا عندي dot او scalar يا عندي
+
+17
+00:01:17,200 --> 00:01:20,180
+vector ال product لو كان عندي مثلا تلاتة vectors
+
+18
+00:01:20,180 --> 00:01:23,720
+هيكون عندي برضه أنموعة تانية من ال product هيكون
+
+19
+00:01:23,720 --> 00:01:26,160
+في عندي مثلا scalar whichever product برضه نفس
+
+20
+00:01:26,160 --> 00:01:30,160
+القضية ال scalar جامن الناتج الناتج تبع a dot b
+
+21
+00:01:30,160 --> 00:01:33,220
+cross c scalar لإنه b cross c قلنا إيش الناتج
+
+22
+00:01:33,220 --> 00:01:36,080
+تبعها vector a dot vector
+
+23
+00:01:38,530 --> 00:01:42,410
+والنوع التالت او الرابع هيكون هو vector a triple
+
+24
+00:01:42,410 --> 00:01:46,990
+product اللي هو a cross b cross c وهذا انها تشتبع
+
+25
+00:01:46,990 --> 00:01:55,790
+عرض ال vector نجي
+
+26
+00:01:55,790 --> 00:01:58,930
+لل vector product لو انا عندى two vectors احنا
+
+27
+00:01:58,930 --> 00:02:05,030
+قولنا لهم ان انا a cross b بعطينا cمعناه إنه لازم
+
+28
+00:02:05,030 --> 00:02:07,890
+ال vector التالت قيله اتجاه عشان أحد اتجاه ال
+
+29
+00:02:07,890 --> 00:02:10,770
+vector التالت بستخدم ال right hand rule ال right
+
+30
+00:02:10,770 --> 00:02:13,490
+hand rule بتقوله بحط أيدي عن ال vector الأول هو ال
+
+31
+00:02:13,490 --> 00:02:17,290
+A و بلف في اتجاه B وين بي موجودة بلف أيدي عليه
+
+32
+00:02:17,290 --> 00:02:22,670
+فبتصير A cross B تقرين اتجاه C يعني لو أنا كانوا
+
+33
+00:02:22,670 --> 00:02:24,830
+عامد ال vector استعوني بهذا الشكل هم اللي بيدعملهم
+
+34
+00:02:24,830 --> 00:02:30,150
+cross product A وB بروح من A لB أو كان هناك هقول
+
+35
+00:02:30,150 --> 00:02:34,630
+من A لB هى معناه أني بلفبلغوف من اتجاه ال vector
+
+36
+00:02:34,630 --> 00:02:37,290
+الأول للتانى اما بتعمل cross ما بين ال a و ال b
+
+37
+00:02:37,290 --> 00:02:41,630
+فبقول a cross b بطني c لو كان ال b هنا ايش بعمل
+
+38
+00:02:41,630 --> 00:02:46,790
+cross اك؟ a cross b بطلع ال c لتحت كمان ممكن احنا
+
+39
+00:02:46,790 --> 00:02:48,850
+بدل ما نستخدم ال right hand rule هذا اسم ال right
+
+40
+00:02:48,850 --> 00:02:52,490
+hand rule اللي بعمل a cross b بطني c ممكن استخدم
+
+41
+00:02:52,490 --> 00:02:55,070
+ان هي فكرة ال fact في ناس بحبوا البراغي بالذات و
+
+42
+00:02:55,070 --> 00:02:57,350
+انا بحب فكرة البراغي اكتر من ال right hand rule
+
+43
+00:02:58,130 --> 00:03:00,470
+عارف زمان و احنا ببرسات قلنا راحت هغلو و تعمل
+
+44
+00:03:00,470 --> 00:03:02,790
+مشاكل، بيجي الولد على ال .. لازم يدرس على
+
+45
+00:03:02,790 --> 00:03:05,110
+البراندة، بقعد يعمل هيك، يعمل هيك، بيجي الجار و
+
+46
+00:03:05,110 --> 00:03:10,670
+يضربه على الأرض، قعد أشهر لابنته، فبقولك أحسن حاجة
+
+47
+00:03:10,670 --> 00:03:15,010
+هي مين ال .. البرغة بالنسبة للشباب، المرئيش بيطلع،
+
+48
+00:03:15,010 --> 00:03:18,230
+بقول أنا بدي ألف البرغة من تجار A لB، إذا هيك A
+
+49
+00:03:18,230 --> 00:03:23,040
+وB، بلفه هكفلما تلف البرغة اللي هيتحرك هي على فوق
+
+50
+00:03:23,040 --> 00:03:26,520
+A لتحت فانا هاي البرغة تبعي و بديت ألف من A ل B
+
+51
+00:03:26,520 --> 00:03:30,440
+اتجاه هاي A و هاي B هنا فبلف البرغة و انا بطلع و
+
+52
+00:03:30,440 --> 00:03:33,860
+انا بطلع على فوق فهذا اتجاه ال vector التالت واضح؟
+
+53
+00:03:33,860 --> 00:03:36,760
+لو كان العكس لو انا عندي A ل B هاي هذا ال vector
+
+54
+00:03:36,760 --> 00:03:40,120
+التالت اللي فاك تبعي و بدي ألف من A ل B هي هنا A و
+
+55
+00:03:40,120 --> 00:03:44,040
+هاي B بدي ألف اتجاه ال B بنزل البرغة لتحت فهذا
+
+56
+00:03:44,040 --> 00:03:47,560
+بيكون اتجاه ال set يعني إيه ال right hand rule؟
+
+57
+00:03:47,560 --> 00:03:50,830
+إيه إيه الشركات البرغة؟بلوفه هك اذا انا رايحة من A
+
+58
+00:03:50,830 --> 00:03:54,830
+ل B او بلوفه هك اذا رايحة من A ل B اذا كانت B تلات
+
+59
+00:03:54,830 --> 00:03:59,770
+اتجاه اذا هذا هو اللي بيحددلي اتجاه ال vector
+
+60
+00:03:59,770 --> 00:04:04,750
+across ال product نيجي ندرس واحد منهم بالواحد يعني
+
+61
+00:04:04,750 --> 00:04:07,870
+ناخد كيف بتعمل هذا ال product أسوأ ال dot product
+
+62
+00:04:07,870 --> 00:04:10,710
+ولا ال vector product نبدأ بال dot product احنا
+
+63
+00:04:10,710 --> 00:04:15,030
+قلنا A dot B لازم اعطني scalar مقدار هذا ال scalar
+
+64
+00:04:15,030 --> 00:04:20,450
+بساوي المجلده التبع A بالمجلد تبع Bالزاوية اللي
+
+65
+00:04:20,450 --> 00:04:26,750
+بينها يعني لو كان عندي هاي ال vector A وهي ال
+
+66
+00:04:26,750 --> 00:04:31,510
+vector B وهي الزاوية اللي بينهم انا هسميها theta
+
+67
+00:04:31,510 --> 00:04:37,990
+AB هيكون عندى ال product هو magnitude تبع A وال
+
+68
+00:04:37,990 --> 00:04:43,310
+magnitude تبع B فهو جبت برامج الزاوية اللي بينهم
+
+69
+00:04:45,270 --> 00:04:48,610
+يعني مثلًا لو كنت عندي a اللي هو ال vector a، اللي
+
+70
+00:04:48,610 --> 00:04:50,950
+هو ال components، احنا قولنا هذا تمثيل تبع ال
+
+71
+00:04:50,950 --> 00:04:56,210
+vectors، يا مصدر الأقراص وهذه ال X component وY
+
+72
+00:04:56,210 --> 00:05:01,890
+component وZ component، يا بكتبه بشكل اللي هو ax x
+
+73
+00:05:01,890 --> 00:05:07,870
+hat زي ay y hat زي az z hat، كنت فاقناه يكتبها x
+
+74
+00:05:07,870 --> 00:05:12,410
+hat y hat z hat، يا زي ما الكتاب يعملها ax hat ay
+
+75
+00:05:12,410 --> 00:05:18,410
+hat ez hat، أه؟نفس الشيء لل V هذا vector و هاي ال
+
+76
+00:05:18,410 --> 00:05:21,950
+components بتاعته في X و Y و Z انددتوا product
+
+77
+00:05:21,950 --> 00:05:26,510
+بقولوا التالي اندي ال component X مع ال component
+
+78
+00:05:26,510 --> 00:05:31,150
+X doted بشكل اهم هو اللي بقدر اعمل product لكل ال
+
+79
+00:05:31,150 --> 00:05:36,690
+components يعني اذا بدأتوا بتفصيل R
+
+80
+00:05:36,690 --> 00:05:50,460
+dot V هي عبارة عن Ax Ayisn doted مع bx by bz هتكون
+
+81
+00:05:50,460 --> 00:05:57,640
+ال component الأولى مع الأولى بax x hat doted مع
+
+82
+00:05:57,640 --> 00:06:05,960
+bx x hat التانية الأولى مع التانية زائد ax x hat
+
+83
+00:06:05,960 --> 00:06:17,900
+doted مع by y hat زائد ax x hatاكس اكسها دتت مع بي
+
+84
+00:06:17,900 --> 00:06:24,980
+زد زدها و هكذا نبدأ بالاي و ايها دتت مع بي اكس
+
+85
+00:06:24,980 --> 00:06:31,300
+اكسها و هكذا معين؟ لكن في حاجة مهمة جدت في ال dot
+
+86
+00:06:31,300 --> 00:06:34,440
+product قولنا ال dot product تبع اي two components
+
+87
+00:06:34,440 --> 00:06:37,940
+بيعطينا قيمة الأول و قيمة التانية في جيب الزاوية
+
+88
+00:06:37,940 --> 00:06:42,340
+اللي بينهم احنا ال XYZ معله فده Cartesian
+
+89
+00:06:42,340 --> 00:06:56,670
+CoordinateX Y و Z أسوأ طالع ولا داخل هى X هى Y X Y
+
+90
+00:06:56,670 --> 00:07:01,870
+Z باخد ال right hand rule هنا عند X hat عند Y hat
+
+91
+00:07:01,870 --> 00:07:09,010
+و عند Z hat هدولة بتسميهم unit vectors X hat و Y
+
+92
+00:07:09,010 --> 00:07:15,470
+hat و Z hatماذا يعني ان المجموعة تبقى واحدة يعني
+
+93
+00:07:15,470 --> 00:07:22,050
+اذا اجيب X hat مجموعة يتحكم واحدة لأن المجموعة
+
+94
+00:07:22,050 --> 00:07:26,950
+هتعرف عليه جزر التربيه ل X hat dot X hat اذا كنت
+
+95
+00:07:26,950 --> 00:07:30,530
+تسعى معنا dot product ايش معناه رابع عن جزر
+
+96
+00:07:30,530 --> 00:07:33,550
+التربيه المجموعة تبقى الها اول ومجموعة تبقى التاني
+
+97
+00:07:33,550 --> 00:07:37,770
+تجيب سواء بينهم اللي يبقى رابع عن كسين اللي يتسين
+
+98
+00:07:37,770 --> 00:07:45,490
+تجيب تسين اداش واحدجيب تمام إذا و غير بينهم Zero X
+
+99
+00:07:45,490 --> 00:07:49,470
+hat
+
+100
+00:07:49,470 --> 00:07:54,470
+مجنته تبعها واحد ال Y hat مجنته تبعها واحد ال Z
+
+101
+00:07:54,470 --> 00:07:58,670
+hat مجنته تبعها واحد فاندي X hat dot X hat واحد
+
+102
+00:07:58,670 --> 00:08:03,990
+بينما X hat dot Y hat ماتساوش اللي حطيتلكميها في
+
+103
+00:08:03,990 --> 00:08:07,800
+ال group لإنه عادي مجنته تبع X hat هو واحدفي
+
+104
+00:08:07,800 --> 00:08:11,020
+مجموعة y hat واحد في جيب التوية الزاوية بينه مقدر
+
+105
+00:08:11,020 --> 00:08:16,200
+كتان درجة جيب تان تسعين زيرو اذا انا عندها ده اللي
+
+106
+00:08:16,200 --> 00:08:20,260
+بيحقق هو الشرط اللي هي unit vectors اذا كانوا
+
+107
+00:08:20,260 --> 00:08:22,780
+اتنين متعامدين مع بعض x hat و y hat الشيء اللي
+
+108
+00:08:22,780 --> 00:08:26,020
+بيكون ال total product تبعهم زيرو x hat و z hat ال
+
+109
+00:08:26,020 --> 00:08:30,700
+total product تبعهم زيرو x hat و x hat واحد y hat
+
+110
+00:08:30,700 --> 00:08:37,330
+و y hat واحد z hat و z hat واحداذا بنقول هدولة ال
+
+111
+00:08:37,330 --> 00:08:41,770
+components اي حاجة فيها x hat و y hat اي حاجة فيها
+
+112
+00:08:41,770 --> 00:08:48,710
+0 y hat و x hat 0 x hat و z hat 0 هيظل عند مين
+
+113
+00:08:48,710 --> 00:08:54,090
+اللي هي مثلا ال a
+
+114
+00:08:54,090 --> 00:09:02,310
+y hat a y y hat dot by y hat هيظل عند مين a z z
+
+115
+00:09:02,310 --> 00:09:04,750
+hat dot
+
+116
+00:09:17,660 --> 00:09:20,640
+عشان هيك بيطلعوا معناة كهذه formula
+
+117
+00:09:25,900 --> 00:09:30,520
+زي ال AYBY زي ال AZBZ فإن أي حاجة اي dot تاني ما
+
+118
+00:09:30,520 --> 00:09:32,980
+بين ال components البقيين يعني لو أنا عملت ال dot
+
+119
+00:09:32,980 --> 00:09:37,720
+ما بين ال AX والBY هتكون zero، ماضر؟ إذا البساطة
+
+120
+00:09:37,720 --> 00:09:40,580
+ال dot ال product هو عبارة عن حاصل ال similar
+
+121
+00:09:40,580 --> 00:09:43,200
+components يعني ال X components مع بعض زي ال Y
+
+122
+00:09:43,200 --> 00:09:47,800
+components مع بعض زي ال Z components مع بعض كمان
+
+123
+00:09:47,800 --> 00:09:51,940
+ال dot ال product احنا مش معرفةه بA بB بقصين
+
+124
+00:09:51,940 --> 00:09:54,600
+الزاوية إذا أنا بقدر أعمل ال dot ال product بهذه
+
+125
+00:09:54,600 --> 00:09:59,700
+الطريقةأجيب المجلد تبع A و المجلد تبع B و أدرسه في
+
+126
+00:09:59,700 --> 00:10:02,320
+ال case file يزور بينهم أو إذا كنت عارفة ال
+
+127
+00:10:02,320 --> 00:10:06,180
+components أعمل الهاي الطريقة كما الهاي كما
+
+128
+00:10:06,180 --> 00:10:09,620
+بتساعدني لو أنا كنت عارفة قيم A و B و ال
+
+129
+00:10:09,620 --> 00:10:22,780
+components عامهم أجيب يتزور بينهم معايا؟ طيب إيش
+
+130
+00:10:22,780 --> 00:10:29,940
+فيه من خصائص ال productخصائصه انه ال commutative
+
+131
+00:10:29,940 --> 00:10:34,760
+law ايش يعني ال commutative law انه سواء ضابط a
+
+132
+00:10:34,760 --> 00:10:38,540
+dot b او b dot a لازم يبقى نفس الحاجة و من هنا ده
+
+133
+00:10:38,540 --> 00:10:44,620
+الحقيقة لو انا حضرت هنا b dot a حضرت هنا bx ex هل
+
+134
+00:10:44,620 --> 00:10:48,820
+حد فرقها ايه ولا by ay ماهد اخدناها في المخدرات
+
+135
+00:10:48,820 --> 00:10:50,200
+الماضية مش هيك
+
+136
+00:10:54,090 --> 00:10:57,010
+فى الـ not distributive يعني التوزيع لو انا اول
+
+137
+00:10:57,010 --> 00:11:01,350
+جمعة اندي طلعتها vector A وB وC لو جمعت اول ال B
+
+138
+00:11:01,350 --> 00:11:05,590
+مع ال C عملتلهم dot ال product مع ال A لازم يساوي
+
+139
+00:11:05,590 --> 00:11:08,950
+لو انا عملت اول dot ال product ما بين ال A وB و
+
+140
+00:11:08,950 --> 00:11:13,510
+dot ال product مع ال A وC و جمعت ال نواتي مع بعض
+
+141
+00:11:13,510 --> 00:11:19,410
+يعني زى ما انتوا شايفين أسوأ في البداية جمعت ال B
+
+142
+00:11:19,410 --> 00:11:24,490
+مع ال Cو الناتج او اول عملت dot product ما بين ال
+
+143
+00:11:24,490 --> 00:11:27,410
+a و ال b و ال dot product ما بين ال a و ال c و
+
+144
+00:11:27,410 --> 00:11:30,350
+بعدين جمعتهم مع بعض نفس الناتج طبعا هذا ال
+
+145
+00:11:30,350 --> 00:11:33,350
+magnitude اللي هو a dot a ناتج من اللي اللي هي
+
+146
+00:11:33,350 --> 00:11:36,210
+العلاقة اللي هنا
+
+147
+00:11:41,780 --> 00:11:45,360
+أو من هنا تعني مثل حاجة هتعطينا a في a اللي هو ال
+
+148
+00:11:45,360 --> 00:11:48,220
+magneto في magneto فجبتهم يزول بينهم، قداشر بتعمل
+
+149
+00:11:48,220 --> 00:11:51,620
+تمام يزول بين ال a و ال a، zero، جبتهم zero واحد،
+
+150
+00:11:51,620 --> 00:11:55,560
+اذا ال dot product ل a مع dot m هتسوي ايه تنبيه؟
+
+151
+00:11:55,560 --> 00:11:58,740
+اذا a هي ال magneto، مش بتسوي الجزر التنبيهي ل a
+
+152
+00:11:58,740 --> 00:12:01,300
+dot a، واضح؟
+
+153
+00:12:04,530 --> 00:12:07,370
+و هدا انا حكيتلكم يا ال unit vectors لازم اذا كان
+
+154
+00:12:07,370 --> 00:12:10,530
+ال unit vector معروف انه ال magnitude تبعه ال unit
+
+155
+00:12:10,530 --> 00:12:13,710
+vector تعريفه هو ال unit vector ال magnitude تبعه
+
+156
+00:12:13,710 --> 00:12:16,710
+واحد ف ال dot product مع ال unit vector نفسه
+
+157
+00:12:16,710 --> 00:12:19,610
+بعطيني واحد unit vector و vector و ان unit vector
+
+158
+00:12:19,610 --> 00:12:24,150
+عمودي عليها بيكون zero كي اسف صار لحد هنا؟ هيك
+
+159
+00:12:24,150 --> 00:12:27,690
+احنا خلصنا ال dot product ديش ال cross product ال
+
+160
+00:12:27,690 --> 00:12:29,970
+cross product اللي هو ال vector product كمان
+
+161
+00:12:29,970 --> 00:12:32,250
+سميناه لإنه ال نميش تبعه vector
+
+162
+00:12:35,490 --> 00:12:38,090
+الـ magnitude تبع ال cross product هذا ال
+
+163
+00:12:38,090 --> 00:12:42,910
+magnitude تبعه هو عبارة عن a في b ب sign الزاوية
+
+164
+00:12:42,910 --> 00:12:48,830
+اللي بينهم هذا ال magnitude عشان
+
+165
+00:12:48,830 --> 00:12:53,050
+هذا vector فإيش هيكون فيه الاتجاه تبع ال vector
+
+166
+00:12:53,050 --> 00:12:56,090
+الجديد am يمثل اتجاه ال vector النتج من ال cross
+
+167
+00:12:56,090 --> 00:13:00,370
+product تبع a مع b إذا a cross b هيعطينا ال vector
+
+168
+00:13:00,370 --> 00:13:03,930
+اللي مقداره a في b ب sign الزاوية اللي بينهم
+
+169
+00:13:03,930 --> 00:13:09,980
+واتجاهه اللي هوأيه هذا؟ انا ممكن كمان اعرف ال
+
+170
+00:13:09,980 --> 00:13:12,100
+cross product عن طريق ال determinant بتاع ال
+
+171
+00:13:12,100 --> 00:13:16,640
+matrix A cross B فهو ال determinant بوزر ال unit
+
+172
+00:13:16,640 --> 00:13:18,980
+vectors اللي هي ال partition مثلا في حالتنا احنا
+
+173
+00:13:18,980 --> 00:13:21,940
+مثلا بنعمل ال partition X hat وY hat وZ hat ال
+
+174
+00:13:21,940 --> 00:13:24,360
+component بتاعة ال vector الأول و ال component
+
+175
+00:13:24,360 --> 00:13:26,600
+بتاعة ال vector التاني بتعرفوا تعملوا ال
+
+176
+00:13:26,600 --> 00:13:30,480
+determinant تحسوها ولا في داعي راجعوا مع بعض كله
+
+177
+00:13:30,480 --> 00:13:31,880
+عارف في حد مش عارف
+
+178
+00:13:41,470 --> 00:13:46,390
+هذا اللي هي ال permutative يعني انا عندي اي unit
+
+179
+00:13:46,390 --> 00:13:50,270
+vectors اللي هم مثلا X hat و Y hat و Z hat برتبهم
+
+180
+00:13:50,270 --> 00:13:56,430
+في المحيط دائرة لو انا عندي X hat مشيت حسب توراة
+
+181
+00:13:56,430 --> 00:14:01,890
+الساعة يعني ان كان عندي X hat cross Y hat X hat
+
+182
+00:14:01,890 --> 00:14:07,260
+cross Y hat هبقيني بصة في Z hatلو كان عندي y hat
+
+183
+00:14:07,260 --> 00:14:10,500
+cross z hat هبقى بتلبس في x hat يعني طول ما أنا
+
+184
+00:14:10,500 --> 00:14:14,540
+ماشية في الدائرة في اتجاه اللي هي قرب الساعة بيكون
+
+185
+00:14:14,540 --> 00:14:17,580
+النات الصحيح لو أنا ماشيت عكسها قرب الساعة يعني
+
+186
+00:14:17,580 --> 00:14:22,970
+هبقى Ax cross z hat هبقى بيبطيني minus yزها تكروس
+
+187
+00:14:22,970 --> 00:14:27,550
+ويها تطييني مينوس اكسها ويها تكروس اكسها تطييني
+
+188
+00:14:27,550 --> 00:14:31,110
+مينوس اكسها واضح ان هذه هي الممتدة للتفسيير يعني و
+
+189
+00:14:31,110 --> 00:14:33,390
+احنا أصغر كانت هذه أسفل حاجة من الظباط دوة من خلال
+
+190
+00:14:33,390 --> 00:14:38,310
+دائرة XYZ XZK هذا موجود ثم انا بروسف هذا الاتجاه
+
+191
+00:14:38,310 --> 00:14:41,890
+لما تجيني تنتمي عكس الاتجاه هاتول بيكون اللي هو
+
+192
+00:14:41,890 --> 00:14:42,990
+الإشارة سنة
+
+193
+00:14:47,590 --> 00:14:50,990
+مش الخصائص بتاعة ال cross product اولا ان هو مش
+
+194
+00:14:50,990 --> 00:14:54,810
+commutative يعني معناه اذا قلت a cross b لها تساوي
+
+195
+00:14:54,810 --> 00:14:58,150
+b cross a ليش؟ لان انا اتفق ان اقول a cross b بسكر
+
+196
+00:14:58,150 --> 00:15:02,190
+a على b بيعطيني ال vector بيكروس a بسكر بيكروس a
+
+197
+00:15:02,190 --> 00:15:05,190
+بتعطيني ال vector معله مش نفس الاتجاه اذا ما
+
+198
+00:15:05,190 --> 00:15:08,350
+تساويش في نفس المقدع الاتجاه مش نفس ال vector فإذا
+
+199
+00:15:08,350 --> 00:15:11,450
+هي مش commutative يعني a cross b لها تساوي b cross
+
+200
+00:15:11,450 --> 00:15:16,700
+aAnticommutative يعني انه انا شرحتلكم a cross b
+
+201
+00:15:16,700 --> 00:15:21,000
+بتطلع لفوق و b cross a بتطلع تحت نفس المقضعة فهي
+
+202
+00:15:21,000 --> 00:15:24,180
+anticommutative يعني معناه انه في إشارة سالبة ال
+
+203
+00:15:24,180 --> 00:15:28,660
+vector a cross b بيكون تجاه مثلا ال z hat لكن ال b
+
+204
+00:15:28,660 --> 00:15:33,800
+cross a بيكون تجاه هوفر سالبit is not associative
+
+205
+00:15:33,800 --> 00:15:37,300
+يعني انا بقدرش اوزاها بقدرش اقول ان a cross b
+
+206
+00:15:37,300 --> 00:15:40,400
+cross c انه associative يعني مثلا اول اعمل cross
+
+207
+00:15:40,400 --> 00:15:44,160
+product بين ال a و ال b و بعدين اعمل cross مع c لا
+
+208
+00:15:44,160 --> 00:15:47,920
+تساوي اللي لو عملت cross product b مع c و عملتلها
+
+209
+00:15:47,920 --> 00:15:50,860
+cross product مع a بيساويوش معاك بالسبب ان هذا
+
+210
+00:15:50,860 --> 00:15:55,520
+vector productلكن هي distributive يعني أسوأ عملت
+
+211
+00:15:55,520 --> 00:15:58,940
+أول جماعة ال P مع ال C و عملت ال cross product مع
+
+212
+00:15:58,940 --> 00:16:02,840
+A أو أول عملت cross A cross P بعد ال A cross C نفس
+
+213
+00:16:02,840 --> 00:16:05,840
+النتيجة و قولنا ال vector crossed مع نفسه بعطينا
+
+214
+00:16:05,840 --> 00:16:06,360
+Zero
+
+215
+00:16:10,360 --> 00:16:13,680
+الـtriple product scalar الـtriple product وهذا
+
+216
+00:16:13,680 --> 00:16:16,600
+شفناه قلنا ليش هو scalar triple لأن قلنا في عمدي
+
+217
+00:16:16,600 --> 00:16:19,640
+أول across ال product بيعطينا vector دُتت معايا
+
+218
+00:16:19,640 --> 00:16:22,400
+scalar بيعطينا scalar البساطة ال triple product
+
+219
+00:16:22,400 --> 00:16:25,720
+اللي عبّر عنه برضه ال determinant النتج تبع ال
+
+220
+00:16:25,720 --> 00:16:29,200
+determinant بيعطينا قيمة اللي هو ال triple product
+
+221
+00:16:29,200 --> 00:16:33,620
+برتب ال vector الأول اللي هو ال A السطر الأول ال V
+
+222
+00:16:33,620 --> 00:16:37,460
+السطر التاني و ال C السطر التالت
+
+223
+00:16:55,490 --> 00:17:05,050
+عشان الناس تحفظها بيقولوا back cap يعني مجرد
+
+224
+00:17:05,050 --> 00:17:10,410
+تذكيربس لازم تكون حاصل انه a cross b cross c يعني
+
+225
+00:17:10,410 --> 00:17:13,070
+لو وجدت كرموز تانية حطها على جانب a cross b cross
+
+226
+00:17:13,070 --> 00:17:16,450
+c وقولي back cap back cap ايش معناه ان الترتيب
+
+227
+00:17:16,450 --> 00:17:21,050
+الأولاني هو back والترتيب التاني cap back هيكون ال
+
+228
+00:17:21,050 --> 00:17:26,870
+b مضروب في a dot c والترتيب minus c a dot b يعني
+
+229
+00:17:26,870 --> 00:17:30,750
+انها لازم تعرف حاجة بس عشان تتذكر الترتيب اللي هي
+
+230
+00:17:30,750 --> 00:17:32,650
+back cap واضح؟
+
+231
+00:17:37,420 --> 00:17:42,640
+إن a dot b مضروبة في c vector لها تساوي a مضروفة
+
+232
+00:17:42,640 --> 00:17:46,000
+بي dot c لأنه طبعا زي ما قولنا هدولة كلهم vector
+
+233
+00:17:46,000 --> 00:17:52,040
+فبكون انها مش مساوية اي تشكيل لكن عند a dot b هذا
+
+234
+00:17:52,040 --> 00:17:56,840
+ايش طلع عليه vector مع c بسوء c a dot b هذا مافيش
+
+235
+00:17:56,840 --> 00:18:00,280
+فيها اي مشكلة الترتيب أسوأ أحطت ال a dot b هنا
+
+236
+00:18:00,280 --> 00:18:04,090
+اللي هو صار scalar عفوا ان هادي scalar لانه ضعفبس
+
+237
+00:18:04,090 --> 00:18:06,950
+هو احضرتها دي تبقى النتج مثلا خمسة او خمس عشر او
+
+238
+00:18:06,950 --> 00:18:09,210
+خمس عشر او خمس عشر او خمس عشر او خمس عشر او خمس
+
+239
+00:18:09,210 --> 00:18:11,310
+عشر او خمس عشر او خمس عشر او خمس عشر او خمس عشر او
+
+240
+00:18:11,310 --> 00:18:11,890
+خمس عشر او خمس عشر او خمس عشر او خمس عشر او خمس
+
+241
+00:18:11,890 --> 00:18:14,590
+عشر او خمس عشر او خمس عشر او خمس عشر او خمس عشر او
+
+242
+00:18:14,590 --> 00:18:14,610
+خمس عشر او خمس عشر او خمس عشر او خمس عشر او خمس
+
+243
+00:18:14,610 --> 00:18:22,850
+عشر او خمس عشر او خمس عشر او
+
+244
+00:18:22,850 --> 00:18:29,870
+خمس عشر او خمس عشر او
+
+245
+00:18:29,870 --> 00:18:33,690
+خمسوبدي اعرف ال component بتاعته في اتجاه ال B
+
+246
+00:18:33,690 --> 00:18:37,530
+عشان اعرف ال component بتاعت ال vector A تتجاه ال
+
+247
+00:18:37,530 --> 00:18:42,050
+B هتكون عبارة عن قيمة A كما انتوا اخدتوا في ال ..
+
+248
+00:18:42,050 --> 00:18:45,730
+اي مصطلحات ال component بتاعته في اتجاه ال X hat
+
+249
+00:18:45,730 --> 00:18:48,570
+او ال Y hat بس احنا بدنا نقول ال X اتجاه ال B يعني
+
+250
+00:18:48,570 --> 00:18:52,010
+ال vector A و ال vector B ال component بتاعت A
+
+251
+00:18:52,010 --> 00:18:55,230
+تجاه ال B اللي هي عبارة عن مجموعة A بكساين الزاوية
+
+252
+00:18:55,230 --> 00:19:03,260
+لل B A كساين الزاوية تمام؟إذاً هاي ال component هي
+
+253
+00:19:03,260 --> 00:19:06,540
+عبارة يعني مثلا إنتوا تتذكروا إننا نحن نتحلل أي
+
+254
+00:19:06,540 --> 00:19:10,720
+vector مثلا هاي ال F وكنا نقول هاي ال component في
+
+255
+00:19:10,720 --> 00:19:14,860
+هذا الاتجاه هي θ هي F cos θ في اتجاه مثلا ال X hat
+
+256
+00:19:14,860 --> 00:19:19,180
+وهي ال component هتكون F cos θ في اتجاه ال Y hat
+
+257
+00:19:19,180 --> 00:19:23,280
+فإذا ال component في اتجاه ال B عبارة عن ميل
+
+258
+00:19:23,280 --> 00:19:27,660
+المجموعة تبقى A cos θ AB هاي ال component اللي في
+
+259
+00:19:27,660 --> 00:19:32,880
+هذا الاتجاه هذا إيش معناه؟معناه هي المجمد تبع A في
+
+260
+00:19:32,880 --> 00:19:37,620
+ال magnitude تبع ال B hat ال unit vector اتجاه ال
+
+261
+00:19:37,620 --> 00:19:41,620
+B اللي هو واحد، ده واحد يعني مقدر اضيفه و ايه صح
+
+262
+00:19:41,620 --> 00:19:46,300
+فجبته من الزاوية اللي هي θتا بين ال A و ال B أو
+
+263
+00:19:46,300 --> 00:19:48,380
+هذا ايش قلنا بساوي، اللي هو المجمد تبع ال vector
+
+264
+00:19:48,380 --> 00:19:50,460
+الأول في المجمد تبع ال vector التاني في الزاوية
+
+265
+00:19:50,460 --> 00:19:53,200
+اللي بينهم ووضبت ال product between هدولة two
+
+266
+00:19:53,200 --> 00:19:57,540
+vectors يعني ال component بتاعة A اتجاه ال B هي
+
+267
+00:19:57,540 --> 00:20:00,160
+عبارة عن مجمد ال product ما بين ال Aو ال unit
+
+268
+00:20:00,160 --> 00:20:04,520
+vector في اتجاه ال B انا هتعطيني المجلد تبع ال A
+
+269
+00:20:04,520 --> 00:20:09,080
+اللي هو A مضروف المجلد تبع ال unit vector B hat
+
+270
+00:20:09,080 --> 00:20:11,600
+اللي هو واحد تجيب الزاوية اللي بينهم اللي هي تاتر
+
+271
+00:20:11,600 --> 00:20:15,660
+واضح؟ اذا انا باجيب component لأي vector في اتجاه
+
+272
+00:20:15,660 --> 00:20:20,740
+معين بضربه في ال unit vector في هذا الاتجاه كمان
+
+273
+00:20:20,740 --> 00:20:21,620
+مرة ولا واضح؟
+
+274
+00:20:27,760 --> 00:20:30,820
+طب إذا بدى أعبّر عنه بشكل vector بديش أتعبّر عنه ب
+
+275
+00:20:30,820 --> 00:20:36,440
+component يعني عرفنا إن هذا الطول هو عبارة عن A
+
+276
+00:20:36,440 --> 00:20:42,520
+dot B hat طب أنا بدي اتجاهه، بدأي كل مرة أقول إن
+
+277
+00:20:42,520 --> 00:20:45,000
+هو في اتجاه الـB، لأ أقوم بقول هو اتجاه اللي هو
+
+278
+00:20:45,000 --> 00:20:48,520
+الـB hat زي ما هنا أنا بدي أقول هذه ال component
+
+279
+00:20:48,520 --> 00:20:57,550
+هي في X، vector، هتسوّأ ف و سعي و ستة، X hatعشان
+
+280
+00:20:57,550 --> 00:21:00,390
+اعرف ال component بتاعة اي vector في اتجاه معين
+
+281
+00:21:00,390 --> 00:21:03,050
+بعملها dot product مع unit vector في هذا الاتجاه
+
+282
+00:21:03,050 --> 00:21:13,530
+والاتجاه هيكون هو هذا ال unit vector تشوف
+
+283
+00:21:13,530 --> 00:21:16,810
+أمثلة على المعلومات اللي أخدناها لو كان عندي two
+
+284
+00:21:16,810 --> 00:21:22,590
+vectors A وB وبدى الزاوية اللي بين A وB دي حد
+
+285
+00:21:22,590 --> 00:21:24,350
+بيقدر يحللنا يلا تفضل
+
+286
+00:21:51,800 --> 00:21:55,420
+عشان تجيب الزاوية اللي بينهم بتجيب ال dot product
+
+287
+00:21:55,420 --> 00:21:59,020
+يعني a dot b بتتساوي a magnitude في b magnitude في
+
+288
+00:21:59,020 --> 00:22:02,660
+cosine الزاوية اللي بينهم فبتعمل ال magnitude تبع
+
+289
+00:22:02,660 --> 00:22:06,880
+aوطبعاً كمان بدها جيب اللي هي a dot b اللي هي ال
+
+290
+00:22:06,880 --> 00:22:11,100
+component الأولى في التانية ال a x في b x زائد ال
+
+291
+00:22:11,100 --> 00:22:16,440
+a y في b y تمام
+
+292
+00:22:16,440 --> 00:22:19,840
+إن ال b x zero فعطول طلعت النتج
+
+293
+00:22:43,920 --> 00:23:07,840
+في أي استفسار لحد هنا؟
+
+294
+00:23:10,400 --> 00:23:14,380
+أول حاجة ممكن أجيبها بالـ dot product زي ما عملت
+
+295
+00:23:14,380 --> 00:23:18,720
+زملتكم لكن كمان برضه أقدر أجيبها بطريقة تانية اللي
+
+296
+00:23:18,720 --> 00:23:22,900
+هي برضه ال cross product cross product محاولنا
+
+297
+00:23:22,900 --> 00:23:27,460
+نعرف إن ال magnitude تبع a cross b إيش بساوي الأول
+
+298
+00:23:27,460 --> 00:23:30,200
+a في ال magnitude تبع b في sin زغر اللي بينهم
+
+299
+00:23:30,200 --> 00:23:33,260
+فبجيب ال a cross b اللي هي باستخدام ال determinant
+
+300
+00:23:33,260 --> 00:23:36,640
+هي جبت ال vector الناتج بجيب ال magnitude تبع a
+
+301
+00:23:36,640 --> 00:23:40,080
+cross bوبعدين ايش بقول هذا المجنيد مش بيساوي
+
+302
+00:23:40,080 --> 00:23:43,120
+المجنيد التبع ال A في المجنيد التبع ال B في sign
+
+303
+00:23:43,120 --> 00:23:47,900
+الزاوية فإذا نتزاوى إيش هتكون sign ال inverse اللي
+
+304
+00:23:47,900 --> 00:23:51,060
+هو المجنيد التبع ال A cross B على المجنيد التبع ال
+
+305
+00:23:51,060 --> 00:23:53,560
+A في المجنيد التبع ال .. هنا في بس طيب و sign
+
+306
+00:23:53,560 --> 00:23:58,840
+inverse فلقيت
+
+307
+00:23:58,840 --> 00:24:04,600
+كمان بدي أعمل derivation ده مثال تاني اللي هو أنا
+
+308
+00:24:04,600 --> 00:24:07,780
+لو بدي أجيلهدول الأمثلة اللي كنا خبتولها في
+
+309
+00:24:07,780 --> 00:24:11,700
+الجابرة في المدرسة اللي هو القانون الأول اللي بقول
+
+310
+00:24:11,700 --> 00:24:19,180
+ليه لو كان عندي مصلة زي هيكي أطلعوا A وB وC هدول
+
+311
+00:24:19,180 --> 00:24:24,580
+أطلعوا أنه ال A تربيع بساوي ال C تربيع زاد ال B
+
+312
+00:24:24,580 --> 00:24:29,040
+تربيع minus اتنين B في C في جابرة من الزاوية اللي
+
+313
+00:24:29,040 --> 00:24:33,780
+بعدهم كنا خبتولها ده القانونوكمان عنا اللي هي sign
+
+314
+00:24:33,780 --> 00:24:36,180
+formula اللي هي مشهورة sign formula اللي هي sign
+
+315
+00:24:36,180 --> 00:24:40,340
+الزاوية على ضلع لقبالها sign ال a على a بسوى sign
+
+316
+00:24:40,340 --> 00:24:45,370
+ال b على ال b لقبالهابتساوي sign ال C اللي هي
+
+317
+00:24:45,370 --> 00:24:48,530
+زاوية على الدولة اللي أقبالها بدنا نثبت هدولة ال
+
+318
+00:24:48,530 --> 00:24:52,370
+two formulas طبعا واضح أنه أكيد هنحتاج ال total
+
+319
+00:24:52,370 --> 00:24:55,930
+product فعشان أحتاج ال total product بدي أحدد مين
+
+320
+00:24:55,930 --> 00:24:58,050
+اللي بدي أحط بينهم ال total product واضح أنه في
+
+321
+00:24:58,050 --> 00:25:01,470
+عندي A تربية و B تربية و C تربية بين ال B و ال C
+
+322
+00:25:01,470 --> 00:25:05,470
+اذا أنا بدي أحدد تلاتة مش واحد منهم بدي أخد مجموع
+
+323
+00:25:05,470 --> 00:25:07,770
+هدولة ال vectors إيش مجموع هدولة ال vectors بتبدأ
+
+324
+00:25:07,770 --> 00:25:12,250
+من هنا عند ال A زي ال B زي ال C إيش بيساوي؟ Zero
+
+325
+00:25:13,820 --> 00:25:18,720
+لأن هى ال component بتاعته للمجموع A زي B زي C بها
+
+326
+00:25:18,720 --> 00:25:22,260
+ساوة و سفر طب هى واضح بين ال dot product من مين و
+
+327
+00:25:22,260 --> 00:25:25,980
+B و C فإذا أنا قولت A vector زي B vector زي C
+
+328
+00:25:25,980 --> 00:25:28,980
+vector مش بساوة و سفر بقى نقول التانية اللى انتوا
+
+329
+00:25:28,980 --> 00:25:31,320
+شاطرين و قولتوا هو ال dot product بين ال B و ال C
+
+330
+00:25:31,320 --> 00:25:35,060
+على طرف و بضل طرف التاني مين ال A و باخد دقساتها
+
+331
+00:25:35,060 --> 00:25:40,180
+اللى هى ال dot product تبع هدول ال vectorsأول حاجة
+
+332
+00:25:40,180 --> 00:25:42,580
+بجيب المجموع بتاعهم هدولة ال vectors اللي هم
+
+333
+00:25:42,580 --> 00:25:45,260
+موجودين في ال formula اللي هي ال A و ال B و ال C
+
+334
+00:25:45,260 --> 00:25:48,780
+بعدين بنقول ال two vectors اللي هو ال A و ال C في
+
+335
+00:25:48,780 --> 00:25:53,140
+جهة و ال A في جهة فهيكون B ذات C بسوا منص A بعدين
+
+336
+00:25:53,140 --> 00:25:56,520
+بعمل ال dot product ل ال vectors في نفسهم يعني انا
+
+337
+00:25:56,520 --> 00:26:00,320
+هاخد ال A dot A بقي التربيش هتساوي B ذات C dot B
+
+338
+00:26:00,320 --> 00:26:04,570
+ذات Cمعايا؟ زى ما انتوا شايفين على الصبورة اذا
+
+339
+00:26:04,570 --> 00:26:08,350
+نعدي الطرف هدا هيكون a dot a اللى هو حاطينا a
+
+340
+00:26:08,350 --> 00:26:12,310
+تربية و الطرف هدا b زكى c dotted مع b زكى c
+
+341
+00:26:12,310 --> 00:26:16,010
+اتفاقنا هدولة هيكون ال component الاولى او يعنى
+
+342
+00:26:16,010 --> 00:26:20,190
+هنا vectors عنهم هيكون b dot b و c dot c اللى هو
+
+343
+00:26:20,190 --> 00:26:23,410
+اللى بالنص اللى هو هيكون minus 2 c dot b لإن
+
+344
+00:26:23,410 --> 00:26:29,440
+اتفاقنا c dot b بالساوة c b dot cإذاً a تربيعاش
+
+345
+00:26:29,440 --> 00:26:34,280
+هتساوي P dot P اللي هي P تربيع C dot C، C تربيع وP
+
+346
+00:26:34,280 --> 00:26:37,260
+dot C اللي هي عبارة عن المجنيد تبع الأول في
+
+347
+00:26:37,260 --> 00:26:39,160
+المجنيد التبع التاني في جبتهم الزاوية بينهم، مين
+
+348
+00:26:39,160 --> 00:26:47,740
+جبتهم الزاوية بينهم، اللي هي الزاوية هاي اللي
+
+349
+00:26:47,740 --> 00:26:51,220
+هي عبارة عن 180 minus F عشان تطلعوا هنا إشارة على
+
+350
+00:26:51,220 --> 00:26:52,260
+سنة
+
+351
+00:26:58,770 --> 00:27:03,810
+Ic الزاوية اللى بين P و C هي 180 نقص فبطلع هنا
+
+352
+00:27:03,810 --> 00:27:09,510
+الإشارة السالفة واضح هذا بالنسبة لل formula الأولى
+
+353
+00:27:09,510 --> 00:27:15,430
+نيجي لل formula التانية احنا
+
+354
+00:27:15,430 --> 00:27:21,650
+بنعرف ان ال area مساحة المثلث هو نص الدلعب
+
+355
+00:27:21,650 --> 00:27:25,840
+الارتفاعإذا اشهر من نص الدلع في الارتفاع a cross b
+
+356
+00:27:25,840 --> 00:27:33,560
+نص a cross b اللي هي نص القاعدة في الارتفاع نص b
+
+357
+00:27:33,560 --> 00:27:38,400
+cross c نص c cross a هدا هتقول اللي هي ال area
+
+358
+00:27:38,400 --> 00:27:45,060
+بتاعة ال triangle لو
+
+359
+00:27:45,060 --> 00:27:47,940
+عوضنا عن كل واحدة هتعطينا a في b sin الزاوية اللي
+
+360
+00:27:47,940 --> 00:27:49,900
+بينها دول magnitude طبعا لإن ال area مالها
+
+361
+00:27:49,900 --> 00:27:54,500
+magnitudeمجموعة مجموعة مجموعة مجموعة مجموعة مجموعة
+
+362
+00:27:54,500 --> 00:27:55,120
+مجموعة مجموعة مجموعة مجموعة مجموعة مجموعة مجموعة
+
+363
+00:27:55,120 --> 00:28:01,500
+مجموعة مجموعة مجموعة مجموعة مجموعة مجموعة مجموعة
+
+364
+00:28:01,500 --> 00:28:06,160
+مجموعة مجموعة مجموعة مجموعة مجموعة مجموعة مجموعة
+
+365
+00:28:06,160 --> 00:28:06,400
+مجموعة مجموعة مجموعة مجموعة مجموعة مجموعة مجموعة
+
+366
+00:28:06,400 --> 00:28:06,460
+مجموعة مجموعة مجموعة مجموعة مجموعة مجموعة مجموعة
+
+367
+00:28:06,460 --> 00:28:13,360
+مجموعة مجموعة مجموعة
+
+368
+00:28:13,360 --> 00:28:18,940
+مجموع
+
+369
+00:28:22,940 --> 00:28:27,560
+هذه الأمثلة كلها موجودة عندكم في الكتاب كويس انكوا
+
+370
+00:28:27,560 --> 00:28:31,440
+ترجعوها المثال هذا ايش بقوللي عندك انت تلات نقاط
+
+371
+00:28:31,440 --> 00:28:37,360
+B1 وB2 وB3 كلها تقع على خط واحد يعني زي ما انتوا
+
+372
+00:28:37,360 --> 00:28:43,260
+شايفين مثل هذا المثل هتفقدت من B1 وB2 B1
+
+373
+00:28:43,260 --> 00:28:47,900
+وB2 وB3 وعينها نفس الخط بقوللي
+
+374
+00:28:49,080 --> 00:28:52,460
+to determine the shortest distance between طبعا
+
+375
+00:28:52,460 --> 00:28:55,040
+أول حاجة بقولنا أثبتوا أنهم قاعدين على نفس الخط
+
+376
+00:28:55,040 --> 00:28:58,860
+يعني بي واحد و بي تنين و بي تلاتة أثبتوا أنهم لقوا
+
+377
+00:28:58,860 --> 00:29:02,800
+على نفس الخط و بعد هيكي بدنا نقرر أقصر مسافة ما
+
+378
+00:29:02,800 --> 00:29:06,940
+بين هذا الخط و نقطة اللي هي بي أربعة المقار هذا
+
+379
+00:29:06,940 --> 00:29:12,910
+الشكلعشان أثبت أنهم قاعدين على نفس الحط لازم أثبت
+
+380
+00:29:12,910 --> 00:29:18,090
+أنه ال .. أول حاجة أجيب اللي هي المسافة بين P1 و
+
+381
+00:29:18,090 --> 00:29:22,630
+P2 و المسافة مثلا P بين P2 و P3 صرت عارفة مثلا
+
+382
+00:29:22,630 --> 00:29:26,170
+المسافة بين هاي و هاي إذا هم قاعدين على نفس الحط
+
+383
+00:29:26,170 --> 00:29:30,150
+ال cross product بتاعهم مش هو بيكون zeroفإذا أول
+
+384
+00:29:30,150 --> 00:29:35,050
+حاجة بدي أجيب المسافة مثلا بين P1 و P2 و أصبحنا
+
+385
+00:29:35,050 --> 00:29:38,370
+عارفين إيش ال distance بين P1 و P2 هتكون اللي هي
+
+386
+00:29:38,370 --> 00:29:40,770
+P2 minus P1
+
+387
+00:29:45,960 --> 00:29:55,240
+Rb1b2-Rb1Rab-RaRb2
+
+388
+00:29:55,240 --> 00:30:09,660
+-Rb1Rb2-Rb1Rb2-Rb2
+
+389
+00:30:09,790 --> 00:30:13,910
+هدول اللي احنا بنايهم لسه لجزء التاني بي واحد و بي
+
+390
+00:30:13,910 --> 00:30:17,090
+تلاتة اذا انا ماشي بنا بين بي واحد و بي تلان و بي
+
+391
+00:30:17,090 --> 00:30:19,970
+واحد و بي تلاتة او بي تلان و بي تلاتة مش حد الفرق
+
+392
+00:30:19,970 --> 00:30:25,430
+يعنيلو أخدنا مثلا برضه P1 و P3 R P1 و P3 المسافة
+
+393
+00:30:25,430 --> 00:30:30,470
+بين P1 و P3 اللي قلنا هتكون R P3 minus R P1 اللي
+
+394
+00:30:30,470 --> 00:30:34,590
+احنا عوض minus 3 0 8 و minus اللي هي 5 2 minus 4
+
+395
+00:30:34,590 --> 00:30:38,290
+وهيجبنا R P1 اللي هي المسافة بين النقطة الأولى و
+
+396
+00:30:38,290 --> 00:30:42,530
+التانية و المسافة برضه من الأولى و التالتة لو أحطت
+
+397
+00:30:42,530 --> 00:30:47,790
+الخط صحيح يعني وهي انا افترضت من هنا قاعدين يعني
+
+398
+00:30:49,820 --> 00:30:55,840
+موضع في الواحدة بالنسبة ل ..
+
+399
+00:30:55,840 --> 00:31:00,920
+هجيب هدول المسافة mE1 وmE2 ومسافة mE1 وmE2 وmE3 او
+
+400
+00:31:00,920 --> 00:31:03,200
+زي ما قلتلكم مسافة mE1 وmE3
+
+401
+00:31:09,110 --> 00:31:11,690
+هجيب ال cross product إذا طلع ال cross product له
+
+402
+00:31:11,690 --> 00:31:15,510
+يساوي zero اذا هم مش قاعدين على نفس الحط لكن لو ال
+
+403
+00:31:15,510 --> 00:31:19,250
+cross product تبعهم سفر هيكون بساوي سفر بيكونوا في
+
+404
+00:31:19,250 --> 00:31:23,450
+نفس الحط لأنه احنا اشهرنا cross product A cross B
+
+405
+00:31:23,450 --> 00:31:28,250
+نفس المتبع هيعبارة عن A بB فسه عم يساوي الرابعين
+
+406
+00:31:29,850 --> 00:31:33,270
+إذا كانت الزاوية 0 ثاني الـ 00 فال cross product
+
+407
+00:31:33,270 --> 00:31:36,310
+سفر، لو ماكانتش بالساعة و سفر مش هيكون ال cross
+
+408
+00:31:36,310 --> 00:31:38,490
+product بساعة و سفر، احنا بنيها تكون الزاوية بينهم
+
+409
+00:31:38,490 --> 00:31:41,370
+سفر عشان يقع نفس الحط، الحط، إذا ال cross product
+
+410
+00:31:41,370 --> 00:31:46,340
+طلع سفر معناه أنه معينة نفس الحط، معايا؟لما نجي
+
+411
+00:31:46,340 --> 00:31:49,960
+نعمل cross product بالفعل بيطلع صفر إذا هم ال B1
+
+412
+00:31:49,960 --> 00:31:54,320
+وB2 وB3 وقعين على نفس الخط إذا الجثة الأول أثبتنا
+
+413
+00:31:54,320 --> 00:31:57,380
+كيف بيقع على نفس الخط أنه جبت المسافة بين كل نقطة
+
+414
+00:31:57,380 --> 00:32:00,660
+و التانية و بعدين جبت cross product بين هدول
+
+415
+00:32:00,660 --> 00:32:04,540
+المسافات طلع صفر معناه أنهم بالفعل قاعدين على نفس
+
+416
+00:32:04,540 --> 00:32:08,440
+الخط ما طلع الصفر معناه لأ في بينهم زاويةيعني مش
+
+417
+00:32:08,440 --> 00:32:12,000
+هو عيني على نفس الخط الجزء التاني هو نبيتنا أقصر
+
+418
+00:32:12,000 --> 00:32:18,640
+مسافة ما بين النقطة P4 و الخط اللي هم وقعين عليها
+
+419
+00:32:18,640 --> 00:32:22,200
+النقطة يعني ما بين الخط اللي وقع عليه النقطة P1 و
+
+420
+00:32:22,200 --> 00:32:28,160
+P2 و P3 و بين الخط اللي وقع عليه النقطة P4 النقطة
+
+421
+00:32:28,160 --> 00:32:31,520
+P4 هذا هو الخط اللي هم وقعين عليه فاندي فيه نقطة
+
+422
+00:32:31,520 --> 00:32:34,940
+P4 عرف ال axis بتاعي
+
+423
+00:32:37,860 --> 00:32:45,310
+أقصر مسافة بين ال V4 وهذا بحط أقصر مسافة بينهماللي
+
+424
+00:32:45,310 --> 00:32:48,490
+هي هتكون المسافة العمودية و لا لا أقصر مسافة هي
+
+425
+00:32:48,490 --> 00:32:52,290
+المسافة العمودية هاي الخط اللي بين ال P1 و P2 و P3
+
+426
+00:32:52,290 --> 00:32:55,490
+أي هذا الخط اللي أسفلنا هم قاعين كلهم عليه وهي
+
+427
+00:32:55,490 --> 00:33:00,570
+نقطة P4 بدي أن هي هاي المسافة أقصر مسافة بين P4 و
+
+428
+00:33:00,570 --> 00:33:03,890
+P الخط طبعا واضح أنه لازم نحتاج في هاي الحالة
+
+429
+00:33:03,890 --> 00:33:07,630
+cross product لأنه بدي أنا مسافة عمودية هتكون ال
+
+430
+00:33:07,630 --> 00:33:10,730
+cross product بين الخط اللي هو P1 و P4 اللي هو
+
+431
+00:33:10,730 --> 00:33:13,290
+احنا حسبناه تبقى و أنا بديه على الجزء التاني اللي
+
+432
+00:33:13,290 --> 00:33:14,450
+هو بين P1 و P4
+
+433
+00:33:17,220 --> 00:33:20,400
+لأنه لازمني أعرف هاي المسافة عشان أقدر أحدد ال D
+
+434
+00:33:20,400 --> 00:33:23,900
+لأن ال D إيش هتكون هذا اللي هو ال .. ال .. ال
+
+435
+00:33:23,900 --> 00:33:26,700
+water و هاي الزاوية الثالثة فبقدر أجيبه من ما
+
+436
+00:33:26,700 --> 00:33:28,980
+عرفتي اللي هو ال water و الزاوية اللي هو بالمعنى
+
+437
+00:33:28,980 --> 00:33:33,580
+أخر اللي هو ال prostrate part هتكون المسافة D هي
+
+438
+00:33:33,580 --> 00:33:37,380
+هاي المسافة R بي واحد بي أربعة اللي هو ال water في
+
+439
+00:33:37,380 --> 00:33:42,000
+صيني الزاوية معايا؟ اه انتوا تعرفوا هاي الأشياء
+
+440
+00:33:42,800 --> 00:33:46,060
+اللي عبارة عن مين؟ R في صين الزاوية هي عبارة عن
+
+441
+00:33:46,060 --> 00:33:50,780
+هوقع ال cross product بين R بي واحد بي أربع مع
+
+442
+00:33:50,780 --> 00:33:54,660
+مين؟ مع unit vector في اتجاه هذا الاتجاه نفس
+
+443
+00:33:54,660 --> 00:34:00,100
+الفكرة اللي احنا عملناها بالهيكل هذه عبارة عن R بي
+
+444
+00:34:00,100 --> 00:34:05,960
+واحد بي أربع في ال unit vector اللي في اتجاه ال بي
+
+445
+00:34:05,960 --> 00:34:12,360
+واحد بي اتنين بيجوز في صين ثتر
+
+446
+00:34:16,370 --> 00:34:20,490
+ما يعني هذا؟ هذا واضح أن مجموعة الـ cross product
+
+447
+00:34:20,490 --> 00:34:23,490
+بين هذين الفكتورين مجموعة الـ cross product بين
+
+448
+00:34:23,490 --> 00:34:26,290
+هذين الفكتورين المجموعة الأولة في المجموعة التانية
+
+449
+00:34:26,290 --> 00:34:30,450
+في صيني زي ولي بينهم فلما أضعها ر بي واحد بي أربعة
+
+450
+00:34:30,450 --> 00:34:35,590
+صين ستة وأضيف unit vector هو في اتجاهب1 ب2 هتكون
+
+451
+00:34:35,590 --> 00:34:39,790
+في الواقع ال magnitude ل cross ال product بين r ب1
+
+452
+00:34:39,790 --> 00:34:42,970
+ب4 cross it across ما اللي هو ال unit vector في
+
+453
+00:34:42,970 --> 00:34:47,730
+اتجاه b1 b2 عشان اجيب ال unit vector في اتجاه ال
+
+454
+00:34:47,730 --> 00:34:51,950
+b1 b2 ايش هيكون ال vector على ال magnitude تبعه
+
+455
+00:34:51,950 --> 00:34:56,550
+احنا شفنا ايش تعريف ال unit vector لأي
+
+456
+00:34:56,550 --> 00:35:02,730
+vector ال unit vector في اتجاه ال a لو سميته a
+
+457
+00:35:03,400 --> 00:35:06,100
+عبارة عن الـ vector A أخدناه في المتحضرة الهزيمية
+
+458
+00:35:06,100 --> 00:35:11,460
+الموجودة بـ A عشان أجيب لينت فيكتور احنا وصلنا
+
+459
+00:35:11,460 --> 00:35:16,620
+المهدي shorted distance يعبارة عن ال cross product
+
+460
+00:35:16,620 --> 00:35:22,380
+ما بين المسافة R ب 1 ب 4 المجموعات تبعهاالـ
+
+461
+00:35:22,380 --> 00:35:26,400
+crossed مع مين مع اللي هو ال unit vector فتجاه P1
+
+462
+00:35:26,400 --> 00:35:31,160
+P2 اللي هو إيش هيساوي ال vector PRP1P2 ال
+
+463
+00:35:31,160 --> 00:35:36,820
+magnitude تباع PRP1P2 هنعوض عنه و هيطلع معي اللي
+
+464
+00:35:36,820 --> 00:35:40,920
+هو النتج D اللي هي shortest distance بين الخط اللي
+
+465
+00:35:40,920 --> 00:35:46,800
+وقع عليه النقطة P1 P2 و P3 و النقطة P4 واضح؟
+
+466
+00:35:51,560 --> 00:35:54,800
+فهذا المثال احنا اتعلمنا انه فيه right hand rule
+
+467
+00:35:54,800 --> 00:36:01,500
+يعني عند cross product بين two vectors بيعطينا ال
+
+468
+00:36:01,500 --> 00:36:06,410
+vector التالت في ال rectangular coordinateلازم
+
+469
+00:36:06,410 --> 00:36:08,850
+يكون عندي ال right hand rule rectangular
+
+470
+00:36:08,850 --> 00:36:12,030
+coordinate بتطبقلي ال right hand rule يعني x cross
+
+471
+00:36:12,030 --> 00:36:20,030
+y هتعطينا z y cross z هتعطيني x z cross x y z زد
+
+472
+00:36:20,030 --> 00:36:24,870
+cross x هتعطينا y تمام؟ مي من هدولة بتحققش فيها ال
+
+473
+00:36:24,870 --> 00:36:27,690
+rectangular coordinate يعني مي من فيها ان ال x
+
+474
+00:36:27,690 --> 00:36:33,110
+cross y بتعطينا شيء poster z يعني لو استخدمت ال
+
+475
+00:36:33,110 --> 00:36:37,740
+right hand rule خلّيني ابدا في الأولىx cross y
+
+476
+00:36:37,740 --> 00:36:43,040
+واضحة زت اتجاه صحيح نيجي للتانية x cross y اتجاه
+
+477
+00:36:43,040 --> 00:36:50,380
+اضحك هي ريحتنا التانية الخاطئة بيتحققش في المشكلة
+
+478
+00:36:50,380 --> 00:36:58,540
+c x cross y زت اللي تحت لنيجي ل x cross y اتجاه
+
+479
+00:36:58,540 --> 00:37:03,950
+اكس تحت درفعها ل y اتجاه زت فادةاللي بعدها x cross
+
+480
+00:37:03,950 --> 00:37:08,110
+مع y هذا
+
+481
+00:37:08,110 --> 00:37:11,750
+الشكل هتعطينا z عشان هيك أنا بحب البرامي أكتر
+
+482
+00:37:11,750 --> 00:37:16,050
+بعدين الأخيرة اللي هي x برضه across y هتعطينا اللي
+
+483
+00:37:16,050 --> 00:37:26,050
+هي اتجاه z قبل
+
+484
+00:37:26,050 --> 00:37:35,790
+الأخرL الأخيرة E X X cross Y هتكون ال Z لجوه صح
+
+485
+00:37:35,790 --> 00:37:40,430
+كلامكم X cross Y هتعطينا اتجاه Z لو برضه ال E غلط
+
+486
+00:37:40,430 --> 00:37:45,330
+لأن X cross Y هتكون في هذا الاتجاه ال Z صح كلامكم
+
+487
+00:37:45,330 --> 00:37:50,050
+هي X cross Y هي X لفوق سكرتها على ال Y هيكون تجاه
+
+488
+00:37:50,050 --> 00:37:54,250
+ال Z لبرا ف B و E التنتين فيهم مشكلة مش
+
+489
+00:37:54,250 --> 00:37:55,710
+rectangular coordinate
+
+490
+00:37:59,150 --> 00:38:03,350
+هذا السؤال كل هذا طبعا تطبيقات لل vector analysis
+
+491
+00:38:03,350 --> 00:38:08,850
+عندنا جسم بيلف عمال و هذا جسم عند النط بيه و قاعد
+
+492
+00:38:08,850 --> 00:38:12,470
+بيلف طبعا ال rigid body يعني زي حجر حجر و قاعد
+
+493
+00:38:12,470 --> 00:38:16,770
+بيلف حوالين اللي هو المصار اللي انتوا شايفينه ب
+
+494
+00:38:16,770 --> 00:38:20,310
+angular velocity مقدرها omega radian per second
+
+495
+00:38:20,310 --> 00:38:25,890
+اتلف
+
+496
+00:38:25,890 --> 00:38:30,300
+حوالينهذا ال axis اللى بيقرق في ال origin zero زى
+
+497
+00:38:30,300 --> 00:38:34,040
+ما هو مضطح قدامنا في ال figure قولنا خلّينا نقول R
+
+498
+00:38:34,040 --> 00:38:38,060
+هي المسافة اللى هي distance vector من zero ل P
+
+499
+00:38:42,250 --> 00:38:46,050
+الواقع تبع اللي هو وضع ال particle يعني هذا ال
+
+500
+00:38:46,050 --> 00:38:48,350
+position vector ال position تبع ال P ماحنا عرفناش
+
+501
+00:38:48,350 --> 00:38:50,390
+معانا ال position vector انه انا لو عندي object
+
+502
+00:38:50,390 --> 00:38:53,630
+بتحدد مكانه بالنسبة لل origin ال distance between
+
+503
+00:38:53,630 --> 00:38:58,130
+two objects فال distance او ال position تبع ال P
+
+504
+00:38:58,130 --> 00:39:01,250
+بالنسبة لل origin هذا هو ال R هي عند ال origin
+
+505
+00:39:01,250 --> 00:39:06,030
+وهذا هو ال axis اللي بتلف حجر او ال object وR اللي
+
+506
+00:39:06,030 --> 00:39:08,330
+هي position vector تبع النقطة P
+
+507
+00:39:12,610 --> 00:39:15,310
+the velocity v of the body at B، ال velocity
+
+508
+00:39:15,310 --> 00:39:18,330
+تعرفها، يمكن أخدتها بالفيزيا، هي ال magnitude
+
+509
+00:39:18,330 --> 00:39:23,110
+تبعها D في Omega، اللي هي هذه المسافة D في قيمة
+
+510
+00:39:23,110 --> 00:39:28,590
+Omega أو عبارة عن R، magnitude، اللي هي D من هي R
+
+511
+00:39:28,590 --> 00:39:34,050
+في sin θ، صح؟Rsinθ في Omega اللى عبارة عن مين
+
+512
+00:39:34,050 --> 00:39:37,650
+Rsinθ Omega اللى هى المجنتى في ال magnitude لو
+
+513
+00:39:37,650 --> 00:39:41,290
+بتستعمل مجنتى تبع U هى المجنتى ل Omega cross R
+
+514
+00:39:41,290 --> 00:39:46,610
+بشكل عن ال velocity V او U هى عبارة عن Omega cross
+
+515
+00:39:46,610 --> 00:39:50,390
+R اذا ما كنتوا عارفش يعني فى ال physics فده هى
+
+516
+00:39:50,390 --> 00:39:55,200
+يعني U magnitude هى عبارة عنقيمة ال velocity هي D
+
+517
+00:39:55,200 --> 00:39:58,420
+في R في Omega وطبعا ال units كمان بتأكدكم ان هذا
+
+518
+00:39:58,420 --> 00:40:01,060
+الحاجة صحيح اللي هو العلاقة بين ال angular
+
+519
+00:40:01,060 --> 00:40:04,780
+velocity و ال linear velocity ال linear velocity U
+
+520
+00:40:04,780 --> 00:40:08,940
+اللي هي اللي عندكم نقطة بعضها بحسبها علاقتها بال
+
+521
+00:40:08,940 --> 00:40:12,880
+angular velocity اللي V بتساوي ال distance ما بين
+
+522
+00:40:12,880 --> 00:40:16,660
+ال object و ال axis اللي بيلوف حواليها مضروف في
+
+523
+00:40:16,660 --> 00:40:19,580
+قيمة اللي هي ال angular velocity ال distance دي
+
+524
+00:40:19,580 --> 00:40:23,230
+ايش اللي مستعدها؟ مترفي omega radian per second
+
+525
+00:40:23,230 --> 00:40:26,190
+فإيش هتكون unit meter per second اللي هي ال linear
+
+526
+00:40:26,190 --> 00:40:29,550
+velocity اذا V بتاسع لهذه اللي هي ال linear
+
+527
+00:40:29,550 --> 00:40:32,550
+velocity لل object بتاعة كل نقطة و ال omega اللي
+
+528
+00:40:32,550 --> 00:40:36,810
+هي ال radian velocity اذا بشكل عام اللي هي ال
+
+529
+00:40:36,810 --> 00:40:39,510
+linear velocity عبارة عن omega اللي هي ال angular
+
+530
+00:40:39,510 --> 00:40:42,210
+velocity crossed مع R ليه هاي ال R؟
+
+531
+00:40:46,280 --> 00:40:49,000
+بقول إذا كان الجسم بلف تلاتة radian per second
+
+532
+00:40:49,000 --> 00:40:52,880
+عطانا ال magneto تبع ال Omega هو about an axis
+
+533
+00:40:52,880 --> 00:40:58,120
+parallel to يعني عطاني انه بلف بأمجا مقدارها تلاتة
+
+534
+00:40:58,120 --> 00:41:03,860
+حوالين axis موازي ال axis او موازيلخط أو يعني ل ..
+
+535
+00:41:03,860 --> 00:41:09,560
+ل .. ل vector قيمته a x hat minus 2 a y hat زي 2 z
+
+536
+00:41:09,560 --> 00:41:13,320
+hat انا اللي مهمي بيعني الاتجاه ال Y يعني بتجيب ال
+
+537
+00:41:13,320 --> 00:41:16,240
+Y .. ال .. الاتجاه ال W ال vector تبع ال W
+
+538
+00:41:16,240 --> 00:41:20,120
+المجموعة تبعها و اتجاهها المجموعة التبعها أطانيها
+
+539
+00:41:20,120 --> 00:41:23,460
+3 radian per second اتجاهها هيكون موازية لاتجاه
+
+540
+00:41:23,460 --> 00:41:27,530
+الخط اللي أطانيهايعني بقدر اقول ان اتجاه ال
+
+541
+00:41:27,530 --> 00:41:31,390
+angular velocity هو ال vector هذا مقسم على ال
+
+542
+00:41:31,390 --> 00:41:37,030
+magnitude تبعه فبجيب ال omega vector صح؟معايا هو
+
+543
+00:41:37,030 --> 00:41:40,890
+اعطانى ال unit القيمة تاعت omega قيمتها تلاتة
+
+544
+00:41:40,890 --> 00:41:44,590
+radian per second واتجاهها موازن اتجاه ال axis
+
+545
+00:41:44,590 --> 00:41:47,990
+موازن هذا الاتجاه اذا انتجاه هو هيك فهذا اتجاه ال
+
+546
+00:41:47,990 --> 00:41:51,510
+axis لو بقول موازن ال x hat مشهور تجاهها ال x hat
+
+547
+00:41:51,510 --> 00:41:56,070
+فهو مواطن هذا ال vector هو ax hat minus 2ay hat زي
+
+548
+00:41:56,070 --> 00:42:00,450
+2az hat موازن اتجاه ال omegaعشان اجيب الاتجاه
+
+549
+00:42:00,450 --> 00:42:03,270
+ماقدرش استخدم vector بدي unit vector هيكون ال
+
+550
+00:42:03,270 --> 00:42:05,850
+vector علي مجنته بتبعه بتن اتجاه ال omega اذا ال
+
+551
+00:42:05,850 --> 00:42:09,250
+omega s بتاعها في كل بياناتها مقدارها تلاتة و
+
+552
+00:42:09,250 --> 00:42:12,330
+اتجاهها اللي هو هذا ال unit vector علي مجنته ..
+
+553
+00:42:12,330 --> 00:42:15,170
+هذا السواق متعفن اسفه هذا ال vector علي ال .. علي
+
+554
+00:42:15,170 --> 00:42:18,110
+المجنته بتبعه اللي هو ال unit vector في اتجاه هذا
+
+555
+00:42:18,110 --> 00:42:23,410
+ال axis عرفنا كل المعلومات علي omegaإذا ال object
+
+556
+00:42:23,410 --> 00:42:27,390
+هذا بلوف على نقطة تلاتة radian per second موازق
+
+557
+00:42:27,390 --> 00:42:31,410
+لهذا ال access and passing through a point ال
+
+558
+00:42:31,410 --> 00:42:35,470
+object .. ال .. ال .. ال access هذا passing ال
+
+559
+00:42:35,470 --> 00:42:38,950
+access اللي هو يعطينا موازق له passing through هذه
+
+560
+00:42:38,950 --> 00:42:42,670
+النقطة اللي هي اتنين ومانثلثة وواحد determine ال
+
+561
+00:42:42,670 --> 00:42:46,350
+velocity عند هذه النقطة إيش لازمني أنا عشان أجيب
+
+562
+00:42:46,350 --> 00:42:49,510
+ال velocity قلنا omega cross r omega ويعرفنا كل
+
+563
+00:42:49,510 --> 00:42:54,210
+بياناتهابضل على اليمين R بدي أجيب ال R R هي عبارة
+
+564
+00:42:54,210 --> 00:42:58,210
+عن مين ال position ما بين النقطة B و ال zero فإذا
+
+565
+00:42:58,210 --> 00:43:03,890
+Rش هتكون B minus O بي إحنا عارفينها و عارفين ال O
+
+566
+00:43:03,890 --> 00:43:07,310
+فبجيب ال R و أقعد طول بعمل ال plus product بجيب ال
+
+567
+00:43:07,310 --> 00:43:10,590
+velocity واضح؟ إذا أنا هيدا تفتيق مباشرة برضه وين
+
+568
+00:43:10,590 --> 00:43:14,400
+أنا بستخدم ال plus productأحنا شوفنا كذا مثال لحد
+
+569
+00:43:14,400 --> 00:43:17,120
+اللي هي طويل فانحتاج الـ spectral analysis وكيف
+
+570
+00:43:17,120 --> 00:43:20,140
+ممكن أستعين في تطبيق له استخدمناه في الجبرا
+
+571
+00:43:20,140 --> 00:43:24,760
+واستخدمناه هنا في ال rigid body rotation اذا خلنا
+
+572
+00:43:24,760 --> 00:43:28,620
+نشوف اللي حكيناه حكيته شفاهي أول حاجة بتاع المطيني
+
+573
+00:43:28,620 --> 00:43:31,220
+omega اللي هي المجنون تبعها هي ال direction تبعها
+
+574
+00:43:32,150 --> 00:43:35,130
+أذا بقدر أقول إن الـ ω vector هي ال magnitude
+
+575
+00:43:35,130 --> 00:43:38,610
+تبعها في اللي هو ال direction اللي هي ω تبعه
+
+576
+00:43:38,610 --> 00:43:41,910
+بتلاتة ال magnitude تبعه بالصفة برضه بتطلع بتلاتة
+
+577
+00:43:41,910 --> 00:43:45,990
+لإن جزر ال 1 زي 4 زي 4 تسعة بتروح التلاتة مع
+
+578
+00:43:45,990 --> 00:43:47,890
+التلاتة بتبقى اللي هي 1 من السان على السان هاي
+
+579
+00:43:47,890 --> 00:43:51,310
+جيبنا ال ω دل عليها أجيب ال R اللي هي RB منصة R0
+
+580
+00:43:51,310 --> 00:43:56,450
+هاي جيبنا ال R فال polystylene هي ω cross R وجيبنا
+
+581
+00:43:56,450 --> 00:44:00,890
+ال polystyleneهك احنا خلصنا الجزء الاول من اللى هو
+
+582
+00:44:00,890 --> 00:44:06,810
+ال vector analysis فى اي استفسار بس احنا بدنا
+
+583
+00:44:06,810 --> 00:44:10,130
+ياكوا ترجعولنا المعلومات اللى أخدناها زى ما شفنا
+
+584
+00:44:10,130 --> 00:44:13,670
+احنا شفنا مفتقاطه فى ال vector analysis شفنا كمان
+
+585
+00:44:13,670 --> 00:44:17,370
+فى rigid body rotation وقبل هيك شفنا relative
+
+586
+00:44:17,370 --> 00:44:21,650
+velocity في المحاضرة الماضية شفنا مثال اللى هو كيف
+
+587
+00:44:21,650 --> 00:44:24,690
+حساب relative velocity باستعانة فى اللى هو ال
+
+588
+00:44:24,690 --> 00:44:24,890
+vectors
+
+589
+00:44:38,820 --> 00:44:43,040
+الشبطر التاني هيميزنا بين ال coordinates احنا لحد
+
+590
+00:44:43,040 --> 00:44:45,060
+دلوقت هبنحكي عن ال Cartesian coordinates اذا انتم
+
+591
+00:44:45,060 --> 00:44:49,320
+متبهين هبنحكي عن X Y Z اللي قال قادم هنشوف برضه ال
+
+592
+00:44:51,850 --> 00:44:54,710
+الـ cylindrical coordinate يعني هنتعرف على ال
+
+593
+00:44:54,710 --> 00:44:57,890
+coordinates البقية و كيف انا انقل من ال Cartesian
+
+594
+00:44:57,890 --> 00:45:01,510
+coordinate ل ال spherical coordinate و لعكس و كيف
+
+595
+00:45:01,510 --> 00:45:03,830
+انقل برضه من ال Cartesian ل ال cylindrical و لعكس
+
+596
+00:45:03,830 --> 00:45:06,530
+او من spherical ل cylindrical و cylindrical ل
+
+597
+00:45:06,530 --> 00:45:08,390
+spherical ان شاء الله
+
diff --git a/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/rVD36L-6n9Y_postprocess.srt b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/rVD36L-6n9Y_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..39a1a5410626bc11f3d7cdfbe9c48a2803cee183
--- /dev/null
+++ b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/rVD36L-6n9Y_postprocess.srt
@@ -0,0 +1,1816 @@
+1
+00:00:20,790 --> 00:00:23,050
+بسم الله الرحمن الرحيم السلام عليكم ورحمة الله
+
+2
+00:00:23,050 --> 00:00:25,850
+وبركاته احنا اليوم ان شاء الله هنفضله chapter two
+
+3
+00:00:25,850 --> 00:00:29,430
+اللي بيحكي عن أنواع ال coordinate system احنا ال
+
+4
+00:00:29,430 --> 00:00:31,770
+chapter الأول بس شفنا ال Cartesian coordinate اللي
+
+5
+00:00:31,770 --> 00:00:35,370
+هو ال XYZ أو بيسموه rectangular coordinate ان شاء
+
+6
+00:00:35,370 --> 00:00:37,570
+الله هنشوف احنا ال coordinate الشديدة اللي هي ال
+
+7
+00:00:37,570 --> 00:00:40,310
+spherical و الcylindrical ونشوف كيف تحويل من
+
+8
+00:00:40,310 --> 00:00:43,570
+coordinate ل coordinate تاني بس قبل ما نبدأ بدي
+
+9
+00:00:43,570 --> 00:00:46,250
+اسألكوا سؤال رولاقة في ال chapter الماضي
+
+10
+00:00:49,970 --> 00:00:58,570
+زي هي كتبت مش ال quiz عشان نشوف معايا ايه الطولة
+
+11
+00:00:58,570 --> 00:01:05,150
+دلوقت اثبتت ان انا cross ال 2
+
+12
+00:01:19,380 --> 00:01:29,340
+ده ال C cross A cross B سواء على
+
+13
+00:01:29,340 --> 00:01:42,580
+السريع هذا
+
+14
+00:01:42,580 --> 00:01:45,420
+أخر issue هنا المحاضرة الماضية المفروض يكون لسه
+
+15
+00:01:45,420 --> 00:01:46,320
+علق في ذهنكم
+
+16
+00:02:02,890 --> 00:02:04,830
+حلصت؟ متفضل
+
+17
+00:02:34,220 --> 00:02:40,360
+كيف اعرفت ان P X C P X L كيف
+
+18
+00:02:40,360 --> 00:02:40,880
+اعرفت ان P X C P L كيف اعرفت ان P X C P L كيف
+
+19
+00:02:40,880 --> 00:02:41,140
+اعرفت ان P X C P L كيف اعرفت ان P X C P L كيف
+
+20
+00:02:41,140 --> 00:02:41,740
+اعرفت ان P X C P L كيف اعرفت ان P X C P L كيف
+
+21
+00:02:41,740 --> 00:02:42,360
+اعرفت ان P X C P L كيف اعرفت ان P X C P L كيف
+
+22
+00:02:42,360 --> 00:02:46,260
+اعرفت ان P X C P L كيف اعرفت ان P X C P L كيف
+
+23
+00:02:46,260 --> 00:02:50,960
+اعرفت ان P X C P L كيف اعرفت ان P X C P L كيف
+
+24
+00:02:50,960 --> 00:02:57,300
+اعرفت ان P X C P L كيف اعرفت ان P X C P L كيف
+
+25
+00:02:57,300 --> 00:03:03,310
+اعرفت ان P X C P L كيف اعرفت انأنا هى قصدي عمودي
+
+26
+00:03:03,310 --> 00:03:08,270
+صح كلامك ممتازة لإن ليش هو A مش D ولا F أنا أعطيتك
+
+27
+00:03:08,270 --> 00:03:11,670
+معلومة بتقول بيكورسي بيساوي A لأ بس احنا أخدنا
+
+28
+00:03:11,670 --> 00:03:15,090
+معلومة ان اي دي اي .. two vectors بتطلع من كتر
+
+29
+00:03:15,090 --> 00:03:18,530
+عمودة اه دي و هى ايه ايه تسمي التجارب ايه تسمي
+
+30
+00:03:18,530 --> 00:03:24,350
+التجارب عمودة هل
+
+31
+00:03:24,350 --> 00:03:27,850
+أنا قولت ان عمودي على ال vector بتطلع من بيكورسي
+
+32
+00:03:29,110 --> 00:03:33,410
+إذا فينا two vectors B وC cross product تطلع بكتر
+
+33
+00:03:33,410 --> 00:03:39,650
+عمودي عليهم صحيح أنا دولة على plan B cross C تطلع
+
+34
+00:03:39,650 --> 00:03:43,470
+لنا واحد عمودي عليهم بس هل هذا العمودي عليهم مش
+
+35
+00:03:43,470 --> 00:03:48,790
+بينه زي و بين إيه نعرف إنش ممكن يكون و لأ أول حاجة
+
+36
+00:03:48,790 --> 00:03:52,590
+بعرفش إن ال cross product تبعهم هو إيه ولا بعرف
+
+37
+00:03:52,590 --> 00:03:56,890
+إنه الناتج تبعهم اللي هو عمودي عليهم برضه في اتجاه
+
+38
+00:03:56,890 --> 00:04:00,670
+إيههذه المعلومات ماعرفتاش، لكن دي معلومات احنا
+
+39
+00:04:00,670 --> 00:04:04,990
+أخدناها عن ال triple cross product و لا لأ، إيش
+
+40
+00:04:04,990 --> 00:04:08,570
+كانت؟ أعلمتكوا إياها؟ إيش هي كانت ال .. ال .. ال
+
+41
+00:04:08,570 --> 00:04:13,610
+slogan اللي بنتعلمها أو نحكيها؟ مين قارب الحرب؟ مش
+
+42
+00:04:13,610 --> 00:04:18,870
+مشكلة، بس ساعتك خلاص احنا قولنا backup، تتذكرينها
+
+43
+00:04:18,870 --> 00:04:21,910
+و لا لأ؟ backup، يلا و عملنا backup
+
+44
+00:04:33,130 --> 00:04:37,730
+الشكل اللي اعطيتكم اليه هو a cross b cross c بعبر
+
+45
+00:04:37,730 --> 00:04:42,650
+عنه back cap ايه عمل الهاتف هنا ايه كله في عنده
+
+46
+00:04:42,650 --> 00:04:50,790
+gene vector مضروبة
+
+47
+00:04:50,790 --> 00:04:52,710
+في a dot c
+
+48
+00:05:05,500 --> 00:05:12,400
+بنفتح ال bus وهو A على
+
+49
+00:05:12,400 --> 00:05:16,400
+غراره بدنا نعمل هذه بس نساط بدنا نخيل أن هذا ال A
+
+50
+00:05:16,400 --> 00:05:19,100
+وهذا ال B وC
+
+51
+00:05:23,440 --> 00:05:26,900
+يعني الـA هي هنا لما كان عند التاني هو اللي طلع
+
+52
+00:05:26,900 --> 00:05:32,560
+يعني هنا الـC بحيث بقى الـC ومين بحيث انهم الـdot
+
+53
+00:05:32,560 --> 00:05:41,200
+product اللي هو الأول والتالت B dot A minus S على
+
+54
+00:05:41,200 --> 00:05:46,740
+تلك اللي هو التالت اللي هو التالت اللي هو الـA فين
+
+55
+00:05:46,740 --> 00:05:52,580
+اللي هو مين الـA اللي هو B عندنا dot L هي عندنا C
+
+56
+00:06:00,590 --> 00:06:13,590
+ممتازة ممتازة ماينوس ممتازة
+
+57
+00:06:13,590 --> 00:06:15,770
+ماينوس ماينوس ماينوس ماينوس ماينوس ماينوس ماينوس
+
+58
+00:06:15,770 --> 00:06:16,070
+ماينوس ماينوس ماينوس ماينوس ماينوس ماينوس ماينوس
+
+59
+00:06:16,070 --> 00:06:16,090
+ماينوس ماينوس ماينوس ماينوس ماينوس ماينوس ماينوس
+
+60
+00:06:16,090 --> 00:06:22,610
+ماينوس ماينوس ماينوس ماينوس ماينوس
+
+61
+00:06:22,610 --> 00:06:28,600
+ماينA.B هي نفسها B.A فعندى هذا ال term و term
+
+62
+00:06:28,600 --> 00:06:32,480
+الأخير اللى طلعنا عليهم متشابهان هيروحوا مع بعضهم
+
+63
+00:06:32,480 --> 00:06:37,300
+تحت سطحهم عشان يمتشابهان فهنا فى عندى اللى هو A.B
+
+64
+00:06:37,300 --> 00:06:42,480
+و A.B هنا فى عندى minus و عندى plus هذا ال term و
+
+65
+00:06:42,480 --> 00:06:45,760
+هذا ال term فالنص العظيم احنا قولنا dot ال product
+
+66
+00:06:45,760 --> 00:06:50,370
+مع لهبقدر اعمله انه associated علي A ب B بيساوي B
+
+67
+00:06:50,370 --> 00:06:55,710
+بC و هدا كي بروحوا مع بعض فاسد اش ناتج بيساوي C
+
+68
+00:06:55,710 --> 00:07:00,330
+واضح اولا ان احنا مش لازم نحفظ ان A cross B
+
+69
+00:07:00,330 --> 00:07:05,070
+بتعطينا C و B cross C بتعطينا A هدا مجرد احنا
+
+70
+00:07:05,070 --> 00:07:10,090
+للشرح بستخدمهم رموز لكن B cross C يمكن يكون اي
+
+71
+00:07:10,090 --> 00:07:11,190
+vector واضح
+
+72
+00:07:17,850 --> 00:07:25,750
+عشان تنتبهوا لهذه النقطة يعني اولا
+
+73
+00:07:25,750 --> 00:07:30,450
+كان عندى فيه vector a وعارفة ال vector b و vector
+
+74
+00:07:30,450 --> 00:07:34,790
+c وانطلب منى اجيب ال volume اللى هدولة vectors
+
+75
+00:07:34,790 --> 00:07:39,010
+بيحصرونه ايش ده يكون ال vector ال volume ال volume
+
+76
+00:07:39,010 --> 00:07:43,390
+ل object اللى هدولة تلاتة vectors بيحصرونه ايش
+
+77
+00:07:43,390 --> 00:07:53,240
+هيكون هذا ال volumeماذا سيكون ال volume؟ اذا
+
+78
+00:07:53,240 --> 00:07:58,460
+أخذت كورس ال product لأتنين، المدنيتر تبعهم
+
+79
+00:07:58,460 --> 00:08:03,540
+سيعطينا ال area موجودة مع ال B ويعطينا ال volume
+
+80
+00:08:03,540 --> 00:08:07,260
+فال product ال triple هو A dot B cross C سيعطينا
+
+81
+00:08:07,260 --> 00:08:08,080
+ال volume
+
+82
+00:08:16,140 --> 00:08:20,860
+هذا طبعا هو scalar لإن بي كرو سي هيعطينا vector ال
+
+83
+00:08:20,860 --> 00:08:24,480
+vector puted مع ال a هيعطينا scalar quantity اللي
+
+84
+00:08:24,480 --> 00:08:28,280
+هي ال volume تبع متواز الأضلاع اللي بيحصروها دولة
+
+85
+00:08:28,280 --> 00:08:33,300
+التلاتة vector واضح؟
+
+86
+00:08:33,300 --> 00:08:39,060
+مش
+
+87
+00:08:39,060 --> 00:08:42,100
+كمان شيء اندراجا فيها المعلومات السابقة
+
+88
+00:08:44,730 --> 00:08:47,950
+واخدنا احنا اللي هي مساحة المثلث المحاضرة الماضية
+
+89
+00:08:47,950 --> 00:08:50,730
+اللي هو نص ال a dot b مثلا اللي هو ال two vectors
+
+90
+00:08:50,730 --> 00:08:54,570
+المصدر القاعدة
+
+91
+00:08:54,570 --> 00:08:58,010
+نيجي لها المحاضرة اليوم اللي هو ال coordinate
+
+92
+00:08:58,010 --> 00:09:01,390
+system إذا واضحة فيها الأمور هلأ إذا إن هو إنها
+
+93
+00:09:01,390 --> 00:09:04,290
+تشتبع وإنفعن نيجي لها
+
+94
+00:09:14,530 --> 00:09:22,490
+الحلقة اليوم سوف نتكلم عن ال coordinates نبدأ
+
+95
+00:09:22,490 --> 00:09:25,370
+بتذكير أن هنا فينا three types of coordinate
+
+96
+00:09:25,370 --> 00:09:29,330
+system N القارتيجين او rectangular coordinate اللي
+
+97
+00:09:29,330 --> 00:09:38,470
+هو احنا بمثله بال X Y Z X Y Z اكتر عنهم ال heart
+
+98
+00:09:38,470 --> 00:09:43,220
+هذا في جهة ان هو كل واحد منهمعشان احنا اتفانى احنا
+
+99
+00:09:43,220 --> 00:09:46,580
+بحط اكس هات على طول او اي اكس زي اكتر اي برضه
+
+100
+00:09:46,580 --> 00:09:53,640
+عليها هات تمام او انه الcircular coordinate
+
+101
+00:09:53,640 --> 00:09:56,580
+الcircular اللى هو نفسه ال cylindrical coordinate
+
+102
+00:09:56,580 --> 00:09:58,940
+الcircular cylindrical coordinate يعني باختصار
+
+103
+00:09:58,940 --> 00:10:02,620
+نقدر نقول cylindrical coordinate بيكون القاعدة على
+
+104
+00:10:02,620 --> 00:10:07,440
+شكل دائرة وله اتجاه طويل غالبا بتحطه على ال z axis
+
+105
+00:10:07,440 --> 00:10:13,570
+فانه kind of a partition هو ال XYZالسفريكال
+
+106
+00:10:13,570 --> 00:10:18,610
+كواردنات الراو
+
+107
+00:10:18,610 --> 00:10:26,370
+و الفاي و السفريكال
+
+108
+00:10:26,370 --> 00:10:29,910
+كواردنات
+
+109
+00:10:29,910 --> 00:10:39,150
+السفريكال كواردنات سفير الار الراديوس الذاوية
+
+110
+00:10:39,150 --> 00:10:44,210
+الفاي و الذاوية الفيتربتمثل هذا ال coordinate اذا
+
+111
+00:10:44,210 --> 00:10:48,350
+نحكي عن Cartesian بنحكي عن XYZ عن cylindrical
+
+112
+00:10:48,350 --> 00:10:53,930
+بنحكي عن رو فاي زد أسفريكال بحكي R ثتا فاي هدول ال
+
+113
+00:10:53,930 --> 00:10:56,410
+system نسميهم orthogonal systems ليش orthogonal
+
+114
+00:10:56,410 --> 00:11:00,290
+systems هدول اللي غصب عنهم لازم بحكي عن Y بيكون في
+
+115
+00:11:00,290 --> 00:11:04,190
+عند Z orthogonal يعني هدول ال coordinate التلاتة
+
+116
+00:11:04,190 --> 00:11:07,270
+متعاملين على بعض يعني ال X و ال Y متعاملين على Z
+
+117
+00:11:07,270 --> 00:11:12,350
+ال رو و ال Z متعاملين على بعضهنا الـR عمودية في ما
+
+118
+00:11:12,350 --> 00:11:17,290
+هو الـ system هنا x,y,z هو الأساس و الـR هي عبارة
+
+119
+00:11:17,290 --> 00:11:21,930
+عن ال vector بيسميه ال radius لدى ال system اذا ال
+
+120
+00:11:21,930 --> 00:11:25,090
+Cartesian coordinate لأنهم دايما بيكونوا متشوه
+
+121
+00:11:25,090 --> 00:11:29,290
+لبربندوكي العالم ابدا
+
+122
+00:11:29,290 --> 00:11:32,430
+بال Cartesian coordinate زي الرسم اللي انا اقسمته
+
+123
+00:11:41,270 --> 00:11:45,670
+عشان أقلب قليل الـ Center بس هنا نشوف المنظر أكثر
+
+124
+00:11:45,670 --> 00:11:50,710
+ألواناً فينا ال Cartesian coordinate اللي هي ال X
+
+125
+00:11:50,710 --> 00:11:54,450
+Y Z احنا قولنا فينا component في اتجاه ال X و بقى
+
+126
+00:11:54,450 --> 00:11:56,690
+في اتجاه ال Y ممكنش بداها ال Z قولنا ماهو اللي و
+
+127
+00:11:56,690 --> 00:12:00,290
+ده بيكون ايه عشان orthogonal يعني ال X عمودي على
+
+128
+00:12:00,290 --> 00:12:04,950
+ال Y و ال Y عمودي على ال Z ax hat dot ax hat
+
+129
+00:12:04,950 --> 00:12:08,990
+تعطينا واحد اكت ax hat dot ay hat إيش بتساوي؟ سفر
+
+130
+00:12:08,990 --> 00:12:13,740
+خدنا المحاضرة الماضيةنجلع اي vector position في
+
+131
+00:12:13,740 --> 00:12:16,680
+هذا ال system احنا قلنا ايش ال position بحدد لموضع
+
+132
+00:12:16,680 --> 00:12:20,260
+object في النظام انا مثلا نفترض اني عندى نقطة هنا
+
+133
+00:12:20,260 --> 00:12:22,360
+و بدى اجيب ال position تبعها هنا ال vector ايه
+
+134
+00:12:22,360 --> 00:12:25,740
+بمثله ال position vector بين ال origin و بين
+
+135
+00:12:25,740 --> 00:12:32,020
+النقطة في ال space هذه لها three components واحدة
+
+136
+00:12:32,020 --> 00:12:35,780
+في اتجاه ال X واحدة في اتجاه ال Y واحدة في اتجاه
+
+137
+00:12:35,780 --> 00:12:42,880
+ال Zاسقب أول حاجة لهذه ال coordinate هيكون واحد في
+
+138
+00:12:42,880 --> 00:12:46,200
+ال XY plane والتاني وانت تجهز في هذه ال components
+
+139
+00:12:46,200 --> 00:12:51,680
+بتاعك بAZZ hat والتاني اللي سقطت في ال XY اللي هي
+
+140
+00:12:51,680 --> 00:12:57,200
+لها two components واحدة AXX hat والتانية AYY hat
+
+141
+00:12:57,450 --> 00:13:01,430
+أذا هذا هو ال vector تبعي هاي ال X component هاي
+
+142
+00:13:01,430 --> 00:13:04,770
+ال Y component وهي ال Z component اللي هو الجمع
+
+143
+00:13:04,770 --> 00:13:09,250
+هيكون هذا هو ال vector تبعي مجموعة AX ساقات AY
+
+144
+00:13:09,250 --> 00:13:13,510
+ساقات AZ تمام شوفنا برضه المحاضرة الماضية جمال
+
+145
+00:13:19,650 --> 00:13:22,790
+الـ X coordinate بروح minus infinity ل plus
+
+146
+00:13:22,790 --> 00:13:26,170
+infinity ال Y coordinate بروح minus infinity ل
+
+147
+00:13:26,170 --> 00:13:29,670
+plus infinity ال Z بروح minus infinity ل plus
+
+148
+00:13:29,670 --> 00:13:34,350
+infinity عشان أعبر عن أي vector A في ال Cartesian
+
+149
+00:13:34,350 --> 00:13:41,270
+يا بالأقواص هذه بقول A vector بساوي
+
+150
+00:13:41,270 --> 00:13:46,130
+فدي معناها ال X component فال Y component وهي Z
+
+151
+00:13:46,130 --> 00:13:53,650
+component بتساويهذا الشكل يعني
+
+152
+00:13:53,650 --> 00:13:57,730
+يا بكتبها في هذا الشكل يا بالشكل التاني معناه هذا
+
+153
+00:13:57,730 --> 00:14:01,930
+ال vector تبعي
+
+154
+00:14:01,930 --> 00:14:06,510
+هدول احنا اتفقنا ان x hat و y hat و z hat هم ال
+
+155
+00:14:06,510 --> 00:14:09,570
+unit vectors في كل اتجاه من الاتجاهات التلاتة نجي
+
+156
+00:14:09,570 --> 00:14:11,210
+ل ال cylindrical coordinate ال cylindrical
+
+157
+00:14:11,210 --> 00:14:15,490
+coordinate يعني ال raw ال raw تيجي من zero ل
+
+158
+00:14:15,490 --> 00:14:21,790
+infinityمن zero ل infinity روه تتمجلها من zero ل
+
+159
+00:14:21,790 --> 00:14:26,710
+infinity فاى اللى هى الزاوية فاى من zero ل two pi
+
+160
+00:14:26,710 --> 00:14:30,450
+تقلق حوالين الدائرة and روه تروح من zero ل
+
+161
+00:14:30,450 --> 00:14:37,770
+infinity فاى اللى هى الزاوية ما بين ال x axis و ال
+
+162
+00:14:37,770 --> 00:14:42,920
+روه تجاه ال روه في حقيقة فاىإذا ال raw فاى بتروح
+
+163
+00:14:42,920 --> 00:14:47,300
+من zero لحد two pi ننتبه ان هي ما بين ال x axis و
+
+164
+00:14:47,300 --> 00:14:51,780
+ال rawز من minus infinity ل plus infinity يعني
+
+165
+00:14:51,780 --> 00:14:55,280
+السيلندر بتاعتي بتغطي ال space كله زي ما ال XY
+
+166
+00:14:55,280 --> 00:14:58,320
+بيغطي ال space كله لأن X بتروح من minus infinity ل
+
+167
+00:14:58,320 --> 00:15:00,940
+plus infinity و Y من minus infinity ل plus
+
+168
+00:15:00,940 --> 00:15:02,980
+infinity و Z من minus infinity ل plus infinity
+
+169
+00:15:02,980 --> 00:15:06,140
+هتغطي كل space نفس القضية السيلندر تاعت لما أقول
+
+170
+00:15:06,140 --> 00:15:10,480
+ال row بتروح من zero ل infinity و بتلف two pi و
+
+171
+00:15:10,480 --> 00:15:12,740
+بتروح من minus infinity ل plus infinity اذا برضه
+
+172
+00:15:12,740 --> 00:15:14,040
+غطت كل space
+
+173
+00:15:17,780 --> 00:15:19,460
+نفس الحاجة الـ vector في الـ cylindrical
+
+174
+00:15:19,460 --> 00:15:21,980
+coordinate بتعبّر عنه يا بشكل اللي هو ال
+
+175
+00:15:21,980 --> 00:15:25,820
+parentheses اللي هي row hat phi hat z hat يعني دي
+
+176
+00:15:25,820 --> 00:15:30,500
+ال a vector بتساوي a row a phi a z أو a row row
+
+177
+00:15:30,500 --> 00:15:37,020
+hat زغط a phi phi hat زغط a z z hat طبعا
+
+178
+00:15:37,020 --> 00:15:39,120
+احنا مجموعة طبعا ال vector في ال Cartesian
+
+179
+00:15:39,120 --> 00:15:41,940
+coordinate أخدناها من الحاضر الماضي وانقش اي
+
+180
+00:15:41,940 --> 00:15:44,940
+مجموعة .. اي مجموعة يبدأ اي vector انقش بالساعة
+
+181
+00:15:44,940 --> 00:15:50,870
+المجموعة يقول square rootلـ A Dot A فالـ Cartesian
+
+182
+00:15:50,870 --> 00:15:55,710
+Coordinate هيكون الجزر التربيهي AX تربيه زي الـ AY
+
+183
+00:15:55,710 --> 00:15:59,210
+تربيه زي الـAZ تربيه هذا الـ magnitude تبقى الـ
+
+184
+00:15:59,210 --> 00:16:03,550
+vector في الـ Cartesian Coordinate نجي للـ
+
+185
+00:16:03,550 --> 00:16:05,930
+cylindrical coordinate لإن هو موضوع جديد علينا
+
+186
+00:16:05,930 --> 00:16:09,690
+هيكون ال magnitude مش بيساوي
+
+187
+00:16:15,800 --> 00:16:19,700
+الـ magnitude هيكون الجزر التربيعي ل a dot a في
+
+188
+00:16:19,700 --> 00:16:23,540
+هذه الحلقة مش هيطلع لنا a rho تربيع زي ال a في
+
+189
+00:16:23,540 --> 00:16:27,220
+تربيع زي ال a زي التربيع لإن ال unit vectors هدولة
+
+190
+00:16:27,220 --> 00:16:31,280
+فقط a rho dot a rho بيعطينا واحد لكن a rho dot a
+
+191
+00:16:31,280 --> 00:16:32,720
+five بيعطينا أسفل لإن هم orthogonal
+
+192
+00:16:53,990 --> 00:16:58,710
+أي واحدة من الـ cross product أو cross termsالـ
+
+193
+00:16:58,710 --> 00:17:02,550
+cross terms لأن ال product a dot a ممكن تكون في
+
+194
+00:17:02,550 --> 00:17:06,710
+عند a رو رو هات dot مع a فاي فاي هات هتعطيني سفر
+
+195
+00:17:06,710 --> 00:17:10,030
+لإيش لأن ال رو هات و الفاي هات مالهم orthogonal
+
+196
+00:17:10,030 --> 00:17:13,370
+هتعطيني زرع كمان برضه بناخد اللي هي العلاقة
+
+197
+00:17:13,370 --> 00:17:20,490
+الدائرية اللي هي ال cross product رو هات فاي هات و
+
+198
+00:17:20,490 --> 00:17:23,950
+زد هات فانا أجعل ال cross product رو هات cross فاي
+
+199
+00:17:23,950 --> 00:17:24,950
+هتعطيني زد هات
+
+200
+00:17:32,820 --> 00:17:36,860
+عشان اي issue في اتجاه المعاكس هيكون قدام اشارة
+
+201
+00:17:36,860 --> 00:17:37,340
+سالبة
+
+202
+00:17:42,330 --> 00:17:45,210
+العلاقة بين ال Cartesian و ال cylindrical هذا مهم
+
+203
+00:17:45,210 --> 00:17:47,430
+كتير لي أعرف كيف أروح من ال Cartesian ل ال
+
+204
+00:17:47,430 --> 00:17:50,470
+cylindrical و ال cylindrical ل ال Cartesian هذه كم
+
+205
+00:17:50,470 --> 00:17:54,990
+مرة النقطة في ال space اللي هي بتمثلني مكانها
+
+206
+00:17:54,990 --> 00:17:57,450
+أسواق بقدر أعبر عنه بال Cartesian أو ال
+
+207
+00:17:57,450 --> 00:17:58,050
+cylindrical
+
+208
+00:18:03,040 --> 00:18:05,740
+بقدر أعبر عنه أسوأ بالـ Cartesian أو بالـ
+
+209
+00:18:05,740 --> 00:18:08,600
+Cylindrical التاني لازم يعطوه نفس المفهوم لأن
+
+210
+00:18:08,600 --> 00:18:12,460
+الموضوع لاتغيرش لها المقطة هنا هي الطبة بتاعته ده
+
+211
+00:18:12,460 --> 00:18:16,120
+عقوم البشر تبعها أسوأ أعبرت عنه بالـ Cartesian أو
+
+212
+00:18:16,120 --> 00:18:19,260
+بالـ Cylindrical لازم يخلف الموضوع لازم يكون نفس
+
+213
+00:18:19,260 --> 00:18:23,180
+الأشياء بس هنا هدفة عشان نشوف شغلها قابل ال XYZ و
+
+214
+00:18:23,180 --> 00:18:27,300
+ال Raw و الYZ اذا أي موضوع لنقطة بقدر أعبر عنه كده
+
+215
+00:18:27,300 --> 00:18:30,000
+بقدر أعبر عنه بالـ Cepherical و لازم يكون نفس
+
+216
+00:18:30,000 --> 00:18:34,840
+الأشياء فمش لازم نرتبطنجلال كارتيجين الموضوع عبارة
+
+217
+00:18:34,840 --> 00:18:38,500
+عن x component زي ال y component زي ال z component
+
+218
+00:18:38,500 --> 00:18:44,340
+نجلال الفائز سلندريكال السلندريكال هو الراو و
+
+219
+00:18:44,340 --> 00:18:48,980
+الفايد يتحددوا الزاوية فايد ما بين ال x و الراو و
+
+220
+00:18:48,980 --> 00:18:54,090
+ال z componentهالبسشن أول حاجة بعمله two
+
+221
+00:18:54,090 --> 00:18:57,530
+components واحدة في ال x y plan اللي هسميها ال raw
+
+222
+00:18:57,530 --> 00:19:01,450
+والتانية في ال z plan اللي هي z ضلت اذا ان ال z
+
+223
+00:19:01,450 --> 00:19:04,630
+ضلت زي ما هي يعني بال component اللي هي z ضلت زي
+
+224
+00:19:04,630 --> 00:19:08,890
+ما هي ال raw بقدر ايش أسوي فيه اعطيه two
+
+225
+00:19:08,890 --> 00:19:12,430
+components واحدة في ال x direction وفحدة في ال y
+
+226
+00:19:12,430 --> 00:19:16,910
+direction في ال x direction وفي ال y direction فهي
+
+227
+00:19:16,910 --> 00:19:21,600
+ال components عمها ال x زائد ال yإذاً ال raw عبارة
+
+228
+00:19:21,600 --> 00:19:26,880
+عن x و y هي ال raw vector عبارة عن مجموع x x hat و
+
+229
+00:19:26,880 --> 00:19:30,860
+y y hat فإذا ما بالتالي ال magnitude تبع ال raw
+
+230
+00:19:30,860 --> 00:19:35,560
+إيش هيكون الجزر التربيه ل x x hat أيوة x تربيه زاد
+
+231
+00:19:35,560 --> 00:19:40,280
+y تربيه تمام شكرا إذاً ال raw هو عبارة عن ال
+
+232
+00:19:40,280 --> 00:19:45,940
+radius تبع الدائرة اللي تمثل القاعدة بتاعة
+
+233
+00:19:45,940 --> 00:19:51,450
+السيلينغادائرة مش احنا بقول R تبع الدائرة R تربيه
+
+234
+00:19:51,450 --> 00:19:54,290
+هو عبارة عن X تربيه زي Y تربيه التمام اللي ماتو
+
+235
+00:19:54,290 --> 00:19:57,870
+شايفينه اذا ال raw تربيه او روه هو جزر تربيه ل X
+
+236
+00:19:57,870 --> 00:20:00,430
+تربيه زي Y تربيه او من الرسم اللي احنا شايفين
+
+237
+00:20:00,430 --> 00:20:04,030
+متأكدين ان ال raw هي عبارة عن raw vector هي عبارة
+
+238
+00:20:04,030 --> 00:20:09,930
+عن X X hat زي Y Y hat تمام اذا ال raw البساطة هي
+
+239
+00:20:09,930 --> 00:20:13,110
+عبارة عن جزر تربيه ل X تربيه زي Y تربيه نجي لل Phi
+
+240
+00:20:13,110 --> 00:20:16,730
+ال Phi قلنا هي عبارة عن الزاوية المابين ال X axis
+
+241
+00:20:16,730 --> 00:20:21,460
+و ال rawايش الزاوية هاي بتكون فيها إن هي ال X و هي
+
+242
+00:20:21,460 --> 00:20:24,220
+ال Y و هم متعمدين هم مانساش إن هم متعمدين ال X و
+
+243
+00:20:24,220 --> 00:20:29,000
+ال Y ال X و ال Y متعمدين بقدر أقول إن هى عبارة عن
+
+244
+00:20:29,000 --> 00:20:33,760
+هذا الوطر فال X و هى ال Y هي ما لها هى المقابل و
+
+245
+00:20:33,760 --> 00:20:38,020
+هى المجاور فهتكون tan inverse Y على X لإن التاني
+
+246
+00:20:38,020 --> 00:20:45,140
+الفائش هيكون Y على X إذا فهي tan inverse Y على X و
+
+247
+00:20:45,140 --> 00:20:47,840
+Z احنا اتفقنا إن هي نفس ال components الاسواق في
+
+248
+00:20:47,840 --> 00:20:51,030
+ال Xcoordinate x,y,z coordinate او صندوق
+
+249
+00:20:51,030 --> 00:20:54,310
+الكوارينتز الـ z نفسه مفقفين على بعض ممكن تشتغل
+
+250
+00:20:54,310 --> 00:21:00,510
+اوى تم اذا احنا قولنا رو هتساوي جزر التربية ل X
+
+251
+00:21:00,510 --> 00:21:04,830
+تربية زي Y تربية في هي تل inverse Y على X و Z
+
+252
+00:21:04,830 --> 00:21:08,390
+بتساوي Z فبنيجي لو احنا بدك تكتب X بدلالة اللي هو
+
+253
+00:21:08,390 --> 00:21:15,090
+ال رو و الفي هى ال X X هتساوي رو جبت دلال من الفي
+
+254
+00:21:16,170 --> 00:21:19,710
+الـ X component للـ Raw زي ما احنا اخدتوا تحليل اي
+
+255
+00:21:19,710 --> 00:21:24,250
+vector الحاضر الماضي كمان شفنا هى vector ايه؟ ايش
+
+256
+00:21:24,250 --> 00:21:27,650
+تحليله لو كان هنا في زاوية؟ هذه اللى هى ال X
+
+257
+00:21:27,650 --> 00:21:30,230
+component عظمها يمكننا نسميها X وهي ال X component
+
+258
+00:21:30,230 --> 00:21:36,530
+بس ايش هى X الواطنة؟ هى A Cosine of Phi صح؟ اللى
+
+259
+00:21:36,530 --> 00:21:39,150
+هى ال magnitude لو انا بتطبع ال X magnitude و Y
+
+260
+00:21:39,150 --> 00:21:44,990
+magnitude هتكون ايه؟ A Sin Yهي اتجاهها في ال Xها
+
+261
+00:21:44,990 --> 00:21:54,070
+وهي اتجاهها في ال Yها ال Phi هذا هو ال Y component
+
+262
+00:21:54,070 --> 00:21:57,330
+تمام؟
+
+263
+00:21:57,330 --> 00:22:00,610
+إذا
+
+264
+00:22:00,610 --> 00:22:05,810
+ال X component هي برعه روه صين الفي و Y برعه روه
+
+265
+00:22:05,810 --> 00:22:09,130
+صين الفي صح؟ لأن هذه هي ال components ال X
+
+266
+00:22:09,130 --> 00:22:10,930
+component بتاعة ال روه
+
+267
+00:22:14,810 --> 00:22:18,870
+الـ X هي عبارة عن رو شتم الفاية والـ Y هي عبارة عن
+
+268
+00:22:18,870 --> 00:22:23,450
+رو صين اي فاية الـ
+
+269
+00:22:23,450 --> 00:22:27,570
+A ال raw hat يعني ال unit vector اللي في اتجاه ال
+
+270
+00:22:27,570 --> 00:22:31,910
+raw برضه هيكون لتو components واحدة في اتجاه اللي
+
+271
+00:22:31,910 --> 00:22:36,390
+هسميها X hat و Y hat و هنا فاية ايش علاقة X hat ب
+
+272
+00:22:36,390 --> 00:22:38,990
+raw hat نفس العلاقة بتاعة ال vector بس هنا ال unit
+
+273
+00:22:38,990 --> 00:22:43,510
+المجموعة تبع ال raw hat ايش هيكونالراو هات هو
+
+274
+00:22:43,510 --> 00:22:47,970
+مجموعة
+
+275
+00:22:47,970 --> 00:22:54,150
+الراو كوساين الفار ايش المجموعة تبع الراو هات؟
+
+276
+00:22:54,150 --> 00:23:00,370
+واحد ايش هتكون ال X هات هتكون كوساين الفار انت
+
+277
+00:23:00,370 --> 00:23:05,070
+تجيب العقل العكسي الراو هات الراو هات هو two
+
+278
+00:23:05,070 --> 00:23:08,570
+components واحدة في تجاه ال X هات واحدة في تجاه ال
+
+279
+00:23:08,570 --> 00:23:13,540
+Y هاتاتجاه ال X hat ايش هتكون؟ المجليتور التبع ال
+
+280
+00:23:13,540 --> 00:23:18,200
+raw hat جيب تمام الزاوية، اذا ال component بتاعك
+
+281
+00:23:18,200 --> 00:23:23,280
+اتجاه ال X hat هي بساطة cos⁻⁾، لو بدأ احكي على Y
+
+282
+00:23:23,280 --> 00:23:29,260
+component، المجليتور التبع ال raw hat ايش هيكون؟
+
+283
+00:23:29,260 --> 00:23:36,510
+واحد، cosY⁻⁾Y، واضح ما قال ايش هت؟إذا نعندي رو هات
+
+284
+00:23:36,510 --> 00:23:40,350
+هي عبارة عن أسعار الفاية لإنها component في تجاه
+
+285
+00:23:40,350 --> 00:23:44,170
+ال X اللي هي المجنفة تقع رو هات في جبهة من الزاوية
+
+286
+00:23:44,170 --> 00:23:49,310
+رو هات مجنفة واحد هي أسعار الفاية X hat ثم أسعار
+
+287
+00:23:49,310 --> 00:23:52,030
+الفاية و إحدها تفس الأشياء ل A فاية A فاية و إحد
+
+288
+00:23:52,030 --> 00:23:55,330
+تجاه ال A فاية احنا هذا الorthogonal coordinate
+
+289
+00:23:55,330 --> 00:24:00,670
+الواحد عمودي هي تجاه ال رو هات وتجاه الفاية هت
+
+290
+00:24:00,670 --> 00:24:03,470
+العمودي عليها أنت تجاه الفاية من Zero ل Two Pi
+
+291
+00:24:03,740 --> 00:24:10,140
+عمودي عليها لو أنا رجعت رسمة الدائرة دائرة
+
+292
+00:24:10,140 --> 00:24:17,300
+هلاقي ان الروحة تنالو فيها نفس بالدائرة عمودي على
+
+293
+00:24:17,300 --> 00:24:30,280
+الروحة رسمت
+
+294
+00:24:30,280 --> 00:24:39,360
+الدائرة عمودي على الروحةال radius تبعهم عمود
+
+295
+00:24:39,360 --> 00:24:43,400
+على عمودي
+
+296
+00:24:43,400 --> 00:24:44,480
+عمودي عمودي عمودي عمودي عمودي عمودي عمودي عمودي
+
+297
+00:24:44,480 --> 00:24:45,600
+عمودي عمودي عمودي عمودي عمودي عمودي عمودي عمودي
+
+298
+00:24:45,600 --> 00:24:45,820
+عمودي عمودي عمودي عمودي عمودي عمودي عمودي عمودي
+
+299
+00:24:45,820 --> 00:24:46,360
+عمودي عمودي عمودي عمودي عمودي عمودي عمودي عمودي
+
+300
+00:24:46,360 --> 00:24:46,420
+عمودي عمودي عمودي عمودي عمودي عمودي عمودي عمودي
+
+301
+00:24:46,420 --> 00:24:57,240
+عمودي عمودي عمودي عمودي عم
+
+302
+00:25:01,720 --> 00:25:05,880
+هي ال component في اتجاه ال X هتكون في اتجاه ال Y
+
+303
+00:25:05,880 --> 00:25:08,840
+في اتجاه ال X بس هتكون واحدة في اتجاه ال X في
+
+304
+00:25:08,840 --> 00:25:13,020
+اتجاه ال minus X لو بدأ احل ال components والزاوية
+
+305
+00:25:13,020 --> 00:25:22,960
+بتاعتهم هي ال Phi بيجي على الاسم Phi hat I minus
+
+306
+00:25:22,960 --> 00:25:29,900
+hat I من هنا ال X Yزي ال X هنا I من هنا ال Y
+
+307
+00:25:37,920 --> 00:25:44,900
+الزاوية هيجب ترم الـPi هو اتجاه الـY hatوالـ sin
+
+308
+00:25:44,900 --> 00:25:48,440
+هيكون في تجاه ال X بس هتكون في سالب ال X hat لأن
+
+309
+00:25:48,440 --> 00:25:51,420
+تجاهها هي .. انا عاملا بحلل Phi hat هيكون Y
+
+310
+00:25:51,420 --> 00:25:56,660
+component موجبة و X component سالبة عشان أسهل واحد
+
+311
+00:25:56,660 --> 00:25:59,740
+يتذكرها طبعا انتوا هيتطلبوا منكم لو تحللوا على
+
+312
+00:25:59,740 --> 00:26:02,540
+الرسمة يمكنوا تجيبوها دول ال coordinates بس كمان
+
+313
+00:26:02,540 --> 00:26:06,300
+عشان تتذكر انك عاملة حاجة صح ولا لا هتلاحظ ان Y ال
+
+314
+00:26:06,300 --> 00:26:10,440
+Phi hat component هي ال differential لل raw hatأنا
+
+315
+00:26:10,440 --> 00:26:13,260
+جبت ال differential تبع ال row هتش هتعطيلي minus
+
+316
+00:26:13,260 --> 00:26:16,520
+sine of I ال X component و ال sine of Phi هي
+
+317
+00:26:16,520 --> 00:26:24,920
+cosine ال Phi طبعا
+
+318
+00:26:24,920 --> 00:26:28,560
+ال Z hat هي نفسها ال Z hat احنا اتفقنا على هكم
+
+319
+00:26:28,560 --> 00:26:33,160
+الأول يعني كل الشغل عندنا هو في الدائرة في الدائرة
+
+320
+00:26:33,160 --> 00:26:36,160
+بتاعة السلم ده ال Z component بتطابقوا على بعض لكن
+
+321
+00:26:36,160 --> 00:26:39,000
+ال X component و ال Y component هي قد صاروا بدلهم
+
+322
+00:26:39,000 --> 00:26:39,380
+row
+
+323
+00:26:46,180 --> 00:26:49,600
+العلاقة رو بقدر اكتبها في دلالة ال X و Y فاي بقدر
+
+324
+00:26:49,600 --> 00:26:53,200
+اكتبها في دلالة ال X و Y و Z هي نفس ال Z كما بقدر
+
+325
+00:26:53,200 --> 00:26:56,100
+اكتب اللي هو ال row vector او يعني ال X component
+
+326
+00:26:56,100 --> 00:27:02,000
+اتجاه دلالة ال رو و الفاي و Y دلالة ال رو و الفاي
+
+327
+00:27:02,000 --> 00:27:03,260
+و Z دلالة ال Z
+
+328
+00:27:07,580 --> 00:27:13,360
+هذا ما شرحته بس سايموس مع الرسمة هاي ال X hat كيف
+
+329
+00:27:13,360 --> 00:27:17,480
+بدي أعبر عنها بدلالة ال raw hat هاي ال X hat هاي
+
+330
+00:27:17,480 --> 00:27:21,040
+اتجاه ال raw hat وهذا اتجاه ال minus Phi hat لإيش؟
+
+331
+00:27:21,040 --> 00:27:24,260
+لأن هاي ال X و هاي ال Y Phi هات ايش اتجاهها لفوق
+
+332
+00:27:24,260 --> 00:27:33,540
+اتجاهها counter clockwise هاي
+
+333
+00:27:33,540 --> 00:27:40,280
+ال X بتاعتها بدلالةالراو هات والفاي هات احنا اللى
+
+334
+00:27:40,280 --> 00:27:46,560
+عملناها قبل شوية اللى هى الراو هات بدلت ال X و ال
+
+335
+00:27:46,560 --> 00:27:50,200
+Y هات ال X هات و ال Y هات انت بدل ال X هات بدلت ال
+
+336
+00:27:50,200 --> 00:27:56,420
+راو و الفاي هى ال X هى ال X direction وهد طبعا
+
+337
+00:27:56,420 --> 00:27:58,720
+اللى هو ال راو ديركشن اللى هو اتجاه ال radius بتاع
+
+338
+00:27:58,720 --> 00:28:03,220
+ال circuit و الفاي هات هي اتجاه لفوق بس هتكون في
+
+339
+00:28:03,220 --> 00:28:07,660
+ال minus انه بدل انا ال Xحللها 2 component واحدة
+
+340
+00:28:07,660 --> 00:28:10,640
+في اتجاه ال raw و واحدة في اتجاه ال phi فالحلقة
+
+341
+00:28:10,640 --> 00:28:14,040
+هتكون في minus ال phi الفتجاه ال raw هتكون طبعا
+
+342
+00:28:14,040 --> 00:28:17,920
+هذه الزاوية في هي نفس هذه الزاوية في من التناظر
+
+343
+00:28:17,920 --> 00:28:21,920
+هذا نفس الخط فهذا الخط بوازي هذا الخط اللي هو ال x
+
+344
+00:28:21,920 --> 00:28:26,460
+component ال x اي x حتة الفتجاه ال raw hat هتكون
+
+345
+00:28:26,460 --> 00:28:33,470
+cosine ال phi raw hat واضح فالتجاهالـ Phi هتكون
+
+346
+00:28:33,470 --> 00:28:38,130
+sin Phi minus Phi hat لأن Phi hat ماله counter
+
+347
+00:28:38,130 --> 00:28:43,670
+clockwise على محيط الدائرةميجي لل y component a y
+
+348
+00:28:43,670 --> 00:28:47,850
+hat هذا هي ال y hat a y hat هي ال raw hat اللي هو
+
+349
+00:28:47,850 --> 00:28:50,950
+في اتجاه ال radius و ال phi hat ما قلنا هي اتجاهها
+
+350
+00:28:50,950 --> 00:28:54,290
+الصحيح اللي هي counter clockwise نفس الحاجة قلنا
+
+351
+00:28:54,290 --> 00:28:57,490
+ال a y اللي هي two components واحدة في اتجاه ال
+
+352
+00:28:57,490 --> 00:29:00,970
+raw hat واحدة في اتجاه ال x hat لو بدي أشوف وين هي
+
+353
+00:29:00,970 --> 00:29:07,670
+ال phi هلاقي ال phi هي الزاوية اللي هنا تمام؟
+
+354
+00:29:18,350 --> 00:29:25,230
+عشان بتأكد من الزاوية اذا عملنا تناظر هادي من
+
+355
+00:29:25,230 --> 00:29:31,890
+التوازي بتساوي هذه الزاوية هي نفس الفاية وهي تتنين
+
+356
+00:29:31,890 --> 00:29:33,390
+هاي وهي تتنين هاي
+
+357
+00:29:38,410 --> 00:29:42,570
+تمام فإذا ال y component في ندي اللي هي ال raw hat
+
+358
+00:29:42,570 --> 00:29:46,170
+اللي هتكون sine ال phi raw hat وعندي في اتجاه ال
+
+359
+00:29:46,170 --> 00:29:49,830
+plus ال phi hat اللي هي cosine ال phi pie hat طبعا
+
+360
+00:29:49,830 --> 00:29:53,890
+ال is it hat هي نفسها ال is it hat إذا إحنا شفنا
+
+361
+00:29:53,890 --> 00:29:59,540
+كيف أنا بقدر أكتهالراو هات دلالة ال X و ال Y
+
+362
+00:29:59,540 --> 00:30:03,160
+component و نبسطها هى الراو هات فده الاتجاه فهيكون
+
+363
+00:30:03,160 --> 00:30:06,300
+له component في اتجاه ال X اللى هى cosine فى X hat
+
+364
+00:30:06,300 --> 00:30:12,620
+واحدة في اتجاه ال Y اللى هى راو هات magnitude اللى
+
+365
+00:30:12,620 --> 00:30:17,640
+هى واحد sine فى Y hat و الفاي هات بقدر برضه اعملها
+
+366
+00:30:17,640 --> 00:30:21,740
+انه هحطها اتجاه المماس للدائرة و اعملها ال X و ال
+
+367
+00:30:21,740 --> 00:30:25,020
+Y component و عشان للتسكير قلتلكم مش هلاقيها انها
+
+368
+00:30:25,020 --> 00:30:29,000
+differentialفاي هات هي ال differential ل raw hat
+
+369
+00:30:29,000 --> 00:30:32,980
+فهتكون minus الفاي X hat زي ال cosine في و Y hat و
+
+370
+00:30:32,980 --> 00:30:36,020
+Z component نفس الحاجة تمام؟
+
+371
+00:30:40,520 --> 00:30:42,860
+و هنا نفس الشيء اذا لاحظتم ان العلاقة برضه بينهم
+
+372
+00:30:42,860 --> 00:30:46,200
+differential ال X hat و ال Y hat عند ال X hat
+
+373
+00:30:46,200 --> 00:30:50,120
+كوسين الفايرو hat مانساين فاير رحمكم الله يصلح
+
+374
+00:30:50,120 --> 00:30:53,840
+حالكم فاير هات التفاضل تبع حتيني اللي هي minus
+
+375
+00:30:53,840 --> 00:30:57,940
+التفاضل لإن الكوسين تفاضله minus هتكون plus sign و
+
+376
+00:30:57,940 --> 00:31:01,660
+هنا هتكون ال sign هتكون plus cosine لإن في عندي
+
+377
+00:31:01,660 --> 00:31:05,650
+minus بينهم بالعلاقةأحنا بحفظها الناس فقط لل رو
+
+378
+00:31:05,650 --> 00:31:08,070
+والفاي لأنها أسفة على طول ال differential هنا
+
+379
+00:31:08,070 --> 00:31:11,250
+بتتذكروا ان في minus ال differential بين ال X و ال
+
+380
+00:31:11,250 --> 00:31:17,350
+Y يعني اي vector قلنا بقدر اكتبه بدلالة ال XYZ او
+
+381
+00:31:17,350 --> 00:31:20,690
+بقدر اكتبه بدلالة ال رو و الفاي و ال Z عندى انا هى
+
+382
+00:31:20,690 --> 00:31:23,250
+ال vector اللى هو ال position vector اللى له
+
+383
+00:31:23,250 --> 00:31:25,890
+component في ال X direction و في ال Y و في ال Z
+
+384
+00:31:25,890 --> 00:31:28,890
+وعندي في ال cylindrical coordinate هيكون له
+
+385
+00:31:28,890 --> 00:31:32,960
+component في ال رو و الفاي و ال Zعشان انا اكتب ال
+
+386
+00:31:32,960 --> 00:31:36,020
+vector هذا اللى هو بالكارتيجين دلالة ال
+
+387
+00:31:36,020 --> 00:31:38,940
+cylindrical coordinate ده اتذكر ال unit vector كيف
+
+388
+00:31:38,940 --> 00:31:42,260
+علاقتها ب ال cylindrical components ال x hat هي
+
+389
+00:31:42,260 --> 00:31:46,180
+cos φ رو hat minus sin فاي فاي hat و ال y hat هي
+
+390
+00:31:46,180 --> 00:31:49,320
+عبارة عن sin فاي رو hat زايد cos فاي فاي hat و ال
+
+391
+00:31:49,320 --> 00:31:55,220
+z hat هي نفس ال z hat اذا بعود ع ال ax و ال ay و
+
+392
+00:31:55,220 --> 00:31:58,120
+ال az و بعدين بجمع ال components بتاعت
+
+393
+00:32:01,000 --> 00:32:05,180
+هي اول حاجة باجي لل a vector هو ميديا عن ax وبعود
+
+394
+00:32:05,180 --> 00:32:10,260
+على ال ax hat ال E cosine ال phi rho hat minus sin
+
+395
+00:32:10,260 --> 00:32:17,500
+phi phi hat زائد ay و بعود على ال y hat دي بsin
+
+396
+00:32:17,500 --> 00:32:25,220
+phi rho hat زائد cosine phi phi hat زائد a z z hat
+
+397
+00:32:25,220 --> 00:32:28,870
+هاي ال component مش هتتغير هتطلع زي مينلكن هنلاحظ
+
+398
+00:32:28,870 --> 00:32:32,490
+أنه ظهرت ال raw hat مرتين و ال phi hat مرتين باخد
+
+399
+00:32:32,490 --> 00:32:36,770
+ال raw hat عامل مشترك هيكون في عندي ax cos phi زي
+
+400
+00:32:36,770 --> 00:32:41,490
+ay sin phi و في عندي ال phi component يعني minus
+
+401
+00:32:41,490 --> 00:32:47,840
+ax sin phi و في عندي ay cos phiإذاً هي ال raw
+
+402
+00:32:47,840 --> 00:32:52,240
+component A raw هتساوي Ax cos فهذا احنا اصلا
+
+403
+00:32:52,240 --> 00:32:55,780
+مابنتوقعينه ال A raw نفس الحالة هتكون لها
+
+404
+00:32:55,780 --> 00:33:00,560
+component اتجاه ال X واحدة اتجاه ال Y Ax cos فزاية
+
+405
+00:33:00,560 --> 00:33:04,960
+Ay sin فهو ال A ف هتكون minus Ax sin فزاية Ay cos
+
+406
+00:33:04,960 --> 00:33:10,840
+فهو ال AZ بيها ال AZبس ان هي كدت اكتب ال vector
+
+407
+00:33:10,840 --> 00:33:13,700
+position في ال Cartesian coordinate احوله من ال
+
+408
+00:33:13,700 --> 00:33:15,480
+Cartesian coordinate اذا كنت عارف ال components
+
+409
+00:33:15,480 --> 00:33:19,940
+عادوا في ال X و Y و Z و هتتحلل ال ax ل two
+
+410
+00:33:19,940 --> 00:33:22,980
+components واحدة في ال rho واحدة في ال phi و ال y
+
+411
+00:33:22,980 --> 00:33:25,620
+هتتحلل two components واحدة في ال rho واحدة في ال
+
+412
+00:33:25,620 --> 00:33:29,720
+phi و ال z هتظلها زي ما هي فبطلع عندي لكل واحدة من
+
+413
+00:33:29,720 --> 00:33:31,840
+ال components عادوا من ال vector في اتجاه ال rho
+
+414
+00:33:31,840 --> 00:33:35,150
+hat و ال phi hat و ال z hatتجاه الـ Phi 2
+
+415
+00:33:35,150 --> 00:33:37,850
+components وتجاه الـ Phi 2 components والـ Z تظهر
+
+416
+00:33:37,850 --> 00:33:41,730
+زي ما هي تمام صار واضح ايش اللي بنعمله هذا كله
+
+417
+00:33:41,730 --> 00:33:45,890
+بنقدر معبر عنه بال transfer matrix انا بقدر اكتب
+
+418
+00:33:45,890 --> 00:33:49,790
+العلاقة بين ال A Rho وال A Phi وال A Z وال A X وال
+
+419
+00:33:49,790 --> 00:33:52,410
+A Y وال A Z بتبدأت ال matrix احنا قولنا ان ال A
+
+420
+00:33:52,410 --> 00:33:57,350
+Rho ايش بتساوي كو سين الفي X سين الفي A Y دولة
+
+421
+00:33:57,350 --> 00:34:01,670
+اللي هي ال ال ال ال raw hat dot X A hat X hat وهد
+
+422
+00:34:01,670 --> 00:34:06,540
+ال raw hat dot Y hatوهنا ال FI هتكون عندى ال
+
+423
+00:34:06,540 --> 00:34:10,780
+matrix ما نص FI وصل فى 0001 لإن ال acid هى نفس ال
+
+424
+00:34:10,780 --> 00:34:15,150
+acidمن cylindrical ل cartesian يعني إذا كنت عارفة
+
+425
+00:34:15,150 --> 00:34:19,230
+ال a rho a phi a z وبدل a x a y a z هتكون اللي هي
+
+426
+00:34:19,230 --> 00:34:22,570
+cosine of phi minus sine of phi cosine of phi and
+
+427
+00:34:22,570 --> 00:34:26,750
+cosine of phi العلاقة بين ال matrix بتاعت اللي هي
+
+428
+00:34:26,750 --> 00:34:29,470
+من ال cartesian ل ال cylindrical أو من ال
+
+429
+00:34:29,470 --> 00:34:33,050
+cylindrical ل ال cartesian هي عبارة عن اللي هي ال
+
+430
+00:34:33,050 --> 00:34:36,570
+inverse matrix لإن لو بدي اقول بدي انا اكتب ال
+
+431
+00:34:36,570 --> 00:34:39,620
+cartesian بدلات ال cylindrical ايش بدي اعمل؟اك واي
+
+432
+00:34:39,620 --> 00:34:41,360
+واي واي واي واي واي واي واي واي واي واي واي واي
+
+433
+00:34:41,360 --> 00:34:44,020
+واي واي واي واي واي واي واي واي واي واي واي واي
+
+434
+00:34:44,020 --> 00:34:48,440
+واي واي واي واي
+
+435
+00:34:48,440 --> 00:34:49,760
+واي واي واي واي واي واي واي واي واي واي واي واي
+
+436
+00:34:49,760 --> 00:34:52,320
+واي واي واي واي واي واي واي واي واي واي واي واي
+
+437
+00:34:52,320 --> 00:34:52,500
+واي واي واي واي واي واي واي واي واي واي واي واي
+
+438
+00:34:52,500 --> 00:34:53,340
+واي واي واي واي واي واي واي واي واي واي واي واي
+
+439
+00:34:53,340 --> 00:34:53,720
+واي واي واي واي واي واي واي واي واي واي واي واي
+
+440
+00:34:53,720 --> 00:34:56,320
+واي واي واي واي واي واي واي واي واي واي واي واي
+
+441
+00:34:56,320 --> 00:35:03,920
+واي واي واي واي واي واي
+
+442
+00:35:03,920 --> 00:35:07,830
+واي واي واي وعشان اعمل هيك انا بدي هذا ال vector
+
+443
+00:35:07,830 --> 00:35:14,030
+اش باخد ال inverse تبع ال M بعد M inverse اللي هي
+
+444
+00:35:14,030 --> 00:35:18,270
+بساطة هتطلع بس ال vector اللي احنا شفناها قبل هيك
+
+445
+00:35:22,200 --> 00:35:25,860
+هي طبعا اي component من هدول ال components ببساطة
+
+446
+00:35:25,860 --> 00:35:27,580
+لو انا في ال cylindrical و انا بده اروح ل
+
+447
+00:35:27,580 --> 00:35:30,520
+Cartesian هيكون كل واحد من هدول ال elements هيكون
+
+448
+00:35:30,520 --> 00:35:35,960
+ax dot a rawhat ax dot phi hat x hat dot z hat هده
+
+449
+00:35:35,960 --> 00:35:39,420
+هتكون y hat dot rawhat y hat dot phi hat y hat dot
+
+450
+00:35:39,420 --> 00:35:43,400
+z hat z hat dot rawhat z hat dot phi hat z hat dot
+
+451
+00:35:43,400 --> 00:35:48,320
+z hat هنخل الصفر اكتر لنقاء القادم عشان هدول بتحكم
+
+452
+00:35:48,320 --> 00:35:54,180
+مع المهندسمحمد اجعالنا موجود هى اتحدى دموعى
+
+453
+00:35:54,180 --> 00:35:56,980
+المحاضرات كفاية لكم العافية وان شاء الله بنشوفكم
+
+454
+00:35:56,980 --> 00:35:58,060
+لقاء القادم
+
diff --git a/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/ryHc6fpOqQU_postprocess.srt b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/ryHc6fpOqQU_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..a3673485bd1571177db33d500bc00bc8352b59c1
--- /dev/null
+++ b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/ryHc6fpOqQU_postprocess.srt
@@ -0,0 +1,1976 @@
+1
+00:00:21,680 --> 00:00:24,420
+بسم الله الرحمن الرحيم السلام عليكم ورحمة الله
+
+2
+00:00:24,420 --> 00:00:28,160
+وبركاته احنا اليوم ان شاء الله هنكمل موضوعنا في ال
+
+3
+00:00:28,160 --> 00:00:32,380
+vector analysis احنا وصلنا لمحاضرة الماضية لما
+
+4
+00:00:32,380 --> 00:00:35,800
+شوفنا ال curl وشوفنا Stokes theorem ال Stokes
+
+5
+00:00:35,800 --> 00:00:38,840
+theorem قالت ان ال clause integral over L او ال
+
+6
+00:00:38,840 --> 00:00:41,940
+circulation بساوى ال surface integral ل ال curl في
+
+7
+00:00:41,940 --> 00:00:45,860
+DSوقفنا عند الأمثلة وقلنا ان شاء الله بنشوف بعض
+
+8
+00:00:45,860 --> 00:00:48,580
+الأمثلة فاليوم طلب مننا مثلا determine the curl of
+
+9
+00:00:48,580 --> 00:00:51,660
+vector field اللي احنا طبعا بيقولنا ال curl لازم
+
+10
+00:00:51,660 --> 00:00:54,760
+يكون مع ال vector وقدرش اعمل curl ل scalar مالهوش
+
+11
+00:00:54,760 --> 00:00:59,000
+معنى احنا نبقى vector field بيه P وQ وT ويجيبهم ال
+
+12
+00:00:59,000 --> 00:01:02,440
+curl بيه ما احنا شوفناه قبل هيك هذا المثال هذا في
+
+13
+00:01:02,440 --> 00:01:06,080
+ال Cartesian ال Q في ال cylindrical وC في ال
+
+14
+00:01:06,080 --> 00:01:11,710
+spherical طب احنا خلينا نشوف الحال تبعنانبدأ بيه
+
+15
+00:01:11,710 --> 00:01:14,310
+اللي هو ال Cartesian coordinate لإن المثال أولا هو
+
+16
+00:01:14,310 --> 00:01:17,190
+Cartesian احنا قلنا ال kill هو عبارة عن
+
+17
+00:01:17,190 --> 00:01:20,210
+determinant هو حط جواب على طول هذا جانب ال
+
+18
+00:01:20,210 --> 00:01:24,030
+determinant احنا
+
+19
+00:01:24,030 --> 00:01:31,690
+عندنا ال determinant بتقول X hat Y hat Z hat D
+
+20
+00:01:31,690 --> 00:01:37,760
+body X D body Yأحنا شفناهم بهذا الشكل نفس الشيء
+
+21
+00:01:37,760 --> 00:01:43,780
+للـ spherical و الـcylindrical بعدين عنده هي PX PY
+
+22
+00:01:43,780 --> 00:01:50,340
+PZ هذا دوامين تغيروا كده احنا قبل ان ندetermine
+
+23
+00:01:50,340 --> 00:01:54,860
+ايش بنسويه بناخد الصفر الأول و العمود الأول اللي
+
+24
+00:01:54,860 --> 00:02:00,000
+بنتمسله هو يتوفرنا ال X هتكون هنا فانترو الطرف
+
+25
+00:02:03,030 --> 00:02:09,610
+بعدين ماقصها على كل واحد دي بي زت باي بي واي
+
+26
+00:02:09,610 --> 00:02:18,530
+مايناس دي بي واي باي بي زت مايناس واي هات مايناس
+
+27
+00:02:32,350 --> 00:02:45,810
+أن تفتحه باسم cap هيعطينا dPy-dPx-dPy-dPy-dPy-dPy
+
+28
+00:02:45,810 --> 00:02:46,510
+-dPy-dPy-dPy-dPy-dPy-dPy-dPy-dPy-dPy-dPy-dPy-dPy
+
+29
+00:02:46,510 --> 00:02:49,850
+-dPy-dPy-dPy-dPy-dPy-dPy-dPy-dPy-dPy-dPy-dPy-dPy
+
+30
+00:02:49,850 --> 00:02:56,430
+-dPy-dPy-dPy-dPy-dPy-dPy-dPy-dPy-dPy
+
+31
+00:02:56,430 --> 00:03:00,610
+-dPyباعتمد على ثلاث coordinates باعتمد على x و y و
+
+32
+00:03:00,610 --> 00:03:03,850
+z يعني هو variable as a function of x and y and z
+
+33
+00:03:03,850 --> 00:03:08,790
+مابتش مفاضة بيه بيه z هذا ال x component ال z
+
+34
+00:03:08,790 --> 00:03:15,350
+component فقط function في x و z يعني بيه x هلاقيها
+
+35
+00:03:15,350 --> 00:03:23,390
+function of x و y و z بيه z function of x و z و
+
+36
+00:03:23,390 --> 00:03:33,310
+بيه y بتساوزيهطبعا انا دى py by dz هدحقه مش هى ال
+
+37
+00:03:33,310 --> 00:03:40,910
+one component ثالثة وين؟ بس فى الحلها نموج يعنى
+
+38
+00:03:40,910 --> 00:03:48,970
+عكس بس هو عكس الترتيب عكس d by x y by z minus d by
+
+39
+00:03:48,970 --> 00:03:54,690
+z by dx بحكي عن الحل بتاعي بس بحكي عنه slide يعنى
+
+40
+00:03:54,690 --> 00:04:00,270
+الحل على slideطيب بس معاكوسة لما هي نفس الاشي طبعا
+
+41
+00:04:00,270 --> 00:04:04,030
+الاشي احنا بدنا نزوّق ال BY وE من كل الجهات بيبقى
+
+42
+00:04:04,030 --> 00:04:07,170
+BY بيبقى DX بيبقى لنا اللي هي ال components
+
+43
+00:04:07,170 --> 00:04:10,930
+الباقية احنا قمنا ال DBZ بس ترمز على X و Z يعني هو
+
+44
+00:04:10,930 --> 00:04:13,870
+في عندي DBZ by DY بيساوي سكر زي ما هاي بعضه سكر
+
+45
+00:04:13,870 --> 00:04:21,670
+بينما DBX by DZ في عندي أكملية على ال Z فهتكون X
+
+46
+00:04:21,670 --> 00:04:30,170
+ترمزية في YDPZ by DX هي اعتمادية Z ويظل عندى minus
+
+47
+00:04:30,170 --> 00:04:36,150
+DX by DX by DY هي اتنين X تربية Z ويظهر نتيجة DX
+
+48
+00:04:36,150 --> 00:04:43,630
+تربية Y minus Z Y hat minus X تربية Z Z hat تمام؟
+
+49
+00:04:43,630 --> 00:04:51,510
+في اي سؤال لحد هناك؟ نفس العملية بنكررها في ال
+
+50
+00:04:51,510 --> 00:04:57,330
+cylindrical و ال spherical كواردناتبجيب نوع ال
+
+51
+00:04:57,330 --> 00:04:57,610
+curve
+
+52
+00:05:07,920 --> 00:05:10,780
+مش هعملها من كلهم يعني لإن بس عمل المثال الأولاني
+
+53
+00:05:10,780 --> 00:05:15,180
+ال B و ال T نفس الحاجة بتشيبوا ال kern تبع ال Q
+
+54
+00:05:15,180 --> 00:05:17,000
+اللي هو ال cylindrical coordinate اللي عرفناه
+
+55
+00:05:17,000 --> 00:05:20,500
+المحاضرة الماضية نفس القضية لكرن ال T اللي هو سفر
+
+56
+00:05:20,500 --> 00:05:23,580
+السيندركال كواردين نيجي لالمثال اللي أقنعه المثال
+
+57
+00:05:23,580 --> 00:05:28,320
+اللي أقنعه بتقولي F A بتسوي رو كسين الفي رو هات
+
+58
+00:05:28,320 --> 00:05:33,720
+ذات سين الفي في هات يعني مالها موجودة وين في ال
+
+59
+00:05:33,720 --> 00:05:37,190
+cylindrical coordinateهذا الـ function أو ال field
+
+60
+00:05:37,190 --> 00:05:41,190
+ال vector field A معرف بالـ cylindrical coordinate
+
+61
+00:05:41,190 --> 00:05:45,310
+بالدلالة row of I evaluate ال circulation قلنا هذا
+
+62
+00:05:45,310 --> 00:05:47,990
+ال clause integral ال line integral برضه اسمه
+
+63
+00:05:47,990 --> 00:05:51,590
+circulation ال clause line integral ل a dot dl
+
+64
+00:05:51,590 --> 00:05:55,270
+around the bastion in the figure يعني بده قيمة ال
+
+65
+00:05:55,270 --> 00:05:58,930
+circulation في هذا الفيجربعدين confirm using
+
+66
+00:05:58,930 --> 00:06:00,730
+Stokes theorem يعني أول مرة بدي أعمل ال
+
+67
+00:06:00,730 --> 00:06:04,370
+circulation أخد ال line integral و بعدين أتحقق منه
+
+68
+00:06:04,370 --> 00:06:07,190
+باستخدام اللي هو Stokes theorem بتقوللي ال
+
+69
+00:06:07,190 --> 00:06:09,970
+circulation اللي هو ال clause line integral ل a
+
+70
+00:06:09,970 --> 00:06:13,550
+dot dl بساوي ال surface integral ل k l a dot ds
+
+71
+00:06:13,550 --> 00:06:16,350
+نفس الحاجة هنعمل خطوة خطوة زي ما عملنا في ال
+
+72
+00:06:16,350 --> 00:06:20,680
+divergence theoremDivision of closed surface
+
+73
+00:06:20,680 --> 00:06:25,160
+integral A dot DS بتساوي ال volume integral ل
+
+74
+00:06:25,160 --> 00:06:26,720
+divergent A
+
+75
+00:06:29,730 --> 00:06:33,230
+نشيل ال line integral a dot dl معناه انش بس لو بده
+
+76
+00:06:33,230 --> 00:06:36,630
+اعمل ال bus كله حوالين كل bus واحد واحد يعني هاخد
+
+77
+00:06:36,630 --> 00:06:41,370
+ال bus من a ل b زاد ال bus من b ل c زاد ال bus من
+
+78
+00:06:41,370 --> 00:06:46,090
+c ل d زاد ال bus من d ل a ل a فهيك بيكون انا عملت
+
+79
+00:06:46,090 --> 00:06:49,330
+ال circulation كله اذا بده اكمل اول هذا ال bus و
+
+80
+00:06:49,330 --> 00:06:51,510
+بعدين هذا ال bus و بعدين هذا ال bus و بعدين هذا ال
+
+81
+00:06:51,510 --> 00:06:55,790
+bus بخلص ال circulation نبدأ بال bus الأول هو من a
+
+82
+00:06:55,790 --> 00:07:01,230
+ل bمن A ل B ايش هنا ال line DL هنا DL احنا كل مرة
+
+83
+00:07:01,230 --> 00:07:06,710
+نعرف ال DL ايش ال DL هنا معايا ايش ال DL في هذا ال
+
+84
+00:07:06,710 --> 00:07:11,650
+bus DL ايش
+
+85
+00:07:11,650 --> 00:07:18,810
+DL ايش بتساوي في هذا ال bus دي فا قرأت اه هدا قرأت
+
+86
+00:07:18,810 --> 00:07:23,070
+دي فا ايه قرأت دي فا لإن هذا ماله ال course الصغير
+
+87
+00:07:23,070 --> 00:07:28,500
+لقبل D5فبتكون رو دي فاي اذا دي L هنا هي رو دي فاي
+
+88
+00:07:28,500 --> 00:07:34,120
+واتجاهها وين احنا فاي هات اتجاهها بهالي هذا minus
+
+89
+00:07:34,120 --> 00:07:38,480
+فاي هات او اذا اخدت انه فاي هات ودراعي ايه يعني
+
+90
+00:07:38,480 --> 00:07:40,640
+حالة من الحزين يابا الدراعي ان اقول minus فاي هات
+
+91
+00:07:40,640 --> 00:07:43,480
+او دراعي اتجاهي يعني اذا قعدت من A لB خلاص باخدت
+
+92
+00:07:43,480 --> 00:07:49,240
+فاي هات فإذا ماعندي دي L دي عبارة عن رو دي رو دي
+
+93
+00:07:49,240 --> 00:07:49,680
+فاي
+
+94
+00:07:52,350 --> 00:07:55,950
+وعندي اللي هو ال vector a ال vector a في اللي في
+
+95
+00:07:55,950 --> 00:07:59,530
+الجهة الفيهات هي اللي في الجهة الفيهات اللي هي
+
+96
+00:07:59,530 --> 00:08:02,670
+sign الفيهات فإذا أنا طبت ال product فهي sign
+
+97
+00:08:02,670 --> 00:08:06,030
+الفيهات إذا أنا طبت ال product فهي sign الفيهات
+
+98
+00:08:06,030 --> 00:08:10,070
+إذا أنا طبت ال product فهي sign الفيهات إذا أنا
+
+99
+00:08:10,070 --> 00:08:12,330
+طبت ال product فهي sign الفيهات إذا أنا طبت ال
+
+100
+00:08:12,330 --> 00:08:15,270
+product فهي sign الفيهات إذا أنا طبت ال product
+
+101
+00:08:15,270 --> 00:08:15,530
+فهي sign الفيهات إذا أنا طبت ال product فهي sign
+
+102
+00:08:15,530 --> 00:08:15,670
+الفيهات إذا أنا طبت ال product فهي sign الفيهات
+
+103
+00:08:15,670 --> 00:08:17,380
+product فهي sign الفيهات إذا أنا طA مُحطوة على
+
+104
+00:08:17,380 --> 00:08:22,120
+الرسمة قيمة هذا الـ circle قيمة روه ثابتة على 2
+
+105
+00:08:22,120 --> 00:08:26,600
+فهوض عن روه ب2 إذا هذه هتكون 2 بضبط عند التكامل
+
+106
+00:08:26,600 --> 00:08:31,660
+على sign فاي دي فاي من أين؟ من A ل B A عند أي
+
+107
+00:08:31,660 --> 00:08:36,500
+زاوية؟ A عند الزاوية اللي هي الستين و B عند
+
+108
+00:08:36,500 --> 00:08:41,440
+الزاوية اللي هي التلاتين فهكامل
+
+109
+00:08:41,440 --> 00:08:46,790
+من ستين لتلاتين فإذا نعيد البعث الأولانيهو الـ
+
+110
+00:08:46,790 --> 00:08:54,990
+integral طبعا ال raw اللي قلنا اتنين التكامل
+
+111
+00:08:54,990 --> 00:09:05,430
+من ستين لتلتين لقولنا sine of five D five إسرائيل
+
+112
+00:09:05,430 --> 00:09:14,410
+ال side اشتغلوها minus cosine من ستين لتلتينالسنة
+
+113
+00:09:14,410 --> 00:09:20,290
+و اتنين minus cosine التلاتين زائد cosine الستين
+
+114
+00:09:20,290 --> 00:09:27,510
+هذه اللي هي نص وهي جزء التلاتة على اتنين صح؟ جبت
+
+115
+00:09:27,510 --> 00:09:31,090
+من التلاتين لو احنا جبناها هون بال calculator
+
+116
+00:09:31,090 --> 00:09:37,430
+هيعطيني الجواب اللي هو قدامنا minus جزء التلاتة
+
+117
+00:09:37,430 --> 00:09:40,410
+زائد واحد minus جزء التلاتة زائد واحد
+
+118
+00:09:48,300 --> 00:09:52,380
+عشان هاد بالنسبالي بحث الأولاني البحث التانى اللى
+
+119
+00:09:52,380 --> 00:10:00,360
+هو من B ل C من B ل C مين اللى بيقول HDL هنا HDL
+
+120
+00:10:00,360 --> 00:10:04,560
+هم مين اللى بيغير مين اللى بروح من ال 2 ل 5 دي رو
+
+121
+00:10:04,560 --> 00:10:09,560
+برافو عليكم و اتجاهة روهاد دي رو روهاد فى عندكم
+
+122
+00:10:09,560 --> 00:10:12,560
+وانت اتجاه الرو فى عندكم وانت اتجاه الرو اذا ال A
+
+123
+00:10:12,560 --> 00:10:19,070
+dot DL هتعطينارو كوسايم الفاي دي رو رو كوسايم
+
+124
+00:10:19,070 --> 00:10:36,670
+الفاي دي رو رو
+
+125
+00:10:36,670 --> 00:10:38,150
+كوسايم الفاي دي رو رو كوسايم الفاي دي رو رو كوسايم
+
+126
+00:10:38,150 --> 00:10:41,190
+الفاي دي رو رو كوسايم الفاي دي رو رو كوسايم الفاي
+
+127
+00:10:41,190 --> 00:10:42,050
+دي رو رو كوسايم الفاي دي رو رو كوسايم الفاي دي رو
+
+128
+00:10:42,050 --> 00:10:49,830
+دي رو رو كوسايم الفاي دي رو رو كوأخر حاجة رو
+
+129
+00:10:49,830 --> 00:10:59,690
+دي فايف رو دي فايف رو دي فايف رو دي فايف رو دي
+
+130
+00:10:59,690 --> 00:11:03,870
+فايف رو دي فايف رو دي فايف رو دي فايف رو دي فايف
+
+131
+00:11:03,870 --> 00:11:04,550
+رو دي فايف رو دي فايف رو دي فايف رو دي فايف رو دي
+
+132
+00:11:04,550 --> 00:11:07,060
+فايف رو دي فايف رو دي فايف رو دي فايف رو دي فايفو
+
+133
+00:11:07,060 --> 00:11:11,500
+هتتغير من 5 ل 2 هيكون نفس الـ integral هذا بس
+
+134
+00:11:11,500 --> 00:11:15,900
+هيكون التغير ل DL من 5 ل 2 و بطلع معايا ال
+
+135
+00:11:15,900 --> 00:11:20,640
+circulation زي ما احنا شايفين على الصورة انه ال
+
+136
+00:11:20,640 --> 00:11:23,560
+circulation ل A ل DL او ال circulation ل ال vector
+
+137
+00:11:23,560 --> 00:11:26,660
+field A هت احنا بسميه ال circulation ل vector
+
+138
+00:11:26,660 --> 00:11:34,120
+field A بساوي 4.941 تمام؟ اذا هيك هيه معنى ال
+
+139
+00:11:34,120 --> 00:11:38,060
+circulation اللي بتعمل على كل lineبجمع الـ lines
+
+140
+00:11:38,060 --> 00:11:43,440
+كلهم بطلالي الناتج الواحدة طب هو بده يعني نحقق من
+
+141
+00:11:43,440 --> 00:11:45,540
+هذا الحكي ال Stokes theorem يعني أنا ببدأ أجيب
+
+142
+00:11:45,540 --> 00:11:50,580
+برضه ال curl A و أجيب ال DS و كامل على ال surface
+
+143
+00:11:50,580 --> 00:11:53,960
+integral و نعمل ال S اللي هو اللي محيطه ال line هي
+
+144
+00:11:53,960 --> 00:11:57,600
+ال surface هاي
+
+145
+00:11:57,600 --> 00:12:01,240
+ال surface هتا ال surface اللي محيطه هاي جزء يعني
+
+146
+00:12:01,240 --> 00:12:04,660
+زي كأنها قطعة أرضال surface تبع الأرض هو هاي
+
+147
+00:12:04,660 --> 00:12:07,440
+الطاولة أنا قبل هيك حكيتلكم هاي الطاولة هذا هو ال
+
+148
+00:12:07,440 --> 00:12:10,540
+surface اللي هو سطح الطاولة وال line اللي هو
+
+149
+00:12:10,540 --> 00:12:15,080
+الحدود بتاعة الطاولة إنت احنا عملنا الحدود كملنا
+
+150
+00:12:15,080 --> 00:12:17,940
+على ال line إنت بنكامل على ال surface معناها
+
+151
+00:12:17,940 --> 00:12:21,950
+بتجيبني ال norm تبع ال surface لازمني الإنهاتلازم
+
+152
+00:12:21,950 --> 00:12:26,270
+نيد ال unit vector العمودي على ال surface و في
+
+153
+00:12:26,270 --> 00:12:31,410
+هالحالة انها تني لإنها بيكون XYZZ هيكون ال norm
+
+154
+00:12:31,410 --> 00:12:36,110
+على ال surface هو Z hat اذا ان احنا عرفنا DS هتكون
+
+155
+00:12:36,110 --> 00:12:40,450
+DS اتجاهها لإنها طب مين هي ال DS لو انا اخدت هذا
+
+156
+00:12:40,450 --> 00:12:47,350
+القطاع هذا القطاع ايش هذا قيمته هتقول ان انا حكيت
+
+157
+00:12:47,350 --> 00:12:47,930
+ايش قيمته
+
+158
+00:12:51,200 --> 00:12:57,540
+دى رو دى
+
+159
+00:12:57,540 --> 00:13:00,900
+رو دى فاي
+
+160
+00:13:18,030 --> 00:13:21,150
+نرجع احنا عندنا ال vector لازمنا اجيب اول حاجة
+
+161
+00:13:21,150 --> 00:13:28,330
+كيرم ال a كيرم ال a قولنا بس أخد يا اللي هو
+
+162
+00:13:28,330 --> 00:13:31,930
+determinant يا بكون حفظاهم ال x hat ده تكون dz by
+
+163
+00:13:31,930 --> 00:13:37,650
+dy minus dy by dz minus dy يعني اللي واحد ممكن
+
+164
+00:13:37,650 --> 00:13:39,870
+يتخيلها determinant يا بقى حفظاهم يا بحط ال
+
+165
+00:13:39,870 --> 00:13:43,270
+determinant و بجيب الكيرم ال product ديش انسى انه
+
+166
+00:13:43,270 --> 00:13:45,690
+بس عندي raw component و phi component يعني لو انا
+
+167
+00:13:45,690 --> 00:13:50,420
+أخدت ال determinantأو x hat, y hat, z hat, and d
+
+168
+00:13:50,420 --> 00:13:57,620
+by dx لأن كلمه هو اللي قبل, d by dy, d by dz, and
+
+169
+00:13:57,620 --> 00:14:04,340
+دي قلنا رو كمبارز، أظن
+
+170
+00:14:04,340 --> 00:14:08,080
+في كان عندنا واحد على رو بره، واحد على رو و في رو
+
+171
+00:14:08,080 --> 00:14:10,200
+إيه، إيه رو صح؟
+
+172
+00:14:12,120 --> 00:14:15,440
+أسهل ال dx أنا بحاصها أكتر بس ال raw يعني ده
+
+173
+00:14:15,440 --> 00:14:21,700
+أرجعها شوية بس واحد على ال raw وده بال raw ال raw
+
+174
+00:14:21,700 --> 00:14:26,120
+مضروبة في ال five halves هاي ال raw halves وهي ال
+
+175
+00:14:26,120 --> 00:14:29,500
+raw five halves وهي إيه اس ال halves هاي كلنا يجب
+
+176
+00:14:29,500 --> 00:14:34,180
+أننا dy ب raw dy ب five dy ب z لإنها احنا في
+
+177
+00:14:34,180 --> 00:14:40,020
+cylindrical coordinate فعندي a raw رو a five وز من
+
+178
+00:14:40,020 --> 00:14:49,650
+هناطبعا تقفل على ال .. التنميسات برضه
+
+179
+00:14:49,650 --> 00:14:52,310
+سهل الواحد يتذكرها يعني لما انا تخسنكم كنت دول ا
+
+180
+00:14:52,310 --> 00:14:55,470
+.. يعني اخلص اعملهم .. حتى لو نقوم ب book مثلا
+
+181
+00:14:55,470 --> 00:14:57,830
+احنا مش هيقوم نقوم ب book بقول .. بس هيقوم مع بعض
+
+182
+00:14:57,830 --> 00:15:02,490
+ال .. ال formulas بتاخد وقت تفتح و تدور على ال
+
+183
+00:15:02,490 --> 00:15:07,350
+formulas واحد على room دي room انا قبلها دي قيمة
+
+184
+00:15:07,350 --> 00:15:07,950
+ال a
+
+185
+00:15:12,770 --> 00:15:17,550
+Row component هي تداري تسار وزير وRow component هي
+
+186
+00:15:17,550 --> 00:15:18,210
+تداري تسار وزير وRow component هي تداري تسار وزير
+
+187
+00:15:18,210 --> 00:15:18,550
+وRow component هي تداري تسار وزير وRow component
+
+188
+00:15:18,550 --> 00:15:20,290
+هي تداري تسار وزير وRow component هي تداري تسار
+
+189
+00:15:20,290 --> 00:15:23,350
+وزير وRow component هي تداري تسار وزير وRow
+
+190
+00:15:23,350 --> 00:15:28,970
+component هي تداري تسار وزير وRow
+
+191
+00:15:28,970 --> 00:15:30,330
+component هي تداري تسار وزير وRow component هي
+
+192
+00:15:30,330 --> 00:15:30,670
+وRow component هي تداري تسار وزير وRow component
+
+193
+00:15:30,670 --> 00:15:34,150
+هي تداري تسار
+
+194
+00:15:34,150 --> 00:15:36,830
+وزير وRow component هي تداري تسار وزير وRow
+
+195
+00:15:36,830 --> 00:15:38,710
+component هي تداري تسار وRow
+
+196
+00:15:46,750 --> 00:15:50,590
+هيكون عندى ال raw hat component هسكر نفس الاشياء
+
+197
+00:15:50,590 --> 00:15:55,630
+هدا هتكون zero هيكون عندى raw sin ف دي زد مش ده
+
+198
+00:15:55,630 --> 00:15:58,350
+يعني اقعد اكتبهم من هنا واضح ان مافيش عند اي z
+
+199
+00:15:58,350 --> 00:16:01,890
+dependence عندى raw sin ف مافيش اي ادمة ازد هتكون
+
+200
+00:16:01,890 --> 00:16:05,550
+zero كل هاي ال components هنا zero دي ف zero minus
+
+201
+00:16:05,550 --> 00:16:11,570
+d raw sin ف by دي زد zero minus raw fi hatوهو ال
+
+202
+00:16:11,570 --> 00:16:15,110
+term التاني هيكون التفاض بالنسبة ل row 0 و نفس
+
+203
+00:16:15,110 --> 00:16:21,470
+الحاجة row cos ف D z هيكمل بسوا 0 اخر term اللي هو
+
+204
+00:16:21,470 --> 00:16:27,850
+z hat هسكره هيكون عندى زائد z hat هيكون عندى row
+
+205
+00:16:27,850 --> 00:16:31,550
+cos ف D ف ال row بتطلع لفره و ال cos تفضلها
+
+206
+00:16:31,550 --> 00:16:33,830
+بالنسبة لفيه هيكون minus sin ف
+
+207
+00:16:37,780 --> 00:16:42,400
+بهاي بهاي مع نصهاي بهاي هتطلع ال sign الفاية D rho
+
+208
+00:16:42,400 --> 00:16:50,320
+by D rho هتكون واحدة اذا
+
+209
+00:16:50,320 --> 00:16:55,000
+أنا انت هتذاكر ال O ستلاقيتها اذا
+
+210
+00:16:55,000 --> 00:16:59,180
+هذا ال tip هتمنى انه بس عند ال Z component بيبقى
+
+211
+00:16:59,180 --> 00:17:04,740
+ففاضل هيك هيقولنا انه هتعطينا انا عكست عكست
+
+212
+00:17:04,740 --> 00:17:10,980
+الاتجاهالهدف هي رو دي ساين في دي ست دي ساين في دي
+
+213
+00:17:10,980 --> 00:17:16,880
+فاي اللي هي كسان فاي مش عارفة بس اه بس بدك اعكس
+
+214
+00:17:16,880 --> 00:17:20,380
+الاتجاه مش ممكن تبين عاملا هدا في هدا عشان انا
+
+215
+00:17:20,380 --> 00:17:23,560
+احكي مش هدا في هدا و أسهلها في هدا فتفاضل مع هدا
+
+216
+00:17:23,560 --> 00:17:27,400
+هيكبطي نص ساين في فاي نحو plus minus اعكس الاتجاه
+
+217
+00:17:33,810 --> 00:17:37,190
+فاكرنا هدولة هي في هي ماينوس هي في هي في هي هتكون
+
+218
+00:17:37,190 --> 00:17:41,850
+تفضلها اللي هي sign of I وهي ما هي هتعطيني ال
+
+219
+00:17:41,850 --> 00:17:46,150
+minus ال rock طلعت جره ويه ال cosine تصير minus ال
+
+220
+00:17:46,150 --> 00:17:52,930
+I اذا انتهم اللي ده لعندي واحد على long فيه لو
+
+221
+00:17:52,930 --> 00:17:57,630
+دخلت ال minus ده جوا sign of I ساقت
+
+222
+00:18:19,930 --> 00:18:22,330
+هذه هي فكرة ان اخذ الـ Kern
+
+223
+00:18:27,760 --> 00:18:30,620
+طبعا إذا عندي يبقى واحد على رو في واحد زائد رو
+
+224
+00:18:30,620 --> 00:18:35,880
+ثانية في و احنا كمان اتفقنا ان دي اس ايش قيمتها رو
+
+225
+00:18:35,880 --> 00:18:43,620
+دي في دي رو فعمل dot product ل A dot DS هيعطيني
+
+226
+00:18:43,620 --> 00:18:46,460
+اللي هو طبعا لإن هزد component هزد component
+
+227
+00:18:46,460 --> 00:18:50,740
+هعطيني هذا المقدر مضروف في رو دي في دي رو عندي
+
+228
+00:18:50,740 --> 00:18:55,900
+التكامل على رو dot product تبعهم هقسم منيها شوية
+
+229
+00:18:56,680 --> 00:19:01,620
+على ال surface في double integral واحد على رو في
+
+230
+00:19:01,620 --> 00:19:09,940
+واحد زائد رو sign ال five في رو دي رو دي five ال
+
+231
+00:19:09,940 --> 00:19:14,380
+رو بتروح مع ال رو عند ال رو كانت من وم تتكمل لوين
+
+232
+00:19:14,380 --> 00:19:20,580
+القصد كان تبعي من اتنين لخمسة اتنين لخمسة فعند ال
+
+233
+00:19:20,580 --> 00:19:25,930
+رو بتعطيتروح من اتنين لخمسة والـ Phi من تلاتين
+
+234
+00:19:25,930 --> 00:19:36,990
+لستين من
+
+235
+00:19:36,990 --> 00:19:42,530
+حفاظة الـ Phi sin Phi D Phi تحفظ عطيني minus
+
+236
+00:19:42,530 --> 00:19:47,090
+cosine Phi من تلاتين لستين
+
+237
+00:19:55,240 --> 00:19:59,000
+مضروب في تكامل واحد زائد رو دي رو بتعرفوا النقطة
+
+238
+00:19:59,000 --> 00:20:02,640
+الجامعة تتكامل بكمل كل واحد على حد يعني بكمل أول
+
+239
+00:20:02,640 --> 00:20:07,800
+هو دي رو بعدين بكمله رو دي رو الواحد هي فتاني دي
+
+240
+00:20:07,800 --> 00:20:13,120
+رو تكاملها رو زائد رو دي رو اللي رو تربير على
+
+241
+00:20:13,120 --> 00:20:20,560
+اتنين وهدولة ال limits عامهم من اتنين لخمسين minus
+
+242
+00:20:20,560 --> 00:20:25,460
+وsin الستين كده يجب ان تكون ستين نصوهو نتجارب تقوم
+
+243
+00:20:25,460 --> 00:20:30,900
+بالتلاتين هو جزر التلاتة على الدنيا مطروف في خمسة
+
+244
+00:20:30,900 --> 00:20:37,560
+ماقص تانين حلاتة زائد نص في خمسة وعشرين ماقص أربعة
+
+245
+00:20:37,560 --> 00:20:40,860
+هذا
+
+246
+00:20:40,860 --> 00:20:43,540
+بس تجميعه بيعطينا الرقم اللي أمامنا اللي هو أربعة
+
+247
+00:20:43,540 --> 00:20:46,900
+point تسعة أربعة واحدة اللي هو بالتمان بساوي
+
+248
+00:20:46,900 --> 00:20:52,180
+الجواب اللي حصلنا عليه من ال circulationواضح؟ يعني
+
+249
+00:20:52,180 --> 00:20:55,300
+إذا أنا بس بحب ال integration أعمله مرة واحدة باخد
+
+250
+00:20:55,300 --> 00:20:57,940
+اللي هو ال care لل A dot DS أنا بس هعمل
+
+251
+00:20:57,940 --> 00:21:00,620
+integration مرة واحدة مفرقش معايا باخد ال
+
+252
+00:21:00,620 --> 00:21:03,460
+circulation و بدي أعمل أربع مرات integral على كل
+
+253
+00:21:03,460 --> 00:21:12,620
+line في أي استفسار لحد هنا؟ في أي استفسار؟
+
+254
+00:21:12,620 --> 00:21:16,640
+في أي استفسار؟ واضح للجميع؟
+
+255
+00:21:25,690 --> 00:21:29,290
+بدنا لل vector field A عندى vector field A اللى
+
+256
+00:21:29,290 --> 00:21:31,850
+قلناه ممكن يكون فى المستقبل يعنى هنسير هدولة كل
+
+257
+00:21:31,850 --> 00:21:36,390
+الأشياء اللى بتعلمها بس نحط بدلهم E أو H يعني
+
+258
+00:21:36,390 --> 00:21:38,790
+المفروض ان نكون اتعلمنا كتير هاي ال integration
+
+259
+00:21:38,790 --> 00:21:41,790
+لإنه مش هنرجع نقيد التكاملات او مفهومها او اش
+
+260
+00:21:41,790 --> 00:21:44,990
+بتاعى هنطبقها على طول عم الذاكرين أخدنا stocks
+
+261
+00:21:44,990 --> 00:21:47,750
+theorem أخدنا ال divergence theorem أخدنا ال curl
+
+262
+00:21:47,750 --> 00:21:51,150
+أخدنا ال divergence فاحنا هنقول انه لو أنا عندى
+
+263
+00:21:51,150 --> 00:21:55,150
+vector field Aأحنا قبل هيك حكينا انه divergence
+
+264
+00:21:55,150 --> 00:21:58,790
+الكيرل بساوة zero احنا بقول لو فرجيني explicit ان
+
+265
+00:21:58,790 --> 00:22:02,270
+هذا الحكي صحيح that is the divergence of the curl
+
+266
+00:22:02,270 --> 00:22:06,790
+of any vector field is zero وكمان فرجينا انه curl
+
+267
+00:22:06,790 --> 00:22:09,190
+ل grade ال V بساوة zero هدول احنا حكيناهم في ال
+
+268
+00:22:09,190 --> 00:22:14,070
+identity بتاعة ال curl curl ال gradient بساوة zero
+
+269
+00:22:14,070 --> 00:22:17,710
+ل ال scalar field و ال divergence ل ال vector
+
+270
+00:22:17,710 --> 00:22:22,120
+field بساوة zeroبقول لأ سبتي ليه x plus d يعني بدي
+
+271
+00:22:22,120 --> 00:22:25,220
+تعمليه خطوة خطوة يعني بدي أجيب أول curl لل a أقول
+
+272
+00:22:25,220 --> 00:22:29,820
+أن a هي مثلا ax, ay يا z أجيب ال curl تبعها و بعد
+
+273
+00:22:29,820 --> 00:22:33,120
+ما أجيب ال curl تبعها أجيب ال divergence تبعها
+
+274
+00:22:33,120 --> 00:22:38,600
+واضح؟ والتانية اللي بدي curl agreed ال V بيسوا
+
+275
+00:22:38,600 --> 00:22:41,160
+zero يعني أجيب أول ال gradient لل V اللي هو in a
+
+276
+00:22:41,160 --> 00:22:43,560
+scalar field بقولنا ال gradient in a scalar field
+
+277
+00:22:43,560 --> 00:22:51,630
+يعني هيكون مثلا dv by dx x hat دي by دي yVy في Y
+
+278
+00:22:51,630 --> 00:22:57,690
+hat زائد D V by DZ في Z hat بعدين أخد اللي لها ال
+
+279
+00:22:57,690 --> 00:23:02,670
+kern نبدأ ب divergence kernel ال R عندنا ال R قلنا
+
+280
+00:23:02,670 --> 00:23:08,210
+نفترضها مثلا بدي أخد الكارتيجة انها Ax X hat زائد
+
+281
+00:23:08,210 --> 00:23:13,950
+Ay Y hat زائد Az Z hat اخد ال kernel تبعه kernel
+
+282
+00:23:13,950 --> 00:23:18,010
+ال A يعني انا بكون حافظه يعني بتقدر اتخيله و بحطه
+
+283
+00:23:18,010 --> 00:23:18,330
+determinant
+
+284
+00:23:21,700 --> 00:23:25,700
+نفس الحكي يعني أحيان بطلب منك أنك تحليها مش بال ..
+
+285
+00:23:25,700 --> 00:23:28,660
+تسبتيها بال .. بال Cartesian هنا مش الشرط تبقى
+
+286
+00:23:28,660 --> 00:23:32,200
+تبقى تبقى تبقى تسبتيها في ال .. ال spherical عشان
+
+287
+00:23:32,200 --> 00:23:34,700
+نفهم أنك تفهم كيف تعمل مع ال spherical coordinate
+
+288
+00:23:34,700 --> 00:23:37,840
+أو بال cylindrical coordinate لكن أنا مش مشارقة
+
+289
+00:23:37,840 --> 00:23:41,520
+حاسسة أخد أصفر واحدة اللي هي ال Cartesian يعني سهل
+
+290
+00:23:41,520 --> 00:23:47,020
+أنه سرجعها من الذاكرة d by dx, d by dy, d by dz
+
+291
+00:23:47,020 --> 00:23:55,610
+and dxay a z يعني هيكون ايش هيكون النتج x hat في d
+
+292
+00:23:55,610 --> 00:24:08,370
+ay y dx minus d ax by dy minus y hat d az by dx
+
+293
+00:24:08,370 --> 00:24:13,770
+minus d ax by dz plus z hat
+
+294
+00:24:34,180 --> 00:24:35,580
+DxyDxyDxyDxyDxyDxyDxyDxyDxyDxyDxyDxyDxyDxyDxyDxyDxyDxyDxyDxyDxyDxy
+
+295
+00:24:48,850 --> 00:24:53,650
+محنا اتفقنا ان كل الاشي zero مش نفس ال unit يعني x
+
+296
+00:24:53,650 --> 00:24:56,310
+hat dot x hat هتعطي نوع ات لكن x hat dot y hat
+
+297
+00:24:56,310 --> 00:25:01,210
+هيكون zero اذا هيتلقى معايا ال d by dx التفاضل x
+
+298
+00:25:01,210 --> 00:25:06,350
+component و ال d by dy يعني هان النتش هيكون dgx by
+
+299
+00:25:06,350 --> 00:25:13,690
+dx ذات dgy by dy ذات dgz by dz
+
+300
+00:25:24,220 --> 00:25:29,200
+الفاضل d by dx هيكون
+
+301
+00:25:29,200 --> 00:25:35,800
+في عندى ال second derivative لأ ال ay by dx هيكون
+
+302
+00:25:35,800 --> 00:25:46,140
+عندى minus d ax by dx dy الترم التانى هيكون في
+
+303
+00:25:46,140 --> 00:25:52,480
+عندى d اتنين az by dy dx minus
+
+304
+00:26:08,340 --> 00:26:11,600
+طبعاً طبعاً طبعاً طبعاً طبعاً طبعاً
+
+305
+00:26:41,220 --> 00:26:47,140
+الـ x هي
+
+306
+00:26:47,140 --> 00:26:55,490
+dAz by dx minus dAy by dzأنا عاملة shift ايه لكل
+
+307
+00:26:55,490 --> 00:27:05,910
+حاجة انا عاملة shift A X hat انا بمسكت الصف الأولى
+
+308
+00:27:05,910 --> 00:27:11,310
+لأ صح انا عاملة انا D سنة ل shift عمود واحد يعني
+
+309
+00:27:11,310 --> 00:27:20,110
+انا سكت هدولة dAZ by dy minus dAY by dz minus Y
+
+310
+00:27:20,110 --> 00:27:23,350
+hat عاملة shift عمود واحد انا dAZ
+
+311
+00:27:41,520 --> 00:27:46,560
+معقول يعني مش علينا عمل shift عموالـ x hat هو dAz
+
+312
+00:27:46,560 --> 00:27:51,580
+by dy minus dAy by dz minus y hat هو dAz by dx
+
+313
+00:27:51,580 --> 00:27:57,220
+minus dAx by dz وAz hat component هتكون dAy by dx
+
+314
+00:27:57,220 --> 00:28:03,840
+minus dAx by dy نجي التفاضل هلأ مش حاجبه مرة بصحى
+
+315
+00:28:03,840 --> 00:28:12,020
+في الحلقة بيجي x by dx انفاضل اللي هي ال x
+
+316
+00:28:12,020 --> 00:28:24,540
+component هتكونDGX by DXDY minus DAZ by
+
+317
+00:28:24,540 --> 00:28:31,440
+DXDY minus DAY by
+
+318
+00:28:31,440 --> 00:28:33,380
+DXDZ
+
+319
+00:28:39,430 --> 00:28:49,550
+by by by by by by by by
+
+320
+00:28:49,550 --> 00:28:51,690
+by by by by by by by by by by by by by by by by by
+
+321
+00:28:51,690 --> 00:28:54,750
+by by by by by by by
+
+322
+00:28:54,750 --> 00:28:56,470
+by by by by by by by by by by by by by by by by by
+
+323
+00:28:56,470 --> 00:28:56,710
+by by by by by by by by by by by by by by by by by
+
+324
+00:28:56,710 --> 00:28:56,930
+by by by by by by by by by by by by by by by by by
+
+325
+00:28:56,930 --> 00:28:56,970
+by by by by by by by by by by by by by by by by by
+
+326
+00:28:56,970 --> 00:28:58,130
+by by by by by by by by by by by by by by by by by
+
+327
+00:28:58,130 --> 00:29:03,590
+by by
+
+328
+00:29:11,960 --> 00:29:19,120
+بروحوا مع بعض، نفس الحاجة دي تلين از by dx dy احنا
+
+329
+00:29:19,120 --> 00:29:24,220
+دي تلين از by dy dx بروحوا مع بعض عند هذا ال term
+
+330
+00:29:24,220 --> 00:29:31,120
+اللي هو فيه دلتر بيه ay by dx dz هنظرها لتاعة مرة،
+
+331
+00:29:31,120 --> 00:29:35,880
+بروحوا مع بعض كمان عند ال term اللي هو اللي اتبقى
+
+332
+00:29:40,230 --> 00:29:45,570
+D2AX YDY DZ وظهر كرامرة هنا و الإشارات تلتة تروح
+
+333
+00:29:45,570 --> 00:29:50,430
+لـ 0 إذاً هيك احنا أثبتنا إن بالفعل diverse curl A
+
+334
+00:29:50,430 --> 00:29:59,130
+بيساوي 0 واضح؟ نفس الحاجة لcurl gradient V نعملها
+
+335
+00:29:59,130 --> 00:30:10,970
+مع بعض curl gradient V على إن V scalar Aدل ال V
+
+336
+00:30:10,970 --> 00:30:21,270
+هتسوى DVY DX X HAT زي ال DVY DY Y HAT زي ال DVY DZ
+
+337
+00:30:21,270 --> 00:30:25,730
+Z HAT هذا scalar كتير لكن متغير فانت ده على X Y Z
+
+338
+00:30:25,730 --> 00:30:29,150
+ناخد
+
+339
+00:30:29,150 --> 00:30:36,450
+الكام فعندي هذا vector ناخد الكام ده
+
+340
+00:30:36,450 --> 00:30:36,870
+ال gradient
+
+341
+00:30:47,670 --> 00:30:59,730
+هيكون كيرل F X hat Y hat Z hat دي Y دي X دي Y دي Y
+
+342
+00:30:59,730 --> 00:31:05,330
+دي Z دي
+
+343
+00:31:05,330 --> 00:31:07,130
+Y دي Y دي Z دي Y دي Y دي Z دي Y دي Y دي Z دي Y دي
+
+344
+00:31:07,130 --> 00:31:07,370
+Z دي Y دي Y دي Z دي Y دي Y دي Z دي Y دي Y دي Z دي
+
+345
+00:31:07,370 --> 00:31:15,510
+Y دي Y دي Y دي Y دي Y دdV by dy و dV by dz لو
+
+346
+00:31:15,510 --> 00:31:26,490
+أخدنا ال X hat حياتينا دي تلاني D by dy dz minus
+
+347
+00:31:26,490 --> 00:31:34,430
+ال X hat يعني minus D تلاني دي أو دلتا BAB by dy
+
+348
+00:31:34,430 --> 00:31:42,100
+dzهذا الـ term هو 0 واضح؟ انا اخدت الـ x component
+
+349
+00:31:42,100 --> 00:31:46,860
+هيعطيني second derivative ل v بالنسبة ل y و z
+
+350
+00:31:46,860 --> 00:31:51,420
+minus second derivative ل v بالنسبة ل dy و dz
+
+351
+00:31:51,420 --> 00:31:57,480
+مفرقش معايا لأي function لو اخدتله اول d by dx و
+
+352
+00:31:57,480 --> 00:32:01,180
+بعدين اخدتله v by dy هذه لازم يتساوي لو اخدت
+
+353
+00:32:01,180 --> 00:32:07,170
+التقاضة بالنسبة ل y و بعدين تضعف بالنسبة ل xواضح
+
+354
+00:32:07,170 --> 00:32:13,810
+ال component دي ال y hat y hat هيكون عند d تربيه
+
+355
+00:32:13,810 --> 00:32:25,550
+dy dx dz minus d تربيه dy dx dz عند z hat
+
+356
+00:32:25,550 --> 00:32:33,760
+component هيكون عند تلت تربيه dy dx dyمينوس دلتر
+
+357
+00:32:33,760 --> 00:32:36,640
+بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+358
+00:32:36,640 --> 00:32:42,700
+بيه بيه بيه بيه بيه بيه بيه بيه
+
+359
+00:33:05,870 --> 00:33:15,370
+ليه جمال موضوع تاني اللي هو Laplacian قبل
+
+360
+00:33:15,370 --> 00:33:18,630
+ما اعمل Laplacian بتعطيكم مثال من عندى من ال notes
+
+361
+00:33:18,630 --> 00:33:24,630
+فانا بروح ل Laplacian
+
+362
+00:33:24,630 --> 00:33:30,810
+انا
+
+363
+00:33:30,810 --> 00:33:41,010
+مثال لو انا عنديهو V vector بساوي K half دي هيكو
+
+364
+00:33:41,010 --> 00:33:48,910
+تجيبولي diverse ال V لو
+
+365
+00:33:48,910 --> 00:33:59,170
+كان عندي V تساوي X I half زي Y J half زي Z K half
+
+366
+00:33:59,170 --> 00:34:06,330
+بدي diverse ال VI hat و J hat و K hat هما X hat و
+
+367
+00:34:06,330 --> 00:34:10,150
+Y hat و Z hat تعرفوهم ولا ارجع X hat و Y hat و Z
+
+368
+00:34:10,150 --> 00:34:21,570
+hat X hat و Y hat ممكن اسميهم برضه اي جي كي تبقى
+
+369
+00:34:21,570 --> 00:34:29,750
+تعرف اي مين قد
+
+370
+00:34:29,750 --> 00:34:30,350
+ايش قيمته
+
+371
+00:34:45,060 --> 00:34:53,100
+ع السريع قولولي أول سؤال إيه جوابه؟ برافو
+
+372
+00:34:53,100 --> 00:34:56,500
+لإيش احنا اتفقنا ان ال diver معاه لازم يكون دي
+
+373
+00:34:56,500 --> 00:35:04,700
+source يا بيصله thinking يا energy يا بيطلع ال
+
+374
+00:35:04,700 --> 00:35:07,840
+field اللي قداني واضحش بقى اتجاهه في ال key heart
+
+375
+00:35:07,840 --> 00:35:11,120
+اذا غبتي أن هذا اتجاه هو ال key heart
+
+376
+00:35:14,660 --> 00:35:20,140
+هي Z hat و Z hat يعني مش قاعدين على K hat دول ال
+
+377
+00:35:20,140 --> 00:35:24,160
+main vectors و انا بعمل switch غالبة بينهم I hat و
+
+378
+00:35:24,160 --> 00:35:30,760
+J hat و K hat و نفسهم X hat و Y hat و Z hat نفسهم
+
+379
+00:35:30,760 --> 00:35:36,140
+اذا اتجاه ال field اتجاه Z hat اذا مافيش
+
+380
+00:35:36,140 --> 00:35:40,260
+divergence فيه بدون مغلب حالي و اعمل divergence
+
+381
+00:35:40,260 --> 00:35:46,190
+الجواب بيكون zeroطيب الفكتور هذا يكون واحد واحد
+
+382
+00:35:46,190 --> 00:35:56,230
+واحد واحد واحد واحد واحد واحد واحد واحد
+
+383
+00:35:56,230 --> 00:35:56,890
+واحد واحد واحد واحد واحد واحد واحد واحد واحد واحد
+
+384
+00:35:56,890 --> 00:35:57,230
+واحد واحد واحد واحد واحد واحد واحد واحد واحد واحد
+
+385
+00:35:57,230 --> 00:36:01,490
+واحد واحد واحد واحد واحد واحد واحد واحد واحد واحد
+
+386
+00:36:01,490 --> 00:36:03,750
+واحد واحد واحد واحد واحد واحد واحد واحد واحد واحد
+
+387
+00:36:03,750 --> 00:36:03,770
+واحد واحد واحد واحد واحد واحد واحد واحد واحد واحد
+
+388
+00:36:03,770 --> 00:36:04,190
+واحد واحد واحد واحد واحد واحد واحد واحد واحد واحد
+
+389
+00:36:04,190 --> 00:36:04,210
+واحد واحد واحد واحد واحد واحد واحد واحد واحد واحد
+
+390
+00:36:24,170 --> 00:36:25,570
+DYDYDYDXVXDBYDYDVZYDVZ
+
+391
+00:36:29,330 --> 00:36:35,290
+ثالث واحد وثالث ثالث
+
+392
+00:36:35,290 --> 00:36:39,270
+واحد وثالث واحد وثالث ثالث واحد وثالث ثالث واحد
+
+393
+00:36:39,270 --> 00:36:41,150
+وثالث واحد وثالث واحد وثالث واحد وثالث واحد وثالث
+
+394
+00:36:41,150 --> 00:36:41,190
+وثالث واحد وثالث واحد وثالث واحد وثالث واحد وثالث
+
+395
+00:36:41,190 --> 00:36:42,170
+وثالث واحد وثالث واحد وثالث واحد وثالث واحد وثالث
+
+396
+00:36:42,170 --> 00:36:43,090
+وثالث واحد وثالث واحد وثالث واحد وثالث واحد
+
+397
+00:36:58,550 --> 00:37:06,010
+تقدر أخبرك تمان أخر مثال هو لو كان عندي D بيساوي
+
+398
+00:37:06,010 --> 00:37:12,870
+minus Y X hat plus
+
+399
+00:37:12,870 --> 00:37:20,270
+X Y hat بدي ال curve تبعك احنا كذا مثال اليوم
+
+400
+00:37:20,270 --> 00:37:23,030
+أخدنا على ال curve بس مش رلط اننا نعمل اخر مرة
+
+401
+00:37:23,030 --> 00:37:32,970
+curve بيه قلنا إيش بيساويx hat y hat z hat فبقيت
+
+402
+00:37:32,970 --> 00:37:40,870
+نعملها كتير اذا حد يجي يطلع يطلع يالا مانعش مش هلأ
+
+403
+00:37:40,870 --> 00:37:43,690
+اخد اللي هو الكل لما احتملنا يالا انا اقولكم كذا
+
+404
+00:37:43,690 --> 00:37:48,810
+مرة الكل دي
+
+405
+00:37:48,810 --> 00:37:55,790
+by dx دي by dx دي by dx دي by dx دي by dx دي by dx
+
+406
+00:37:55,790 --> 00:37:56,090
+x دي by x دي by x دي by x دي by x دي by x دي by x
+
+407
+00:37:56,090 --> 00:38:07,500
+دي by x دd by dx by dy dy dz عندي minus y و x و 0
+
+408
+00:38:07,500 --> 00:38:13,440
+ممتازة هناخد ال x hat component ليه هتقولي zero
+
+409
+00:38:13,440 --> 00:38:19,860
+minus zero لإنه dx by dz zero minus
+
+410
+00:38:19,860 --> 00:38:26,830
+y hat minus y hat بس المهم أنه نروح التجارب صح-Y
+
+411
+00:38:26,830 --> 00:38:37,650
+hat هيكون 0DX0-0 ذات Z hat يكون واحد ومايناس
+
+412
+00:38:37,650 --> 00:38:42,090
+ومايناس ويصير plus واحد هيكون اثنين Z hat إذا ال
+
+413
+00:38:42,090 --> 00:38:46,050
+curling تبعه بيسوي الصفر هي عند ال curling حوالين
+
+414
+00:38:46,050 --> 00:38:50,410
+ال Z axis بيعملوه باتجاه ال curling Z hat
+
+415
+00:39:02,620 --> 00:39:05,480
+أحنا هذا كله لحظة ال eta ناس كتير بيسموه ال first
+
+416
+00:39:05,480 --> 00:39:10,000
+derivative صح هو divergence و curl و gradient بس
+
+417
+00:39:10,000 --> 00:39:13,100
+ال first derivative لإن أنا بفضل بس مرة واحدة و d
+
+418
+00:39:13,100 --> 00:39:17,180
+by dx, d by dy, d by dz، في كل الأحوال أسوأ أخدت
+
+419
+00:39:17,180 --> 00:39:20,840
+ال gradient ولا ال divergence ولا ال curl اللي
+
+420
+00:39:20,840 --> 00:39:24,240
+هنشوفه هال eta اللي هو ال aplacian أو اللي هو
+
+421
+00:39:24,240 --> 00:39:24,840
+second derivative
+
+422
+00:39:46,010 --> 00:39:51,390
+أو second derivative اول واحد هنشوفه بال second
+
+423
+00:39:51,390 --> 00:39:55,070
+derivative اللي هو لابلاسيان لابلاسيان هو بساطة هو
+
+424
+00:39:55,070 --> 00:39:59,450
+دل ال divergence يعني انا باخد دل ال gradient اصلا
+
+425
+00:39:59,450 --> 00:40:02,070
+divergence دل ال gradient لما انا عاجز scalar
+
+426
+00:40:02,070 --> 00:40:05,670
+field وعندي ال gradient دي لو لما اخد هذا بكتر صار
+
+427
+00:40:05,670 --> 00:40:09,630
+بكتر حتى انا شوفت في المثال مصممة مصانعاتهذا ال
+
+428
+00:40:09,630 --> 00:40:13,150
+vector لما أخده ال divergence إيش بيصير؟ دل تربية
+
+429
+00:40:13,150 --> 00:40:22,130
+لإنه grade ال V دي
+
+430
+00:40:22,130 --> 00:40:27,950
+V بيكتب دي V بيكتب DX X hat دي Y بيكتب Y Y hat دي
+
+431
+00:40:27,950 --> 00:40:32,050
+V بيكتب Z Z hat لما أجي أعمله ال product مع اللي
+
+432
+00:40:32,050 --> 00:40:38,180
+هو الدل هيكون DX X hatبي دي V بي دي X هتصير second
+
+433
+00:40:38,180 --> 00:40:42,540
+derivative ل V بالنسبة ل X ال second term هيكون
+
+434
+00:40:42,540 --> 00:40:45,720
+second derivative بالنسبة ل Y و ال third term هو
+
+435
+00:40:45,720 --> 00:40:49,140
+second derivative بالنسبة ل Z عشان هيك احنا بنسمي
+
+436
+00:40:49,140 --> 00:40:53,300
+ال second derivative او ل plus يعني اذا دلتر بيه V
+
+437
+00:40:53,300 --> 00:40:57,200
+هو ل plus V الناس باختصار بيسموه ل plus ل V لما
+
+438
+00:40:57,200 --> 00:41:02,520
+تسمع كلمة ل plus V هو دلتر بيه Vلو لاحظنا اللي
+
+439
+00:41:02,520 --> 00:41:06,900
+بلاسن هو scalar لانه انا عملنا product between two
+
+440
+00:41:06,900 --> 00:41:09,620
+vectors و ال product between two vectors ده لانه
+
+441
+00:41:09,620 --> 00:41:17,660
+scalar فالنتج هو scalar a quantity
+
+442
+00:41:17,660 --> 00:41:24,760
+حلتها
+
+443
+00:41:24,760 --> 00:41:27,240
+في ال cylindrical coordinate احنا شفنا هذا الحكي
+
+444
+00:41:27,240 --> 00:41:31,210
+أثبتناه في اللي هو ال Cartesian coordinateالـ
+
+445
+00:41:31,210 --> 00:41:33,570
+Cartesian Coordinate اللي بلاس برضه بقدر أكتبه
+
+446
+00:41:33,570 --> 00:41:35,650
+بالـ cylindrical و بقدر أكتبه بالـ cephalical
+
+447
+00:41:35,650 --> 00:41:39,910
+coordinate بنفس الطريقة أكتب ال grade ال V و بعدين
+
+448
+00:41:39,910 --> 00:41:43,190
+أعمل diverge ل grade ال V بحصل على ال place ال V
+
+449
+00:41:43,190 --> 00:41:46,010
+في ال cylindrical coordinate و نفس الحاجة في ال
+
+450
+00:41:46,010 --> 00:41:50,350
+cephalical coordinate قالت لو أنا بدي أحكي على
+
+451
+00:41:50,350 --> 00:41:53,470
+أنمواء ال fields لو كان ان ال field اسمه harmonic
+
+452
+00:41:54,390 --> 00:41:56,970
+It's said to be in a given region if the Laplacian
+
+453
+00:41:56,970 --> 00:42:00,550
+vanish in that region يعني إذا كان ال Laplace ل V
+
+454
+00:42:00,550 --> 00:42:04,550
+بيساوة Zero ع طول بقول V ماله Harmonic بتعرفوا ال
+
+455
+00:42:04,550 --> 00:42:09,450
+Harmonic صح؟ إذا أول ما بشوف إنه لو حسبت الدل ل V
+
+456
+00:42:09,450 --> 00:42:14,070
+بيساوة Zero بقول إذا V تبعي هو Harmonic function ع
+
+457
+00:42:14,070 --> 00:42:18,490
+طول عشان أفحص إنه Harmonic ولا لأ ع طول بقول إنه
+
+458
+00:42:18,490 --> 00:42:21,990
+دل تربيع V إذا سوات Zero بقول Harmonic ال second
+
+459
+00:42:21,990 --> 00:42:26,680
+derivative لل vectorدل تلبية ال vector بس second
+
+460
+00:42:26,680 --> 00:42:29,780
+derivative ل ال vector بقدر أعيد كتابته بهذه
+
+461
+00:42:29,780 --> 00:42:34,300
+الطريقة احنا
+
+462
+00:42:34,300 --> 00:42:38,580
+في ال .. لما ناخد نفسه ال equation كتير هيطلع معنا
+
+463
+00:42:38,580 --> 00:42:42,920
+kill .. kill .. kill .. kill .. kill .. kill ..
+
+464
+00:42:42,920 --> 00:42:44,620
+kill .. kill .. kill .. kill .. kill .. kill ..
+
+465
+00:42:44,620 --> 00:42:46,040
+kill .. kill .. kill .. kill .. kill .. kill ..
+
+466
+00:42:46,040 --> 00:42:46,840
+kill .. kill .. kill .. kill .. kill .. kill ..
+
+467
+00:42:46,840 --> 00:42:47,040
+kill .. kill .. kill .. kill .. kill .. kill ..
+
+468
+00:42:47,040 --> 00:42:48,500
+kill .. kill .. kill .. kill .. kill .. kill ..
+
+469
+00:42:48,500 --> 00:42:49,180
+kill .. kill .. kill .. kill .. kill .. kill ..
+
+470
+00:42:49,180 --> 00:42:51,480
+kill ..
+
+471
+00:43:19,110 --> 00:43:20,510
+-DelTarbiyaDelTarbiyaDelTarbiyaDelDivergeA
+
+472
+00:43:20,510 --> 00:43:21,910
+-KerKerFieldDelTarbiyaDelTarbiyaDelTarbiyaDelTarbiyaDelTarbiya
+
+473
+00:43:26,300 --> 00:43:32,420
+النتيجة الواضحة قدامنا هيكون delta PA بتساوي delta
+
+474
+00:43:32,420 --> 00:43:35,860
+PA X X hat لأن مسحنا مش ال identity تعطيه العوام
+
+475
+00:43:35,860 --> 00:43:39,520
+دلتر بيه اه هو التفاعد ال second derivative او
+
+476
+00:43:39,520 --> 00:43:45,540
+دلتر بيه الا اه دلتر بيه اه يعني ورعان دكتور بيه
+
+477
+00:43:45,540 --> 00:43:50,120
+اكس اكس هات زائد ا و وايها زائد ا جدر بيه اكس اكس
+
+478
+00:43:50,120 --> 00:43:50,520
+هات زائد ا جدر بيه اكس هات زائد ا جدر بيه اكس هات
+
+479
+00:43:50,520 --> 00:43:51,900
+زائد ا جدر بيه اكس هات زائد ا جدر بيه اكس هات زائد
+
+480
+00:43:51,900 --> 00:43:53,180
+ا جدر بيه اكس هات زائد ا جدر بيه اكس هات زائد ا جد
+
+481
+00:43:53,240 --> 00:43:56,040
+هتسيب دل تربية على كل component من دول components
+
+482
+00:43:56,040 --> 00:43:59,820
+طبعا ال vector .. الدل تربية لل vector field هي
+
+483
+00:43:59,820 --> 00:44:04,980
+vector لأن دل التربية هي scalar D2 by DX2 D2 by
+
+484
+00:44:04,980 --> 00:44:07,180
+DY2 أو .. بس يعني هذه
+
+485
+00:44:21,910 --> 00:44:29,230
+دل تربيه في الواقع هي دل ضد دل هيكون D تربيه by DX
+
+486
+00:44:29,230 --> 00:44:34,950
+تربيه ذات D تربيه by DY تربيه ذات D تربيه راج DZ
+
+487
+00:44:34,950 --> 00:44:41,970
+واضح؟ لأن دل إيش هي؟ D by DX إزها ذات D by DY
+
+488
+00:44:41,970 --> 00:44:45,830
+وإيها ذات D by DZ إزها
+
+489
+00:44:58,770 --> 00:45:05,110
+هتعطينا D2YDX2 ثقة D2YDY تربية ثقة D2YDZ تربية فمن
+
+490
+00:45:05,110 --> 00:45:08,290
+هذه التربية A هيكون عندنا ال components اللي
+
+491
+00:45:08,290 --> 00:45:14,310
+أمامنا و كما اتفقنا هو هيكون vector P ممكن أعبر
+
+492
+00:45:14,310 --> 00:45:22,410
+عليه بهذه الطريقة أو أعبر عنه بهذه الطريقة يعطيكوا
+
+493
+00:45:22,410 --> 00:45:25,910
+العافية و ان شاء الله بنتبع اللقاء القادم السلام
+
+494
+00:45:25,910 --> 00:45:26,250
+عليكم
+
diff --git a/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/ryHc6fpOqQU_raw.json b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/ryHc6fpOqQU_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..38b39517f8ebd233a490389f34f33c6337702f22
--- /dev/null
+++ b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/ryHc6fpOqQU_raw.json
@@ -0,0 +1 @@
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"end": 780.9, "text": "دى رو دى رو دى فاي", "tokens": [3215, 7578, 12602, 2407, 11778, 7578, 12602, 2407, 11778, 7578, 6156, 47302], "avg_logprob": -0.6796875, "compression_ratio": 1.1071428571428572, "no_speech_prob": 0.0, "words": [{"start": 771.2, "end": 771.5, "word": "دى", "probability": 0.382080078125}, {"start": 771.5, "end": 771.74, "word": " رو", "probability": 0.730712890625}, {"start": 771.74, "end": 777.54, "word": " دى", "probability": 0.619384765625}, {"start": 777.54, "end": 780.32, "word": " رو", "probability": 0.662353515625}, {"start": 780.32, "end": 780.52, "word": " دى", "probability": 0.890869140625}, {"start": 780.52, "end": 780.9, "word": " فاي", "probability": 0.5037841796875}], "temperature": 1.0}, {"id": 31, "seek": 82641, "start": 798.03, "end": 826.41, "text": "نرجع احنا عندنا ال vector لازمنا اجيب اول حاجة كيرم ال a كيرم ال a قولنا بس أخد يا اللي هو determinant يا بكون حفظاهم ال x hat ده تكون dz by dy minus dy by dz minus dy يعني اللي واحد ممكن يتخيلها 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"probability": 0.47265625}, {"start": 2450.88, "end": 2451.7, "word": " يعني", "probability": 0.64013671875}, {"start": 2451.7, "end": 2452.32, "word": " اذا", "probability": 0.7025146484375}, {"start": 2452.32, "end": 2452.78, "word": " دلتر", "probability": 0.75714111328125}, {"start": 2452.78, "end": 2453.0, "word": " بيه", "probability": 0.7018229166666666}, {"start": 2453.0, "end": 2453.3, "word": " V", "probability": 0.95947265625}, {"start": 2453.3, "end": 2453.62, "word": " هو", "probability": 0.9541015625}, {"start": 2453.62, "end": 2453.74, "word": " ل", "probability": 0.94091796875}, {"start": 2453.74, "end": 2454.12, "word": " plus", "probability": 0.93212890625}, {"start": 2454.12, "end": 2454.42, "word": " V", "probability": 0.9892578125}, {"start": 2454.42, "end": 2454.92, "word": " الناس", "probability": 0.9222005208333334}, {"start": 2454.92, "end": 2455.5, "word": " باختصار", "probability": 0.83330078125}, {"start": 2455.5, "end": 2456.04, "word": " بيسموه", "probability": 0.87265625}, {"start": 2456.04, "end": 2456.18, "word": " ل", "probability": 0.88330078125}, {"start": 2456.18, "end": 2456.62, "word": " plus", "probability": 0.947265625}, {"start": 2456.62, "end": 2456.84, "word": " ل", "probability": 0.6953125}, {"start": 2456.84, "end": 2457.0, "word": " V", "probability": 0.9736328125}, {"start": 2457.0, "end": 2457.2, "word": " لما", "probability": 0.912353515625}, {"start": 2457.2, "end": 2457.5, "word": " تسمع", "probability": 0.8103841145833334}, {"start": 2457.5, "end": 2457.8, "word": " كلمة", "probability": 0.9016927083333334}, {"start": 2457.8, "end": 2457.92, "word": " ل", "probability": 0.35791015625}, {"start": 2457.92, "end": 2458.2, "word": " plus", "probability": 0.97705078125}, {"start": 2458.2, "end": 2458.44, "word": " V", "probability": 0.9814453125}, {"start": 2458.44, "end": 2458.86, "word": " هو", "probability": 0.88916015625}, {"start": 2458.86, "end": 2459.28, "word": " دلتر", "probability": 0.980712890625}, {"start": 2459.28, "end": 2459.64, "word": " بيه", "probability": 0.96533203125}, {"start": 2459.64, "end": 2460.06, "word": " V", "probability": 0.98291015625}], "temperature": 1.0}, {"id": 88, "seek": 248958, "start": 2462.04, "end": 2489.58, "text": "لو لاحظنا اللي بلاسن هو scalar لانه انا عملنا product between two vectors و ال product between two vectors ده لانه scalar فالنتج هو scalar a quantity حلتها في ال cylindrical coordinate احنا شفنا هذا الحكي أثبتناه في اللي هو ال Cartesian coordinate", "tokens": [1211, 2407, 20193, 5016, 19913, 8315, 13672, 1829, 4724, 15040, 3794, 1863, 31439, 39684, 5296, 7649, 3224, 1975, 8315, 6225, 42213, 8315, 1674, 1296, 732, 18875, 4032, 2423, 1674, 1296, 732, 18875, 11778, 3224, 5296, 7649, 3224, 39684, 6156, 6027, 29399, 7435, 31439, 39684, 257, 11275, 11331, 1211, 2655, 11296, 8978, 2423, 28044, 15888, 15670, 1975, 5016, 8315, 13412, 5172, 8315, 23758, 21542, 4117, 1829, 5551, 12984, 3555, 2655, 8315, 3224, 8978, 13672, 1829, 31439, 2423, 22478, 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{"start": 2486.6, "end": 2486.82, "word": " هذا", "probability": 0.8896484375}, {"start": 2486.82, "end": 2487.24, "word": " الحكي", "probability": 0.8111979166666666}, {"start": 2487.24, "end": 2487.82, "word": " أثبتناه", "probability": 0.8241373697916666}, {"start": 2487.82, "end": 2487.98, "word": " في", "probability": 0.85107421875}, {"start": 2487.98, "end": 2488.26, "word": " اللي", "probability": 0.8203125}, {"start": 2488.26, "end": 2488.44, "word": " هو", "probability": 0.9677734375}, {"start": 2488.44, "end": 2488.54, "word": " ال", "probability": 0.8076171875}, {"start": 2488.54, "end": 2488.92, "word": " Cartesian", "probability": 0.69287109375}, {"start": 2488.92, "end": 2489.58, "word": " coordinate", "probability": 0.7978515625}], "temperature": 1.0}, {"id": 89, "seek": 251346, "start": 2491.07, "end": 2513.47, "text": "الـ Cartesian Coordinate اللي بلاس برضه بقدر أكتبه بالـ cylindrical و بقدر أكتبه بالـ cephalical coordinate بنفس الطريقة أكتب ال grade ال V و بعدين أعمل diverge ل grade ال V بحصل على ال place ال V في ال cylindrical coordinate و نفس الحاجة في ال cephalical coordinate قالت لو أنا بدي أحكي على أنمواء ال fields لو كان ان ال field اسمه harmonic", "tokens": [6027, 39184, 22478, 42434, 39620, 473, 13672, 1829, 4724, 15040, 3794, 4724, 43042, 3224, 4724, 28543, 2288, 5551, 4117, 2655, 3555, 3224, 20666, 39184, 28044, 15888, 4032, 4724, 28543, 2288, 5551, 4117, 2655, 3555, 3224, 20666, 39184, 45026, 4947, 804, 15670, 44945, 36178, 41950, 16572, 28671, 5551, 4117, 2655, 3555, 2423, 7204, 2423, 691, 4032, 39182, 9957, 5551, 25957, 1211, 18558, 432, 5296, 7204, 2423, 691, 4724, 5016, 36520, 15844, 2423, 1081, 2423, 691, 8978, 2423, 28044, 15888, 15670, 4032, 8717, 36178, 21542, 26108, 3660, 8978, 2423, 45026, 4947, 804, 15670, 50239, 2655, 45164, 41850, 4724, 16254, 5551, 5016, 4117, 1829, 15844, 14739, 2304, 2407, 16606, 2423, 7909, 45164, 25961, 16472, 2423, 2519, 24525, 2304, 3224, 32270], "avg_logprob": -0.28230930890067146, 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0.9893798828125}, {"start": 2673.79, "end": 2674.35, "word": " راج", "probability": 0.239471435546875}, {"start": 2674.35, "end": 2674.95, "word": " DZ", "probability": 0.654296875}, {"start": 2674.95, "end": 2676.59, "word": " واضح؟", "probability": 0.770751953125}, {"start": 2676.59, "end": 2676.93, "word": " لأن", "probability": 0.38482666015625}, {"start": 2676.93, "end": 2677.21, "word": " دل", "probability": 0.830078125}, {"start": 2677.21, "end": 2677.41, "word": " إيش", "probability": 0.6630859375}, {"start": 2677.41, "end": 2678.03, "word": " هي؟", "probability": 0.6473388671875}, {"start": 2678.03, "end": 2678.27, "word": " D", "probability": 0.56640625}, {"start": 2678.27, "end": 2678.73, "word": " by", "probability": 0.269775390625}, {"start": 2678.73, "end": 2679.27, "word": " DX", "probability": 0.99365234375}, {"start": 2679.27, "end": 2680.05, "word": " إزها", "probability": 0.5962320963541666}, {"start": 2680.05, "end": 2680.93, "word": " ذات", "probability": 0.756591796875}, {"start": 2680.93, "end": 2681.15, "word": " D", "probability": 0.91357421875}, {"start": 2681.15, "end": 2681.49, "word": " by", "probability": 0.98046875}, {"start": 2681.49, "end": 2681.97, "word": " DY", "probability": 0.814453125}, {"start": 2681.97, "end": 2682.57, "word": " وإيها", "probability": 0.63824462890625}, {"start": 2682.57, "end": 2683.17, "word": " ذات", "probability": 0.95263671875}, {"start": 2683.17, "end": 2683.53, "word": " D", "probability": 0.9873046875}, {"start": 2683.53, "end": 2683.85, "word": " by", "probability": 0.96826171875}, {"start": 2683.85, "end": 2684.39, "word": " DZ", "probability": 0.88037109375}, {"start": 2684.39, "end": 2685.83, "word": " إزها", "probability": 0.8759765625}], "temperature": 1.0}, {"id": 96, "seek": 272625, "start": 2698.77, "end": 2726.25, "text": "هتعطينا D2YDX2 ثقة D2YDY تربية ثقة D2YDZ تربية فمن هذه التربية A هيكون عندنا ال components اللي أمامنا و كما اتفقنا هو هيكون vector P ممكن أعبر عليه بهذه الطريقة أو أعبر عنه بهذه الطريقة يعطيكوا العافية و ان شاء الله بنتبع اللقاء القادم السلام عليكم", "tokens": [3224, 2655, 3615, 9566, 1829, 8315, 413, 17, 56, 35, 55, 17, 38637, 28671, 413, 17, 56, 35, 56, 6055, 2288, 21292, 3660, 38637, 28671, 413, 17, 56, 35, 57, 6055, 2288, 21292, 3660, 6156, 27842, 29538, 16712, 2288, 21292, 3660, 316, 39896, 30544, 43242, 8315, 2423, 6677, 13672, 1829, 5551, 2304, 10943, 8315, 4032, 9122, 15042, 1975, 2655, 5172, 4587, 8315, 31439, 39896, 30544, 8062, 430, 3714, 43020, 5551, 3615, 3555, 2288, 47356, 39627, 24192, 41950, 16572, 28671, 34051, 5551, 3615, 3555, 2288, 18871, 3224, 39627, 24192, 41950, 16572, 28671, 37495, 9566, 1829, 4117, 14407, 18863, 31845, 10632, 4032, 16472, 13412, 16606, 21984, 44945, 2655, 3555, 3615, 13672, 4587, 16606, 25062, 18513, 2304, 21136, 37440, 25894, 24793], "avg_logprob": -0.2846638590347867, "compression_ratio": 1.8705357142857142, "no_speech_prob": 2.2649765014648438e-06, "words": [{"start": 2698.7699999999995, "end": 2699.6299999999997, "word": "هتعطينا", "probability": 0.7977091471354166}, {"start": 2699.6299999999997, "end": 2700.49, "word": " D2YDX2", "probability": 0.4804484049479167}, {"start": 2700.49, "end": 2700.97, "word": " ثقة", "probability": 0.1635303497314453}, {"start": 2700.97, "end": 2701.95, "word": " D2YDY", "probability": 0.853125}, {"start": 2701.95, "end": 2702.43, "word": " تربية", "probability": 0.58721923828125}, {"start": 2702.43, "end": 2702.69, "word": " ثقة", "probability": 0.814697265625}, {"start": 2702.69, "end": 2703.67, "word": " D2YDZ", "probability": 0.93779296875}, {"start": 2703.67, "end": 2704.71, "word": " تربية", "probability": 0.93994140625}, {"start": 2704.71, "end": 2705.11, "word": " فمن", "probability": 0.5224609375}, {"start": 2705.11, "end": 2705.31, "word": " هذه", "probability": 0.478759765625}, {"start": 2705.31, "end": 2705.97, "word": " التربية", "probability": 0.7940673828125}, {"start": 2705.97, "end": 2706.23, "word": " A", "probability": 0.56982421875}, {"start": 2706.23, "end": 2706.71, "word": " هيكون", "probability": 0.7467041015625}, {"start": 2706.71, "end": 2707.17, "word": " عندنا", "probability": 0.79833984375}, {"start": 2707.17, "end": 2707.39, "word": " ال", "probability": 0.93896484375}, {"start": 2707.39, "end": 2707.87, "word": " components", "probability": 0.9228515625}, {"start": 2707.87, "end": 2708.29, "word": " اللي", "probability": 0.865966796875}, {"start": 2708.29, "end": 2708.87, "word": " أمامنا", "probability": 0.8436279296875}, {"start": 2708.87, "end": 2709.25, "word": " و", "probability": 0.86083984375}, {"start": 2709.25, "end": 2709.37, "word": " كما", "probability": 0.2557373046875}, {"start": 2709.37, "end": 2709.89, "word": " اتفقنا", "probability": 0.83984375}, {"start": 2709.89, "end": 2710.11, "word": " هو", "probability": 0.77587890625}, {"start": 2710.11, "end": 2710.53, "word": " هيكون", "probability": 0.72216796875}, {"start": 2710.53, "end": 2711.03, "word": " vector", "probability": 0.75341796875}, {"start": 2711.03, "end": 2711.69, "word": " P", "probability": 0.85693359375}, {"start": 2711.69, "end": 2713.93, "word": " ممكن", "probability": 0.792724609375}, {"start": 2713.93, "end": 2714.31, "word": " أعبر", "probability": 0.803466796875}, {"start": 2714.31, "end": 2714.51, "word": " عليه", "probability": 0.5166015625}, {"start": 2714.51, "end": 2714.77, "word": " بهذه", "probability": 0.668212890625}, {"start": 2714.77, "end": 2715.23, "word": " الطريقة", "probability": 0.97509765625}, {"start": 2715.23, "end": 2715.47, "word": " أو", "probability": 0.87060546875}, {"start": 2715.47, "end": 2715.87, "word": " أعبر", "probability": 0.8389892578125}, {"start": 2715.87, "end": 2716.09, "word": " عنه", "probability": 0.910888671875}, {"start": 2716.09, "end": 2716.35, "word": " بهذه", "probability": 0.96240234375}, {"start": 2716.35, "end": 2718.45, "word": " الطريقة", "probability": 0.9832356770833334}, {"start": 2718.45, "end": 2722.41, "word": " يعطيكوا", "probability": 0.740576171875}, {"start": 2722.41, "end": 2722.89, "word": " العافية", "probability": 0.9264322916666666}, {"start": 2722.89, "end": 2723.03, "word": " و", "probability": 0.978515625}, {"start": 2723.03, "end": 2723.07, "word": " ان", "probability": 0.69384765625}, {"start": 2723.07, "end": 2723.19, "word": " شاء", "probability": 0.974609375}, {"start": 2723.19, "end": 2723.23, "word": " الله", "probability": 0.9287109375}, {"start": 2723.23, "end": 2723.67, "word": " بنتبع", "probability": 0.7769775390625}, {"start": 2723.67, "end": 2724.05, "word": " اللقاء", "probability": 0.79638671875}, {"start": 2724.05, "end": 2724.59, "word": " القادم", "probability": 0.8933919270833334}, {"start": 2724.59, "end": 2725.91, "word": " السلام", "probability": 0.787109375}, {"start": 2725.91, "end": 2726.25, "word": " عليكم", "probability": 0.86572265625}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2727.648, "duration_after_vad": 2478.213124999989}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/tMFy3zzwo94.srt b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/tMFy3zzwo94.srt
new file mode 100644
index 0000000000000000000000000000000000000000..ca4d826a919bf089e430ed391a5ecacea226c5da
--- /dev/null
+++ b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/tMFy3zzwo94.srt
@@ -0,0 +1,2077 @@
+1
+00:00:20,860 --> 00:00:23,300
+بسم الله الرحمن الرحيم السلام عليكم ورحمة الله و
+
+2
+00:00:23,300 --> 00:00:26,160
+بركاته إحنا اليوم إن شاء الله راح نتابع موضوعنا 
+
+3
+00:00:26,160 --> 00:00:29,240
+إحنا في المحاضرات الماضية شفنا أمثلة كيف ممكن نحسب 
+
+4
+00:00:29,240 --> 00:00:32,560
+الـmagnetic field من عدة elements ومور فيها 
+
+5
+00:00:32,560 --> 00:00:36,080
+التيار زي الـ filament اللي لها finite length  الـ
+
+6
+00:00:36,080 --> 00:00:40,080
+filament اللي لها length infinity و infinity من جهتين
+
+7
+00:00:40,330 --> 00:00:42,790
+بعدين شفنا من الـ plane شفنا من الـ ring شفنا من الـ
+
+8
+00:00:42,790 --> 00:00:47,250
+solenoid اللي يعتبرنا إن الـ ring هي element من الـ
+
+9
+00:00:47,250 --> 00:00:50,910
+solenoid بعدين كملنا على الـ Biot-Savart و اليوم
+
+10
+00:00:50,910 --> 00:00:54,070
+هنشوف أمثلة كمان على حساب الـ magnetic field يعني
+
+11
+00:00:54,070 --> 00:00:56,770
+مثلا ما أنا حكيتلكم على ذلك سابقا إن الـ concept
+
+12
+00:00:56,770 --> 00:01:00,970
+بتاع كل chapter هو واضح لكن كل اللي إحنا بنحكي فيه
+
+13
+00:01:00,970 --> 00:01:04,230
+هي أمثلة عامة توضح الـ concept كيف إحنا نستخدم هذا الـ
+
+14
+00:01:04,230 --> 00:01:08,690
+concept وكيف إحنا نطبقه فإحنا شفنا في المحاضرات
+
+15
+00:01:08,690 --> 00:01:12,890
+السابقة إن الـ magnetic field بشكل عام بيساوي نص K
+
+16
+00:01:12,890 --> 00:01:19,330
+cross A and hat  K اللي هو اتجاه التيار A and hat
+
+17
+00:01:19,330 --> 00:01:23,410
+اللي هو الـ normal اللي على الـ plane في اتجاه النقطة
+
+18
+00:01:23,410 --> 00:01:26,900
+الرئيسية عندها الـ magnetic field طبعا فإحنا إيش
+
+19
+00:01:26,900 --> 00:01:29,740
+بقولنا أول مثال بيعني طبعا إيه؟ لأن فينا two planes
+
+20
+00:01:29,740 --> 00:01:35,060
+واحد عند z equal 0 واحد هذا z axis هذا الاتجاه هو
+
+21
+00:01:35,060 --> 00:01:39,400
+z axis فهذا عند z equal 0 وهنا عند z equal 4 يعني
+
+22
+00:01:39,400 --> 00:01:43,820
+المسافة بين الـ two planes هي 4 الـ plane اللي عند z
+
+23
+00:01:43,820 --> 00:01:48,460
+equal 0 بيحمل تيار K مقداره minus 10 ax hat واضح
+
+24
+00:01:48,460 --> 00:01:52,180
+إن هو واخد الـ x يعني إيه اللي هيطلع من الـ plane هتكون باتجاه الـ
+
+25
+00:01:52,180 --> 00:02:00,780
+x طبعا والتيار داخل والتيار هو الـ x معناه إن التيار
+
+26
+00:02:00,780 --> 00:02:04,700
+داخل هي K هي اتجاه التيار وهي الـ x فزائد هيكون 
+
+27
+00:02:04,700 --> 00:02:09,980
+minus minus عشرة x hat بينما هنا شماله طالع
+
+28
+00:02:09,980 --> 00:02:16,620
+فهيكون عشرة x hat طبعا الـ K هي الـ units بتاعتها
+
+29
+00:02:16,620 --> 00:02:20,060
+amps per meter زي ما شوفنا في مثال لما جبنا الـ
+
+30
+00:02:20,060 --> 00:02:27,050
+magnetic field اللي بيعملونه في الـ surface طبعا طالب مننا
+
+31
+00:02:27,050 --> 00:02:33,410
+نحسب عند نقطة x1 y1 z1 هذه إحنا الـ 0
+
+32
+00:02:33,410 --> 00:02:39,270
+0 0 هنا نقل الـ origin عندي x1 y1 z1 ومنها تكون z
+
+33
+00:02:39,270 --> 00:02:45,490
+هو الـ axis يعني مثلا هنا هذه النقطة بتاعتنا 1 1 1
+
+34
+00:02:45,490 --> 00:02:49,370
+x1 y1 z1
+
+35
+00:02:52,220 --> 00:02:55,120
+لو استخدمنا المعادلة العامة أو استخدمنا معادلتنا 
+
+36
+00:02:55,120 --> 00:02:58,040
+السابقة إن تحت وفوق الـ plane زي ما حكينا في محاضرات
+
+37
+00:02:58,040 --> 00:03:03,260
+الماضية لازم نحصل على نتيجة عند لو أخدت... هسمي الـ H
+
+38
+00:03:03,260 --> 00:03:07,500
+اللي عند الـ origin H0 المجال اللي فيه الناتج من الـ
+
+39
+00:03:07,500 --> 00:03:09,780
+current اللي في الـ plane اللي عند الـ origin هسميه 
+
+40
+00:03:09,780 --> 00:03:13,260
+H0 والمجال اللي فيه الناتج من الـ current اللي على 
+
+41
+00:03:13,260 --> 00:03:18,000
+الـ plane اللي عنده 4 زي تسوء 4 هسميه H4 بس
+
+42
+00:03:18,000 --> 00:03:23,320
+التمييز عند الـ H0 هستحضر المعادلة K من نصف K cross
+
+43
+00:03:23,320 --> 00:03:27,120
+A and hat كمان مرة نذكر حالنا K باتجاه مجال الـ 
+
+44
+00:03:27,120 --> 00:03:30,860
+current و A and hat هو العمود اللي على الـ plane و
+
+45
+00:03:30,860 --> 00:03:35,840
+بين الـ plane ونقطة اسمها المجال K في حالتنا هي
+
+46
+00:03:35,840 --> 00:03:41,040
+قداش منها نص عشرة A x hat عوض عنها A and hat من هي 
+
+47
+00:03:41,040 --> 00:03:44,320
+العمودي على الـ plane لحد النقطة من هيكون اللي في
+
+48
+00:03:44,320 --> 00:03:51,250
+اتجاه الـ z hat فإيش هيكون الـ cross لأنها هي 
+
+49
+00:03:51,250 --> 00:03:55,770
+اتجاهها ومجابب z hat لكون سبوردك في الـ x والـ z
+
+50
+00:03:55,770 --> 00:04:01,250
+ماله minus y هيكون عند الـ plus حسب ضبط المصدر في
+
+51
+00:04:01,250 --> 00:04:08,070
+العشرة خمسة ay hat a على الـ parameter الـ parameter الـ parameter
+
+52
+00:04:08,070 --> 00:04:12,990
+الـ parameter الـ parameter الـ parameter الـ parameter الـ parameter الـ parameter
+
+53
+00:04:12,990 --> 00:04:13,270
+الـ parameter الـ parameter الـ parameter الـ parameter الـ parameter الـ parameter
+
+54
+00:04:13,270 --> 00:04:14,970
+الـ parameter الـ parameter الـ parameter الـ parameter الـ parameter الـ parameter
+
+55
+00:04:14,970 --> 00:04:17,050
+الـ parameter الـ parameter الـ parameter الـ parameter الـ parameter الـ parameter
+
+56
+00:04:17,050 --> 00:04:19,500
+الـ parameter الـ parameter الـ parameter الـ parameter الـ parameter القيمة K
+
+57
+00:04:19,500 --> 00:04:28,020
+أداش عشرة x hat A and hat عبارة عن minus z hat سالب z
+
+58
+00:04:28,020 --> 00:04:35,720
+hat الـ cross product بين x و z هو سالب y hat سالب
+
+59
+00:04:35,720 --> 00:04:40,100
+وسالب تصبح plus نصف عشرة خمسة فخمسة y hat amps 
+
+60
+00:04:40,100 --> 00:04:45,280
+per meter إذا الاثنين أعطوني عند النقطة نقدر الـ
+
+61
+00:04:45,280 --> 00:04:48,460
+magnetic field خمسة واتجاه واتجاه y hat
+
+62
+00:04:52,830 --> 00:04:57,430
+تمام إذا أنت الاثنين أعطوني بصفر إذا الـ total field
+
+63
+00:04:57,430 --> 00:05:02,430
+مش هيكون مجموعهم يعني عشرة y hat تمام ويجي لأ
+
+64
+00:05:02,430 --> 00:05:07,490
+النقطة الثانية النقطة الثانية قول لي أنا بدي x صفر
+
+65
+00:05:07,490 --> 00:05:15,870
+y minus 3  z عشرة يعني somewhere هنا
+
+66
+00:05:15,870 --> 00:05:22,730
+x صفر y minus 3 z عشرة على افتراض إن هي النقطة 
+
+67
+00:05:22,730 --> 00:05:25,330
+الـ origin أو يعني في أي مكان الـ origin على
+
+68
+00:05:25,330 --> 00:05:28,270
+أساس إن الـ planes هم اكبر يعني مش بضرورة هكذا يعني
+
+69
+00:05:28,270 --> 00:05:31,950
+هذا الإشارة بس مبتدأ بالـ planes وهذا الإشارة إن
+
+70
+00:05:31,950 --> 00:05:38,610
+مبتدأ الـ planes واضح فهذه النقطة هي 0-3 10 لسه
+
+71
+00:05:38,610 --> 00:05:42,370
+planes اللي قلتلكم بتمد هكذا infinity في كل اتجاه
+
+72
+00:05:42,370 --> 00:05:50,960
+في الـ x y infinity هنا عند الـ z equals 0 وهنا عند
+
+73
+00:05:50,960 --> 00:05:55,360
+الـ z equals 4 تمام بدنا نعيد نفس الخطوات وفي هذه
+
+74
+00:05:55,360 --> 00:05:58,720
+الحالة إيش الاختلاف هيكون؟ نيجي لـ H node اللي هو الـ
+
+75
+00:05:58,720 --> 00:06:02,440
+field الناتج من الـ plane عند الـ 0 K لا زالت minus 
+
+76
+00:06:02,440 --> 00:06:07,120
+10 x hat والـ N hat ماله plus z hat فهيعطينا نفس
+
+77
+00:06:07,120 --> 00:06:13,080
+النتيجة ناقص عشرة وz hat هيعطيني خمسة ay hat
+
+78
+00:06:13,080 --> 00:06:17,880
+amps per meter نيجي للـ plane الثاني من عند الـ 4 K
+
+79
+00:06:17,880 --> 00:06:23,530
+عشرة من الـ A and hat؟ الـ plus z hat الـ plus z hat
+
+80
+00:06:23,530 --> 00:06:27,950
+فاندي أنا الـ plus عشرة والـ plus z hat الـ cross 
+
+81
+00:06:27,950 --> 00:06:32,210
+product بينهم minus y هيعطيني الـ minus خمسة y hat 
+
+82
+00:06:32,210 --> 00:06:36,270
+يعني الأولى نهاية قيمة جزئها والثاني minus إيش الـ
+
+83
+00:06:36,270 --> 00:06:41,110
+result  سهر؟ إذا لما كان النقطة بين الـ two planes
+
+84
+00:06:41,110 --> 00:06:45,530
+حصلنا على field واحد منهم تيار داخل والثاني طالع
+
+85
+00:06:46,150 --> 00:06:50,770
+باتجاه التيارات معاكسة لما برا كانت النتيجة بتساوي 0
+
+86
+00:06:50,770 --> 00:06:53,950
+جابوا لما يكونوا التيارات كلهم داخلين أو التيارات
+
+87
+00:06:53,950 --> 00:06:57,330
+مع بعض طالعين عيدوا يعني هذه الأمثلة اللي ممكن 
+
+88
+00:06:57,330 --> 00:07:01,930
+تشوفها في الامتحانات لو بدى أغير في السؤال صح؟
+
+89
+00:07:01,930 --> 00:07:06,830
+وضح؟ 
+
+90
+00:07:17,760 --> 00:07:22,040
+نيجي للي هو الـ Toroid الـ Toroid هو عبارة عن حلقة
+
+91
+00:07:22,040 --> 00:07:26,440
+ملفوف حولها سلك وهذا السلك مور فيه current زي ما
+
+92
+00:07:26,440 --> 00:07:31,280
+أنتم شايفين هي السلك بدخل فيه تيار بهذا الاتجاه و
+
+93
+00:07:31,280 --> 00:07:36,320
+بيطلع من السلك الثاني بدال ما يبني تكفيد في نقطة مالها
+
+94
+00:07:36,320 --> 00:07:41,660
+في هذه المنطقة في قلب الـ Toroid في قلب الـ Toroid زي
+
+95
+00:07:41,660 --> 00:07:46,280
+ما أنتم شايفين مثلا عند اللي هي النقطة رو مع بعض
+
+96
+00:07:46,280 --> 00:07:49,720
+رو من الـ origin قداش يكون الـ magnetic field
+
+97
+00:07:49,720 --> 00:07:54,360
+المعروفة اللي هو الـ Rho not هي المسافة أو الـ
+
+98
+00:07:54,360 --> 00:07:58,760
+center أو نصف القطر ما بين الـ origin لو هي نص
+
+99
+00:07:58,760 --> 00:08:02,740
+المسافة بتاعة الـ ring بالتمام هي Rho not يعني إذا
+
+100
+00:08:02,740 --> 00:08:12,580
+اعتبرنا إحنا شايفين هذا الـ Rho not هذه كلها أنت 
+
+101
+00:08:12,580 --> 00:08:16,850
+مسميها المسافة من هنا إلى هنا هي Rho not فهي عند أي
+
+102
+00:08:16,850 --> 00:08:19,690
+نقطة عامة تكون هنا الـ ring هنا الـ ring هنا الـ Rho
+
+103
+00:08:19,690 --> 00:08:22,950
+ما بين الـ origin والنقطة اللي عامة بحسب بنتها الـ
+
+104
+00:08:22,950 --> 00:08:26,030
+magnetic field فبنعرف إحنا الـ magnetic field اللي
+
+105
+00:08:26,030 --> 00:08:28,910
+بتاعها بيكون لفرعين اللي هو الـ inside والـ outside
+
+106
+00:08:28,910 --> 00:08:34,130
+للـ toroid inside مثلا على مسافة Rho زي ما حكى نستخدم
+
+107
+00:08:34,130 --> 00:08:38,230
+الـ Ampere's circuital law بسوق I enclosed 
+
+108
+00:08:39,230 --> 00:08:43,410
+طب H dot dl H dot dl H الاتجاه كيف؟ إحنا الـ 
+
+109
+00:08:43,410 --> 00:08:45,730
+current بدنا نتبع اتجاه الـ current عشان نعرف اتجاه 
+
+110
+00:08:45,730 --> 00:08:51,910
+الـ magnetic field الـ current هي فيك تاخد لورا
+
+111
+00:08:51,910 --> 00:08:56,930
+فبلف إيدي على اتجاه الـ current بلاقي إن الـ magnetic
+
+112
+00:08:56,930 --> 00:09:00,670
+field فيه اتجاه واضح؟ كيف عرفنا اتجاه الـ magnetic
+
+113
+00:09:00,670 --> 00:09:03,830
+field؟ لفيت إيدي في اتجاه الـ current حلاقي إن الـ
+
+114
+00:09:03,830 --> 00:09:06,830
+magnetic field اتجاهه في الـ toroid معناه هذه الاتجاه
+
+115
+00:09:11,810 --> 00:09:15,910
+واضح كيف نحدده؟ إذا اتجاهه هو في طريقة مين؟ الـ Phi
+
+116
+00:09:15,910 --> 00:09:23,890
+hat اتجاه المنطقية اتجاه الـ Phi hat طبعا الـ dl إيش
+
+117
+00:09:23,890 --> 00:09:32,250
+هتكون؟ two by row او 
+
+118
+00:09:32,250 --> 00:09:35,330
+يعني لو أخذنا الـ element row d5 ده كمل على الـ d5
+
+119
+00:09:35,330 --> 00:09:39,820
+اللي هي two by تبع النبت اكبر ان الـ row ثابتة و
+
+120
+00:09:39,820 --> 00:09:41,820
+باخد الـ element الـ element إيش هيكون الـ row دي
+
+121
+00:09:41,820 --> 00:09:45,160
+5 بكمل الـ 5 من 0 لـ two pi فهذا h dot dl
+
+122
+00:09:45,160 --> 00:09:49,320
+إيش هتعطينا اتش two by row طب I enclosed قداش كم
+
+123
+00:09:49,320 --> 00:09:52,560
+تهيه enclosed هو I الداخل هيبقى معناه يابس I بتلوف
+
+124
+00:09:52,560 --> 00:09:56,540
+على كم حلقة؟ على N حلقات فـ I الـ enclosed هتكون N في 
+
+125
+00:09:56,540 --> 00:10:01,520
+I أو I المولدة لـ magnetic field تبعنا هي N في I
+
+126
+00:10:04,040 --> 00:10:08,500
+إذا إيش هيكون H؟ بيساوي N في I على 2 by R هذا هو
+
+127
+00:10:08,500 --> 00:10:12,960
+المجال field inside الـ toroid في Rho ما بيلعب Rho not
+
+128
+00:10:12,960 --> 00:10:18,740
+ناقص A اللي هي A من هي هذه كلها اللي هو نص القطر 
+
+129
+00:10:18,740 --> 00:10:23,580
+فهذه 
+
+130
+00:10:23,580 --> 00:10:27,640
+الـ مجال field inside اللي هي Rho not ناقص A و Rho not
+
+131
+00:10:27,640 --> 00:10:33,640
+زائد A أساس إن الدمية كله A2A نص القطر A فإذا هذه
+
+132
+00:10:33,640 --> 00:10:37,200
+الـ region إيش بعرفها Rho not ناقص A أو Rho not زائد A
+
+133
+00:10:37,200 --> 00:10:40,640
+فهذه الـ region اللي هي inside الـ toroid المجال فيه 
+
+134
+00:10:40,640 --> 00:10:46,240
+بيساوي Ni على 2π Rho not بسيطة من أهم سلوكهنا جوا بس 
+
+135
+00:10:46,240 --> 00:10:49,460
+هالمجال إضافة معلومة لزيادة اللي هحكيها إن 
+
+136
+00:10:49,460 --> 00:10:54,300
+لو أخذنا approximation واعتبرنا إن الـ two pi
+
+137
+00:10:54,300 --> 00:10:57,940
+مثلا عند اللي هي يعني إن sickness تبع الـ toroid
+
+138
+00:10:57,940 --> 00:11:01,720
+صغير بالنسبة لطوله يعني كله بقدر اتقربه لـ two pi
+
+139
+00:11:01,720 --> 00:11:04,940
+Rho not يعني الـ a هذه ناقص أو a صغيرة كثير
+
+140
+00:11:04,940 --> 00:11:10,820
+بالنسبة لـ Rho not يعني ممكن اهملها اعتبرها إن
+
+141
+00:11:10,820 --> 00:11:15,040
+كلها بقدر أعبر عنها two by Rho not باش هيكون اللي
+
+142
+00:11:15,040 --> 00:11:19,800
+هو أداش approximate Ni على two by Rho not اللي
+
+143
+00:11:19,800 --> 00:11:23,180
+هي two by Rho not بدأت سميها اللي هي طول الـ toroid
+
+144
+00:11:23,770 --> 00:11:28,390
+طوله هيكون فإذا ما هيكون n I على L و N على L اللي 
+
+145
+00:11:28,390 --> 00:11:31,510
+هي n per unit length فإذا ما هيكون اتش
+
+146
+00:11:31,510 --> 00:11:35,070
+approximate بتساوي N في I اللي هي بالتمام المجال field
+
+147
+00:11:35,070 --> 00:11:37,910
+اللي حسبناه من يوم الـ solenoid متذكرينه هنا في 
+
+148
+00:11:37,910 --> 00:11:41,050
+الـ solenoid المجال field الـ inside هو عدد اللفات per
+
+149
+00:11:41,050 --> 00:11:43,710
+unit length في الـ current اللي مور فيه الـ solenoid
+
+150
+00:11:43,710 --> 00:11:48,440
+متذكرين إذا ما بنقدر نقول إن الـ solenoid هو حالة
+
+151
+00:11:48,440 --> 00:11:50,960
+خاصة من الـ toroid لإن إحنا لما عملنا الـ 
+
+152
+00:11:50,960 --> 00:11:54,520
+approximation حصلنا على شكل الـ magnetic field اللي
+
+153
+00:11:54,520 --> 00:11:59,020
+ناتج في قلب الـ solenoid طب بدنا outside الـ magnetic
+
+154
+00:11:59,020 --> 00:12:04,580
+field outside اللي هو الـ toroid زي ما هو طالب مننا
+
+155
+00:12:04,580 --> 00:12:07,300
+inside و outside حيكون في عندنا current
+
+156
+00:12:07,300 --> 00:12:11,200
+enclosed يعني حيكون هنا n I minus n I بيساوي
+
+157
+00:12:11,200 --> 00:12:17,770
+0 فإذا ما حيكون magnetic field بيساوي 0 إحنا بدنا
+
+158
+00:12:17,770 --> 00:12:20,990
+نلاقاتها نعرف الـ magnetic flux density الـ magnetic
+
+159
+00:12:20,990 --> 00:12:25,450
+flux density  B
+
+160
+00:12:25,450 --> 00:12:28,570
+اللي هي الـ magnetic flux density بعرفها بدلالة الـ
+
+161
+00:12:28,570 --> 00:12:31,950
+H إنها بتساوي ميو نوت H H اللي هو الـ magnetic
+
+162
+00:12:31,950 --> 00:12:35,010
+field intensity أو الـ field intensity أو الـ
+
+163
+00:12:35,010 --> 00:12:39,730
+magnetic field و B اللي هي الـ density فالـ density 
+
+164
+00:12:39,730 --> 00:12:44,030
+هي ميو نوت في H ميو نوت بنسميها Permeability
+
+165
+00:12:45,210 --> 00:12:49,770
+السماحية للـ space إن ماله يسمح لـ magnetic field
+
+166
+00:12:49,770 --> 00:12:54,390
+إن يدخل فيه ميو نوت للـ free space أو الـ vacuum لو
+
+167
+00:12:54,390 --> 00:12:57,150
+قمنا الـ not بتصير الـ ميو لأي material زي ما عملنا
+
+168
+00:12:57,150 --> 00:13:01,130
+في الـ electric field ابسلون نوت بتكون للـ space الـ
+
+169
+00:13:01,130 --> 00:13:04,350
+free space أو الـ vacuum بتدلون الـ not اللي هتكون
+
+170
+00:13:04,350 --> 00:13:09,030
+ابسلون لأي material إذا الـ ميو نوت هي مقدار 
+
+171
+00:13:09,030 --> 00:13:12,130
+السماحية لهذا الـ space أو هذه الـ media إنها تسمح لـ
+
+172
+00:13:12,130 --> 00:13:13,730
+magnetic field يمر فيها
+
+173
+00:13:16,950 --> 00:13:21,
+
+201
+00:15:15,630 --> 00:15:18,530
+زي ما أنتو شايفينه هي هال surface اللي بنعمل عليه
+
+202
+00:15:18,530 --> 00:15:23,110
+close integral  إشعاعاني Q enclosed ما راح تش سكرت على
+
+203
+00:15:23,110 --> 00:15:27,030
+حالة خطوط القوة خطوط المجال لكن في ال magnetic
+
+204
+00:15:27,030 --> 00:15:32,210
+field هنلاحظ أن ال close integral لـ D ضد S بتساوي
+
+205
+00:15:32,210 --> 00:15:37,440
+صفر، دائما بيكون ال flux like closed surface احنا 
+
+206
+00:15:37,440 --> 00:15:40,460
+ده ال flux اللي قولنا عرفنا اللي هو بصين مش closed
+
+207
+00:15:40,460 --> 00:15:44,140
+surface لأي surface P dot DS سميناه ال flux لكن لو
+
+208
+00:15:44,140 --> 00:15:48,340
+عرفناه على closed surface integral هيعطينا صفر معنى
+
+209
+00:15:48,340 --> 00:15:52,880
+هيك أن خطوط المجال بتسكر على نفسها بتروح و بتسكر
+
+210
+00:15:52,880 --> 00:15:57,320
+على نفسها هو لا يمكن احصل على حاجة بتسميها ال
+
+211
+00:15:57,320 --> 00:16:03,340
+monopole اللي هو magnetic لحاله north pole أو south 
+
+212
+00:16:03,340 --> 00:16:07,140
+pole ليش؟ لإن لو أنا طلعت على ال magnet هاي magnet
+
+213
+00:16:07,140 --> 00:16:11,520
+هاي له south و north pole أخد جزء من نقطته هاتني
+
+214
+00:16:11,520 --> 00:16:16,580
+كمان ع طول south و north أقطع دايما هاتني south و
+
+215
+00:16:16,580 --> 00:16:19,980
+north قد ما أقطع هاتني south و north لكن بالنسبة
+
+216
+00:16:19,980 --> 00:16:23,420
+لل charge ممكن أحصل على positive chargenegative
+
+217
+00:16:23,420 --> 00:16:26,900
+charge electron او بروتون هدولة موجودية الطبيعة
+
+218
+00:16:26,900 --> 00:16:30,680
+لكن ال magnet قد ما حاولوا أنهم يصغروا فيه اللي
+
+219
+00:16:30,680 --> 00:16:34,960
+يظل عندهم north و south poles و لزالوا بيحاولوا
+
+220
+00:16:34,960 --> 00:16:40,500
+يعملوا magnet اللي بس له خاصية ال north او ال
+
+221
+00:16:40,500 --> 00:16:50,000
+south شو هيستفيده؟ كل العلم له أسرار و علوم استفيد
+
+222
+00:16:50,000 --> 00:16:50,740
+أشياء كتير
+
+223
+00:16:54,620 --> 00:16:58,800
+طبعا إيش بيستفيدوا؟ يعني بالنسبة لهم لل .. لل
+
+224
+00:16:58,800 --> 00:17:01,740
+magnet إذا أنا بقدر أتحكم بإني بس أحصل على North
+
+225
+00:17:01,740 --> 00:17:05,420
+واحد، إن أحصل على magnet flux رايحة مش مولقة عن
+
+226
+00:17:05,420 --> 00:17:08,600
+نفسها، أكيد يعني إلها تطبيقات كتير ولا زال في ..
+
+227
+00:17:08,600 --> 00:17:12,260
+ولا زال في الطب، إنه يحصلوا على اللي واحد منهم،
+
+228
+00:17:12,260 --> 00:17:15,240
+فإيش هم بعودوا عنها لحد الآن؟ هم لسه مش قادرين
+
+229
+00:17:15,240 --> 00:17:18,520
+إنه يعملوها نقطة لحالها، بيعملوا very soon و
+
+230
+00:17:18,520 --> 00:17:22,860
+طوييييل طويييل طوييل جداً بيصير كأنه في عندهم اللي
+
+231
+00:17:22,860 --> 00:17:27,480
+هو ال north أو ال south pole طبعاً طويل مش معناه
+
+232
+00:17:27,480 --> 00:17:29,800
+infinite طويل بالنسبة لل application أو ال
+
+233
+00:17:29,800 --> 00:17:31,420
+wavelengths اللي احنا بنحكي عنهم لل
+
+234
+00:17:31,420 --> 00:17:34,460
+electromagnetic signal قداش هو الطول هذا ما هو
+
+235
+00:17:34,460 --> 00:17:38,820
+نسبي أكبر من أو أقل من اللي هي الطول north فطوله
+
+236
+00:17:38,820 --> 00:17:41,780
+بيختاروه أن يكون طول محدد فبيقدر يعمل approximate
+
+237
+00:17:41,780 --> 00:17:43,560
+north و approximate south
+
+238
+00:17:50,870 --> 00:17:53,350
+بذات هيدور بالسنت جو بنقول له عندها ال clause
+
+239
+00:17:53,350 --> 00:17:56,710
+Integra b dot ds بالسوء zero أنه ما فيش عندنا اللي
+
+240
+00:17:56,710 --> 00:18:04,590
+هي ال monopole إذا
+
+241
+00:18:04,590 --> 00:18:07,310
+ال clause Integra ل b dot ds هي بقدر أستخدم ال
+
+242
+00:18:07,310 --> 00:18:10,800
+divergence theorem أولاً ال close integral لأي field
+
+243
+00:18:10,800 --> 00:18:13,640
+دو ال DS بيساوي ال volume integral ل diverge ال
+
+244
+00:18:13,640 --> 00:18:18,360
+field DV بس تحنينها ل ال magnetic flux هيعطينا ال
+
+245
+00:18:18,360 --> 00:18:20,900
+volume integral ل diverge B DV بيساوي 0، إذا 
+
+246
+00:18:20,900 --> 00:18:25,740
+diverge ال B بيساوي 0، إذا diverge ال B بيبدأ يساوي
+
+247
+00:18:25,740 --> 00:18:28,140
+0، إيش معناه diverge ال B بيساوي 0؟ ما فيش هنا
+
+248
+00:18:28,140 --> 00:18:33,570
+monopole؟ تشكل تفاقنا؟ divergence E بتساوي رو على
+
+249
+00:18:33,570 --> 00:18:38,750
+إبسيلون أو Q على إبسلون قلنا إيش معناه؟ إبسلون رو
+
+250
+00:18:38,750 --> 00:18:42,570
+على إبسلون لإن في عندي charge مو نتشارج يعني
+
+251
+00:18:42,570 --> 00:18:45,390
+positive أو negative charge في عندي source اللي
+
+252
+00:18:45,390 --> 00:18:48,650
+بيروح عليه زي ما قلنا الميه و ال sink اللي هي
+
+253
+00:18:48,650 --> 00:18:54,830
+القرق تبع الحفية ميه بتروح عليه أو بتطلع منه هي ال
+
+254
+00:18:54,830 --> 00:18:58,130
+divergence معناه الكلش اللي معناه حاجة بتلف
+
+255
+00:19:01,370 --> 00:19:04,050
+تفهيص ل maxwell equations و غالباً بيجيكوا سؤال في
+
+256
+00:19:04,050 --> 00:19:08,650
+الامتحان النهائي أنكوا تلاحظوه يعني تتذكرينه ولا
+
+257
+00:19:08,650 --> 00:19:13,710
+ما حضرتوش؟ في ال ده اللي هو two forms ما قدروا ال
+
+258
+00:19:13,710 --> 00:19:16,330
+integral form و ال differential form يعني مثلاً
+
+259
+00:19:16,330 --> 00:19:19,650
+نبدأ بمين؟ بجاوسلو جاوسلو يعني ال differential
+
+260
+00:19:19,650 --> 00:19:24,660
+form اللي هو دا في الجديد بتسويره صحيح؟ لما تكون D
+
+261
+00:19:24,660 --> 00:19:28,720
+بيصير E E و E مالها homogenous ايسو تروبيك اش
+
+262
+00:19:28,720 --> 00:19:34,060
+بتصير E أو diverge ال E بيصير ρو على E صح؟ هذا
+
+263
+00:19:34,060 --> 00:19:37,840
+بالنسبة لل divergence أو ال point form بيسمونه ال
+
+264
+00:19:37,840 --> 00:19:42,140
+clause integral لـ D ضد S بتساوي Q أو ال volume
+
+265
+00:19:42,140 --> 00:19:46,140
+integral ρو VDV بنساوي ال integral form من أين
+
+266
+00:19:46,140 --> 00:19:48,720
+بنجيبهم احنا؟ من ال divergence theorem
+
+267
+00:19:54,750 --> 00:19:58,370
+القانون الأولى هو gauss law القانون الثاني هو
+
+268
+00:19:58,370 --> 00:20:01,970
+divergence P بالسوء 0 أو ال clause integral على ال
+
+269
+00:20:01,970 --> 00:20:04,830
+surface ل P dot DS بالسوء 0 اللي هي ال flux ال
+
+270
+00:20:04,830 --> 00:20:09,230
+total flux الطالع من ال surface بالسوء صفر ما فيش
+
+271
+00:20:09,230 --> 00:20:13,490
+existence للمنوبول non existence of magnetic
+
+272
+00:20:13,490 --> 00:20:21,140
+monobol كل ال E بالسوء 0 اللي هي برضه جيبناها من ال
+
+273
+00:20:21,140 --> 00:20:23,500
+close line integral a dot dl متذكرين ال work
+
+274
+00:20:23,500 --> 00:20:26,920
+قلنا بصوص صفر إذا هذه بتعتمدش على ال boss عفواً ال
+
+275
+00:20:26,920 --> 00:20:30,940
+work بتعتمدش على ال boss a dot dl إذا معناه فيه
+
+276
+00:20:30,940 --> 00:20:33,620
+عندي conservativeness of the electrostatic field
+
+277
+00:20:38,400 --> 00:20:41,380
+Conservation، فمتذكّرينه؟ قلنا هذا معناه إنه إيده
+
+278
+00:20:41,380 --> 00:20:44,360
+و الديقال بتساوي zero إنه لو أخدت المسار أي اتجاه
+
+279
+00:20:44,360 --> 00:20:48,360
+بيكون نفس الحاجة، بتمدش على البعض، وهذا بنقول إنه
+
+280
+00:20:48,360 --> 00:20:52,730
+فينا conservativeness ل ال electrostatic field كرل
+
+281
+00:20:52,730 --> 00:20:56,170
+ال H بيستوي J اللي هو Amberslaw أو ل close
+
+282
+00:20:56,170 --> 00:21:00,090
+integral ل LH دو ال DL هي طبعاً من هي المشطق اللي
+
+283
+00:21:00,090 --> 00:21:03,290
+هي هي ال form من وين برضه من Stokes theorem ال
+
+284
+00:21:03,290 --> 00:21:06,790
+line integral هدولة تمتع من Stokes theorem ل close
+
+285
+00:21:06,790 --> 00:21:09,890
+line integral بيستوي ال surface integral لكرل ال E
+
+286
+00:21:09,890 --> 00:21:14,330
+دو ال DS فكرل ال E بتساوي 0 هنا نفس الاصدارية ال
+
+287
+00:21:14,330 --> 00:21:17,630
+closed integral H to DL اشتقناها المحاضرة الماضية
+
+288
+00:21:17,630 --> 00:21:20,950
+من Stokes theorem تعطينا برضه surface integral كرل
+
+289
+00:21:20,950 --> 00:21:26,050
+ال E ل H to DS و هذا بالساوي اللي هو ال enclosed
+
+290
+00:21:26,050 --> 00:21:28,330
+current اللي هو عبارة عن surface integral J to DS
+
+291
+00:21:28,330 --> 00:21:32,290
+فبالتالي سنتجنا ان كرل ال H بتساوي J وهذا سمينا
+
+292
+00:21:32,290 --> 00:21:36,770
+unbearable متذكرينهم؟ هدول لازم تحفظوهم ما فيش فيهم
+
+293
+00:21:36,770 --> 00:21:42,810
+مزح اللي هو ال four Maxwell's equations بسموهم
+
+294
+00:21:42,810 --> 00:21:48,770
+عمدان الكهرو استاتيك، العمدان تعونها، إذا ما حفظتيش
+
+295
+00:21:48,770 --> 00:21:52,950
+واحد منهم نهد البنيان، فلازم تحفظوا الأربع، و
+
+296
+00:21:52,950 --> 00:21:57,010
+تتذكروا إيش معانيهم ولا إيش استخدمناهم وإيش 
+
+297
+00:21:57,010 --> 00:21:57,790
+صفقتةم
+
+298
+00:22:02,090 --> 00:22:05,270
+زي ما احنا ال electric field قلنا فيه اللي هو ال
+
+299
+00:22:05,270 --> 00:22:08,570
+scalar potential، هنا فيه كمان عندنا scalar
+
+300
+00:22:08,570 --> 00:22:12,230
+potential و vector potential، من وين اجوا هدولتين؟
+
+301
+00:22:12,230 --> 00:22:16,010
+احنا قلنا كارل ال E بيساوي 0، بتذكرين؟ كارل ال E
+
+302
+00:22:16,010 --> 00:22:18,310
+بيساوي 0، إذا نعطيه اصفة انتاجنا له إيش بتساوي
+
+303
+00:22:18,310 --> 00:22:23,730
+minus grade V هذه المعادلة مرقت علينا قلنا curl E
+
+304
+00:22:23,730 --> 00:22:27,870
+لإيه مالهوش curl ال E اللي هو diverge فيه اللي هو
+
+305
+00:22:27,870 --> 00:22:31,350
+mono charge يا بيطلع منها يا بيدخل فيها لكن ال
+
+306
+00:22:31,350 --> 00:22:33,970
+curl تبعه بيثاوزيرو لإن هو conservative field
+
+307
+00:22:33,970 --> 00:22:37,890
+ف curl هو zero فقلنا إذا E إيش بيثاو لإن curl ال
+
+308
+00:22:37,890 --> 00:22:40,650
+grade بيثاوزيرو إذا إن هو عبارة عن minus grade ال
+
+309
+00:22:40,650 --> 00:22:44,540
+V لو قلنا divergence بيه بيه بيه بيه بيه بيه بيه
+
+310
+00:22:44,540 --> 00:22:47,780
+بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+311
+00:22:47,780 --> 00:22:50,440
+بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+312
+00:22:50,440 --> 00:22:50,480
+بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+313
+00:22:50,480 --> 00:22:50,500
+بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+314
+00:22:50,500 --> 00:23:07,940
+بيه بيه بيه بيه بيه بي
+
+315
+00:23:08,900 --> 00:23:11,600
+أو يعني هذا هو amber's law ال line integral ال
+
+316
+00:23:11,600 --> 00:23:15,840
+close line integral أيها ل أكتر دي ألف بتساوي ال I
+
+317
+00:23:15,840 --> 00:23:18,940
+enclosed اللي منها نتجنا كل أتش بتساوي جي جي
+
+318
+00:23:18,940 --> 00:23:23,000
+enclosed افتراضي لو افترضنا أن جي كانت سفر جي
+
+319
+00:23:23,000 --> 00:23:26,800
+enclosed بتساوي سفر إذا كل أتش بده يساوي zero
+
+320
+00:23:26,800 --> 00:23:29,980
+مقدار ال enclosed current بتساوي سفر زي المثال
+
+321
+00:23:29,980 --> 00:23:32,980
+كوكسيا الكيبل اللي داخل كانت اللي جوا مثلاً طالع
+
+322
+00:23:32,980 --> 00:23:36,100
+و الثاني داخل فطلع برا
+
+323
+00:23:40,110 --> 00:23:48,210
+القران بيساوي سفر صح هاي ال coaxial أو 
+
+324
+00:23:48,210 --> 00:24:00,030
+برضه ال Troy برا معناه أنه مجموعة بتذكرين
+
+325
+00:24:00,030 --> 00:24:04,650
+ال current كان zero هنا فقلنا هيكون ال magnetic
+
+326
+00:24:04,650 --> 00:24:09,830
+field مجموع ال currents I minus I بيساوي سفر، أنت
+
+327
+00:24:09,830 --> 00:24:12,950
+ذاكرينه؟ إذا من هاي ambers law، إيش بقدر أقربها
+
+328
+00:24:12,950 --> 00:24:17,990
+ل كرل ال H؟ بتساوي سفر في
+
+329
+00:24:17,990 --> 00:24:20,430
+هاي الحالة، إذا أنا برضه قلت كرل ال H بتساوي سفر
+
+330
+00:24:20,430 --> 00:24:24,230
+كحالة أن ال current بتساوي سفر، بقدر أقول أن ال
+
+331
+00:24:24,230 --> 00:24:28,500
+H إيش بتساوي؟ كيرل لـ Gradient بيساوي 0 إذا بقدر
+
+332
+00:24:28,500 --> 00:24:31,960
+أقول الـ H في هالحلقة إيش بتساوي صمي Gradient ل
+
+333
+00:24:31,960 --> 00:24:36,060
+field حسب مين VM عشان أميزه عامين اللي هو ال
+
+334
+00:24:36,060 --> 00:24:38,860
+scalar potential تبع ال electric field إذا الـ H
+
+335
+00:24:38,860 --> 00:24:42,540
+بقدر أقول بكتبها بدلالة أو بقدر أعبر عنها الدلالة
+
+336
+00:24:42,540 --> 00:24:45,560
+scalar magnetic potential أو magnetic scalar
+
+337
+00:24:45,560 --> 00:24:49,060
+potential VM و لو أنا رجعت لها اللي هي diverse
+
+338
+00:24:49,060 --> 00:24:52,300
+كيرل
+
+339
+00:24:52,300 --> 00:25:02,070
+لـ H بيساوي 0 إذا الـ H إيش بتساوي - Vm Vm
+
+340
+00:25:02,070 --> 00:25:08,650
+Vm
+
+341
+00:25:08,650 --> 00:25:15,930
+Vm Vm
+
+342
+00:25:15,930 --> 00:25:19,820
+Vm Vm Vm Vm Vm Vm لكن لو كانت بتاعت متعالى in
+
+343
+00:25:19,820 --> 00:25:23,460
+homogenous and non isotropic يعني بتاعت متعالى ال
+
+344
+00:25:23,460 --> 00:25:26,680
+X,Y,Z بقدرش أدخلها بسهولة في قلب ال divergence نحن
+
+345
+00:25:26,680 --> 00:25:37,640
+عاليه ال divergence ال B بتساوي 0 بس
+
+346
+00:25:37,640 --> 00:25:42,840
+اعتبرناها أن هي بتركز على ال space بقدر أقول أضرب
+
+347
+00:25:42,840 --> 00:25:48,270
+ال new node فبتصير برضه diverge الـ H ساوي زيرو اصول
+
+348
+00:25:48,270 --> 00:25:56,030
+العالمين و التأثير احنا
+
+349
+00:25:56,030 --> 00:26:00,550
+قلنا H من الكيل في حالة ان الجيب ساوة زيرو في حالة
+
+350
+00:26:00,550 --> 00:26:07,270
+ان الجيب ساوة زيرو كرل الـ H ساوة زيرو معناه أن
+
+351
+00:26:07,270 --> 00:26:12,490
+الـ H شو بتساوي minus del V تمام زي كتر فيه لو
+
+352
+00:26:12,490 --> 00:26:14,650
+عوضنا عنها في هذه المعادلة إيش هيصير هنا
+
+353
+00:26:24,630 --> 00:26:35,570
+بس في حالة جيب تساوي 0 و من
+
+354
+00:26:35,570 --> 00:26:38,650
+diverse B قلنا أن بي بقدر اكتبها بدلالة اللي هو ال
+
+355
+00:26:38,650 --> 00:26:42,170
+vector magnetic potential اللي هي بي بتساوي كرل ال
+
+356
+00:26:42,170 --> 00:26:47,970
+A الـ vector-magnet field و الـ scalar-magnet field
+
+357
+00:26:47,970 --> 00:26:51,430
+الـ scalar-magnet field في حالة فقط أن J بيساوي 0
+
+358
+00:26:51,430 --> 00:26:54,990
+كل الـ H بيصير بيساوي 0 إذاً الـ H إذا بقدر أعبر
+
+359
+00:26:54,990 --> 00:26:57,950
+عنها بدلالة اللي هو scalar .. magnetic scalar
+
+360
+00:26:57,950 --> 00:27:03,330
+potential minus grade ال V يعني ال B بتساوي ال
+
+361
+00:27:03,330 --> 00:27:06,190
+divergence ال B دايماً بيساوي 0 إذا بقدر أقول إن ال
+
+362
+00:27:06,190 --> 00:27:08,730
+B بكتبها بدلالة مين كل ال H
+
+363
+00:27:11,640 --> 00:27:14,880
+من أول جيبنا هدول المعادلات احنا عارفين ان بي
+
+364
+00:27:14,880 --> 00:27:21,300
+بترتبط بقاتش بدلالة مين الـ mu0 و احنا عرفنا ..
+
+365
+00:27:21,300 --> 00:27:28,300
+تأول ال slides .. حديني أطلع منهم
+
+366
+00:27:28,300 --> 00:27:34,320
+.. هاي
+
+367
+00:27:34,320 --> 00:27:37,540
+تعريفنا ل .. اللي هو ال magnetic field
+
+368
+00:27:50,220 --> 00:27:54,160
+أول ما أخذنا ال magnetic field أنت ذاكرين اشتقناه
+
+369
+00:27:54,160 --> 00:27:57,000
+و لقينا ان ال magnetic field عندها نقطة النتجة من
+
+370
+00:27:57,000 --> 00:28:03,040
+current بعبر عنها بدلالة اللي هو ال clause
+
+371
+00:28:03,040 --> 00:28:07,920
+integral I dot DL cross ARH بتاع ال verb IR التربية
+
+372
+00:28:07,920 --> 00:28:11,760
+إيش البرمج من ال H و ال B ال B بتساوي H على Mu
+
+373
+00:28:11,760 --> 00:28:18,530
+node إذا ما قدر أجيب ال P من H صح؟ إذا H بيه تساوي
+
+374
+00:28:18,530 --> 00:28:21,650
+بيه على ميو نوت بقدر أجيب بيه إذا بيه إيش بيه
+
+375
+00:28:21,650 --> 00:28:26,970
+تساوي أو عوضنا بميو نوت في هذا الحكي بس صح عندنا
+
+376
+00:28:26,970 --> 00:28:31,490
+أسعرنا ميو نوت I
+
+401
+00:30:30,450 --> 00:30:33,190
+هذه المعلومات إلا إذا كان هناك أي استفسار في أي
+
+402
+00:30:33,190 --> 00:30:37,630
+استفسار من المعلومات اليوم الإضافية اللي تعلمناها
+
+403
+00:30:37,630 --> 00:30:42,570
+بس الـ B بي هي عبارة عن Mu node H من H ماحنا عارفين
+
+404
+00:30:42,570 --> 00:30:46,510
+العلاقة تقيمها مع بعض إيش هي H فاعود عن H بيه بي
+
+405
+00:30:46,510 --> 00:30:50,210
+على Mu node فهو بتعطينا قيمة B شوية الجبر بقدر
+
+406
+00:30:50,210 --> 00:30:54,790
+أحصل على قيمة A هاي
+
+407
+00:30:54,790 --> 00:30:57,500
+المعلومة الجديدة اللي اليوم تعلمناها Given the
+
+408
+00:30:57,500 --> 00:31:00,120
+magnetic vector potential A أعطانا قيمة ال
+
+409
+00:31:00,120 --> 00:31:02,820
+magnetic vector potential A أنه minus rotor B على
+
+410
+00:31:02,820 --> 00:31:07,800
+أربع في اتجاه الـ Z hat wither per meter Calculate
+
+411
+00:31:07,800 --> 00:31:12,160
+the total magnetic flux crossing the surface Phi
+
+412
+00:31:12,160 --> 00:31:15,100
+بيتساوى باي على اثنين رو من واحد للاثنين و Z من
+
+413
+00:31:15,100 --> 00:31:19,780
+Zero لخمسة الـ surface تبعي cylindrical تخيلوا أنها
+
+414
+00:31:19,780 --> 00:31:22,180
+سلندر وشقاحنا السلندر بالطول
+
+415
+00:31:26,810 --> 00:31:29,870
+وين بدو يكون هذا الـ plan ع الـ y axis صح؟ لو أنا
+
+416
+00:31:29,870 --> 00:31:35,110
+عندي سمدة وين 
+
+417
+00:31:35,110 --> 00:31:44,850
+الـ y على 2؟ raw من قيمته من 1 لـ 2 و الـ z من 0 لـ 5
+
+418
+00:31:44,850 --> 00:31:49,390
+هذا الـ plan اللي بدو يحتاجه واضح؟
+
+419
+00:31:53,200 --> 00:31:56,620
+هو إيش بده؟ Calculate the total magnetic flux
+
+420
+00:31:56,620 --> 00:32:00,120
+crossing the surface أنا رسمته اللي هو الـ 5 يساوي
+
+421
+00:32:00,120 --> 00:32:07,480
+باي على اثنين سيلندر عندي 5 من 0 لـ 2 باي أنا بدي
+
+422
+00:32:07,480 --> 00:32:09,980
+الـ plan قاعد علميا يعني باي على اثنين اللي هي على
+
+423
+00:32:09,980 --> 00:32:13,880
+الـ y axis بالتمام على الـ y axis روه بده من 1 لـ 2
+
+424
+00:32:13,880 --> 00:32:18,760
+وزد من 0 لـ 5 طب يا أنا طريقتين إنهم ممكن يحلوا الـ
+
+425
+00:32:18,760 --> 00:32:21,300
+flux اللي هي من آخر slide احنا قلنا بقدر أجيب الـ
+
+426
+00:32:21,300 --> 00:32:24,860
+flux من a عشان أنتجره لـ b.ds أو الـ close line
+
+427
+00:32:24,860 --> 00:32:28,060
+أنتجره لـ a.dl الثاني اللي لازم يعطيهم الـ flux لازم
+
+428
+00:32:28,060 --> 00:32:31,080
+يعطيهم نفس النتيجة نبدأ بالأولى اللي هي الـ flux في
+
+429
+00:32:31,080 --> 00:32:36,120
+الساوي الـ surface أنتجره لـ b.ds b هو ما عطينا منه الـ
+
+430
+00:32:36,120 --> 00:32:39,520
+vector potential a واحنا عارفين أن الـ vector الـ ..
+
+431
+00:32:39,520 --> 00:32:44,980
+الـ .. الـ magnetic flux density اللي هي b بتساوي كل
+
+432
+00:32:44,980 --> 00:32:48,360
+الـ a إذا بيبقى أقدر أجيبها من الـ curve الـ A اللي هو
+
+433
+00:32:48,360 --> 00:32:50,920
+أنه اتطلعت من اللي عندي بس Z component يعني لو
+
+434
+00:32:50,920 --> 00:32:54,220
+عملت الـ determinant بس هتطلع لي واحدة أولاً باعتمد
+
+435
+00:32:54,220 --> 00:32:56,500
+على رو حدشن تان فيه يعني باعتمد على رو و Z
+
+436
+00:32:56,500 --> 00:32:59,640
+component فلو أخدت اللي هو الـ curve في الـ
+
+437
+00:32:59,640 --> 00:33:02,580
+cylindrical coordinate بتظل عند الـ component اللي
+
+438
+00:33:02,580 --> 00:33:09,480
+هي D minus D A Z على D رو Phi hat نفضل بالنسبة لـ
+
+439
+00:33:09,480 --> 00:33:17,370
+رو هتعطينا minus اثنين في روع الاربعة بيصير نص والـ
+
+440
+00:33:17,370 --> 00:33:22,350
+raw بتروح اللي هي .. sorry الاثنين بس بتروح فبقدر
+
+441
+00:33:22,350 --> 00:33:27,210
+عندي raw على اثنين by hatو عندي minus بتروح مع الـ
+
+442
+00:33:27,210 --> 00:33:31,050
+minus فإذا صارت رو على اثنين فاي هات فالتفاضلها
+
+443
+00:33:31,050 --> 00:33:34,410
+اللي هي اثنين رو على اربع بتصير رو على اثنين والـ
+
+444
+00:33:34,410 --> 00:33:37,750
+الناقص بتروح مع الناقص بتكون إذا الـ vector P
+
+445
+00:33:37,750 --> 00:33:41,370
+بيساوي رو على اثنين فاي هات و الـ surface إيش الـ
+
+446
+00:33:41,370 --> 00:33:43,970
+surface هنا بتذكرى؟ لإيش هو أن هذا الـ surface مين
+
+447
+00:33:43,970 --> 00:33:46,750
+لسه هبتنقل دي five فلو أخدت أنا element مين اللي
+
+448
+00:33:46,750 --> 00:33:49,790
+بتغيره؟ الـ raw لأنها بتتغير من الواحد للاثنين
+
+449
+00:33:49,790 --> 00:33:55,050
+والزد فدي هتكون دي raw ودي زد إذا الـ surface تبعي
+
+450
+00:33:55,050 --> 00:33:59,010
+دي raw دي z واتجاههم اللي الـ norm اللي عليه هو الـ
+
+451
+00:33:59,010 --> 00:34:03,970
+raw هيكون اللي في تجاه الـ phi hat الـ norm عليه
+
+452
+00:34:03,970 --> 00:34:05,150
+اللي هو phi hat
+
+453
+00:34:08,420 --> 00:34:13,080
+دس رو دي رو دي زد فاي هات نجيب الـ flux اللي هو
+
+454
+00:34:13,080 --> 00:34:16,760
+طلبه اللي هو الـ total magnetic flux بتصيب سوى الـ
+
+455
+00:34:16,760 --> 00:34:21,000
+surface integral لـ P dot DS P dot DS بتعطينا رو
+
+456
+00:34:21,000 --> 00:34:23,680
+على اثنين دي رو دي زد رو من هو اللي هو اللي بتروح
+
+457
+00:34:23,680 --> 00:34:29,680
+من واحد للاثنين و زد من zero لخمسة DZ هتعطينا خمسة والـ
+
+458
+00:34:29,680 --> 00:34:33,600
+الرو هتعطينا رو تربيع على اثنين من اللي هو واحد
+
+459
+00:34:33,600 --> 00:34:36,880
+للاثنين بعوض عنهم بيطلع عندي خمس عشر على أربع أو
+
+460
+00:34:36,880 --> 00:34:44,460
+اللي بيصيب يتساوى تلاتة وخمسة وسبعين بالمئة نيجي
+
+461
+00:34:44,460 --> 00:34:47,020
+للطريقة الثانية اللي هي الـ close line integral
+
+462
+00:34:47,020 --> 00:34:50,580
+لـ A دو DL الرسم اللي أنا رسمته هي موجود برضه على
+
+463
+00:34:50,580 --> 00:34:51,000
+الـ slide
+
+464
+00:35:08,240 --> 00:35:11,040
+عشان أجيب الـ line integra مانعش بده أكمل على كل
+
+465
+00:35:11,040 --> 00:35:15,120
+path من هدوله الـ path فهي احنا معلميهم واحد،
+
+466
+00:35:15,120 --> 00:35:18,780
+اثنين، ثلاثة، أربعة فالـ close line integral هيكون
+
+467
+00:35:18,780 --> 00:35:21,680
+إيش مجموعة هسميهم بصي واحد زي بصي اثنين زي بصي
+
+468
+00:35:21,680 --> 00:35:25,580
+ثلاثة زي بصي أربعة اللي هو الـ integration على الـ
+
+469
+00:35:25,580 --> 00:35:28,320
+line الأول زي الـ integration على الـ line الثاني زي
+
+470
+00:35:28,320 --> 00:35:29,700
+الـ integration على الـ line الثالث زي الـ
+
+471
+00:35:29,700 --> 00:35:32,160
+integration على الـ line الرابع فهيك بيعطيني الـ
+
+472
+00:35:32,160 --> 00:35:35,460
+close boss فسميناهم بصي واحد بصي اثنين بصي ثلاثة
+
+473
+00:35:35,460 --> 00:35:39,820
+بصي أربعة الحاجة اللي بتسهل عليا أنه إحنا عندنا a
+
+474
+00:35:39,820 --> 00:35:44,910
+dot dl a إيش تجاه z hat فاللي هيضل عندي اللي في
+
+475
+00:35:44,910 --> 00:35:48,790
+اتجاه الـ z hat لأنه dot product اللي مش في اتجاه
+
+476
+00:35:48,790 --> 00:35:54,150
+الـ z hat مش هيكون zero عند الـ line هنا قداش دي z z
+
+477
+00:35:54,150 --> 00:35:59,010
+hat هنا دي z minus z hat يعني الاثنين هدولة أربعة
+
+478
+00:35:59,010 --> 00:36:02,510
+في اتجاه الـ z hat الـ dot product ليه سوى zero لكن
+
+479
+00:36:02,510 --> 00:36:08,150
+واحد وثلاثة رو hat رو hat فواحد وثلاثة عطوب
+
+480
+00:36:08,150 --> 00:36:14,140
+يبعطوني zero من مي من الـ dot product فإذا 1 و 3 صفر
+
+481
+00:36:14,140 --> 00:36:18,240
+من الـ product و product بيظل عند مين؟ 2 و 4 فمن
+
+482
+00:36:18,240 --> 00:36:25,940
+كامل على 2 و 4 طبعا هناخد الـ a التي هي minus root
+
+483
+00:36:25,940 --> 00:36:33,090
+of b على 4 a زد hat بأوض عنها في هذا الـ bus هذا الـ
+
+484
+00:36:33,090 --> 00:36:36,930
+bus قداش قيمة row واحد اللي هو اثنين فبعود عن الـ
+
+485
+00:36:36,930 --> 00:36:40,270
+row بواحد في هذا الـ bus إيش الـ row هتكون اثنين
+
+486
+00:36:40,270 --> 00:36:44,810
+فبعود عن الـ row اثنين طبعا ناقص ربع بطلعها برا أنا
+
+487
+00:36:44,810 --> 00:36:48,130
+بكمل بالنسبة لمين الـ line تبعي دي زدهات وبرضه الـ
+
+488
+00:36:48,130 --> 00:36:50,450
+row بتطلع برا لأنها constant على طول هذا الـ bus
+
+489
+00:36:50,450 --> 00:36:54,240
+row constant واحد قيمتها فأعوض عنها واحد تربيع
+
+490
+00:36:54,240 --> 00:36:57,580
+والزيت بتكامل من Zero لخمسة الثاني هنا الـ bus
+
+491
+00:36:57,580 --> 00:37:00,980
+هتكون رو تربيع من اثنين تربيع والـ bus بيجي من
+
+492
+00:37:00,980 --> 00:37:05,540
+خمسة لصفر في diesel لو كملت بيطلع معايا نفس الجواب
+
+493
+00:37:05,540 --> 00:37:10,140
+واضح؟ إذا أنا أسوأ استخدمت اللي هي الـ flux بيساوي
+
+494
+00:37:10,140 --> 00:37:14,920
+الـ surface integral لـ B dot DS أو استخدمنا الـ flux
+
+495
+00:37:14,920 --> 00:37:18,500
+بيساوي الـ cloth line integral لـ A dot DL لازم
+
+496
+00:37:18,500 --> 00:37:23,780
+يعطينا نفس الجواب المثال الثاني بتقول احنا بتذكروا
+
+497
+00:37:23,780 --> 00:37:29,000
+اشتقنا اللي هو الـ magnetic field الناتج من الـ
+
+498
+00:37:29,000 --> 00:37:33,380
+plane يعني الـ plane بمورفي surface current density
+
+499
+00:37:33,380 --> 00:37:37,560
+K اشتقنها أنه فوق البلان وتحت البلان فوق البلان
+
+500
+00:37:37,560 --> 00:37:43,640
+تساوى نص كي اكس هات وتحت البلان تساوى ماينوس نص كي
+
+501
+00:37:43,640 --> 00:37:48,640
+اكس هات أو يعني above ب law اللي هي عند صد أكبر من
+
+502
+00:37:48,640 --> 00:37:52,640
+صفر و صد أقل من صفر باستخدام mean under's law كيف
+
+503
+00:37:52,640 --> 00:37:55,140
+ممكن أنا أحصل على نفس النتيجة يعني نقلنا .. يعني
+
+504
+00:37:55,140 --> 00:37:59,580
+نستخدم كذا طريقة لإن ممكن نطلب مني أطل .. يعني
+
+505
+00:37:59,580 --> 00:38:02,200
+أحصل عليها كذا طريقة أن كيف لو أنا استخدمت الـ
+
+506
+00:38:02,200 --> 00:38:06,320
+vector magnetic potential إيش عرفنا المجلة الـ
+
+507
+00:38:06,320 --> 00:38:10,440
+potential ناتج من مين؟ من vector which charge
+
+508
+00:38:10,440 --> 00:38:13,540
+current density surface current density أنه قولنا
+
+509
+00:38:13,540 --> 00:38:18,100
+دي ايه أو يعني a vector قولنا الـ integral على الـ
+
+510
+00:38:18,100 --> 00:38:21,720
+surface صح؟ هيك أنا رجب أقول لكم القانون اللي قولنا
+
+511
+00:38:21,720 --> 00:38:26,200
+انشقنا من بيه بس أنا مش عارفش كل اشتقاق اللي هو دي
+
+512
+00:38:26,200 --> 00:38:31,800
+أو أقول دي ايه يساوي surface integral لـ mu not k
+
+513
+00:38:31,800 --> 00:38:39,780
+على 4 by R في دي اسمفا إيه إذا هي التكامل دي ايه؟
+
+514
+00:38:39,780 --> 00:38:46,270
+بتحسبني كدس على four by R والـ K اللي هي مفروض
+
+515
+00:38:46,270 --> 00:38:50,510
+given لنا والـ DS وبقدر أجيب اللي هو المفروض أن
+
+516
+00:38:50,510 --> 00:38:52,570
+أجيب المجمد اللي فيه الأسواق في نقطة above الـ
+
+517
+00:38:52,570 --> 00:38:56,210
+surface أو below الـ surface مين DS؟ هي DS على الـ
+
+518
+00:38:56,210 --> 00:39:00,650
+plan DS هي قاعدة وين في الـ plan تبعي؟ على Z equals
+
+519
+00:39:00,650 --> 00:39:05,830
+0 معناه بيمتد وين؟ في الـ XY إذا الـ element تبعي دي
+
+520
+00:39:05,830 --> 00:39:09,170
+X prime دي Y prime لأنه قاعدة النقطة X prime و Y
+
+521
+00:39:09,170 --> 00:39:15,220
+prime بعده عن الـ origin عند x' y' و z0 وهاخد أن
+
+522
+00:39:15,220 --> 00:39:21,220
+دي x' ودي y' إذا دي s هتكون دي x' ودي y' ودي
+
+523
+00:39:21,220 --> 00:39:25,380
+البعد تبعها اللي هو مين x' y' النقطة اللي بدأ ايس
+
+524
+00:39:25,380 --> 00:39:30,200
+عندها الـ magnetic field هي 00z فبتنقل ر ر قلنا
+
+525
+00:39:30,200 --> 00:39:33,860
+دائما هي عبارة عن r-r' اللي هو وين أنا بدأ ايس الـ
+
+526
+00:39:33,860 --> 00:39:38,500
+magnetic minus بعد الـ element أو الـ source هيكون
+
+527
+00:39:40,130 --> 00:39:43,370
+أول حاجة هي الـ K التي هي K Y A Y hat اللي هو نفس
+
+528
+00:39:43,370 --> 00:39:48,910
+المثال كان معروف لنا أن الـ K K Y Y hat وعندي اللي
+
+529
+00:39:48,910 --> 00:39:53,090
+هي DS زي ما اتفقنا دي X prime Dy prime وR إيش
+
+530
+00:39:53,090 --> 00:39:57,350
+بتساوي الـ R magnitude هي جزر التربيع لـ R minus R
+
+531
+00:39:57,350 --> 00:40:00,410
+prime الـ R بدأيسي عندها الـ magnetic field هي 00Z
+
+532
+00:40:00,410 --> 00:40:03,890
+minus الـ R prime اللي هو أن عندي الـ element X
+
+533
+00:40:03,890 --> 00:40:07,610
+prime Y prime 0 فبتكون الجزر التربيع لـ X prime
+
+534
+00:40:07,610 --> 00:40:12,010
+تربيع زي Y تربيع primeY prime تربيع زي Z تربيع
+
+535
+00:40:12,010 --> 00:40:15,350
+تمام هذه R magnitude لأن هو نطوب من الـ R magnitude
+
+536
+00:40:15,350 --> 00:40:23,730
+ده بس إذا دي A أشبه ساومي ونط K Y Y hat فدي قسم
+
+537
+00:40:23,730 --> 00:40:28,630
+يمين دي X prime دي Y prime على 4 Pi الجزر التربية
+
+538
+00:40:28,630 --> 00:40:33,030
+لـ X prime تربيع زي Y prime تربيع زي Z تربيع برايم
+
+539
+00:40:33,030 --> 00:40:37,330
+تمام لو بدي أجيب الـ magnetic field density اللي هي
+
+540
+00:40:37,330 --> 00:40:42,150
+دي A أشبه تكون كل دي A بأجيبها لو أنا طلعت عند الـ ay
+
+541
+00:40:42,150 --> 00:40:48,410
+hat والـ kern بس بتضلوا الاعتمادية عميل اعتمادية
+
+542
+00:40:48,410 --> 00:40:53,060
+على الـ z فقط الاعتمادية بأجيب الـ kern الاعتمادية على
+
+543
+00:40:53,060 --> 00:40:56,000
+الـ z فهذا الـ component الوحيد اللي بالضبط عندي الي
+
+544
+00:40:56,000 --> 00:41:02,240
+minus dy by dz x hat من الـ determinant تبع الـ kern
+
+545
+00:41:02,240 --> 00:41:07,020
+بحسبها بأجيب اللي هو التفاضل بالنسبة لـ z بتصير
+
+546
+00:41:07,020 --> 00:41:12,580
+القوة 3 على 2 التفاضل بيصير عندي minus نص اللي
+
+547
+00:41:12,580 --> 00:41:17,560
+هببطلها لفوق وبعدين باطفلها ليه كمان نص واحد
+
+548
+00:41:17,560 --> 00:41:19,820
+فبيصير منص تلاتة ع اتنين تنزل تحت بقوة تلاتة ع
+
+549
+00:41:19,820 --> 00:41:22,500
+اتنين والتفاضل ما يبق داخل القوس اللي هي نزلت
+
+550
+00:41:22,500 --> 00:41:29,090
+فبيصير عندي زد في البسط واضح من وين إجت والنص راحت
+
+551
+00:41:29,090 --> 00:41:32,410
+مع الاثنين اللي إجت من الزت تفضل عادي بتعرفوا أه في
+
+552
+00:41:32,410 --> 00:41:35,370
+ده أكتب على اللوح ولا عارفينه إذا في الـ دي أول حاجة
+
+553
+00:41:35,370 --> 00:41:39,950
+بتيجي ناقص نص من وين من ده فاضل المقام وكمان اثنين
+
+554
+00:41:39,950 --> 00:41:44,010
+إجت من اثنين زت فالاتنين بتروح مع النص وبيضل عند زت
+
+555
+00:41:44,010 --> 00:41:46,370
+في البص بتقول تحتها بتصير القوة ثلاثة على اثنين
+
+556
+00:41:46,370 --> 00:41:51,680
+لأنه كمان ناقص واحد إذا هذه هي الـ DB بعد بقى أجيب
+
+557
+00:41:51,680 --> 00:41:58,060
+الـ B من مكان ما هو الـ infinity لـ plus infinity لو
+
+558
+00:41:58,060 --> 00:42:00,460
+عملنا التكامل طبعا إذا أنتم لاحظتوا هذا double
+
+559
+00:42:00,460 --> 00:42:04,120
+integral dx prime dy prime و dx prime تربيع و y
+
+560
+00:42:04,120 --> 00:42:09,530
+prime تربيع مقدر أحولها من كارتيزيا لدولر لأن
+
+561
+00:42:09,530 --> 00:42:13,510
+أسهل في الـ boolean بيحوظ
+
+562
+00:42:13,510 --> 00:42:17,310
+عها بـ row دي رو دي فاي الـ prime لأن عشان نحافظ
+
+563
+00:42:17,310 --> 00:42:22,140
+عليها و X تربيع زي Y تربيع هي رو الـ prime تربيع و
+
+564
+00:42:22,140 --> 00:42:26,420
+الـ row بتروح من 0 لـ infinity والـ 5 من 0 لـ 2π
+
+565
+00:42:26,420 --> 00:42:30,560
+فبتصير سهل جدا يعني التكامل تبع الـ D5 بعطيني 2π
+
+566
+00:42:30,560 --> 00:42:33,100
+بخلص منه بصيحة اللي بيظل عندي row prime D row
+
+567
+00:42:33,100 --> 00:42:36,520
+prime على row prime تربيع زي تربيع بيصير كالها Du
+
+568
+00:42:36,520 --> 00:42:42,200
+على U تربيع زي تربيع قوة 3 على 2 سهل تكملها يعني
+
+569
+00:42:42,200 --> 00:42:45,400
+مجرد الـ trick أكيد أخذتوها في الـ calculus مشهورة
+
+570
+00:42:45,400 --> 00:42:48,420
+هي الـ trick أن أخلص من الـ Cartesian بروح للبولر
+
+571
+00:42:
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/tMFy3zzwo94_postprocess.srt b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/tMFy3zzwo94_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..a4b28174ab43354c61a01aa43ad76bd71912d304
--- /dev/null
+++ b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/tMFy3zzwo94_postprocess.srt
@@ -0,0 +1,2336 @@
+1
+00:00:20,860 --> 00:00:23,300
+بسم الله الرحمن الرحيم السلام عليكم و رحمة الله و
+
+2
+00:00:23,300 --> 00:00:26,160
+بركاته احنا اليوم ان شاء الله راح نتابع موضوعنا
+
+3
+00:00:26,160 --> 00:00:29,240
+احنا المحاضرات الماضية شوفنا امثلة كيف ممكن نحسب
+
+4
+00:00:29,240 --> 00:00:32,560
+ال magnetic field من عدة elements و مور فيها
+
+5
+00:00:32,560 --> 00:00:36,080
+التيار زي ال filament اللي لها finite links ال
+
+6
+00:00:36,080 --> 00:00:40,080
+filament اللي لها اسم infinity و infinity من جهتين
+
+7
+00:00:40,330 --> 00:00:42,790
+بعدين شفنا من ال plane شفنا من ال ring شفنا من ال
+
+8
+00:00:42,790 --> 00:00:47,250
+solenoid اللي يعتبرنا ان ال ring هي element من ال
+
+9
+00:00:47,250 --> 00:00:50,910
+solenoid بعدين كملنا على الكيوكسيا الكامر و اليوم
+
+10
+00:00:50,910 --> 00:00:54,070
+هنشوف أمثلة كمان على حساب ال magnet field يعني
+
+11
+00:00:54,070 --> 00:00:56,770
+مثلا ما انا حكيتلكم على ذلك سابقا ان ال concept
+
+12
+00:00:56,770 --> 00:01:00,970
+بتاع كل chapter هو واضحلكن كل اللي احنا بنحكي فيه
+
+13
+00:01:00,970 --> 00:01:04,230
+هي أمثلة عامة قد ال concept كيف احنا نستخدم هذا ال
+
+14
+00:01:04,230 --> 00:01:08,690
+concept و كيف احنا نطبقه فاحنا شفنا في المحاضرات
+
+15
+00:01:08,690 --> 00:01:12,890
+السابقة انه ال magnetic field بشكل عام بساوي نص K
+
+16
+00:01:12,890 --> 00:01:19,330
+across A and hat K اللي هو اتجاه التيار A and hat
+
+17
+00:01:19,330 --> 00:01:23,410
+اللي هو ال norm اللي على ال plane في اتجاه النقطة
+
+18
+00:01:23,410 --> 00:01:26,900
+الرئيسية عندها ال magnetic fieldطبعا فاحنا ايش
+
+19
+00:01:26,900 --> 00:01:29,740
+بقولنا اول اكس بيعني طبعا ايه لان فينا two planes
+
+20
+00:01:29,740 --> 00:01:35,060
+واحد عند z equal 0 واحد هذا z axis هذا الاتجاه هو
+
+21
+00:01:35,060 --> 00:01:39,400
+z axis فهذا عند z equal 0 وهنا عند z equal 4 يعني
+
+22
+00:01:39,400 --> 00:01:43,820
+المسافة بين ال two planes هي 4 ال plane اللي عند z
+
+23
+00:01:43,820 --> 00:01:48,460
+equal 0 بيحمل طيار k مقداره minus 10 ax hat واضح
+
+24
+00:01:48,460 --> 00:01:52,180
+ان هو ماخد ال x ما اللي هطلع من ال plane هاتجاه ال
+
+25
+00:01:52,180 --> 00:02:00,780
+xطبعا و الطيار داخل الطيار هو ال X معناه ان الطيار
+
+26
+00:02:00,780 --> 00:02:04,700
+داخل هي كيه هي اتجاه الطيار وهي ال X فزاندش بيكون
+
+27
+00:02:04,700 --> 00:02:09,980
+minus minus عشرة X hat بينما هنا أشماله طالع
+
+28
+00:02:09,980 --> 00:02:16,620
+فهيكون عشرة X hat طبعا ال K هي ال units تعونها
+
+29
+00:02:16,620 --> 00:02:20,060
+amps per meter زي ما شوفنا في مثال لما جيبنا ال
+
+30
+00:02:20,060 --> 00:02:27,050
+magnetاللي بيعملون في ال surface طبعا طالب مننا
+
+31
+00:02:27,050 --> 00:02:33,410
+نحسب المجموعات الكثيرة نبطة x1 y1 z1 هاي احنا ال 0
+
+32
+00:02:33,410 --> 00:02:39,270
+0 0 هنا نقل ال origin عندي x1 y1 z1 ومنها تكون z
+
+33
+00:02:39,270 --> 00:02:45,490
+هو ال axis يعني مثلا هنا هاي النقطة بتاعتنا 1 1 1
+
+34
+00:02:45,490 --> 00:02:49,370
+x1 y1 z1
+
+35
+00:02:52,220 --> 00:02:55,120
+لو استخدمنا المعادلة العامة أو استخدمنا معادلتنا
+
+36
+00:02:55,120 --> 00:02:58,040
+السابقة أنه تحت وفوق الـ plan زي ما حكينا بمحادرات
+
+37
+00:02:58,040 --> 00:03:03,260
+المرضى لازم نحصل نتجة عند لو أخدت .. هسمي ال H
+
+38
+00:03:03,260 --> 00:03:07,500
+اللي عند ال origin H0 المجهد اللي فيه الناتج من ال
+
+39
+00:03:07,500 --> 00:03:09,780
+current اللي في ال plan اللي عند ال origin هسميه
+
+40
+00:03:09,780 --> 00:03:13,260
+H0 والمجهد اللي فيه الناتج من ال current اللي على
+
+41
+00:03:13,260 --> 00:03:18,000
+ال plan اللي عنده أربعة زي تسوء أربعة هسميه H4 بس
+
+42
+00:03:18,000 --> 00:03:23,320
+التمييز عند ال H0هستحضر المعادلة K من نصف K cross
+
+43
+00:03:23,320 --> 00:03:27,120
+A and hat كمان مره نذكر حالنا كيلو باتجاه مجلة ال
+
+44
+00:03:27,120 --> 00:03:30,860
+current و A and hat هو العمود اللي على البلاي و
+
+45
+00:03:30,860 --> 00:03:35,840
+بين البلاي و نقطة باسمة المجلة كيلو K في حالتنا هي
+
+46
+00:03:35,840 --> 00:03:41,040
+قداشق منها نص عشر A X hat عوض عنها A and hat من هي
+
+47
+00:03:41,040 --> 00:03:44,320
+العمودي على البلاي لحد النقطة من هيكون اللي في
+
+48
+00:03:44,320 --> 00:03:51,250
+اتجاه البس تفزد hat فإيش هيكون ال crossلأنها هي
+
+49
+00:03:51,250 --> 00:03:55,770
+اتجاهها ومجابب z hat لكون سبوردك في ال x و ال z
+
+50
+00:03:55,770 --> 00:04:01,250
+ماله minus y هيكون عند ال plus حسب ضبط المصدر في
+
+51
+00:04:01,250 --> 00:04:08,070
+العشرة خمسة a y hat a على البرمتر البرمتر البرمتر
+
+52
+00:04:08,070 --> 00:04:12,990
+البرمتر البرمتر البرمتر البرمتر البرمتر البرمتر
+
+53
+00:04:12,990 --> 00:04:13,270
+البرمتر البرمتر البرمتر البرمتر البرمتر البرمتر
+
+54
+00:04:13,270 --> 00:04:14,970
+البرمتر البرمتر البرمتر البرمتر البرمتر البرمتر
+
+55
+00:04:14,970 --> 00:04:17,050
+البرمتر البرمتر البرمتر البرمتر البرمتر البرمتر
+
+56
+00:04:17,050 --> 00:04:19,500
+البرمتر البرمتر البرمتر البرمتر البرمتر البرقيمة K
+
+57
+00:04:19,500 --> 00:04:28,020
+أداش عشرة X hat AN hat عبارة عن minus Z hat سالب Z
+
+58
+00:04:28,020 --> 00:04:35,720
+hat ال cross product بين X و Y هو سالب Y hat سالب
+
+59
+00:04:35,720 --> 00:04:40,100
+و سالب تصبح plus نصف عشرة خمسة فخمسة Y hat amps
+
+60
+00:04:40,100 --> 00:04:45,280
+per meter إذا الاتنين أعطوني عند النقطة نقدر ال
+
+61
+00:04:45,280 --> 00:04:48,460
+magnet field خمسة و تجاه و تجاه Y hat
+
+62
+00:04:52,830 --> 00:04:57,430
+تمام اذا انت نين اعطوني بص تف اذا ال total field
+
+63
+00:04:57,430 --> 00:05:02,430
+مش هيكون مجموهم يعني عشرة y hat تمام ويجي لأ
+
+64
+00:05:02,430 --> 00:05:07,490
+النقطة التانية النقطة التانية قوللي انا بدي x سفر
+
+65
+00:05:07,490 --> 00:05:15,870
+y minus y minus ثلاثة وزد عشرة يعني somewhere هنا
+
+66
+00:05:15,870 --> 00:05:22,730
+x سفر y minus ثلاثةبتتسفر على افتراض انه هي النقطة
+
+67
+00:05:22,730 --> 00:05:25,330
+ال original او يعني في اي مكان ال original على
+
+68
+00:05:25,330 --> 00:05:28,270
+اساس ان ال plans هم اكبار يعني مش بضرورة هكذا يعني
+
+69
+00:05:28,270 --> 00:05:31,950
+هذا الإشارة بس مبتدأ بال plans وهذا الإشارة انه
+
+70
+00:05:31,950 --> 00:05:38,610
+مبتدأ ال plans واضح فهذه النقطة هي 0-3 10 لسه
+
+71
+00:05:38,610 --> 00:05:42,370
+plans اللي قلتلكم بتدين هكذا infinity في كل اتجاه
+
+72
+00:05:42,370 --> 00:05:50,960
+في ال X Y infinityهنا عند ال Z equals 0 وهنا عند
+
+73
+00:05:50,960 --> 00:05:55,360
+ال Z equals R تمام بدنا نعيد نفس الحطوات وفي هذه
+
+74
+00:05:55,360 --> 00:05:58,720
+الحلقة إيش الاختلاف هيكون نيجي ل H node اللي هو ال
+
+75
+00:05:58,720 --> 00:06:02,440
+field الناتج من ال plane عند ال 0 K لا زالة minus
+
+76
+00:06:02,440 --> 00:06:07,120
+10 X hat و ال N hat ماله plus Z hat فهيعطينا نفس
+
+77
+00:06:07,120 --> 00:06:13,080
+النتيجة ناقص عشرة و Z hat هيعطيني خمسة A Y hat
+
+78
+00:06:13,080 --> 00:06:17,880
+amps per meter نيجي للplane التاني من عند الأربع K
+
+79
+00:06:17,880 --> 00:06:23,530
+عشرةمين ال a انهاتى؟ ال plus z hat ال plus z hat
+
+80
+00:06:23,530 --> 00:06:27,950
+فاندي انا ال plus عشرة و ال plus z hat ال cross
+
+81
+00:06:27,950 --> 00:06:32,210
+product بينهم minus y همسيني ال minus خمسة y hat
+
+82
+00:06:32,210 --> 00:06:36,270
+يعني الأولى نهاية قيمة جزتك والتانى minus إيش ال
+
+83
+00:06:36,270 --> 00:06:41,110
+result سهر؟ إذا لما كان النقطة بين ال two planes
+
+84
+00:06:41,110 --> 00:06:45,530
+حصلنا على field واحد منهم تيار داخل والتانى طالع
+
+85
+00:06:46,150 --> 00:06:50,770
+تجاه التيارات معاكسة لما برا كانت النتيجة بتساوي 0
+
+86
+00:06:50,770 --> 00:06:53,950
+جابوا لما يكونوا التيارات كلهم دخلين أو التيارات
+
+87
+00:06:53,950 --> 00:06:57,330
+معاهم طالعين عيدوا يعني هاي الأمثلة اللي ممكن
+
+88
+00:06:57,330 --> 00:07:01,930
+تشوفها في الامتحانات لو بدى أغير في السؤال صح؟
+
+89
+00:07:01,930 --> 00:07:06,830
+وضح؟
+
+90
+00:07:17,760 --> 00:07:22,040
+نيجيلا اللى هو ال Troid ال Troid هو عبارة عن حلقة
+
+91
+00:07:22,040 --> 00:07:26,440
+ملفوف حولها سلك وهذا السلك مور فيه current زى ما
+
+92
+00:07:26,440 --> 00:07:31,280
+انتوا شايفين هى السلك بدخل فيه تيار بهذا الاتجاه و
+
+93
+00:07:31,280 --> 00:07:36,320
+بطلع من السلك التانى بدال مبنى تكفيد فى نقطة مالها
+
+94
+00:07:36,320 --> 00:07:41,660
+فى هذا المنطقة فى قلب ال Troid فى قلب ال Troid زى
+
+95
+00:07:41,660 --> 00:07:46,280
+ما انتوا شايفين مثلا عند اللى هى النقطة رومعلى بعض
+
+96
+00:07:46,280 --> 00:07:49,720
+روه من ال origin قدش يكون ال magnetic field
+
+97
+00:07:49,720 --> 00:07:54,360
+المعرفة اللي هو ال raw node هي المسافة أو ال
+
+98
+00:07:54,360 --> 00:07:58,760
+center أو نصف القطر ما بين ال origin لو ينا نص
+
+99
+00:07:58,760 --> 00:08:02,740
+المسافة بتاعة ال ring بالتمام هي raw node يعني إذا
+
+100
+00:08:02,740 --> 00:08:12,580
+أعتبرنا إحنا شايفين هذا ال raw node؟ هذه كلها أنت
+
+101
+00:08:12,580 --> 00:08:16,850
+مصهاالمسافة من هنا إلى هنا هي رومان فهي عند اي
+
+102
+00:08:16,850 --> 00:08:19,690
+نقطة عامة تكون هنا ال ring هنا ال ring هنا ال raw
+
+103
+00:08:19,690 --> 00:08:22,950
+المابين ال origin والنقطة اللى عامة بحسب بنتها ال
+
+104
+00:08:22,950 --> 00:08:26,030
+magnetic field فبنعرف احنا ال magnetic field اللى
+
+105
+00:08:26,030 --> 00:08:28,910
+بتاعها الفقران اللى هو ال inside و ال outside
+
+106
+00:08:28,910 --> 00:08:34,130
+للترويد inside مثلا على مسافة raw زى ما حكى نستخدم
+
+107
+00:08:34,130 --> 00:08:38,230
+الberslau ال clause integral لHWL بسوق I enclosed
+
+108
+00:08:39,230 --> 00:08:43,410
+طب H dot dl H dot dl H التجاهة كيف؟ احنا ال
+
+109
+00:08:43,410 --> 00:08:45,730
+current بدنا نتبع اتجاه ال current عشان نعرف اتجاه
+
+110
+00:08:45,730 --> 00:08:51,910
+ال magnet field ال current هي فيك تاخد لورا
+
+111
+00:08:51,910 --> 00:08:56,930
+فبلف ايدي على اتجاه ال current بلاقي ان ال magnet
+
+112
+00:08:56,930 --> 00:09:00,670
+field فيه اتجاه واضح؟ كيف عرفنا اتجاه ال magnet
+
+113
+00:09:00,670 --> 00:09:03,830
+field؟ فلف ايدي في اتجاه ال current حلاقي ان ال
+
+114
+00:09:03,830 --> 00:09:06,830
+magnet field اتجاه فال Detroit معناه فدى الاتجاه
+
+115
+00:09:11,810 --> 00:09:15,910
+واضح كيف تحدده؟ اذا اتجاه هو في طريقة مين؟ الـPhi
+
+116
+00:09:15,910 --> 00:09:23,890
+hat اتجاه المنطقية اتجاه الـPhi hat طبعا الال ايش
+
+117
+00:09:23,890 --> 00:09:32,250
+هتكون؟ two by row او
+
+118
+00:09:32,250 --> 00:09:35,330
+يعني لو أخدنا ال element row D5 ده كمل على ال D5
+
+119
+00:09:35,330 --> 00:09:39,820
+اللي هى two byع تبع النبت اكبر ان ال row ثابتة و
+
+120
+00:09:39,820 --> 00:09:41,820
+باخد ال element ال element ايش هيكون ال row دي
+
+121
+00:09:41,820 --> 00:09:45,160
+five بكمل ال five من zero ل two pi فهذا h dot dl
+
+122
+00:09:45,160 --> 00:09:49,320
+ايش هتعطينا اتش two by row طب I enclosed قداش كم
+
+123
+00:09:49,320 --> 00:09:52,560
+تهيه enclosed هو I الداخل هيبقى معناه يابس I بتلوف
+
+124
+00:09:52,560 --> 00:09:56,540
+على اكم حلقة على N حلقات فI ال enclosed هتكون N في
+
+125
+00:09:56,540 --> 00:10:01,520
+I او I المولدة ل ال magnetic field تبعنا هي N في I
+
+126
+00:10:04,040 --> 00:10:08,500
+إذا إيش هيكون H؟ بساوي N في I على 2 by R هذا هو
+
+127
+00:10:08,500 --> 00:10:12,960
+المجلد field inside الـ droid في raw مبالي رو نض
+
+128
+00:10:12,960 --> 00:10:18,740
+minus A اللي هي A من هى هذه كلها اللي هو نص القطار
+
+129
+00:10:18,740 --> 00:10:23,580
+فهذه
+
+130
+00:10:23,580 --> 00:10:27,640
+ال مجلد field inside اللي هي رونوت نقص A و رونوت
+
+131
+00:10:27,640 --> 00:10:33,640
+زائد A أساس ان الدمية كله A2A نص القطر A فإذا هذه
+
+132
+00:10:33,640 --> 00:10:37,200
+ال region إيش بعرفها رونود minus A أو رونود plus A
+
+133
+00:10:37,200 --> 00:10:40,640
+فهذه ال region اللي هي inside ال Troy المجلة فيه
+
+134
+00:10:40,640 --> 00:10:46,240
+بساوي Ni على 2π رونود بسيطة من أهم سلوكهنا جوا بس
+
+135
+00:10:46,240 --> 00:10:49,460
+هال مجلة الإضافة المعلومة لزيادة اللى هحكيها انه
+
+136
+00:10:49,460 --> 00:10:54,300
+لو أخدنا approximation و اعتبرنا انه ال two pi
+
+137
+00:10:54,300 --> 00:10:57,940
+مثلا عند اللى هي يعني انه sickness تبع ال toroid
+
+138
+00:10:57,940 --> 00:11:01,720
+صغير بالنسبة لطوله يعني كله بقدر اتقربه ل two pi
+
+139
+00:11:01,720 --> 00:11:04,940
+Ronald يعني ال a هالدي ناقص او a صغيرة كتير
+
+140
+00:11:04,940 --> 00:11:10,820
+بالنسبة ل ال Ronald يعني ممكن اهملهااعتبرها ان
+
+141
+00:11:10,820 --> 00:11:15,040
+كلها بقدر اعبر عنها two by rho not باش هيكون اللي
+
+142
+00:11:15,040 --> 00:11:19,800
+هو الأدشة approximate ni على two by rho not اللي
+
+143
+00:11:19,800 --> 00:11:23,180
+هي two by rho not بدأت سميها اللي هي طول الترويد
+
+144
+00:11:23,770 --> 00:11:28,390
+طوله هيكون فإذا ما هيكون un I على L و N على L اللى
+
+145
+00:11:28,390 --> 00:11:31,510
+هى un per unit length فإذا ما هيكون اتش
+
+146
+00:11:31,510 --> 00:11:35,070
+approximate بتسوى N في I اللى هى بالتمام المجنفيل
+
+147
+00:11:35,070 --> 00:11:37,910
+اللى حسبناه من ميوم السولانويد متذاكرينه هنا فى
+
+148
+00:11:37,910 --> 00:11:41,050
+السولانويد المجنفيل ال inside هو عدد اللفات per
+
+149
+00:11:41,050 --> 00:11:43,710
+unit length فى ال current اللى مورفه السولانويد
+
+150
+00:11:43,710 --> 00:11:48,440
+متذاكرينإذا ما بنقدر نقول إن السولانويد هو حالة
+
+151
+00:11:48,440 --> 00:11:50,960
+خاصة من الترويد لإن إحنا لما عملنا ال
+
+152
+00:11:50,960 --> 00:11:54,520
+approximation حصلنا على شكل ال magnetic field اللي
+
+153
+00:11:54,520 --> 00:11:59,020
+ناتج في قلب السولانويد طب بدنا outside ال magnetic
+
+154
+00:11:59,020 --> 00:12:04,580
+field outside اللي هو الترويد زي ما هو طالب مننا
+
+155
+00:12:04,580 --> 00:12:07,300
+inside و outside حيكون في عندنا current
+
+156
+00:12:07,300 --> 00:12:11,200
+approximated يعني حيكون هنا an I minus an I بساوة
+
+157
+00:12:11,200 --> 00:12:17,770
+0 فإذا ما حيكون magnetic field بساوة 0احنا بدنا
+
+158
+00:12:17,770 --> 00:12:20,990
+هلاقاتها نعرف ال magnetic flux density ال magnetic
+
+159
+00:12:20,990 --> 00:12:25,450
+flux density بي
+
+160
+00:12:25,450 --> 00:12:28,570
+اللي هي ال magnetic flux density بعرفها بدلالة ال
+
+161
+00:12:28,570 --> 00:12:31,950
+H انها بتساوي ميو نوت H H اللي هو ال magnetic
+
+162
+00:12:31,950 --> 00:12:35,010
+field intensity او ال field intensity او ال
+
+163
+00:12:35,010 --> 00:12:39,730
+magnetic field و بي اللي هي ال density فال density
+
+164
+00:12:39,730 --> 00:12:44,030
+هي ميو نوت في H ميو نوت بنسميها urban mobility
+
+165
+00:12:45,210 --> 00:12:49,770
+السماحية لل space انه ماله يسمح ل magnetic field
+
+166
+00:12:49,770 --> 00:12:54,390
+انه يدخل فيه ميو نوت لل free space او ال vacuum لو
+
+167
+00:12:54,390 --> 00:12:57,150
+قمنا ال note بتصير ال ميو لأي material زي ما عملنا
+
+168
+00:12:57,150 --> 00:13:01,130
+في ال electric field ابسلون نوت بتكون لل space ال
+
+169
+00:13:01,130 --> 00:13:04,350
+free space او ال vacuum بتدلون ال note اللى هتكون
+
+170
+00:13:04,350 --> 00:13:09,030
+ابسلون لأي material اذا ال ميو نوت هي مقدار
+
+171
+00:13:09,030 --> 00:13:12,130
+السماحية لهذا ال space او هذه ال media انها تسمح ل
+
+172
+00:13:12,130 --> 00:13:13,730
+magnetic field يمر فيها
+
+173
+00:13:16,950 --> 00:13:21,830
+الـ units out ميو نوت الهنري بيرميتر هنري بيرميتر
+
+174
+00:13:21,830 --> 00:13:28,310
+أقيمته 4 باعي فعشرة قوة ناقص سبعة هنري بيرميتر ال
+
+175
+00:13:28,310 --> 00:13:30,690
+magnetic flux إيش من عارف ال magnetic flux؟ هي
+
+176
+00:13:30,690 --> 00:13:34,690
+خطوط المجال اللي بتطلع من خلال ال surface أنا عند
+
+177
+00:13:34,690 --> 00:13:38,230
+هاي طيار مثلا طالع من ال facility في غرفي طيار
+
+178
+00:13:38,230 --> 00:13:40,670
+طالع من الصفحة اتجاه ال magnetic field في هذا
+
+179
+00:13:40,670 --> 00:13:45,150
+الاتجاه هتقلب مصنولي اللي هو ال magnetic flux
+
+180
+00:13:45,150 --> 00:13:49,910
+linesمجنتك الـ Flux Lines المجنتك الـ Flux Lines
+
+181
+00:13:49,910 --> 00:13:54,830
+هو عبارة عن الـ Surface Integral ل B Dot DS وقيمة
+
+182
+00:13:54,830 --> 00:13:59,870
+ال units بتاعته Webars ال unit بتاعت ال Flux هي ال
+
+183
+00:13:59,870 --> 00:14:04,070
+Webars B Dot DS لازم تعطيني Webars DS اللي هي
+
+184
+00:14:04,070 --> 00:14:08,090
+مالها متر تربية اذا بي برضه ال units بتاعتها Webar
+
+185
+00:14:08,090 --> 00:14:13,830
+بمتر تربية تمام اذا بي ال units عاونها Webar بمتر
+
+186
+00:14:13,830 --> 00:14:17,860
+تربية اللي هي ال Flux Densityأو الـ magnetic flux
+
+187
+00:14:17,860 --> 00:14:23,640
+density في
+
+188
+00:14:23,640 --> 00:14:26,480
+حاجة مهمة بتفرق ما بين ال electric field و ال
+
+189
+00:14:26,480 --> 00:14:31,420
+magnetic field يعني ال electric field flux أو لو
+
+190
+00:14:31,420 --> 00:14:34,600
+يكون عندي electric field ال flux تبعه هو ال closed
+
+191
+00:14:34,600 --> 00:14:38,760
+integral due to ds ال flux اللي هي حطوط المجال
+
+192
+00:14:38,760 --> 00:14:42,840
+اللي طالعة من ال surface لما يكون closed surface
+
+193
+00:14:42,840 --> 00:14:50,430
+اللي هي المين هاد يقولنالأ بس اشهد المعادلة, gauss
+
+194
+00:14:50,430 --> 00:14:54,290
+law مالكم؟ هيكون Q, اللي هي Q in clause, اذا ال
+
+195
+00:14:54,290 --> 00:14:57,690
+clause انتجرة اللي دي بتقاس بسوا Q ايش معناه هذا
+
+196
+00:14:57,690 --> 00:15:00,350
+الحكيم؟ قولنا ان ممكن احتمالية ان احصل على
+
+197
+00:15:00,350 --> 00:15:04,090
+isolated electric charge وان مش بضرورة الخطوط تغلق
+
+198
+00:15:04,090 --> 00:15:08,630
+نفسهالأن اذا اقلقت نفسي لن تعطيني قيمة Q فهي
+
+199
+00:15:08,630 --> 00:15:12,350
+ستعطيني صفر اذا ال close surface integral D ضد S
+
+200
+00:15:12,350 --> 00:15:15,630
+بيتساوة Q معناها ان انا ممكن احصل على isolated jar
+
+201
+00:15:15,630 --> 00:15:18,530
+زى ما انتوا شايفينه هى هال surface اللى بنعمل عليه
+
+202
+00:15:18,530 --> 00:15:23,110
+close integral اشعطانى Q enclosed ماريشتش سكرت على
+
+203
+00:15:23,110 --> 00:15:27,030
+حالة خطوط القوة خطوط المجال لكن في ال magnetic
+
+204
+00:15:27,030 --> 00:15:32,210
+field هنلاحظ ان ال close integral لD ضد S بتساوة
+
+205
+00:15:32,210 --> 00:15:37,440
+صفرفدائما بيكون ال flux like closed surface احنا
+
+206
+00:15:37,440 --> 00:15:40,460
+ده ال flux اللي قولنا عرفنا اللي هو بصين مش closed
+
+207
+00:15:40,460 --> 00:15:44,140
+surface لأي surface P dot DS سميناه ال flux لكن لو
+
+208
+00:15:44,140 --> 00:15:48,340
+عرفته على closed surface integral هيعطينا سفر معنى
+
+209
+00:15:48,340 --> 00:15:52,880
+هيك ان خطوط المجال بتسكر على نفسها بتروح و بتسكر
+
+210
+00:15:52,880 --> 00:15:57,320
+على نفسها هو لايمكن احصل على حاجة بتسميها ال
+
+211
+00:15:57,320 --> 00:16:03,340
+monopoleاللي هو magnetic لحاله north pole أو south
+
+212
+00:16:03,340 --> 00:16:07,140
+pole ليش؟ لإن لو أنا طلعت على ال magnet هاي magnet
+
+213
+00:16:07,140 --> 00:16:11,520
+هاي له south و north pole أخد جزء من نقطته هاتني
+
+214
+00:16:11,520 --> 00:16:16,580
+كمان ع طول south و north أقطع دايما هاتني south و
+
+215
+00:16:16,580 --> 00:16:19,980
+north قد ما أقطع هاتني south و north لكن بالنسبة
+
+216
+00:16:19,980 --> 00:16:23,420
+لل charge ممكن أحصل على positive chargenegative
+
+217
+00:16:23,420 --> 00:16:26,900
+charge electron او بروتون هدولة موجودية الطبيعة
+
+218
+00:16:26,900 --> 00:16:30,680
+لكن ال magnet قد ما حاولوا انهم يصغروا فيه اللي
+
+219
+00:16:30,680 --> 00:16:34,960
+يظل عندهم north و south poles و لزالوا بيحاولوا
+
+220
+00:16:34,960 --> 00:16:40,500
+يعملوا magnet اللي بس له خاصية ال north او ال
+
+221
+00:16:40,500 --> 00:16:50,000
+south شو هيستفيده؟ كل العلم له أسرار و علوم استفيد
+
+222
+00:16:50,000 --> 00:16:50,740
+أشياء كتير
+
+223
+00:16:54,620 --> 00:16:58,800
+طبعا إيش بيستفيدوا؟ يعني بالنسبالهم لل .. لل
+
+224
+00:16:58,800 --> 00:17:01,740
+magnet إذا أنا بقدر أتحكم بإني بس أحصل على North
+
+225
+00:17:01,740 --> 00:17:05,420
+واحد، إن أحصل على magnet flux رايحة مش مولقة عن
+
+226
+00:17:05,420 --> 00:17:08,600
+نفسها، أكيد يعني إلها تطبيقات كتير ولا زيامة ..
+
+227
+00:17:08,600 --> 00:17:12,260
+ولا زيامة في الطب، إنه يحصلوا على اللي واحد منهم،
+
+228
+00:17:12,260 --> 00:17:15,240
+فإيش هم بعودوا عنها لحد الآتة؟ هم لسه مش عادرين
+
+229
+00:17:15,240 --> 00:17:18,520
+إنه يعملوها نقطة لحالها، بيعملوا very soon و
+
+230
+00:17:18,520 --> 00:17:22,860
+طويييييل طويييل طوييل جدافبيصير كأنه في عندهم اللي
+
+231
+00:17:22,860 --> 00:17:27,480
+هو ال north أو ال south pole طبعا طويل مش معناه
+
+232
+00:17:27,480 --> 00:17:29,800
+infinite طويل بالنسبة لل application أو ال
+
+233
+00:17:29,800 --> 00:17:31,420
+wavelengths اللي أحنا بنحكي عنهم لل
+
+234
+00:17:31,420 --> 00:17:34,460
+electromagnetic signal قداش هو الطول هذا ما هو
+
+235
+00:17:34,460 --> 00:17:38,820
+نسبي أكبر من أو أقل من اللي هي الطول north فطوله
+
+236
+00:17:38,820 --> 00:17:41,780
+بيختاروه أن يكون طول محدد فبيقدر يعمل approximate
+
+237
+00:17:41,780 --> 00:17:43,560
+north و approximate south
+
+238
+00:17:50,870 --> 00:17:53,350
+بذن هيدور بالسنت جو بنقول له عندها ال clause
+
+239
+00:17:53,350 --> 00:17:56,710
+Integra b dot ds بالسوء zero أنه مافيش علنا اللي
+
+240
+00:17:56,710 --> 00:18:04,590
+هي ال monopole إذا
+
+241
+00:18:04,590 --> 00:18:07,310
+ال clause Integra ل b dot ds هي بقدر استخدم ال
+
+242
+00:18:07,310 --> 00:18:10,800
+divergence theoremأولا ال close integral لأي field
+
+243
+00:18:10,800 --> 00:18:13,640
+دو ال DS بيسوي ال volume integral ل diverge ال
+
+244
+00:18:13,640 --> 00:18:18,360
+field DV بس تحنينها ل ال magnetic flux هيعطينا ال
+
+245
+00:18:18,360 --> 00:18:20,900
+volume integral ل diverge B DV بيسوي 0، اذا
+
+246
+00:18:20,900 --> 00:18:25,740
+diverge ال B بيسوي 0، اذا diverge ال B بيبدأ يسوي
+
+247
+00:18:25,740 --> 00:18:28,140
+0، ايش معناه diverge ال B بيسوي 0؟ فيش هنا
+
+248
+00:18:28,140 --> 00:18:33,570
+monopole؟تشكل تفاقنا؟ divergence E بتساوي رو على
+
+249
+00:18:33,570 --> 00:18:38,750
+إبسلون أو Q على إبسلون قولنا إيش معناه؟ إبسلون رو
+
+250
+00:18:38,750 --> 00:18:42,570
+على إبسلون لإن في عندي charge مو نتشارج يعني
+
+251
+00:18:42,570 --> 00:18:45,390
+positive أو negative charge في عندي source اللي
+
+252
+00:18:45,390 --> 00:18:48,650
+بيروح عليه زي ما قالنا الميه و ال sink اللي هي
+
+253
+00:18:48,650 --> 00:18:54,830
+القرق تبع الحفية ميه بتروح عليه أو بتطلع منه هى ال
+
+254
+00:18:54,830 --> 00:18:58,130
+divergence معناه الكلش اللي معناه حاجة بتلف
+
+255
+00:19:01,370 --> 00:19:04,050
+تفهيص ل maxwell equations و غالبا بيجيكوا سؤال في
+
+256
+00:19:04,050 --> 00:19:08,650
+الامتحان نهائي انكوا اتلاحظوه يعنى اتذكرين ولا
+
+257
+00:19:08,650 --> 00:19:13,710
+ماحضرتوش؟ في ال ده اللي هو two forms ماقدروا ال
+
+258
+00:19:13,710 --> 00:19:16,330
+integral form و ال differential form يعني مثلا
+
+259
+00:19:16,330 --> 00:19:19,650
+نبدأ بمين؟ بجاوسلو جاوسلو يعني ال differential
+
+260
+00:19:19,650 --> 00:19:24,660
+form اللي هو دا في الجديد بتسويرهصحيح؟ لما تكون D
+
+261
+00:19:24,660 --> 00:19:28,720
+بيصوى E E و E مالها homogenous ايسو تروبيك اش
+
+262
+00:19:28,720 --> 00:19:34,060
+بتصير E او diverge ال E بيصوى ρو على E صح؟ هذا
+
+263
+00:19:34,060 --> 00:19:37,840
+بالنسبة لل divergence او ال point form بيسمونه ال
+
+264
+00:19:37,840 --> 00:19:42,140
+clause integral ل D ضد S بتساوي Q او ال volume
+
+265
+00:19:42,140 --> 00:19:46,140
+integral ρو VDV بنسوي ال integral form من أين
+
+266
+00:19:46,140 --> 00:19:48,720
+بنجيبهم احنا؟ من ال divergence theorem
+
+267
+00:19:54,750 --> 00:19:58,370
+القانون الأولى هو gauss law القانون الثاني هو
+
+268
+00:19:58,370 --> 00:20:01,970
+divergence P بالسوء 0 أو ال clause integral على ال
+
+269
+00:20:01,970 --> 00:20:04,830
+surface ل P dot DS بالسوء 0 اللي هي ال flux ال
+
+270
+00:20:04,830 --> 00:20:09,230
+total flux الطالع من ال surface بالسوء صفر مافيش
+
+271
+00:20:09,230 --> 00:20:13,490
+existence للمنوبول non existence of magnetic
+
+272
+00:20:13,490 --> 00:20:21,140
+monobol كل ال E بالسوء 0اللي هي برضه جيبناها من ال
+
+273
+00:20:21,140 --> 00:20:23,500
+close line integral a dot dl متذاكرين ال work
+
+274
+00:20:23,500 --> 00:20:26,920
+قولنا بصوص صفر اذا هذى بتعتمدش على ال boss عفوا ال
+
+275
+00:20:26,920 --> 00:20:30,940
+work بتعتمدش على ال boss a dot dl اذا معناه فيه
+
+276
+00:20:30,940 --> 00:20:33,620
+عندى conservativeness of the electrostatic field
+
+277
+00:20:38,400 --> 00:20:41,380
+Conservation، فمتذكرينه؟ قولنا هذا معناه إنه إيده
+
+278
+00:20:41,380 --> 00:20:44,360
+و الديقال بتساوي zero إنه لو أخدت المسار أي اتجاه
+
+279
+00:20:44,360 --> 00:20:48,360
+بيكون نفس الحاجة، بتمدش على البعض، وهذا بنقول إنه
+
+280
+00:20:48,360 --> 00:20:52,730
+فينا conservativeness ل ال electrostatic fieldكرل
+
+281
+00:20:52,730 --> 00:20:56,170
+ال H بيستوي J اللي هو Amberslaw أو ل close
+
+282
+00:20:56,170 --> 00:21:00,090
+integral ل LH دو ال DL هى طبعا من هى المشطق اللى
+
+283
+00:21:00,090 --> 00:21:03,290
+هى هى ال form من وين برضه من Stokes theorem ال
+
+284
+00:21:03,290 --> 00:21:06,790
+line integral هدولة تمتع من Stokes theorem ل close
+
+285
+00:21:06,790 --> 00:21:09,890
+line integral بيستوي ال surface integral لكرل ال E
+
+286
+00:21:09,890 --> 00:21:14,330
+دو ال DSفكرل ال E بتساوي 0 هنا نفس الأصدرية ال
+
+287
+00:21:14,330 --> 00:21:17,630
+closed integral H to DL اشتقناها المحاضرة الماضية
+
+288
+00:21:17,630 --> 00:21:20,950
+من Stokes theorem تعطينا برضه surface integralكرل
+
+289
+00:21:20,950 --> 00:21:26,050
+ال E لH to DS و هذا بالساوية اللي هو ال enclosed
+
+290
+00:21:26,050 --> 00:21:28,330
+current اللي هو عبارة عن surface integral J to DS
+
+291
+00:21:28,330 --> 00:21:32,290
+فبالتالي سنتجنا ان كرل ال H بتساوي J وهذا سمينا
+
+292
+00:21:32,290 --> 00:21:36,770
+unbearable بتذكرينهم؟ هدول لازم تحفظوهم مافيش فيهم
+
+293
+00:21:36,770 --> 00:21:42,810
+مزح اللي هو ال four Maxwell's equationsبسموهم
+
+294
+00:21:42,810 --> 00:21:48,770
+عمدان الكهرو استاتيك، العمدان تعونها، إذا ماحفظتيش
+
+295
+00:21:48,770 --> 00:21:52,950
+واحد منهم نهد البنيان، فلازم تحفظوا الأربع، و
+
+296
+00:21:52,950 --> 00:21:57,010
+تتذكروا إيش معناهم ولا إيش استخدمناهم و إيش
+
+297
+00:21:57,010 --> 00:21:57,790
+صفقاتهم
+
+298
+00:22:02,090 --> 00:22:05,270
+زي ما احنا ال electric field قلنا فيه اللي هو ال
+
+299
+00:22:05,270 --> 00:22:08,570
+scalar potential، هنا فيه كمان عنا scalar
+
+300
+00:22:08,570 --> 00:22:12,230
+potential و vector potential، من وين اجوا هدولتين؟
+
+301
+00:22:12,230 --> 00:22:16,010
+احنا قلنا كارل ال E بيساوي 0، بتذكرين؟ كارل ال E
+
+302
+00:22:16,010 --> 00:22:18,310
+بيساوي 0، اذا نعطيه اصفة انتاجنا له إيش بتساوي
+
+303
+00:22:18,310 --> 00:22:23,730
+minus grade Vهذه المعادلة مرقت علينا قلنا curl E
+
+304
+00:22:23,730 --> 00:22:27,870
+لإيه مالهوش curl ال E اللي هو diverge فيه اللي هو
+
+305
+00:22:27,870 --> 00:22:31,350
+mono charge يا بيطلع منها يا بيدخل فيها لكن ال
+
+306
+00:22:31,350 --> 00:22:33,970
+curl تبعه بيثاوزيرو لإن هو conservative field
+
+307
+00:22:33,970 --> 00:22:37,890
+فcurl هو zero فقلنا إذا E إيش بيثاو لإن curl ال
+
+308
+00:22:37,890 --> 00:22:40,650
+grade بيثاوزيرو إذا إن هو عبارة عن minus grade ال
+
+309
+00:22:40,650 --> 00:22:44,540
+Vلو قلنا divergence بيه بيه بيه بيه بيه بيه بيه
+
+310
+00:22:44,540 --> 00:22:47,780
+بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+311
+00:22:47,780 --> 00:22:50,440
+بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+312
+00:22:50,440 --> 00:22:50,480
+بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+313
+00:22:50,480 --> 00:22:50,500
+بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+314
+00:22:50,500 --> 00:23:07,940
+بيه بيه بيه بيه بيه بي
+
+315
+00:23:08,900 --> 00:23:11,600
+أو يعني هذا هو amber's law ال line integral ال
+
+316
+00:23:11,600 --> 00:23:15,840
+close line integral أيها ل أكتر دي ألف بتساوي ال I
+
+317
+00:23:15,840 --> 00:23:18,940
+enclosed اللي منها سنتجنا كل أتش بتساوي جي جي
+
+318
+00:23:18,940 --> 00:23:23,000
+enclosed افتراضا لو افترضنا ان جي كانت سفر جي
+
+319
+00:23:23,000 --> 00:23:26,800
+enclosed بتساوي سفر اذا كل أتش بده يساوي zero
+
+320
+00:23:26,800 --> 00:23:29,980
+مقدار ال enclosed current بتساوي سفر زي المثال
+
+321
+00:23:29,980 --> 00:23:32,980
+كوكسيا الكيبل اللي داخل كانت اللي جوا مثلا طالع
+
+322
+00:23:32,980 --> 00:23:36,100
+والتاني داخل فطلع برا
+
+323
+00:23:40,110 --> 00:23:48,210
+القران بيساوي سفر صح هاي ال coaxial او
+
+324
+00:23:48,210 --> 00:24:00,030
+برضه ال Troy برا معناه انه مجموعة بتاكرين
+
+325
+00:24:00,030 --> 00:24:04,650
+ال current كان zero هنا فقلنا هيكون ال magnetic
+
+326
+00:24:04,650 --> 00:24:09,830
+fieldمجموع ال currents I minus I بيساوي سفر، انت
+
+327
+00:24:09,830 --> 00:24:12,950
+ذاكرينه؟ اذا من هاي ambers law، ايش بقدر اتقربها
+
+328
+00:24:12,950 --> 00:24:17,990
+لكرر ال H؟ بتساوي سفر في
+
+329
+00:24:17,990 --> 00:24:20,430
+هاي الحالة، اذا انا برضه قولت كرر ال H بتساوي سفر
+
+330
+00:24:20,430 --> 00:24:24,230
+كحالة انه ال current بتساوي سفر، بقدر اقول انه ال
+
+331
+00:24:24,230 --> 00:24:28,500
+H ايش بتساوي؟كيرل لـ Gradient بيساوي 0 إذا بقدر
+
+332
+00:24:28,500 --> 00:24:31,960
+أقول الـ H في هالحلقة إيش بتساوي صمي Gradient ل
+
+333
+00:24:31,960 --> 00:24:36,060
+field حسب مين VM عشان أميزه عامين اللي هو ال
+
+334
+00:24:36,060 --> 00:24:38,860
+scalar potential تبع ال electric field إذا الـ H
+
+335
+00:24:38,860 --> 00:24:42,540
+بقدر أقول بكتبها بدلالة أو بقدر أعبر عنها الدلالة
+
+336
+00:24:42,540 --> 00:24:45,560
+scalar magnetic potential أو magnetic scalar
+
+337
+00:24:45,560 --> 00:24:49,060
+potential VM و لو أنا رجعت لها اللي هي diverse
+
+338
+00:24:49,060 --> 00:24:52,300
+كيرل
+
+339
+00:24:52,300 --> 00:25:02,070
+لـ H بيساوي 0 إذا الـ H إيش بتساوي- Vm Vm
+
+340
+00:25:02,070 --> 00:25:08,650
+Vm
+
+341
+00:25:08,650 --> 00:25:15,930
+Vm Vm
+
+342
+00:25:15,930 --> 00:25:19,820
+Vm Vm Vm Vm Vm Vmلكن لو كانت بتاعت متعالى in
+
+343
+00:25:19,820 --> 00:25:23,460
+homogenous and non isotropic يعني بتاعت متعالى ال
+
+344
+00:25:23,460 --> 00:25:26,680
+X,Y,Z بقدرش أدخلها بسهولة في قلب ال divergence نحن
+
+345
+00:25:26,680 --> 00:25:37,640
+عالية ال divergence ال B بتساوي 0 بس
+
+346
+00:25:37,640 --> 00:25:42,840
+اعتبرناها انها بتركزش على ال space بقدر أقول أضرب
+
+347
+00:25:42,840 --> 00:25:48,270
+ال new node فبتصير برضه divergeالـH ساوة زيرو أصول
+
+348
+00:25:48,270 --> 00:25:56,030
+العالمين والتأثير احنا
+
+349
+00:25:56,030 --> 00:26:00,550
+قلنا H من الكيل في حالة ان الجيب ساوة زيرو في حالة
+
+350
+00:26:00,550 --> 00:26:07,270
+ان الجيب ساوة زيرو كيل الـH ساوة زيرو معناه ان
+
+351
+00:26:07,270 --> 00:26:12,490
+الـH شو بتساوي minus del V تمام زي كتر فيه لو
+
+352
+00:26:12,490 --> 00:26:14,650
+عوضنا عنها في هذه المعادلة إيش هيصير هنا
+
+353
+00:26:24,630 --> 00:26:35,570
+بس في حالة جيب تسوى 0 ومن
+
+354
+00:26:35,570 --> 00:26:38,650
+diverse B قلنا ان بي بقدر اكتبها دلالة اللي هو ال
+
+355
+00:26:38,650 --> 00:26:42,170
+vector magnetic potential اللي هي بي بتسوى كرل ال
+
+356
+00:26:42,170 --> 00:26:47,970
+Aالـ vector-magnet field والـ scalar-magnet field
+
+357
+00:26:47,970 --> 00:26:51,430
+الـ scalar-magnet field في حالة فقط أن J بيساوي 0
+
+358
+00:26:51,430 --> 00:26:54,990
+كل الـ H بيصير بيساوي 0 إذاً الـ H إذا بقدر أعبر
+
+359
+00:26:54,990 --> 00:26:57,950
+عنها الدلالة اللي هو scalar .. magnetic scalar
+
+360
+00:26:57,950 --> 00:27:03,330
+potential minus grade ال V يعني ال B بتساوي ال
+
+361
+00:27:03,330 --> 00:27:06,190
+divergence ال B دايما بيساوي 0 إذا بقدر أقول إن ال
+
+362
+00:27:06,190 --> 00:27:08,730
+B بكتبها الدلالة مين كل ال H
+
+363
+00:27:11,640 --> 00:27:14,880
+من أول جيبنا هدول المعادلات احنا عارفين ان بي
+
+364
+00:27:14,880 --> 00:27:21,300
+بترتبط بقاتش بدلالة مين الـ mu0 و احنا عرفنا ..
+
+365
+00:27:21,300 --> 00:27:28,300
+تأول ال slides .. حديني أطلع منهم
+
+366
+00:27:28,300 --> 00:27:34,320
+.. هاي
+
+367
+00:27:34,320 --> 00:27:37,540
+تعريفنا ل .. اللي هو ال magnetic field
+
+368
+00:27:50,220 --> 00:27:54,160
+أول ما أخدنا ال magnetic field انت ذاكرين اشتقناه
+
+369
+00:27:54,160 --> 00:27:57,000
+و لاقينا ان ال magnetic field عندها نقطة النتجة من
+
+370
+00:27:57,000 --> 00:28:03,040
+current بعبر عنها الدلالة اللي هو ال clause
+
+371
+00:28:03,040 --> 00:28:07,920
+integral I dot DL cross ARH بتاع الverb IR التربية
+
+372
+00:28:07,920 --> 00:28:11,760
+ايش البرمج من ال H و ال B ال B بتساوي H على Mu
+
+373
+00:28:11,760 --> 00:28:18,530
+node اذا ماقدر أجيب ال P من H صح؟إذا H بيه تساوي
+
+374
+00:28:18,530 --> 00:28:21,650
+بيه على ميو نوت بقدر أجيب بيه إذا بيه إيش بيه
+
+375
+00:28:21,650 --> 00:28:26,970
+تساوي أو عوضنا بميو نوت في هذا الحكي بس صح فعنا
+
+376
+00:28:26,970 --> 00:28:31,490
+أسعرنا ميو نوت I D L cross على four by أرثر بيه و
+
+377
+00:28:31,490 --> 00:28:36,090
+هكذا نرجع لمعادلتنا عرفنا ال بيه فإن أحنا عارفين
+
+378
+00:28:36,090 --> 00:28:41,590
+ال H عارفنا ال B تذكرين
+
+379
+00:28:41,590 --> 00:28:45,390
+أديش رقم ال .. هنا أحلى
+
+380
+00:28:50,280 --> 00:28:55,240
+أذا نتعذر من معرفة الـB أشطق الـA طبعا هي الـB هذه
+
+381
+00:28:55,240 --> 00:28:57,460
+هي المعادلة بتاعة الـH اللى أنفرجتكوا يا عقل
+
+382
+00:28:57,460 --> 00:29:00,600
+القليل بيب هتسوى من نقطة على four pi ال line
+
+383
+00:29:00,600 --> 00:29:06,120
+integral IWL IDL cross R على R cube أو R hat على R
+
+384
+00:29:06,120 --> 00:29:11,110
+تربيةمنها احنا بنقدر نشتق انا مش هشتقها هذه كلها
+
+385
+00:29:11,110 --> 00:29:16,490
+خطوات الاشتقاء ان احصل على ال A يعني ارتب ال B من
+
+386
+00:29:16,490 --> 00:29:20,150
+هذا القانون ارتبه و احصله على شكل ال K وبالتالي
+
+387
+00:29:20,150 --> 00:29:24,970
+بقدر احصل على انه ال vector potential بقدر اكتبه
+
+388
+00:29:24,970 --> 00:29:27,910
+على شكله ال line integra اذا كان عند ال current و
+
+389
+00:29:27,910 --> 00:29:33,690
+ال line immunoid IDL على 4 by R او immunoid K DS
+
+390
+00:29:33,690 --> 00:29:41,080
+على 4 by Rأو A لـ Surface لـ Volume U0JDV 4XR
+
+391
+00:29:41,080 --> 00:29:52,600
+واضح؟ هذه خطوات الاشتقاء بس يعني كمان
+
+392
+00:29:52,600 --> 00:29:58,380
+لو استخدمنا علاقة B كيرل A و روحنا لـ Flux الـ
+
+393
+00:29:58,380 --> 00:30:02,410
+Flux عرفنا هو Surface Integra ل B دول DSالـ Stokes
+
+394
+00:30:02,410 --> 00:30:06,570
+theorem هو الحاجة اللي بحبّرها بـ B بكرل الـ A
+
+395
+00:30:06,570 --> 00:30:10,290
+surface integral لكرل A dot DS بحوّلها ل line
+
+396
+00:30:10,290 --> 00:30:13,210
+integral من الـ Stokes theorem line integral plus
+
+397
+00:30:13,210 --> 00:30:15,930
+line integral ل A dot DL إذا ال flux بقدر أعبّر
+
+398
+00:30:15,930 --> 00:30:19,890
+عنه برضه بأنه line integral ل A dot DL يا بقول عنه
+
+399
+00:30:19,890 --> 00:30:23,950
+هو surface integral ل B dot DS أو line integral ال
+
+400
+00:30:23,950 --> 00:30:30,450
+close line integral ل A dot DLناخد شوية أمثلة على
+
+401
+00:30:30,450 --> 00:30:33,190
+هذه المعلومات إلا إذا كان هناك أي استفسار في أي
+
+402
+00:30:33,190 --> 00:30:37,630
+استفسار من المعلومات اليوم الإضافية اللي اتعلمناها
+
+403
+00:30:37,630 --> 00:30:42,570
+بس ال B بي هي عبارة عن Mu node H من H ماحنا عارفين
+
+404
+00:30:42,570 --> 00:30:46,510
+العلاقش تقيمها مع بعض إش هي H فاعود عن H بيه بي
+
+405
+00:30:46,510 --> 00:30:50,210
+على Mu node فهو بتعطينا قيمة B شوية الجبرة بقدر
+
+406
+00:30:50,210 --> 00:30:54,790
+أحصل على قيمة A هاي
+
+407
+00:30:54,790 --> 00:30:57,500
+المعلومة الجديدة اللي اليوم اتعلمناهاGiven the
+
+408
+00:30:57,500 --> 00:31:00,120
+magnetic vector potential A أعطانا قيمة ال
+
+409
+00:31:00,120 --> 00:31:02,820
+magnetic vector potential A أنه minus rotor B على
+
+410
+00:31:02,820 --> 00:31:07,800
+أربع في اتجاه ال Z hat wither per meter Calculate
+
+411
+00:31:07,800 --> 00:31:12,160
+the total magnetic flux crossing the surface Phi
+
+412
+00:31:12,160 --> 00:31:15,100
+بيتساوة باي على اتنين رو من واحد لاتنين و Z من
+
+413
+00:31:15,100 --> 00:31:19,780
+Zero لخمسة ال surface تبعي cylindrical تخيلوا أنها
+
+414
+00:31:19,780 --> 00:31:22,180
+سلندر و شقاحنا السلندر بالطولة
+
+415
+00:31:26,810 --> 00:31:29,870
+وين بدو يكون هذا ال plan ع ال y axis صح؟ لو أنا
+
+416
+00:31:29,870 --> 00:31:35,110
+عندي سمدة وين
+
+417
+00:31:35,110 --> 00:31:44,850
+ال y على 2؟ raw من قيمته من 1 ل 2 و ال z من 0 ل 5
+
+418
+00:31:44,850 --> 00:31:49,390
+هذا ال plan اللي بدو يحتاجه واضح؟
+
+419
+00:31:53,200 --> 00:31:56,620
+هو ايش بده؟ Calculate the total magnetic flux
+
+420
+00:31:56,620 --> 00:32:00,120
+crossing the surface انا رسمته اللى هو ال 5 يساوي
+
+421
+00:32:00,120 --> 00:32:07,480
+باي على اتنين سيلندر عندي 5 من 0 ل 2 باي انا بدي
+
+422
+00:32:07,480 --> 00:32:09,980
+ال plan قاعد علميا يعني باي على اتنين اللى هى على
+
+423
+00:32:09,980 --> 00:32:13,880
+ال y axis بالتمام على ال y axis روه بده من 1 ل 2
+
+424
+00:32:13,880 --> 00:32:18,760
+وزد من 0 ل 5طب يانا طريقتين انهم ممكن يحلوا ال
+
+425
+00:32:18,760 --> 00:32:21,300
+flux اللي هي من آخر slide احنا قلنا بقدر اجيب ال
+
+426
+00:32:21,300 --> 00:32:24,860
+flux من a عشان انتجره لb.ds او ال close line
+
+427
+00:32:24,860 --> 00:32:28,060
+انتجره لa.dl التاني اللي لازم يعطيهم ال flux لازم
+
+428
+00:32:28,060 --> 00:32:31,080
+يعطيهم نفس النتيجة نبدأ بالأولى اللي هي ال flux في
+
+429
+00:32:31,080 --> 00:32:36,120
+الساوي ال surface انتجره لb.ds b هو ماعطينا منه ال
+
+430
+00:32:36,120 --> 00:32:39,520
+vector potential a واحنا عارفين ان ال vector ال ..
+
+431
+00:32:39,520 --> 00:32:44,980
+ال .. ال magnetic flux density اللي هي b بتساوي كل
+
+432
+00:32:44,980 --> 00:32:48,360
+ال aإذا بيبقى أقدر أجيبها من الcurve الـA اللي هو
+
+433
+00:32:48,360 --> 00:32:50,920
+أنه اتطلعت من اللي عندى بس Z component يعني لو
+
+434
+00:32:50,920 --> 00:32:54,220
+عملت ال determinant بس هتطلع لي واحدة أولا باعتمد
+
+435
+00:32:54,220 --> 00:32:56,500
+على رو حدشن تان فيه يعني باعتمد على رو و Z
+
+436
+00:32:56,500 --> 00:32:59,640
+component فلو أخدت اللي هو ال curve في ال
+
+437
+00:32:59,640 --> 00:33:02,580
+cylindrical coordinate بتظل عند ال component اللي
+
+438
+00:33:02,580 --> 00:33:09,480
+هي D minus D A Z على D رو Phi hat نفضل بالنسبة ل
+
+439
+00:33:09,480 --> 00:33:17,370
+رو هتعطينا minus اتنين في روع الاربع بيصير نص و ال
+
+440
+00:33:17,370 --> 00:33:22,350
+raw بتروح اللي هي .. sorry التانين بس بتروح فبقدر
+
+441
+00:33:22,350 --> 00:33:27,210
+عندي raw على اتنين by hatو عندى minus بتروح مع ال
+
+442
+00:33:27,210 --> 00:33:31,050
+minus فإذا صارت رو على اتنين فاي هات فالتفاضلها
+
+443
+00:33:31,050 --> 00:33:34,410
+اللى هى اتنين رو على اربع بتصير رو على اتنين و
+
+444
+00:33:34,410 --> 00:33:37,750
+الناقص بتروح مع الناقص بتكون اذا ال vector P
+
+445
+00:33:37,750 --> 00:33:41,370
+بيساوي رو على اتنين فاي هات و ال surface ايش ال
+
+446
+00:33:41,370 --> 00:33:43,970
+surface هنا بتذكرى؟ لإيش هو ان هذا ال surface مين
+
+447
+00:33:43,970 --> 00:33:46,750
+لسه هبتنقل دى five فلو أخدت انا element مين اللى
+
+448
+00:33:46,750 --> 00:33:49,790
+بتغيره؟ ال raw لإنها بتتغير من الواحد الاتنين
+
+449
+00:33:49,790 --> 00:33:55,050
+والزد فدي هتكون دي raw ودي زدإذا ال surface تبعي
+
+450
+00:33:55,050 --> 00:33:59,010
+دي raw دي z و اتجاههم اللي ال norm اللي عليه هو ال
+
+451
+00:33:59,010 --> 00:34:03,970
+raw هيكون اللي في تجاه ال phi hat ال norm عليه
+
+452
+00:34:03,970 --> 00:34:05,150
+اللي هو phi hat
+
+453
+00:34:08,420 --> 00:34:13,080
+دس رو دي رو دي زد فاي هات نجيب ال flux اللي هو
+
+454
+00:34:13,080 --> 00:34:16,760
+طلبها اللي هو ال total magnetic flux بتصيب سوى ال
+
+455
+00:34:16,760 --> 00:34:21,000
+surface integral ل P dot DS P dot DS بتعطينا رو
+
+456
+00:34:21,000 --> 00:34:23,680
+على اتنين دي رو دي زد رو من هو اللي هو اللي بتروح
+
+457
+00:34:23,680 --> 00:34:29,680
+من واحد لاتنين و زد من zero لخمسةDZ هتعطينا خمسة و
+
+458
+00:34:29,680 --> 00:34:33,600
+الرو هتعطينا رو تربيه على اتنين من اللي هو واحد
+
+459
+00:34:33,600 --> 00:34:36,880
+لاتنين بعوض عنهم بيطلع عندى خمس عاشر على اربع او
+
+460
+00:34:36,880 --> 00:34:44,460
+اللي بيصيب يتساوى تلاتة و خمس سبعين بالمية نيجي
+
+461
+00:34:44,460 --> 00:34:47,020
+للطريقة التانية اللى هى ال close line integral
+
+462
+00:34:47,020 --> 00:34:50,580
+لادو ال DL الرسم اللى انا رسمته هى موجود برضه على
+
+463
+00:34:50,580 --> 00:34:51,000
+ال slide
+
+464
+00:35:08,240 --> 00:35:11,040
+عشان اجيب ال line integra مانعش بده اكمل على كل
+
+465
+00:35:11,040 --> 00:35:15,120
+path من هدوله ال pathفهي احنا معلمينهم واحد،
+
+466
+00:35:15,120 --> 00:35:18,780
+اتنين، تلاتة، اربعة فال close line integral هيكون
+
+467
+00:35:18,780 --> 00:35:21,680
+إيش مجموعة هسميهم بصي واحد زي بصي اتنين زي بصي
+
+468
+00:35:21,680 --> 00:35:25,580
+تلاتة زي بصي اربعة اللي هو ال integration على ال
+
+469
+00:35:25,580 --> 00:35:28,320
+line الأول زي ال integration على ال line التاني زي
+
+470
+00:35:28,320 --> 00:35:29,700
+ال integration على ال line التالت زي ال
+
+471
+00:35:29,700 --> 00:35:32,160
+integration على ال line الرابع فهيك بيعطيني ال
+
+472
+00:35:32,160 --> 00:35:35,460
+close boss فسميناهم بصي واحد بصي اتنين بصي تلاتة
+
+473
+00:35:35,460 --> 00:35:39,820
+بصي اربعة الحاجة اللي بتسهل عليا أنه إحنا عندنا a
+
+474
+00:35:39,820 --> 00:35:44,910
+dot dl a إش تجاه z hatفاللي هيضل عندي اللي في
+
+475
+00:35:44,910 --> 00:35:48,790
+اتجاه ال z hat لأنه dot product اللي مش في اتجاه
+
+476
+00:35:48,790 --> 00:35:54,150
+ال z hat مش هيكون zero عند ال line هنا قداش دي z z
+
+477
+00:35:54,150 --> 00:35:59,010
+hat هنا دي z minus z hat يعني التانين هدولة اربعة
+
+478
+00:35:59,010 --> 00:36:02,510
+في اتجاه ال z hat ال dot product ليه سوى zero لكن
+
+479
+00:36:02,510 --> 00:36:08,150
+واحد و تلاتة رو hat رو hat فواحد و تلاتة عطوب
+
+480
+00:36:08,150 --> 00:36:14,140
+يبعطوني zero من مي من ال dot product فإذا1 و 3 صفر
+
+481
+00:36:14,140 --> 00:36:18,240
+من ال product و product بيظل عند مين؟ 2 و 4 فمن
+
+482
+00:36:18,240 --> 00:36:25,940
+كامل على 2 و 4 طبعا هناخد ال a التي هي minus root
+
+483
+00:36:25,940 --> 00:36:33,090
+of b على 4 a زد hat بأوض عنها في هذا ال busهذا ال
+
+484
+00:36:33,090 --> 00:36:36,930
+bus قدش قيمة row واحد اللي هو اتنين فبعود عن ال
+
+485
+00:36:36,930 --> 00:36:40,270
+row بواحد في هذا ال bus ايش ال row هتكون تنين
+
+486
+00:36:40,270 --> 00:36:44,810
+فبعود عن ال row تنين طبعا ناقص ربع بطلعها برا انا
+
+487
+00:36:44,810 --> 00:36:48,130
+بكمل بالنسبة لمين ال line تبعي دي زدهات و برضه ال
+
+488
+00:36:48,130 --> 00:36:50,450
+row بتطلع برا لانها constant على طول هذا ال bus
+
+489
+00:36:50,450 --> 00:36:54,240
+row constant واحد قيمتهافأعوض عنها واحد تربية
+
+490
+00:36:54,240 --> 00:36:57,580
+والزيت بتكامل من Zero لخمسة التاني هنا ال bus
+
+491
+00:36:57,580 --> 00:37:00,980
+هتكون رو تربية من اتنين تربية و ال bus بيجي من
+
+492
+00:37:00,980 --> 00:37:05,540
+خمسة لسفر في diesel لو كملت بيطلع معايا نفس الجواب
+
+493
+00:37:05,540 --> 00:37:10,140
+واضح؟ اذا أنا أسوأ استخدمت اللي هي ال flux بيساوي
+
+494
+00:37:10,140 --> 00:37:14,920
+ال surface integral ل B dot DS أو استخدمنا ال flux
+
+495
+00:37:14,920 --> 00:37:18,500
+بيساوي ال cloth line integral ل A dot DL لازم
+
+496
+00:37:18,500 --> 00:37:23,780
+يعطينا نفس الجوابالمثال التاني بتقول احنا بتذكروا
+
+497
+00:37:23,780 --> 00:37:29,000
+اشتقنا اللي هو ال magnetic field الناتج من ال
+
+498
+00:37:29,000 --> 00:37:33,380
+plane يعني ال plane بمورفي surface current density
+
+499
+00:37:33,380 --> 00:37:37,560
+Kأشتقنها أنه فوق البلان و تحت البلان فوق البلان
+
+500
+00:37:37,560 --> 00:37:43,640
+تسوى نص كي اكس هات و تحت البلان تسوى ماينوس نص كي
+
+501
+00:37:43,640 --> 00:37:48,640
+اكس هات او يعني above ب law اللي هي عند صد أكبر من
+
+502
+00:37:48,640 --> 00:37:52,640
+صفر و صد أقل من صفر باستخدام mean under's law كيف
+
+503
+00:37:52,640 --> 00:37:55,140
+ممكن أنا أحصل على نفس النتيجة يعني نقلنا .. يعني
+
+504
+00:37:55,140 --> 00:37:59,580
+نستخدم كذا طريقة لإن ممكن نطلب مني أطل .. يعني
+
+505
+00:37:59,580 --> 00:38:02,200
+أحصل عليها كذا طريقة أن كيف لو أنا استخدمت ال
+
+506
+00:38:02,200 --> 00:38:06,320
+vector magnetic potentialأيش عرفنا المجلة ال
+
+507
+00:38:06,320 --> 00:38:10,440
+potential ناتج من مين؟ من vector which charge
+
+508
+00:38:10,440 --> 00:38:13,540
+current density surface current density انه قولنا
+
+509
+00:38:13,540 --> 00:38:18,100
+دي ايه او يعني a vector قولنا ال integral على ال
+
+510
+00:38:18,100 --> 00:38:21,720
+surface صح؟ هيك انا رجب تقولكوا القانون اللي قولنا
+
+511
+00:38:21,720 --> 00:38:26,200
+انشقنا من بيه بس انا مش عارفش كل اشتقاق اللي هو دي
+
+512
+00:38:26,200 --> 00:38:31,800
+او اقول دي ايه يساوي surface integral لmu not k
+
+513
+00:38:31,800 --> 00:38:39,780
+على 4 by R في دي اسمفا إيه إذا هي التكامل دي إيه؟
+
+514
+00:38:39,780 --> 00:38:46,270
+بتحسبني كدس على four by Rو ال K اللي هي مفروض
+
+515
+00:38:46,270 --> 00:38:50,510
+given لنا و ال DS و بقدر اجيب اللي هو المفروض ان
+
+516
+00:38:50,510 --> 00:38:52,570
+اجيب المجمد اللي فيه الأسواق في نقطة above ال
+
+517
+00:38:52,570 --> 00:38:56,210
+surface او below ال surface مين DS؟ هي DS على ال
+
+518
+00:38:56,210 --> 00:39:00,650
+plan DS هي قاعدة وين في ال plan تبعي؟ على Z equals
+
+519
+00:39:00,650 --> 00:39:05,830
+0 معناه بيمتد وين؟ في ال XY اذا ال element تبعي دي
+
+520
+00:39:05,830 --> 00:39:09,170
+X prime دي Y prime لأنه قاعدة النقطة X prime و Y
+
+521
+00:39:09,170 --> 00:39:15,220
+primeبعده عن ال origin عند x' y' و z0 و هاخد انه
+
+522
+00:39:15,220 --> 00:39:21,220
+دي x' و دي y' اذا دي s هتكون دي x' و دي y' و دي
+
+523
+00:39:21,220 --> 00:39:25,380
+البعد تبعها اللي هو مين x' y' النقطة اللي بدأ ايس
+
+524
+00:39:25,380 --> 00:39:30,200
+عندها ال magnetic field هي 00z فبتنقل ر ر قلنا
+
+525
+00:39:30,200 --> 00:39:33,860
+دائما هي عبارة عن r-r' اللي هو وين انا بدأ ايس ال
+
+526
+00:39:33,860 --> 00:39:38,500
+magnetic minus بعد ال element او ال source هيكون
+
+527
+00:39:40,130 --> 00:39:43,370
+أول حاجة هي ال K التي هي K Y A Y hat اللي هو نفس
+
+528
+00:39:43,370 --> 00:39:48,910
+المثال كان معروف لنا ان ال K K Y Y hat وعندي اللي
+
+529
+00:39:48,910 --> 00:39:53,090
+هي DS زي ما اتفقنا دي X prime Dy prime وR ايش
+
+530
+00:39:53,090 --> 00:39:57,350
+بتساوي ال R magnitude هي جزر التربيع ل R minus R
+
+531
+00:39:57,350 --> 00:40:00,410
+prime ال R بدأيسي عندها ال magnetic field هي 00Z
+
+532
+00:40:00,410 --> 00:40:03,890
+minus ال R prime اللي هو ان عندي ال element X
+
+533
+00:40:03,890 --> 00:40:07,610
+prime Y prime 0 فبتكون الجزر التربيع ل X prime
+
+534
+00:40:07,610 --> 00:40:12,010
+تربيع زي Y تربيع primeY prime تربية زي Z تربية
+
+535
+00:40:12,010 --> 00:40:15,350
+تمام هذي R magnitude لإن هو نطوب من ال R magnitude
+
+536
+00:40:15,350 --> 00:40:23,730
+ده بس اذا دي A أشبه ساومي و نط K Y Y hat فدي قسم
+
+537
+00:40:23,730 --> 00:40:28,630
+يمين دي X prime دي Y prime على 4 Pi الجزر التربية
+
+538
+00:40:28,630 --> 00:40:33,030
+ل X prime تربية زي Y prime تربية زي Z تربية برايم
+
+539
+00:40:33,030 --> 00:40:37,330
+تمام لو بدى أجيب ال magnetic field density اللي هي
+
+540
+00:40:37,330 --> 00:40:42,150
+دي A أشبه تكون كل دي Aبجيبها لو انا طلعت عند ال ay
+
+541
+00:40:42,150 --> 00:40:48,410
+hat و ال kern بس بتضلوا الاعتمادية عميل اعتمادية
+
+542
+00:40:48,410 --> 00:40:53,060
+على ال zفقط الاعتمادية بجيب ال kern الاعتمادية على
+
+543
+00:40:53,060 --> 00:40:56,000
+ال z فهذا ال component الوحيد اللي بالضبط عندي الي
+
+544
+00:40:56,000 --> 00:41:02,240
+minus dy by dz x hat من ال determinant تبع ال kern
+
+545
+00:41:02,240 --> 00:41:07,020
+بحسبها بجيب اللي هو التفاضل بالنسبة ل z بتصير
+
+546
+00:41:07,020 --> 00:41:12,580
+القوة 3 على 2 التفاضل بيصير عندي minus نصاللي
+
+547
+00:41:12,580 --> 00:41:17,560
+هبطلها لفوق و بعدين باطفلها ليه كمان منص واحد
+
+548
+00:41:17,560 --> 00:41:19,820
+فبصير منص تلاتة ع اتنين تنزل تحت بقوة تلاتة ع
+
+549
+00:41:19,820 --> 00:41:22,500
+اتنين و التفاضل مايبقى داخل القوس اللي هي تنزلت
+
+550
+00:41:22,500 --> 00:41:29,090
+فبصير عندي زد في البسطواضح من وين إجت والنص راحت
+
+551
+00:41:29,090 --> 00:41:32,410
+مع التنين اللي إجت من الزت تفضل عادي بتعرفوا أه في
+
+552
+00:41:32,410 --> 00:41:35,370
+ده أكتب على اللوح ولا عارفينه إذا في الدي أول حاجة
+
+553
+00:41:35,370 --> 00:41:39,950
+بتيجي ناقص نص من وين من ده فاضل المقام وكمان اتنين
+
+554
+00:41:39,950 --> 00:41:44,010
+إجت من اتنين زت فالتنين بتروح مع النص وبيضل عند زت
+
+555
+00:41:44,010 --> 00:41:46,370
+في البص بتقول تحتها بتصير القوة تلاتة على اتنين
+
+556
+00:41:46,370 --> 00:41:51,680
+لإنه كمان ناقص واحد إذا هذه هي ال DBبعد بقى أجيب
+
+557
+00:41:51,680 --> 00:41:58,060
+ال B من مكان ما هو ال infinity ل plus infinity لو
+
+558
+00:41:58,060 --> 00:42:00,460
+عملنا التقام طبعا إذا انتوا لاحظتوا هذا double
+
+559
+00:42:00,460 --> 00:42:04,120
+integral dx prime dy prime و dx prime تربيه و y
+
+560
+00:42:04,120 --> 00:42:09,530
+prime تربيه مقدر أحولها من كارتيزيا ل دولارلأنه
+
+561
+00:42:09,530 --> 00:42:13,510
+أسهل في ال boolean بيحوظ
+
+562
+00:42:13,510 --> 00:42:17,310
+عها بrow دي رو دي فاي ال prime لإن عشان نحافظ
+
+563
+00:42:17,310 --> 00:42:22,140
+عليها و X تربية زي Y تربية هي رو ال prime التربيةو
+
+564
+00:42:22,140 --> 00:42:26,420
+ال row بتروح من 0 ل infinity و ال 5 من 0 ل 2π
+
+565
+00:42:26,420 --> 00:42:30,560
+فبتصير سهل جدا يعني التكامل تبع ال D5 بعطيني 2π
+
+566
+00:42:30,560 --> 00:42:33,100
+بحلص منه بصيحة اللي بيظل عندي row prime D row
+
+567
+00:42:33,100 --> 00:42:36,520
+prime على row prime تربيع زي تربيع بيصير كالها Du
+
+568
+00:42:36,520 --> 00:42:42,200
+على U تربيع زي تربيع قوة 3 على 2 سهل تكملها يعني
+
+569
+00:42:42,200 --> 00:42:45,400
+مجرد ال trick أكيد أخدتوها في ال calculus مشهورة
+
+570
+00:42:45,400 --> 00:42:48,420
+هي ال trick أن أحلص من ال Cartesian بروح للبولر
+
+571
+00:42:48,420 --> 00:42:52,820
+أسهل التكامل تبعهإذا كملنا التكامل بحصل على
+
+572
+00:42:52,820 --> 00:42:56,540
+الماجنات كثير في نقطة ما لها احنا أخدنا النقطة فوق
+
+573
+00:42:56,540 --> 00:43:02,780
+00z بجيب ال H اللي هي P على ميو نوت بتصير ky على
+
+574
+00:43:02,780 --> 00:43:08,420
+2x hat عشان أجيبها minus z بس كل الكلام بعيده و
+
+575
+00:43:08,420 --> 00:43:12,800
+بحط تدلة اللي هي z ب minus 0 بفتنتج الناتج انه H
+
+576
+00:43:12,800 --> 00:43:18,900
+بتساوي minus ky على 2x hat واضح؟لذا نحصلنا على نفس
+
+577
+00:43:18,900 --> 00:43:24,560
+النتيجة أسوأ بإنه حصدته ب numbers law أو باستخدام
+
+578
+00:43:24,560 --> 00:43:28,140
+اللي هو ال vector potential أيضا يعني اللي بنحكيه
+
+579
+00:43:28,140 --> 00:43:31,720
+في الامتحان في البيت لإن هاي الأشياء هي مش هتكون
+
+580
+00:43:31,720 --> 00:43:36,620
+خارج كتير عن نطاق الامتحان يعنيفإذا إحنا بنوقف لحد
+
+581
+00:43:36,620 --> 00:43:40,400
+هنا بيضلنا حاجة بسيطة جدا من ال chapter بنكملها
+
+582
+00:43:40,400 --> 00:43:43,900
+اللقاء القادم ان شاء الله و نبدأ ال chapter الأخير
+
+583
+00:43:43,900 --> 00:43:46,920
+اللي فيه جزئية بسيطة اللي هنخلصها ان شاء الله مع
+
+584
+00:43:46,920 --> 00:43:48,460
+بعض يعطيكوا العافية
+
diff --git a/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/tMFy3zzwo94_raw.json b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/tMFy3zzwo94_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..7b450d2d2410f9e23aea11e543b8968c124d7151
--- /dev/null
+++ b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/tMFy3zzwo94_raw.json
@@ -0,0 +1 @@
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"end": 1965.36, "text": "طب يانا طريقتين انهم ممكن يحلوا ال flux اللي هي من آخر slide احنا قلنا بقدر اجيب ال flux من a عشان انتجره لb.ds او ال close line انتجره لa.dl التاني اللي لازم يعطيهم ال flux لازم يعطيهم نفس النتيجة نبدأ بالأولى اللي هي ال flux في الساوي ال surface انتجره لb.ds b هو ماعطينا منه ال vector potential a واحنا عارفين ان ال vector ال .. ال .. ال magnetic flux density اللي هي b بتساوي كل ال a", "tokens": [9566, 3555, 7251, 7649, 995, 23032, 16572, 38149, 9957, 16472, 16095, 3714, 43020, 7251, 5016, 1211, 14407, 2423, 19298, 13672, 1829, 39896, 9154, 19753, 34740, 4137, 1975, 5016, 8315, 12174, 1211, 8315, 4724, 28543, 2288, 1975, 7435, 1829, 3555, 2423, 19298, 9154, 257, 6225, 8592, 7649, 16472, 2655, 7435, 2288, 3224, 5296, 65, 13, 16063, 1975, 2407, 2423, 1998, 1622, 16472, 2655, 7435, 2288, 3224, 5296, 64, 13, 67, 75, 16712, 7649, 1829, 13672, 1829, 5296, 31377, 2304, 37495, 9566, 1829, 16095, 2423, 19298, 5296, 31377, 2304, 37495, 9566, 1829, 16095, 8717, 36178, 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double", "probability": 0.2958984375}, {"start": 2520.46, "end": 2520.94, "word": " integral", "probability": 0.2333984375}, {"start": 2520.94, "end": 2521.28, "word": " dx", "probability": 0.414794921875}, {"start": 2521.28, "end": 2521.64, "word": " prime", "probability": 0.486328125}, {"start": 2521.64, "end": 2521.84, "word": " dy", "probability": 0.884765625}, {"start": 2521.84, "end": 2522.4, "word": " prime", "probability": 0.85009765625}, {"start": 2522.4, "end": 2522.76, "word": " و", "probability": 0.82763671875}, {"start": 2522.76, "end": 2523.02, "word": " dx", "probability": 0.78271484375}, {"start": 2523.02, "end": 2523.46, "word": " prime", "probability": 0.849609375}, {"start": 2523.46, "end": 2523.92, "word": " تربيه", "probability": 0.7501220703125}, {"start": 2523.92, "end": 2523.98, "word": " و", "probability": 0.7255859375}, {"start": 2523.98, "end": 2524.12, "word": " y", "probability": 0.92431640625}, {"start": 2524.12, "end": 2524.34, "word": " prime", "probability": 0.865234375}, {"start": 2524.34, "end": 2524.88, "word": " تربيه", "probability": 0.9808349609375}, {"start": 2524.88, "end": 2525.48, "word": " مقدر", "probability": 0.837890625}, {"start": 2525.48, "end": 2526.12, "word": " أحولها", "probability": 0.916748046875}, {"start": 2526.12, "end": 2526.42, "word": " من", "probability": 0.98876953125}, {"start": 2526.42, "end": 2527.32, "word": " كارتيزيا", "probability": 0.5548583984375}, {"start": 2527.32, "end": 2527.92, "word": " ل", "probability": 0.927734375}, {"start": 2527.92, "end": 2528.62, "word": " دولار", "probability": 0.73681640625}], "temperature": 1.0}, {"id": 100, "seek": 254115, "start": 2529.15, "end": 2541.15, "text": "لأنه أسهل في ال boolean بيحوظ عها بrow دي رو دي فاي ال prime لإن عشان نحافظ عليها و X تربية زي Y تربية هي رو ال prime التربية", "tokens": [1211, 33456, 3224, 5551, 3794, 3224, 1211, 8978, 2423, 748, 4812, 282, 4724, 1829, 5016, 2407, 19913, 6225, 11296, 4724, 1892, 11778, 1829, 12602, 2407, 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ال", "probability": 0.95751953125}, {"start": 2565.68, "end": 2565.96, "word": " trick", "probability": 0.984375}, {"start": 2565.96, "end": 2566.16, "word": " أن", "probability": 0.55224609375}, {"start": 2566.16, "end": 2566.6, "word": " أحلص", "probability": 0.9473876953125}, {"start": 2566.6, "end": 2567.04, "word": " من", "probability": 0.9853515625}, {"start": 2567.04, "end": 2567.2, "word": " ال", "probability": 0.84912109375}, {"start": 2567.2, "end": 2567.64, "word": " Cartesian", "probability": 0.737060546875}, {"start": 2567.64, "end": 2567.92, "word": " بروح", "probability": 0.8458658854166666}, {"start": 2567.92, "end": 2568.42, "word": " للبولر", "probability": 0.72021484375}, {"start": 2568.42, "end": 2568.74, "word": " أسهل", "probability": 0.9781494140625}, {"start": 2568.74, "end": 2569.18, "word": " التكامل", "probability": 0.939697265625}, {"start": 2569.18, "end": 2569.58, "word": " تبعه", "probability": 0.86614990234375}], "temperature": 1.0}, {"id": 102, "seek": 259678, "start": 2569.74, "end": 2596.78, "text": "إذا كملنا التكامل بحصل على الماجنات كثير في نقطة ما لها احنا أخدنا النقطة فوق 00z بجيب ال H اللي هي P على ميو نوت بتصير ky على 2x hat عشان أجيبها minus z بس كل الكلام بعيده و بحط تدلة اللي هي z ب minus 0 بفتنتج الناتج انه H بتساوي minus ky على 2x hat واضح؟", "tokens": [28814, 15730, 9122, 42213, 8315, 16712, 4117, 10943, 1211, 4724, 5016, 36520, 15844, 9673, 26108, 8315, 2655, 9122, 12984, 13546, 8978, 8717, 47432, 3660, 19446, 5296, 11296, 1975, 5016, 8315, 5551, 9778, 3215, 8315, 28239, 47432, 3660, 6156, 30543, 7143, 89, 4724, 7435, 1829, 3555, 2423, 389, 13672, 1829, 39896, 430, 15844, 3714, 1829, 2407, 8717, 35473, 39894, 9381, 13546, 28740, 15844, 568, 87, 2385, 6225, 8592, 7649, 5551, 7435, 1829, 3555, 11296, 3175, 710, 4724, 3794, 28242, 2423, 28820, 10943, 45030, 25708, 3224, 4032, 4724, 5016, 9566, 6055, 3215, 37977, 13672, 1829, 39896, 710, 4724, 3175, 1958, 4724, 5172, 2655, 29399, 7435, 28239, 9307, 7435, 16472, 3224, 389, 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2580.72, "word": " P", "probability": 0.322021484375}, {"start": 2580.72, "end": 2581.14, "word": " على", "probability": 0.68505859375}, {"start": 2581.14, "end": 2581.4, "word": " ميو", "probability": 0.68212890625}, {"start": 2581.4, "end": 2581.56, "word": " نوت", "probability": 0.95751953125}, {"start": 2581.56, "end": 2582.12, "word": " بتصير", "probability": 0.8880208333333334}, {"start": 2582.12, "end": 2582.46, "word": " ky", "probability": 0.275146484375}, {"start": 2582.46, "end": 2582.78, "word": " على", "probability": 0.53369140625}, {"start": 2582.78, "end": 2583.56, "word": " 2x", "probability": 0.5665283203125}, {"start": 2583.56, "end": 2583.96, "word": " hat", "probability": 0.5283203125}, {"start": 2583.96, "end": 2584.86, "word": " عشان", "probability": 0.9806315104166666}, {"start": 2584.86, "end": 2585.32, "word": " أجيبها", "probability": 0.941015625}, {"start": 2585.32, "end": 2585.82, "word": " minus", "probability": 0.30029296875}, {"start": 2585.82, "end": 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"probability": 0.9185791015625}], "temperature": 1.0}, {"id": 103, "seek": 261352, "start": 2597.94, "end": 2613.52, "text": "لذا نحصلنا على نفس النتيجة أسوأ بإنه حصدته ب numbers law أو باستخدام اللي هو ال vector potential أيضا يعني اللي بنحكيه في الامتحان في البيت لإن هاي الأشياء هي مش هتكون خارج كتير عن نطاق الامتحان يعني", "tokens": [1211, 15730, 8717, 5016, 36520, 8315, 15844, 8717, 36178, 28239, 31371, 7435, 3660, 5551, 3794, 2407, 10721, 4724, 28814, 1863, 3224, 11331, 9381, 3215, 47395, 4724, 3547, 2101, 34051, 4724, 995, 14851, 9778, 3215, 10943, 13672, 1829, 31439, 2423, 8062, 3995, 36632, 11242, 995, 37495, 22653, 13672, 1829, 44945, 5016, 4117, 1829, 3224, 8978, 2423, 10943, 2655, 5016, 7649, 8978, 2423, 21292, 2655, 5296, 28814, 1863, 8032, 47302, 16247, 8592, 1829, 16606, 39896, 37893, 8032, 2655, 30544, 16490, 9640, 7435, 9122, 2655, 13546, 18871, 8717, 9566, 995, 4587, 2423, 10943, 2655, 5016, 7649, 37495, 22653], "avg_logprob": -0.19677733924860755, "compression_ratio": 1.6153846153846154, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2597.94, "end": 2598.2, "word": "لذا", "probability": 0.33251953125}, {"start": 2598.2, "end": 2598.64, "word": " نحصلنا", "probability": 0.79095458984375}, {"start": 2598.64, "end": 2598.74, "word": " على", "probability": 0.89453125}, {"start": 2598.74, "end": 2598.9, "word": " نفس", "probability": 0.998291015625}, {"start": 2598.9, "end": 2599.66, "word": " النتيجة", "probability": 0.970947265625}, {"start": 2599.66, "end": 2600.46, "word": " أسوأ", "probability": 0.809814453125}, {"start": 2600.46, "end": 2601.42, "word": " بإنه", "probability": 0.75421142578125}, {"start": 2601.42, "end": 2602.06, "word": " حصدته", "probability": 0.83642578125}, {"start": 2602.06, "end": 2602.52, "word": " ب", "probability": 0.77587890625}, {"start": 2602.52, "end": 2603.02, "word": " numbers", "probability": 0.0958251953125}, {"start": 2603.02, "end": 2603.4, "word": " law", "probability": 0.8388671875}, {"start": 2603.4, "end": 2603.86, "word": " أو", "probability": 0.875}, {"start": 2603.86, "end": 2604.56, "word": " باستخدام", "probability": 0.9839680989583334}, {"start": 2604.56, "end": 2604.74, "word": " اللي", "probability": 0.888916015625}, {"start": 2604.74, "end": 2604.96, "word": " هو", "probability": 0.9921875}, {"start": 2604.96, "end": 2605.12, "word": " ال", "probability": 0.97607421875}, {"start": 2605.12, "end": 2605.5, "word": " vector", "probability": 0.9638671875}, {"start": 2605.5, "end": 2606.18, "word": " potential", "probability": 0.94775390625}, {"start": 2606.18, "end": 2607.26, "word": " أيضا", "probability": 0.5328369140625}, {"start": 2607.26, "end": 2607.5, "word": " يعني", "probability": 0.82958984375}, {"start": 2607.5, "end": 2607.6, "word": " اللي", "probability": 0.9755859375}, {"start": 2607.6, "end": 2608.14, "word": " بنحكيه", "probability": 0.87451171875}, {"start": 2608.14, "end": 2608.5, "word": " في", "probability": 0.91064453125}, {"start": 2608.5, "end": 2609.0, "word": " الامتحان", "probability": 0.84873046875}, {"start": 2609.0, "end": 2609.18, "word": " في", "probability": 0.486083984375}, {"start": 2609.18, "end": 2609.72, "word": " البيت", "probability": 0.9684244791666666}, {"start": 2609.72, "end": 2609.94, "word": " لإن", "probability": 0.8899739583333334}, {"start": 2609.94, "end": 2610.12, "word": " هاي", "probability": 0.79638671875}, {"start": 2610.12, "end": 2610.68, "word": " الأشياء", "probability": 0.9879150390625}, {"start": 2610.68, "end": 2611.16, "word": " هي", "probability": 0.77734375}, {"start": 2611.16, "end": 2611.36, "word": " مش", "probability": 0.986328125}, {"start": 2611.36, "end": 2611.72, "word": " هتكون", "probability": 0.9889322916666666}, {"start": 2611.72, "end": 2612.04, "word": " خارج", "probability": 0.9915364583333334}, {"start": 2612.04, "end": 2612.3, "word": " كتير", "probability": 0.9339192708333334}, {"start": 2612.3, "end": 2612.44, "word": " عن", "probability": 0.89404296875}, {"start": 2612.44, "end": 2612.76, "word": " نطاق", "probability": 0.8223876953125}, {"start": 2612.76, "end": 2613.26, "word": " الامتحان", "probability": 0.98623046875}, {"start": 2613.26, "end": 2613.52, "word": " يعني", "probability": 0.849853515625}], "temperature": 1.0}, {"id": 104, "seek": 262846, "start": 2615.02, "end": 2628.46, "text": "فإذا إحنا بنوقف لحد هنا بيضلنا حاجة بسيطة جدا من ال chapter بنكملها اللقاء القادم ان شاء الله و نبدأ ال chapter الأخير اللي فيه جزئية بسيطة اللي هنخلصها ان شاء الله مع بعض يعطيكوا العافية", "tokens": [5172, 28814, 15730, 11933, 5016, 8315, 44945, 30543, 5172, 5296, 24401, 34105, 4724, 1829, 11242, 1211, 8315, 11331, 26108, 3660, 4724, 3794, 1829, 9566, 3660, 10874, 28259, 9154, 2423, 7187, 44945, 24793, 1211, 11296, 13672, 4587, 16606, 25062, 18513, 2304, 16472, 13412, 16606, 21984, 4032, 8717, 44510, 10721, 2423, 7187, 16247, 9778, 13546, 13672, 1829, 8978, 3224, 10874, 11622, 19986, 10632, 4724, 3794, 1829, 9566, 3660, 13672, 1829, 8032, 1863, 9778, 1211, 9381, 11296, 16472, 13412, 16606, 21984, 20449, 45030, 11242, 37495, 9566, 1829, 4117, 14407, 18863, 31845, 10632], "avg_logprob": -0.13671874503294626, "compression_ratio": 1.8156424581005586, "no_speech_prob": 1.3113021850585938e-05, "words": [{"start": 2615.02, "end": 2615.68, "word": "فإذا", "probability": 0.5749104817708334}, {"start": 2615.68, "end": 2615.96, "word": " إحنا", "probability": 0.880859375}, {"start": 2615.96, "end": 2616.34, "word": " بنوقف", "probability": 0.9793294270833334}, {"start": 2616.34, "end": 2616.62, "word": " لحد", "probability": 0.983642578125}, {"start": 2616.62, "end": 2616.9, "word": " هنا", "probability": 0.955078125}, {"start": 2616.9, "end": 2617.44, "word": " بيضلنا", "probability": 0.723046875}, {"start": 2617.44, "end": 2617.76, "word": " حاجة", "probability": 0.9856770833333334}, {"start": 2617.76, "end": 2618.12, "word": " بسيطة", "probability": 0.98955078125}, {"start": 2618.12, "end": 2618.5, "word": " جدا", "probability": 0.990234375}, {"start": 2618.5, "end": 2618.76, "word": " من", "probability": 0.9873046875}, {"start": 2618.76, "end": 2618.96, "word": " ال", "probability": 0.360595703125}, {"start": 2618.96, "end": 2619.28, "word": " chapter", "probability": 0.95556640625}, {"start": 2619.28, "end": 2620.4, "word": " بنكملها", "probability": 0.9114990234375}, {"start": 2620.4, "end": 2620.88, "word": " اللقاء", "probability": 0.9903971354166666}, {"start": 2620.88, "end": 2621.36, "word": " القادم", "probability": 0.9951171875}, {"start": 2621.36, "end": 2621.5, "word": " ان", "probability": 0.5224609375}, {"start": 2621.5, "end": 2621.7, "word": " شاء", "probability": 0.9931640625}, {"start": 2621.7, "end": 2621.92, "word": " الله", "probability": 0.9580078125}, {"start": 2621.92, "end": 2622.46, "word": " و", "probability": 0.9853515625}, {"start": 2622.46, "end": 2622.84, "word": " نبدأ", "probability": 0.8885091145833334}, {"start": 2622.84, "end": 2622.98, "word": " ال", "probability": 0.74609375}, {"start": 2622.98, "end": 2623.28, "word": " chapter", "probability": 0.9658203125}, {"start": 2623.28, "end": 2623.9, "word": " الأخير", "probability": 0.8211263020833334}, {"start": 2623.9, "end": 2624.12, "word": " اللي", "probability": 0.93212890625}, {"start": 2624.12, "end": 2624.38, "word": " فيه", "probability": 0.846435546875}, {"start": 2624.38, "end": 2624.72, "word": " جزئية", "probability": 0.9595947265625}, {"start": 2624.72, "end": 2625.3, "word": " بسيطة", "probability": 0.995703125}, {"start": 2625.3, "end": 2625.44, "word": " اللي", "probability": 0.986328125}, {"start": 2625.44, "end": 2625.98, "word": " هنخلصها", "probability": 0.9842936197916666}, {"start": 2625.98, "end": 2626.08, "word": " ان", "probability": 0.5517578125}, {"start": 2626.08, "end": 2626.28, "word": " شاء", "probability": 0.996337890625}, {"start": 2626.28, "end": 2626.5, "word": " الله", "probability": 0.95751953125}, {"start": 2626.5, "end": 2626.92, "word": " مع", 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/tlgyXNIYaB8.srt b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/tlgyXNIYaB8.srt
new file mode 100644
index 0000000000000000000000000000000000000000..b691a1d38895e090f12422de7f706d36c6bad3aa
--- /dev/null
+++ b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/tlgyXNIYaB8.srt
@@ -0,0 +1,2097 @@
+1
+00:00:22,580 --> 00:00:25,480
+السلام عليكم ورحمة الله وبركاته احنا اليوم هنتبع
+
+2
+00:00:25,480 --> 00:00:29,340
+موضوعنا على أنواع اللي هي القوة أسواق **المنطسية** أو
+
+3
+00:00:29,340 --> 00:00:33,320
+الكهربائية وكيف تأثيرهم على ال particles احنا
+
+4
+00:00:33,320 --> 00:00:36,340
+شوفنا في المحاضر الماضي **أن** يسهل كيف particle تحت
+
+5
+00:00:36,340 --> 00:00:39,960
+أثر القوة **المنطسية** **أنه** بيصير في مدار دائري و ال
+
+6
+00:00:39,960 --> 00:00:44,280
+particle او يعني ال charge في مسار كهربا ..
+
+7
+00:00:44,280 --> 00:00:47,130
+electric field إنها بتسير في اتجاه ال electric
+
+8
+00:00:47,130 --> 00:00:49,310
+field حسب ال charge إذا ال positive معاه إذا ال
+
+9
+00:00:49,310 --> 00:00:54,610
+negative عكسه اليوم هنشوف لو كانت ال force الكلية
+
+10
+00:00:54,610 --> 00:00:56,770
+أسوأ جاي من ال magnetic أو ال electric field
+
+11
+00:00:56,770 --> 00:01:00,390
+تأثيرها على ال particle اللي بتحرك في المجالين
+
+12
+00:01:00,390 --> 00:01:04,170
+المثال اللي أمامنا بقول إن في عندي particle ال
+
+13
+00:01:04,170 --> 00:01:07,530
+charge particle اللي بتتحرك بسرعة منتظمة في نفس
+
+14
+00:01:07,530 --> 00:01:11,470
+سرعة Velocity متدارها أربعة X hat meter per second
+
+15
+00:01:11,470 --> 00:01:15,340
+يعني ال particle بتحرك اتجاه ال X hatفى ال region
+
+16
+00:01:15,340 --> 00:01:17,960
+فى المنطقة اللى فىها ال both electric and magnetic
+
+17
+00:01:17,960 --> 00:01:20,660
+field ال electric field اتجاهه في ال Y وال
+
+18
+00:01:20,660 --> 00:01:24,220
+magnetic في اتجاه ال Z يعني الفاردكر اتجه اتجاه ال
+
+19
+00:01:24,220 --> 00:01:28,020
+X مثلا طالع من الصفحة ال electric field في اتجاه
+
+20
+00:01:28,020 --> 00:01:34,230
+ال Yxyz المجنت في اتجاه z اكسس **أن** ال magnitude تبع
+
+21
+00:01:34,230 --> 00:01:37,090
+ال electric والمجنت ال constant يعني مايعتمدش على
+
+22
+00:01:37,090 --> 00:01:40,370
+الزمان ال electric field القابل يتبع عشرين واتجاه
+
+23
+00:01:40,370 --> 00:01:43,710
+y hat مافيش عشرين كوسين ولا سين ولا تي ولا ..
+
+24
+00:01:43,710 --> 00:01:46,390
+مافيش مايعتمدش على الزمان لأن احنا بناخد course
+
+25
+00:01:46,390 --> 00:01:49,710
+electrostatic مايعتمدش على .. مش electrodynamic
+
+26
+00:01:50,170 --> 00:01:53,570
+فإذا عندنا electric field مقدره عشرين y hat ال max
+
+27
+00:01:53,570 --> 00:01:57,470
+field some constant P0 z hat و بارد **متر** ترابين
+
+28
+00:01:57,470 --> 00:02:01,990
+طالب مننا أن نقرأ قداش قيمة P0 اللي ال velocity of
+
+29
+00:02:01,990 --> 00:02:05,090
+the particle remains constant يعني كم مرة احنا
+
+30
+00:02:05,090 --> 00:02:13,050
+عندنا هاي ال X Y Z هاي ال X Y Z ال particle اتحرك
+
+31
+00:02:13,050 --> 00:02:20,000
+بسرعة متظامة مقدارها أربع X hat متر ثانعندى فى ال
+
+32
+00:02:20,000 --> 00:02:23,640
+region electric field فى اتجاه ال Y hat هى ال E
+
+33
+00:02:23,640 --> 00:02:30,160
+ومفضله 20 Y hat فهى خطوط المجال الكهربائى والمجال
+
+34
+00:02:30,160 --> 00:02:32,980
+المعاطس فى خطوطه فى اتجاه ال Z axis
+
+35
+00:02:41,590 --> 00:02:44,390
+لنشوف ايش .. ايش اللي بيصير لهذا ال particle اللي
+
+36
+00:02:44,390 --> 00:02:49,050
+بيتجه بسرعة متظنة في اتجاه ال X-axis بمعنى اخر هو
+
+37
+00:02:49,050 --> 00:02:52,250
+صار السؤال بطريقة تانية قال لك دي قيمة P not هاي
+
+38
+00:02:52,250 --> 00:02:57,470
+اللي بتخليه يستمر في انه يكون يتحرك بهذه السرعة
+
+39
+00:02:57,470 --> 00:03:02,950
+اللي هي 4X hat قداش قيمة P not اللي بتخلي ال
+
+40
+00:03:02,950 --> 00:03:06,550
+particle يستمر بconstant velocity مقدارها 4X hat
+
+41
+00:03:06,550 --> 00:03:12,030
+متر per secondطبعا احنا عشان المجاليين عندنا
+
+42
+00:03:12,030 --> 00:03:17,350
+قُبتين بيأسروا على ال particle هذا قوة كهربائية و
+
+43
+00:03:17,350 --> 00:03:21,410
+قوة ماناطسية اتنتين بيأسروا على ال particle و
+
+44
+00:03:21,410 --> 00:03:25,030
+مجموعهم لازم يساوي قدرش او فئة ال acceleration
+
+45
+00:03:25,030 --> 00:03:29,650
+بتاعة ال object لكن هو اللي انا بدي اياها ال total
+
+46
+00:03:29,650 --> 00:03:32,650
+force بحيث ان ال particle remains in a constant
+
+47
+00:03:32,650 --> 00:03:35,430
+velocity constant velocity اشمعها ال acceleration
+
+48
+00:03:35,430 --> 00:03:42,240
+بتساوي zeroبأن ال acceleration شو بتساوي؟ دي V بقي
+
+49
+00:03:42,240 --> 00:03:45,920
+80 إذا V كونستانت إذا ال acceleration بتكون Zero
+
+50
+00:03:45,920 --> 00:03:49,480
+إذا هاي لازم تساوي سفر يعني مجموعة two forces
+
+51
+00:03:49,480 --> 00:03:52,320
+بديوا تساوي سفر هاي المعنى إن أنا بدي ال particle
+
+52
+00:03:52,320 --> 00:03:57,180
+اللي طالع مستمر فيه constant فلسطين إن ال electric
+
+53
+00:03:57,180 --> 00:04:01,800
+force شو بتساوي؟ ال charge في ال electric field و
+
+54
+00:04:01,800 --> 00:04:06,120
+هي ال magnetic force هو QV cross P إذا هتكون V
+
+55
+00:04:06,120 --> 00:04:12,000
+cross Pهذا هو قوتنا طبعاً كيولها تساوي zero وبقدر
+
+56
+00:04:12,000 --> 00:04:14,900
+أقسم عليها لأنه chart particle لو صمم ال chart
+
+57
+00:04:14,900 --> 00:04:20,460
+فهذا المعنى هذا الحكي أن E بالها تساوي سالب V
+
+58
+00:04:20,460 --> 00:04:25,520
+across B طب نعوض E إيش هي E ال electric field
+
+59
+00:04:25,520 --> 00:04:33,180
+المقدر 20Y hat minus V اللي هي 4X hat across B
+
+60
+00:04:33,180 --> 00:04:36,100
+اللي هي B not زدها
+
+61
+00:04:37,910 --> 00:04:44,490
+ايش ال cross product بين ال X و ال Z؟ X Z A Y بس
+
+62
+00:04:44,490 --> 00:04:53,830
+موجة ولا سالد؟ لإن موجة بقولنا X Y Z X Y Z هيك
+
+63
+00:04:53,830 --> 00:04:58,690
+موجة، لكن لو العكس بقولنا X Z إذا سالد Y، فهو
+
+64
+00:04:58,690 --> 00:05:03,490
+ستصبح ال plus أربع بي نقطة في اتجاه ال Y هذا، بين
+
+65
+00:05:03,490 --> 00:05:07,100
+بي سالد و سالد بيصبح ال plusطبعا بما انه من نفس
+
+66
+00:05:07,100 --> 00:05:11,100
+الاتجاه اذا ال amplitude لازم يكون متساوى تلف
+
+67
+00:05:11,100 --> 00:05:13,640
+اتجاه ال y hat معناه انه عند العشرين لازم تساوي
+
+68
+00:05:13,640 --> 00:05:16,480
+اربعة بي نوت او بي نوت اشهر سبعة اشهر اربعة هي
+
+69
+00:05:16,480 --> 00:05:20,920
+خمسة اذا عرفنا قيمة اللي هو ال بي نوت اللي بتخلي
+
+70
+00:05:20,920 --> 00:05:27,800
+هذا ال charge particle يظل مستمر في المسار تبعه ب
+
+71
+00:05:27,800 --> 00:05:32,250
+constant velocityواضح؟ هاد ال idea بتاعة إنه أنا
+
+72
+00:05:32,250 --> 00:05:34,350
+لما أحط electric field و magnet فيه ممكن أحصى و
+
+73
+00:05:34,350 --> 00:05:37,170
+أخلص من ال acceleration بيستخدموها أني ممكن أعمل
+
+74
+00:05:37,170 --> 00:05:40,330
+أنموع فلترة فلترة يعني عند particles اللي لهم
+
+75
+00:05:40,330 --> 00:05:44,030
+فلسطة معينة مثلا في هذا المثال ال particle بتحرك
+
+76
+00:05:44,030 --> 00:05:48,150
+باربع x hat بيسلهوش أي drift اي acceleration بيبقى
+
+77
+00:05:48,150 --> 00:05:51,670
+اللي ماشي بخط مستقيم بيبقى اللي ماشي بدون اي
+
+78
+00:05:51,670 --> 00:05:54,410
+trajectory لو في acceleration بيسلهو trajectory
+
+79
+00:05:54,410 --> 00:05:58,370
+بيسلهو ميلانزي أي جسم في ال gravitational force،
+
+80
+00:05:58,370 --> 00:06:02,090
+لو دلوا في constant velocity، بيمشي بمصارع ثابت،
+
+81
+00:06:02,090 --> 00:06:05,250
+لكن مع وجود ال acceleration أشبه له في ال X-axis
+
+82
+00:06:05,250 --> 00:06:10,170
+بيمشي بخط مستقيم، لكن في ال Y-axis أشبه له تسارع،
+
+83
+00:06:10,170 --> 00:06:14,650
+بيبدأ بسرعة عالية، وبعدين تطلع
+
+84
+00:06:14,650 --> 00:06:19,550
+لحدبسيلها ال de-acceleration لحد ما تصير سفر
+
+85
+00:06:19,550 --> 00:06:22,550
+وبعدين بسيلها acceleration مرة تانية في المجال
+
+86
+00:06:22,550 --> 00:06:25,990
+المناطسي اخدتوا هذا في المجال ال gravitational اذا
+
+87
+00:06:25,990 --> 00:06:30,490
+مادام هي بتتحرك ب constant velocity معناه انه هذا
+
+88
+00:06:30,490 --> 00:06:33,790
+ال particle او هم بيستغلوها ان particles معينين
+
+89
+00:06:33,790 --> 00:06:38,300
+اللي هم بسرعة معينةبيحطوه في مجال كهربا وماناطيسي
+
+90
+00:06:38,300 --> 00:06:41,660
+بحيث ان هدول الاتنين يحافظوا على هاي ال constant
+
+91
+00:06:41,660 --> 00:06:44,720
+velocity فبيظلوا في مصار مستقيم البقى ايش
+
+92
+00:06:44,720 --> 00:06:47,740
+بيصيرلهم؟ بيصيرلهم drift فانهم مش ماشيين في هاي ال
+
+93
+00:06:47,740 --> 00:06:52,520
+velocity هيتأثروا في هاي القوة، هيصير في عندهم
+
+94
+00:06:52,520 --> 00:06:55,680
+acceleration، هيتصارعوا فهذا بتسمونه من ألواء
+
+95
+00:06:55,680 --> 00:06:58,380
+filters هفرشيكوا الصورة اللي بتقوم بهذا الشكل
+
+96
+00:06:58,380 --> 00:07:01,160
+عندنا طبعا ال electric field دايما بيودوهم من خلال
+
+97
+00:07:01,160 --> 00:07:05,280
+capacitorsهي في عندنا مثلا capacitor و في عندنا
+
+98
+00:07:05,280 --> 00:07:08,000
+اللي هو مثلا فبكون تجاه ال electric field هي تجاه
+
+99
+00:07:08,000 --> 00:07:11,360
+مصر ال electric field و في عندنا المجال المناطيسي
+
+100
+00:07:11,360 --> 00:07:14,660
+اللي هي طالع من الصفحة ال dot متعمدين على بعض زي
+
+101
+00:07:14,660 --> 00:07:17,420
+المثال تبعنا بالتمام عندنا electric field و magnet
+
+102
+00:07:17,420 --> 00:07:21,800
+field متعمدين على بعض و ال particle مصار عمودي على
+
+103
+00:07:21,800 --> 00:07:25,940
+التانيةالبارتكال اللى له ال constant او ال
+
+104
+00:07:25,940 --> 00:07:29,620
+velocity المحددة هو اللى بيبقى ماشى في خط مستقيم
+
+105
+00:07:29,620 --> 00:07:33,520
+اللى بيسلمهش اى تسارة البقى بيسلمهش تسارة فتشوفوا
+
+106
+00:07:33,520 --> 00:07:37,840
+ال trajectory اللى هو ال object في مجال الجاذبى
+
+107
+00:07:37,840 --> 00:07:41,120
+العربيه هنا الفرق ان ال charge تخلق ممكن كموجة او
+
+108
+00:07:41,120 --> 00:07:46,000
+سالبة عشان هيك ممكن نلاقيها مرة فوق و مرة تحت طبعا
+
+109
+00:07:46,000 --> 00:07:48,840
+عشان نحدد اشيه هذه ال velocity احنا لو أخدنا ال
+
+110
+00:07:48,840 --> 00:07:51,400
+magnitude تبع ال two forces احنا ال magnitude تبع
+
+111
+00:07:51,400 --> 00:07:55,000
+هدولهيعني ال magnet تبقى هال force و force هذه
+
+112
+00:07:55,000 --> 00:08:00,220
+حياتنا ال E بديها تسوى بس كمagnitude ال volume 6
+
+113
+00:08:00,220 --> 00:08:03,920
+في B إذا ال volume بتاعة ال particle اللي بيسرهوش
+
+114
+00:08:03,920 --> 00:08:07,600
+اي drift بيساوي E على B اللي ال acceleration
+
+115
+00:08:07,600 --> 00:08:11,450
+بتاعته بال saucerإذا ال particle بتروحش أي drift
+
+116
+00:08:11,450 --> 00:08:15,190
+أو بتبقى instant velocity هذي من الأشياء اللي ممكن
+
+117
+00:08:15,190 --> 00:08:17,650
+تكون فيها ال multiple choice إن ال velocity بتاعة
+
+118
+00:08:17,650 --> 00:08:19,830
+ال particle اللي بيعنيش من أي drift أو اللي بيسله
+
+119
+00:08:19,830 --> 00:08:23,190
+filtering بيبقى ماشي في مساره، بيكون فيه هنا حرق
+
+120
+00:08:23,190 --> 00:08:26,810
+في ال aperture يعني فيه هنا هذي زي wall زي حاجز
+
+121
+00:08:26,810 --> 00:08:29,970
+وفيه بيكون هول ال particles اللي بتكون constant
+
+122
+00:08:29,970 --> 00:08:33,680
+velocity هي اللي بتطلع من خلال ال hallهي بتسميها
+
+123
+00:08:33,680 --> 00:08:38,060
+ال critical speed اللي لازم عشان هذا ال object يظل
+
+124
+00:08:38,060 --> 00:08:44,200
+ماشي constant بواسطة واضح طب كده مثال لو احنا
+
+125
+00:08:44,200 --> 00:08:48,540
+لدينا two filaments
+
+126
+00:08:48,540 --> 00:08:51,820
+واحدة منهم على شكل infinite line بمور فيها current
+
+127
+00:08:51,820 --> 00:08:55,960
+أي واحد والتاني على شكل loop بمور فيها current أي
+
+128
+00:08:55,960 --> 00:09:00,820
+تانين وبدنا نسبة هي واحدة اللي هي long filamentary
+
+129
+00:09:00,820 --> 00:09:04,930
+Ywhere currying current I1 والتاني اللي هو
+
+130
+00:09:04,930 --> 00:09:09,470
+rectangular loop بحمل current I2 بدنا ان القوة
+
+131
+00:09:09,470 --> 00:09:12,790
+اللي experienced by the loop is given by القوة
+
+132
+00:09:12,790 --> 00:09:17,970
+اللي على ال loop given by F equal minus mu0 I1 I2
+
+133
+00:09:17,970 --> 00:09:22,290
+B على 2π ف1 على rho0 minus 1 على النوت زا اد اين
+
+134
+00:09:22,290 --> 00:09:27,090
+اتجاه روهات الميوترتجاهة في روحات الـinfinite يعني
+
+135
+00:09:27,090 --> 00:09:30,350
+مين هي ال رنود و روحه والإيه ال رنود هي المسافة
+
+136
+00:09:30,350 --> 00:09:33,590
+يعني لو حطينا ال first filament اللي هي ال
+
+137
+00:09:33,590 --> 00:09:38,350
+infinite where عند ال origin رنود هي المسافة ما
+
+138
+00:09:38,350 --> 00:09:44,610
+بين ال infinite line و أول ضلع من أضلع المستطيل هي
+
+139
+00:09:44,610 --> 00:09:50,170
+رنود هذه المسافة أو بعد ال loop القريب عن مين عن
+
+140
+00:09:50,170 --> 00:09:54,530
+ال filament ال infinite lineالـ A هي عبارة عن ميل
+
+141
+00:09:54,530 --> 00:09:59,870
+ال width تبع ال rectangular loop فبيكون الدلع
+
+142
+00:09:59,870 --> 00:10:05,130
+البعيد بعضه عن ال wire مقدار raw node زايد يعني
+
+143
+00:10:05,130 --> 00:10:11,990
+واضح I1 هو التيار الممر في ال infinite line I2 هو
+
+144
+00:10:11,990 --> 00:10:15,390
+ال current الممر في ال rectangular wire اذا احنا
+
+145
+00:10:15,390 --> 00:10:20,090
+طلبين القوة اللي على ميل على ال rectangular loop
+
+146
+00:10:20,090 --> 00:10:20,570
+اللي
+
+147
+00:10:23,420 --> 00:10:26,900
+by the loop is given by .. for experience by the
+
+148
+00:10:26,900 --> 00:10:30,740
+loop is given by بالنسبة هي العلاقة اللي اتأثر
+
+149
+00:10:30,740 --> 00:10:35,790
+فيها ال loopطبعا احنا هلاحظ ان في عندى اكم ويرع في
+
+150
+00:10:35,790 --> 00:10:41,150
+ال loop واحد اتنين تلاتة اربعة كل واحد منهم هيتأثر
+
+151
+00:10:41,150 --> 00:10:45,290
+عليه المجال المناطيسي اللى جاي من ال current اللى
+
+152
+00:10:45,290 --> 00:10:48,750
+مارق في ال loop الفائض اللى ال infinite line اللى
+
+153
+00:10:48,750 --> 00:10:53,610
+هو مورفي I واحد هيأثر على كل واحد بقوة هنسميهم F
+
+154
+00:10:53,610 --> 00:10:58,490
+واحد F تنين F تلاتة F اربعة احنا أخدنا قبل هيك
+
+155
+00:10:58,490 --> 00:11:02,110
+اللى هو القوة بين two lines بتذكرينهاهنشوفها من
+
+156
+00:11:02,110 --> 00:11:07,650
+هذا المثال هنشوفها
+
+157
+00:11:07,650 --> 00:11:12,650
+من هذا المثال هنشوفها من هذا المثال هنشوفها من هذا
+
+158
+00:11:12,650 --> 00:11:12,710
+المثال هنشوفها من هذا المثال هنشوفها من هذا المثال
+
+159
+00:11:12,710 --> 00:11:12,890
+هنشوفها من هذا المثال هنشوفها من هذا المثال
+
+160
+00:11:12,890 --> 00:11:12,910
+هنشوفها من هذا المثال هنشوفها من هذا المثال
+
+161
+00:11:12,910 --> 00:11:12,990
+هنشوفها من هذا المثال هنشوفها من هذا المثال
+
+162
+00:11:12,990 --> 00:11:31,230
+هنشوفها من هذا المثال هنشوفها من هذا المثال هنشوف
+
+163
+00:11:38,400 --> 00:11:45,940
+لو كان عندنا هذه القوة ما بين اللي بيأثر فيها مجال
+
+164
+00:11:45,940 --> 00:11:50,220
+معناطيسي مثلا اللي هو ال wire 2 هذا على ال wire 1
+
+165
+00:11:50,220 --> 00:11:58,400
+I D L cross B احنا كانت QV cross B لتشارج لو صرت
+
+166
+00:11:58,400 --> 00:12:04,110
+lines لو بحكي ع ال lines هيصير بقل QV I D LIDL
+
+167
+00:12:04,110 --> 00:12:07,310
+cross B هو مين المجال المناطيسي اللي ناتج من
+
+168
+00:12:07,310 --> 00:12:11,090
+التيار الآخر يعني لما يكون عندى two lines مذكرين
+
+169
+00:12:11,090 --> 00:12:15,110
+الحكاية ده الحكاية بيمور فيهم currents بس بيفرق
+
+170
+00:12:15,110 --> 00:12:19,350
+اتجاه او يعني إيش هي القوة تجازب أو تنافر هيكون
+
+171
+00:12:19,350 --> 00:12:22,330
+القوة اللى بأثر فيها مثلا في هالحالة اتنين على
+
+172
+00:12:22,330 --> 00:12:27,290
+واحد هي ال current بيمور في واحد بذكركم فيها ال
+
+173
+00:12:27,290 --> 00:12:30,990
+current بيمور في واحد IDL cross مين المجال
+
+174
+00:12:30,990 --> 00:12:35,710
+المناطيسي اللي ناتج من اتنينواضح؟ احنا لأنه كنا
+
+175
+00:12:35,710 --> 00:12:39,610
+باخدنا elements فقلنا بكون في double integral على
+
+176
+00:12:39,610 --> 00:12:42,830
+اللي هو عشان احصل على كل القوة اللي بأثر فيها ال
+
+177
+00:12:42,830 --> 00:12:48,110
+current مش بس ال element I2DI2 كل اللوب I2 اللي
+
+178
+00:12:48,110 --> 00:12:53,770
+مورفي I2 على اللوب المورفي I1 فبكمل مرة كاملا على
+
+179
+00:12:53,770 --> 00:12:57,7
+
+201
+00:14:33,850 --> 00:14:37,310
+الجامعة الـ infinite line قلنا هذا symmetric بستخدم
+
+202
+00:14:37,310 --> 00:14:43,150
+Ampere's law اللي هو closed integral لب أو H dot dl
+
+203
+00:14:43,150 --> 00:14:48,730
+بتساوي الـ enclosed current أتذكرين؟ و dl اللي هو
+
+204
+00:14:48,730 --> 00:14:53,770
+أخدناه بالـ unit lengths فإيش طلع عندنا كله؟ الـ
+
+205
+00:14:53,770 --> 00:14:58,930
+magnetic field الناتج من infinite line μ₀ I
+
+206
+00:14:58,930 --> 00:15:05,530
+على 2π ρ واضح؟ أتذكرينه؟ في اتجاه φ hat فالـ
+
+207
+00:15:05,530 --> 00:15:08,870
+current في هذا الاتجاه دلوقتي هيكون في اتجاه φ
+
+208
+00:15:08,870 --> 00:15:13,660
+hat أتذكرين؟ حسب ده Ampere's law يعني الـ infinite line
+
+209
+00:15:13,660 --> 00:15:16,320
+حلتها حتى الطريقة التالية و أكثر من طريقة حلنا
+
+210
+00:15:16,320 --> 00:15:19,720
+نذكرها infinite line إذا الـ infinite line بس هو
+
+211
+00:15:19,720 --> 00:15:22,200
+أسوأ أسخنان الـ closed integral اكشن و H بتساوي الـ
+
+212
+00:15:22,200 --> 00:15:25,880
+enclosed current اللي هو I enclosed هنا في الحالة
+
+213
+00:15:25,880 --> 00:15:28,960
+يعني I enclosed أي واحد فهيكون إيش هو المسار تبع
+
+214
+00:15:28,960 --> 00:15:31,140
+الـ اكشن؟ اللي هو الـ circle
+
+215
+00:15:34,320 --> 00:15:38,220
+H في اتجاه الـ Φ متأكدين إن دي الـ mean هي 2π لو
+
+216
+00:15:38,220 --> 00:15:44,300
+أخدنا إنه مثلًا R نصف القطر تبع الدائرة هيكون H 2π
+
+217
+00:15:44,300 --> 00:15:50,560
+R بتساوي I enclosed فـ H هتساوي I على 2π R و H
+
+218
+00:15:50,560 --> 00:15:55,560
+شلقتها B بي على μ₀ فهيكون B بتساوي μ₀ I
+
+219
+00:15:55,560 --> 00:15:58,660
+على 2π R سهلة أحلى على اللوح ولا واضح من ذاكرينها 
+
+220
+00:15:59,810 --> 00:16:03,030
+هلاّ إحنا قداش الـ radius بتاع الـ circle هناخده
+
+221
+00:16:03,030 --> 00:16:05,130
+هناخده بالطبع الـ ρ₀ فـ أنا بدي المجال
+
+222
+00:16:05,130 --> 00:16:11,070
+المغناطيسي والمكان عند الضلع واحد فـ إيش هيكون مجله
+
+223
+00:16:11,070 --> 00:16:15,570
+الـ field عند هذه النقطة؟ وعبارة عن B بتساوي μ
+
+224
+00:16:15,570 --> 00:16:19,990
+₀ I اللي هي الـ μ في هذا الـ wire و I واحد على
+
+225
+00:16:19,990 --> 00:16:26,700
+2π في الـ ρ₀ واضح؟ واتجاهه φ hat يعني هو في
+
+226
+00:16:26,700 --> 00:16:29,200
+هذه الحالة في هذه الجهة اللي هو أنا النقطة اللي
+
+227
+00:16:29,200 --> 00:16:33,720
+أنا بتدقيس فيها القوة من اتجاهه ده اتدقيس القوة
+
+228
+00:16:33,720 --> 00:16:33,840
+من اتجاهه ده اتدقيس القوة من اتجاهه ده اتدقيس
+
+229
+00:16:33,840 --> 00:16:35,660
+القوة من اتجاهه ده اتدقيس القوة من اتجاهه ده
+
+230
+00:16:35,660 --> 00:16:41,760
+اتدقيس القوة
+
+231
+00:16:41,760 --> 00:16:48,440
+من اتجاهه
+
+232
+00:16:48,440 --> 00:16:50,960
+ده اتدقيس القوة من اتجاهه ده اتدقيس القوة من
+
+233
+00:16:50,960 --> 00:16:56,000
+اتدقيس القوة من اتدقيسمش هنأجيب Ampere's law إحنا
+
+234
+00:16:56,000 --> 00:17:00,940
+عارفين إنه هيك اتجاه المغناطيس كتير I هي الـ H اللي
+
+235
+00:17:00,940 --> 00:17:06,960
+الـ plus بتكراه الـ H الـ H بتساوي I الـ plus قولنا
+
+236
+00:17:06,960 --> 00:17:14,700
+التاني H بتساوي I على 2πR اللي هي R المغناطيس كتير
+
+237
+00:17:14,700 --> 00:17:20,640
+اللي إحنا عارفين إن اتجاهها هو I بيه هتساوي μ
+
+238
+00:17:20,640 --> 00:17:27,680
+₀ I على طبعًا لو طلعنا على الرسم بتاعتنا إحنا هاي
+
+239
+00:17:27,680 --> 00:17:31,200
+المجال معاكس اتجاه التيار الكلية أشهرنا اتجاهه
+
+240
+00:17:31,200 --> 00:17:35,460
+هكذا داخل فعند هاي النقطة اللي بيكون اتجاهه ده جوا
+
+241
+00:17:35,460 --> 00:17:45,010
+هاي الـ current وهي انجام داخل وطالب واضِر هنا داخلو
+
+242
+00:17:45,010 --> 00:17:48,390
+من الجهة التانية إيش هيكون طرف أنا لو بدأ أخط لو
+
+243
+00:17:48,390 --> 00:17:51,550
+لازم يبص مش لازم هنا هبكون نقاطي هنا هيكون داخل
+
+244
+00:17:51,550 --> 00:17:54,990
+هيكون هو الطرف منها إلى الساعة لما في سنة إحنا
+
+245
+00:17:54,990 --> 00:17:58,250
+عرفنا إن مجرد ما أنا قاعدة يسي هنا إيش هيكون B knot
+
+246
+00:17:58,250 --> 00:18:03,430
+يعني شهية كتير من الوقت بس هعوض عن R بقى إيه إيش الـ
+
+247
+00:18:03,430 --> 00:18:10,390
+ρ ρ knot و  Psychic يعني الحمد لله اشتغلت عليكم
+
+248
+00:18:10,390 --> 00:18:11,970
+هيكون B
+
+249
+00:18:15,390 --> 00:18:23,210
+μ₀ في I واحد على 2π ρ₀ أهنا بالتمام
+
+250
+00:18:23,210 --> 00:18:26,590
+هنا المجال المغناطيسي هنا في اتجاهه اللي هو الواحد
+
+251
+00:18:26,590 --> 00:18:31,550
+تمام في S سبحت هنا إذا هذا المجال المغناطيسي اللي
+
+252
+00:18:31,550 --> 00:18:34,910
+بأثر فيه القرع بـ I واحد على هذا الدلال لو على
+
+253
+00:18:34,910 --> 00:18:39,430
+الدلال الـ بعيد مش هيكون ρ₀ زائد إيه نفس
+
+254
+00:18:39,430 --> 00:18:40,870
+الاتجاه رهاد
+
+255
+00:18:44,620 --> 00:18:48,420
+هو في كل نتفة داخل بس أنا بدي على هذه النقطة وعلى
+
+256
+00:18:48,420 --> 00:18:50,720
+هذه النقطة أنا بدي الـ current الـ force اللي بيأثر
+
+257
+00:18:50,720 --> 00:18:54,820
+فيها المجاري المغناطيسي المتولد من التيار المر في
+
+258
+00:18:54,820 --> 00:18:58,600
+الـ filament الأولى على الدلع الأول ومرة تانية على
+
+259
+00:18:58,600 --> 00:19:05,660
+الدلع التالت نفس الحكاية اللي هيكون المجاري
+
+260
+00:19:05,660 --> 00:19:09,920
+المغناطيسي المتولد في كل نقطة هيكون ده بس هنا هيكون
+
+261
+00:19:09,920 --> 00:19:13,610
+على بعد ρ₀ هنا هيكون على بعد اللي هو ρ₀
+
+262
+00:19:13,610 --> 00:19:18,850
++ A هنا متغير البعد ما بين ρ₀ لـ ρ₀ +
+
+263
+00:19:18,850 --> 00:19:23,070
+A صحيح؟
+
+264
+00:19:23,070 --> 00:19:29,830
+هنشوف
+
+265
+00:19:29,830 --> 00:19:34,470
+القورة هنضغط مسحها داكي عشان ما يدخلش على الواحد
+
+266
+00:19:35,260 --> 00:19:39,180
+نبدأ في الأولى الفرصة الأولى أنها I 2 DL 2
+
+267
+00:19:39,180 --> 00:19:42,740
+اللي هو هدا الـ line الأولاني اللي طوله بتغير من
+
+268
+00:19:42,740 --> 00:19:49,020
+صفر لمين لـ B من صفر لـ B يعني إيش الـ DL بتاعته DZ
+
+269
+00:19:49,020 --> 00:19:56,320
+DL هي DZ Z hat DL DZ Z hat across B اللي هنا
+
+270
+00:19:56,320 --> 00:20:00,800
+شفناها مع بعض هنكون تجاه Z hat قيمتها μ₀ I
+
+271
+00:20:00,800 --> 00:20:06,050
+واحد على 2π ρ₀ إذا عندنا الـ Z هتطير من zero
+
+272
+00:20:06,050 --> 00:20:10,650
+لـ B, Z hat cross Φ hat هتكون موجبة ولا سالبة نفس
+
+273
+00:20:10,650 --> 00:20:19,130
+القضية تذكر إن قلنا ρ Φ Z, Z cross Φ hat
+
+274
+00:20:19,130 --> 00:20:22,850
+هتكون -ρ hat فـ إذا ما هيكون الاتجاه في السالب
+
+275
+00:20:22,850 --> 00:20:27,130
+ρ hat هي أول حاجة التكامل طبعًا زاد سهل هيكون من
+
+276
+00:20:27,130 --> 00:20:31,670
+صفر لـ B نحط بينا B فـ إذا نهاش هيكون ناتج I 2
+
+277
+00:20:31,670 --> 00:20:34,630
+في I 1 في μ₀ في B على طول بـ π ρ₀
+
+278
+00:20:34,630 --> 00:20:38,530
+واتجاهه -ρ hat هذه الـ F على الواحد نفس
+
+279
+00:20:38,530 --> 00:20:42,850
+الكلام بنعيده على F اللي هي قلنا الاطلاع البعيد
+
+280
+00:20:42,850 --> 00:20:45,970
+3 سميناها 3
+
+281
+00:20:50,960 --> 00:20:59,020
+بس الفرقية إنه هنغير قيمة الـ ρ هتكون ρ₀ +
+
+282
+00:20:59,020 --> 00:21:03,020
+أه تمام؟ والـ integration هيكون من مين بدل من zero
+
+283
+00:21:03,020 --> 00:21:07,660
+لـ B هيكون من B لـ zero عن اتجاه الـ current جاي من
+
+284
+00:21:07,660 --> 00:21:11,460
+فوق لتحت هيكون من B لـ zero يعني في تغيرون بسطين
+
+285
+00:21:11,460 --> 00:21:15,760
+إن بدل ρ هتكون ρ₀ + أه والـ current بتغير
+
+286
+00:21:15,760 --> 00:21:20,950
+من اللي هي B لـ zero Z hat cross Φ hat -ρ
+
+287
+00:21:20,950 --> 00:21:25,230
+hat وعندي كمان -B جي من تكامل الـ Z هتعطينا Z
+
+288
+00:21:25,230 --> 00:21:28,830
+من zero لـ B هتعطينا -B فبتصير +ρ hat و
+
+289
+00:21:28,830 --> 00:21:32,550
+الباقي هيكون نفس الشيء μ₀ I1 I2 على 2π
+
+290
+00:21:32,550 --> 00:21:39,410
+ρ₀ + A تمام؟ إذا القوة اللي ناجحة من الـ
+
+291
+00:21:39,410 --> 00:21:46,640
+current المورفي الـ line على الصيد الأول -ρ hat
+
+292
+00:21:46,640 --> 00:21:51,720
+اتجاهها -ρ hat هذه ρ hat لأنه لو أخدناها
+
+293
+00:21:51,720 --> 00:21:58,240
+سليندركا اتجاه الفاية هذه ρ hat صح؟ أخ واحد -
+
+294
+00:21:58,240 --> 00:22:03,780
+ρ hat إيش نوع ρ hat اتجاهه 8 مرة هذا سليندركا
+
+295
+00:22:03,780 --> 00:22:07,820
+يعني إحنا أخدناها هيك المجال المغناطيسي وهذه الـ ρ
+
+296
+00:22:07,820 --> 00:22:10,500
+hat يعني إحنا ماخدين إيش اتجاهها وهذا الفاية
+
+297
+00:22:10,500 --> 00:22:17,510
+سليندركا الكوربينة دي صح؟ إذا هذا هو اتجاه الـ ρ hat
+
+298
+00:22:17,510 --> 00:22:22,450
+وهذا الـ -ρ hat إذا بنطلع على التاني في الـ
+
+299
+00:22:22,450 --> 00:22:26,950
+currents لما يكونوا بنفس الاتجاه عكس المعنى الـ
+
+300
+00:22:26,950 --> 00:22:29,910
+currents بتتفق في نفس اتجاه نوع القوة إيش بتكون
+
+301
+00:22:29,910 --> 00:22:34,670
+تجاذب هذه أنا بتجذب هذا الـ current أنا بيزف هذا الـ
+
+302
+00:22:34,670 --> 00:22:38,230
+current معاه عكس الـ charges لما نقول نجد.. بصي في
+
+303
+00:22:38,230 --> 00:22:41,330
+نجد في الـ charge بالساعة وبتجاذبه يعني عندي تيرين
+
+304
+00:22:41,330 --> 00:22:46,670
+بنفس الاتجاه جاذبوا يعني إذا لاحظت إنه الـ line اللي
+
+305
+00:22:46,670 --> 00:22:51,290
+مور في الـ current أي واحد، إيش بيسويه؟ بالزب،
+
+306
+00:22:51,290 --> 00:22:56,150
+بالزب بيعمل عملية جاذب لـ الـ current اللي بتدفق في
+
+307
+00:22:56,150 --> 00:22:59,550
+الـ line اللي نفس الاتجاه، بيطلع على الـ bait، الـ
+
+308
+00:22:59,550 --> 00:23:02,910
+side of الـ bait، الـ current ماله معاكس الاتجاه إذا
+
+309
+00:23:02,910 --> 00:23:07,570
+إنه repulsive، +ρ hat، واضح؟ إذا هذه كنت
+
+310
+00:23:07,570 --> 00:23:10,730
+تذكروها، لما الـ current مور في الـ two wires، اللي
+
+311
+00:23:10,730 --> 00:23:13,710
+نفس الاتجاه، تجاذب، واحد عكس، تنفر
+
+312
+00:23:18,530 --> 00:23:21,390
+مثبتة experimentally وإحنا كمان هنا شفناها
+
+313
+00:23:21,390 --> 00:23:24,570
+theoretically نظرية لما يكونوا التيارين في نفس
+
+314
+00:23:24,570 --> 00:23:29,450
+الاتجاه هيكون في عملية تجاذب متعاكسين بيكون عملية
+
+315
+00:23:29,450 --> 00:23:34,210
+تنافر ومين ضال عندنا F2 و F4 هنا DL إيش اللي
+
+316
+00:23:34,210 --> 00:23:39,570
+هتكون DL2؟ اللي دي ρ هنا هتكون دي ρ وبتروح من
+
+317
+00:23:39,570 --> 00:23:45,000
+ρ₀ لـ ρ₀ + A نجي نعمل اللي هي
+
+318
+00:23:45,000 --> 00:23:48,620
+afternoon هيكون عندنا التكامل من ρ₀ لـ ρ
+
+319
+00:23:48,620 --> 00:23:52,140
+₀ + A وبدل دي Z إيش هيكون دي ρ ρ hat
+
+320
+00:23:52,140 --> 00:23:55,940
+across B قلت نفسها قولنا نفسها وكلهم داخلين في
+
+321
+00:23:55,940 --> 00:24:00,240
+هالجهة ρ₀ I 1 اتوه بـ ρ Φ hat ρ
+
+322
+00:24:00,240 --> 00:24:05,900
+cross Φ إيش بيكون إياه ρ cross across Φ
+
+323
+00:24:05,900 --> 00:24:11,660
+إيش هتكون Z hat ρ cross Φ Z hat ρ هنكملها من
+
+324
+00:24:11,660 --> 00:24:16,920
+ρ₀ لـ ρ₀ + A لكن هنلاحظ إنه في عند دي ρ
+
+325
+00:24:16,920 --> 00:24:21,140
+على ρ كله بيطلع برا الـ integral هي I 2 و I
+
+326
+00:24:21,140 --> 00:24:27,960
+1 وμ₀ والـ .. الـ .. الـ هي الـ unit
+
+327
+00:24:27,960 --> 00:24:31,720
+vector Z hat على 2π كله بيطلع بضُم عند دي ρ على
+
+328
+00:24:31,720 --> 00:24:34,900
+ρ الـ integration من ρ ₀ لـ ρ ₀ + A دي ρ
+
+329
+00:24:34,900 --> 00:24:38,800
+على ρ اللي هي اللان دي ρ على ρ حيث إن اللي بيضل
+
+330
+00:24:38,800 --> 00:24:43,820
+جوا الـ integral من ρ ₀ لـ ρ ₀ + A كله بيطلع
+
+331
+00:24:43,820 --> 00:24:47,940
+في الـ integer بالـ dρ على ρ يبقى تكون len الـ ρ
+
+332
+00:24:47,940 --> 00:24:53,800
+من ρ ₀ لـ ρ ₀ + A هتكون len الـ ρ ₀ +
+
+333
+00:24:53,800 --> 00:24:59,040
+A - len الـ ρ ₀ اللي هي عبارة عن len الـ ρ
+
+334
+00:24:59,040 --> 00:25:00,760
+₀ + A على
+
+335
+00:25:08,870 --> 00:25:13,770
+القضيب أو على الجزء من الـ rectangle إن هي في تجاه
+
+336
+00:25:13,770 --> 00:25:17,370
+الـ ρ hat الـ current في تجاه الـ ρ hat كانت
+
+337
+00:25:17,370 --> 00:25:20,790
+القوة على تجاه positive Z hat افتنين في تجاه
+
+338
+00:25:20,790 --> 00:25:25,030
+positive Z hat دال من عندنا اللي هو الدلع الأخير
+
+339
+00:25:25,030 --> 00:25:28,890
+اللي هو الرابع نفس الحاجة هتكون mean إن دي ρ دي
+
+340
+00:25:28,890 --> 00:25:32,850
+Z هي دي ρ ρ hat والتكامل هيكون من ρ ₀
+
+341
+00:25:32,850 --> 00:25:34,830
++ A لـ ρ ₀
+
+342
+00:25:37,600 --> 00:25:40,780
+إذن التكامل عندنا من ρ ₀ + A لـ ρ ₀ و
+
+343
+00:25:40,780 --> 00:25:45,100
+دي Z هي دي ρ ρ hat دي الـ .. دي ρ ρ hat
+
+344
+00:25:45,100 --> 00:25:48,460
+cross μ₀ I 1 Φ hat عـ 2π ρ إن الـ
+
+345
+00:25:48,460 --> 00:25:53,000
+ρ hat cross Φ hat إيش هتكون؟ ρ hat cross Φ
+
+346
+00:25:53,000 --> 00:25:57,580
+hat برضه الـ Z hat لكن لما نيجي نعمل الـ integration
+
+347
+00:25:57,580 --> 00:26:05,370
+إيش هيكون عندي؟ ρ hat cross Φ hat ρ hat و Z hat
+
+348
+00:26:05,370 --> 00:26:08,770
+اتنين لما نيجي نكمل برضه نفس الحاجة ما ننساش إن في
+
+349
+00:26:08,770 --> 00:26:12,730
+عند dρ على ρ بس من وين من ρ ₀ + A لـ ρ ρ
+
+350
+00:26:12,730 --> 00:26:18,590
+₀ يعني هيكون عند التكامل dρ على ρ من وين من ρ
+
+351
+00:26:18,590 --> 00:26:21,810
+₀ + A لـ ρ الفرقية بينها أي حيكون في إشارة
+
+352
+00:26:21,810 --> 00:26:25,890
+سالبة عشان أخليها تبين زي هيك هتكون -length
+
+353
+00:26:25,890 --> 00:26:33,520
+ρ + A على ρ ₀ صح هتكون length ρ ₀ على
+
+354
+00:26:33,520 --> 00:26:38,160
+ρ ₀ + A يعني هي تساوي سالب لأن الـ ρ ₀ +
+
+355
+00:26:38,160 --> 00:26:43,560
+A معايا هاي ناجلة من الإشارة السالبة إذا ماحيكون F4
+
+356
+00:26:43,560 --> 00:26:48,700
+بتساوي -μ₀ I1 فـ I2 على 2π لأن ρ ₀ +
+
+357
+00:26:48,700 --> 00:26:54,390
+A على ρ ₀ اتجاه is it that وحدة في اتجاه الـ boost في
+
+358
+00:26:54,390 --> 00:27:00,170
+Z hat والتانية في السانر في Z hat يعني إذا طلعت
+
+359
+00:27:00,170 --> 00:27:04,010
+بلاحظ إذا كان في عندي قضيب في اتجاه الـ current
+
+360
+00:27:04,010 --> 00:27:08,410
+تبعه عمودي على الـ current اللي بمر فيه السبب
+
+361
+00:27:08,410 --> 00:27:11,610
+المسبب لـ magnetic field اللي بيحدث في القوة هتكون
+
+362
+00:27:11,610 --> 00:27:17,030
+القوة مالها موازية بسميها قوة موازية يعني افعل هذا
+
+363
+00:27:17,030 --> 00:27:23,030
+القضي مالها موازية لاتجاه التيار و F4 موازي يعني
+
+364
+00:27:23,030 --> 00:27:26,170
+anti-parallel يعني هذه بالاتجاه Z hat ت الاتجاه
+
+365
+00:27:26,170 --> 00:27:30,750
+السالب Z hat بس مالها parallel إذا لو كان التيار
+
+366
+00:27:30,750 --> 00:27:34,550
+التيارين في نفس الاتجاه هتكون attractive واحد
+
+367
+00:27:34,550 --> 00:27:38,490
+معاكس هتكون repulsive لو كان اتجاه التيار ماله
+
+368
+00:27:38,490 --> 00:27:42,110
+عمودي على اتجاه المجال المغناطيسي أو يعني عمودي
+
+369
+00:27:42,110 --> 00:27:47,870
+على اتجاه التيار هيكون إيش نوع القوة موازية بعتمد
+
+370
+00:27:47,870 --> 00:27:52,590
+إذا بعيدة ولا قريبة، إذا بعيد التيار هتكون في نفس
+
+371
+00:27:52,590 --> 00:27:56,770
+الاتجاه، إذا التيار بقترب بتكون في ع
+
+401
+00:29:52,670 --> 00:29:55,930
+أكبر، يعني هذا رينود ماله أقل من هذا، يعني هذا كله
+
+402
+00:29:55,930 --> 00:30:01,010
+على بعض ماله مجد، بس كذا الإشارة السالبة والظهر
+
+403
+00:30:01,010 --> 00:30:06,450
+السالب، إذا إيش قلنا؟ attractive، بالظبط قعدت،
+
+404
+00:30:06,450 --> 00:30:11,110
+ما نصرها، attractive،
+
+405
+00:30:11,110 --> 00:30:14,490
+attractive، قعدت بالظبط، كله قعدت بالظبط، كله 
+
+406
+00:30:14,490 --> 00:30:18,200
+نحيه، ال total force مالها attractive هي ال total
+
+407
+00:30:18,200 --> 00:30:22,560
+force of total اللي هي مجموعهم كلهم واحد واثنين و
+
+408
+00:30:22,560 --> 00:30:26,160
+ثلاثة وأربعة لقينا أن ثلاثة وأربعة cancel مع بعض
+
+409
+00:30:26,160 --> 00:30:29,280
+بيساوي بعض في المقدار والإشارة سالبة ضال عندي
+
+410
+00:30:29,280 --> 00:30:34,980
+واحد ويا اللي هو أربعة اثنين واحد وثلاثة مجموعهم
+
+411
+00:30:34,980 --> 00:30:39,280
+كلهم attractive إيش طبيعي هذه ال robots مالها أبعد
+
+412
+00:30:39,280 --> 00:30:43,700
+المسافة أبعد لكن هذه أقرب فإيش طبيعي أن يكون ال
+
+413
+00:30:43,700 --> 00:30:47,120
+attractive أقوى من ال passive فمجموعهم هيكون ال
+
+414
+00:30:47,120 --> 00:30:51,340
+total force هي attractive تجاهها minus rho hat
+
+415
+00:30:51,340 --> 00:30:56,820
+واضحة؟ طب آخر حاجة اللي هي ال magnetic torque and
+
+416
+00:30:56,820 --> 00:31:01,060
+moment تعريف
+
+417
+00:31:01,060 --> 00:31:04,360
+أول حاجة ال torque أنتم متذكرين ال torque هي R
+
+418
+00:31:04,360 --> 00:31:09,100
+cross F متذكرينه؟ حطيت العزوم؟ torque or mechanical
+
+419
+00:31:09,100 --> 00:31:12,300
+moment of force on a loop is the vector product of
+
+420
+00:31:12,300 --> 00:31:16,480
+the force and the moment arm اللي هو زراع العزم
+
+421
+00:31:16,480 --> 00:31:20,460
+بنسميه، ذاكرين كنتوا بتسموه زراع العزم والعزم و
+
+422
+00:31:20,460 --> 00:31:24,880
+القوة، طب إذا عندنا ال torque هو حاصل أو ال cross
+
+423
+00:31:24,880 --> 00:31:29,580
+product لزراع العزم R cross F اللي هي القوة
+
+424
+00:31:29,580 --> 00:31:30,880
+المؤثرة
+
+425
+00:31:34,790 --> 00:31:41,330
+لو احنا بنطبق هذا الحكي على sliding يعني تقريبًا
+
+426
+00:31:41,330 --> 00:31:44,450
+نفس الشكل اللي احنا شفناه بس هنغير اتجاهات ال
+
+427
+00:31:44,450 --> 00:31:50,650
+loop والقوة مش التوح اللي هنا عليه القوة بس هذا
+
+428
+00:31:50,650 --> 00:31:55,470
+ال rectangular loop هيكون له طول L وعرضه W وبدنا
+
+429
+00:31:55,470 --> 00:31:57,590
+نحطه في uniform magnetic field ما هو المثال اللي
+
+430
+00:31:57,590 --> 00:32:00,570
+طبعًا جبنا القوة عليه كان loop في مجال مغناطيسي
+
+431
+00:32:00,570 --> 00:32:04,210
+متظن، من وين جاي؟ عارفين احنا من وين جاي، جاي من 
+
+432
+00:32:04,210 --> 00:32:07,470
+solenoid coil فكان loop موجود في مجال 
+
+433
+00:32:07,470 --> 00:32:11,150
+مغناطيسي متظن داخل في قلب الصفحة صح؟ نفس ال loop
+
+434
+00:32:11,150 --> 00:32:13,670
+بس احنا هنغير ال coordinates، loop موجود في مجال
+
+435
+00:32:13,670 --> 00:32:17,600
+مغناطيسي طوله L وعرضه W in order for magnetic
+
+436
+00:32:17,600 --> 00:32:21,240
+field B from this figure ويتنقل.. طبعًا خلنا نشوف
+
+437
+00:32:21,240 --> 00:32:24,340
+إيش الوضع تبعنا إيش شكل ال force وإيش شكل ال
+
+438
+00:32:24,340 --> 00:32:27,060
+magnetic field هنا ال magnetic field مش طالع من 
+
+439
+00:32:27,060 --> 00:32:32,500
+برة الصفحة في نفس الصفحة يعني مش عمودي على كل أطراف 
+
+440
+00:32:32,500 --> 00:32:37,980
+المستطيل كان المثل اللي أخذناه قبل قليل ال loop
+
+441
+00:32:37,980 --> 00:32:42,000
+هيك والمجال المغناطيسي ماله عمودي على كل أطراف ال
+
+442
+00:32:42,000 --> 00:32:47,100
+loop هنا ال magnetic field بهذا الاتجاه عمودي فقط
+
+443
+00:32:47,100 --> 00:32:50,960
+على الضلعين اللي هنا لكن في نفس اتجاه التيار اللي
+
+444
+00:32:50,960 --> 00:32:55,580
+في ال.. أو يعني في نفس اللي هو اتجاه أو يعني اللي
+
+445
+00:32:55,580 --> 00:32:59,640
+تبع الضلعين اللي فوق وتحت طبعًا؟ طبعًا التيار
+
+446
+00:32:59,640 --> 00:33:02,520
+يعطينا اتجاه التيار يعني هنا بيكون ال magnetic في
+
+447
+00:33:02,520 --> 00:33:05,960
+اتجاه التيار هنا بس في عكس اتجاه التيار هي التيار
+
+448
+00:33:05,960 --> 00:33:11,660
+اتجاه السهم هذا اللي ممر في اللوغ طوله L عرضه W
+
+449
+00:33:15,490 --> 00:33:20,050
+القوة اللي على CD و AB احنا إيش عرفنا القوة قلنا؟
+
+450
+00:33:20,050 --> 00:33:25,790
+عبارة عن IL IL اللي هو ال current بور في cross B
+
+451
+00:33:25,790 --> 00:33:28,990
+في نماذجهم في نفس الاتجاه ال cross product بتاعهم
+
+452
+00:33:28,990 --> 00:33:33,550
+zero صح؟ ما فيش زاوية وتسعين درجة بينهم صفر الزاوية
+
+453
+00:33:33,550 --> 00:33:38,490
+بينهم sin 00 نفس الشيء هنا الزاوية بينهم 180 هيك
+
+454
+00:33:38,490 --> 00:33:41,790
+cross product صفر إذا القوة اللي بيأثرها المجال
+
+455
+00:33:41,790 --> 00:33:48,110
+المغناطيسي على ضلع CD على ضلع AB ماله صفر لكن القوة
+
+456
+00:33:48,110 --> 00:33:53,850
+اللي على ال BC و DA معها لا تساوي صفر لأن ال I وال
+
+457
+00:33:53,850 --> 00:33:56,970
+B في بينهم زاوية تسعين درجة ف I cross B في
+
+458
+00:33:56,970 --> 00:34:02,170
+زاوية بينهم لا تساوي صفر أو يعني أنه فيه زاوية فهو
+
+459
+00:34:02,170 --> 00:34:06,530
+فيه زاوية بس يعني أنه مش صفر أوي بتبقى إذا ال
+
+460
+00:34:06,530 --> 00:34:09,550
+total force هتكون لو أنا بحسب ال total force زي
+
+461
+00:34:09,550 --> 00:34:14,990
+ما عملنا هيكون فينا two sides اللي هي ال force two
+
+462
+00:34:14,990 --> 00:34:19,230
+sides قلنا ال force فيهم صفر بتلقى اللي هو ال two
+
+463
+00:34:19,230 --> 00:34:23,090
+loops اللي عندنا هو بسميهم صفر واحد اثنين ثلاثة
+
+464
+00:34:23,090 --> 00:34:25,390
+أربعة يعني فعندنا ال woman's side
+
+465
+00:34:29,280 --> 00:34:32,500
+هيكون عندها ال loop الأولاني اللي هو I DL cross B
+
+466
+00:34:32,500 --> 00:34:37,000
+أو ال side الأولاني ذات I ال integral من 4 على 1
+
+467
+00:34:37,000 --> 00:34:42,220
+DL cross B هنا هيكون من 0 لأقل، مش من 0 لأقل،
+
+468
+00:34:42,220 --> 00:34:46,160
+لأنها من 0 لأقل لاتجاه التيار وهذا الاتجاه، هنا
+
+469
+00:34:46,160 --> 00:34:52,260
+هيكون من أقل لـ 0 إذا
+
+470
+00:34:52,260 --> 00:34:56,540
+ال integral الأولاني هيكون I ال integral من 0
+
+471
+00:34:56,540 --> 00:35:06,120
+لأقل، وإتجاهه؟ dy dz
+
+472
+00:35:06,120 --> 00:35:10,620
+z z hat cross B dy z z hat cross B ف dy z إيش
+
+473
+00:35:10,620 --> 00:35:14,940
+حاططينا في هالحالة L وضل ال cross product بين اللى 
+
+474
+00:35:14,940 --> 00:35:19,240
+هي z و B هنا نيجي كم مرة I ال integral من L لـ
+
+475
+00:35:19,240 --> 00:35:25,420
+0 اتجاه التيار من L لـ 0 واتجاهه z hat
+
+476
+00:35:29,220 --> 00:35:34,600
+z من ال لـ 0 z هتكروس B بضوء z هتعطينا هنا سالب
+
+477
+00:35:34,600 --> 00:35:37,760
+ال y يعني هنا هتعطينا ال y وهنا سالب ال y وهنا z
+
+478
+00:35:37,760 --> 00:35:41,700
+هتكروس B وهنا z هتكروس B نفس القيام تبهين معايا
+
+479
+00:35:41,700 --> 00:35:49,180
+عندي I I z اللي هي من 0 لـ L هتعطينا I L إيش بضلع
+
+480
+00:35:49,180 --> 00:35:55,480
+هنا z هتكروس B وهنا هيكون minus I L z هتكروس B
+
+481
+00:35:55,480 --> 00:35:58,720
+نفس المقدار واتجاهه ماله مخالف
+
+482
+00:36:02,490 --> 00:36:06,130
+القوة الأولى إيش هتعطينا أي أو ال term الأولاني
+
+483
+00:36:06,130 --> 00:36:11,410
+هتعطينا I L z hat cross B وال term الثاني هتعطينا
+
+484
+00:36:11,410 --> 00:36:20,030
+minus I L z hat cross B ما هو ب cross my total
+
+485
+00:36:20,030 --> 00:36:26,070
+force صفر لكن لو طلعنا الدقة مش هنلاحظ أن ال object
+
+486
+00:36:26,070 --> 00:36:30,330
+هذا ساكن مش هيكون في حالة سكون، القوة لو تكون 
+
+487
+00:36:30,330 --> 00:36:34,030
+ساكنة، المفروض يا إما بيكون في.. بيمشي بسرعة منتظمة
+
+488
+00:36:34,030 --> 00:36:36,310
+يا ساكن، هنا مش قلنا إنه قاعد بيتحرك بسرعة 
+
+489
+00:36:36,310 --> 00:36:41,490
+منتظمة، إيش بسّله؟ بلوف، ليش بلوف؟ لأن النقطتين
+
+490
+00:36:41,490 --> 00:36:44,370
+هدول مش قاعدين على نفس العمود، يعني لو قاعدين على 
+
+491
+00:36:44,370 --> 00:36:48,070
+نفس.. النقطة بيأثروا على نفس النقطة، هيكون في 
+
+492
+00:36:48,070 --> 00:36:52,210
+توازن، هي cancel بعض ومش هيصير أي دوران لأقلّه،
+
+493
+00:36:52,210 --> 00:36:55,970
+لكن الواضح أن واحدة والثانية في بينهم مسافة، 
+
+494
+00:36:55,970 --> 00:37:01,990
+واحدة اتجاهها، اللي هي عكس اتجاه الثاني، اتعكس B، 
+
+495
+00:37:01,990 --> 00:37:05,030
+والثانية في اتجاه المعاكس، ال magnitude تبعهم إذا 
+
+496
+00:37:05,030 --> 00:37:08,190
+معلوم متساوي، لو بدأت طالع على ال magnitude، لو
+
+497
+00:37:08,190 --> 00:37:15,520
+سميتها هذه F mod ال magnitude بتاع التنتين هي ساوي 
+
+498
+00:37:15,520 --> 00:37:21,020
+I L ال magnitude بتاع B والـ z هتكروس 
+
+499
+00:37:21,020 --> 00:37:27,380
+الاتجاه بتاع B هو اللي هيعطينا الاتجاه تبع ال F0
+
+500
+00:37:27,380 --> 00:37:33,480
+تمام؟ إذا عندنا ال magnitude يعني هو اسمها F0
+
+501
+00:37:33,480 --> 00:37:39,880
+vector minus F0 فدي كلها اسمها F0 vector minus 
+
+502
+00:37:39,880 --> 00:37:44,600
+F mod إذا المقدار تبع F mod هو I L في مين في
+
+503
+00:37:44,600 --> 00:37:47,460
+المجموعة تبع B فانحنا هيتولد z hat cross اتجاه
+
+504
+00:37:47,460 --> 00:37:51,180
+ال B لهم مثلاً x hat أو احنا متبعين الاتجاه المحلي
+
+505
+00:37:51,180 --> 00:37:55,640
+المواضع إذا F mod لهم نفس المقدار مش هو عيين على
+
+506
+00:37:55,640 --> 00:38:00,220
+نفس الأسطحة نفس النقطة هو حط القوة مش نفس الحط
+
+507
+00:38:00,220 --> 00:38:04,260
+فبالتالي فيه هيتولد torque واحدة منهم F mod واحدة
+
+508
+00:38:04,260 --> 00:38:07,820
+minus F mod في إشارة سالبة بينهم تاني
+
+509
+00:38:10,290 --> 00:38:14,670
+عشان هيك قلنا هذا بيسببلنا ازدواج وبيعملنا عزم 
+
+510
+00:38:14,670 --> 00:38:18,570
+ازدواج وهيلف ال loop في وجود المجال المغناطيسي لسه 
+
+511
+00:38:18,570 --> 00:38:24,510
+ال torque احنا بنعرف إيش هو F knot في اللي هو
+
+512
+00:38:24,510 --> 00:38:27,390
+الزراع ال arm ال magnitude دي دي بالكم احنا قلنا
+
+513
+00:38:27,390 --> 00:38:32,430
+هو R cross F يعني ال magnitude تبع R في F F اللي 
+
+514
+00:38:32,430 --> 00:38:37,890
+هي أنا F knot سميناها والزراع تبعنا هيكون ال بالة
+
+515
+00:38:37,890 --> 00:38:42,770
+التنتين لو مدينا هذا على طوله هي هتكون الزراع إيش 
+
+516
+00:38:42,770 --> 00:38:47,530
+بيساوي هاذ الزاوية هتكون نفسها Alpha هيكون الزراع 
+
+517
+00:38:47,530 --> 00:38:53,950
+أو هذا العمود بينهم إيش بيساوي W Sin Alpha واضِر W
+
+518
+00:38:53,950 --> 00:38:56,530
+Sin Alpha مش هذا اللي على فول هذا اللي هو الزراع
+
+519
+00:38:56,530 --> 00:39:01,390
+اللي بينهم هيكون إيش W Sin Alpha هاذ الزاوية
+
+520
+00:39:01,390 --> 00:39:05,290
+بتساوي نفس الزاوية اللي هنا معايا أسمها ولا
+
+521
+00:39:05,290 --> 00:39:05,990
+بأضحك؟
+
+522
+00:39:15,340 --> 00:39:23,280
+هذه تكمل هذه وهذه تكمل هذه فهذه Alpha هذه
+
+523
+00:39:23,280 --> 00:39:28,700
+تكمل هذه وهذه تكمل هذه فهذه Alpha وهذا اللي أنا 
+
+524
+00:39:28,700 --> 00:39:34,100
+بده إيش هيكون Sine Alpha إيش بيساوي يظهر اللي 
+
+525
+00:39:34,100 --> 00:39:40,920
+أنا بدّه مثلاً X على W فـ X بيساوي W Sine Alpha
+
+526
+00:39:40,920 --> 00:39:43,000
+واضح؟ هاذ ال R تبعه هو 
+
+527
+00:39:46,650 --> 00:39:51,470
+التوك بيساوي قيمة F not اللي هو الشيء اللي بتساوي 
+
+528
+00:39:51,470 --> 00:40:00,180
+IL في B في BT W sin α اللي هو الذراع القوة فإيش لو 
+
+529
+00:40:00,180 --> 00:40:03,940
+أنا بدي أجيب الترتيب تبع T أو ال magnitude بدي
+
+530
+00:40:03,940 --> 00:40:06,480
+أخطّه بدون bold احنا قلنا بدون bold هذا magnitude
+
+531
+00:40:06,480 --> 00:40:10,520
+ال bold بتكون vector أو أن أخطّه بين اللي هي ال
+
+532
+00:40:10,520 --> 00:40:13,660
+absolute هاذ اللي باليه فهي magnitude يعني هاذ نفس
+
+533
+00:40:13,660 --> 00:40:20,140
+هاذ فـ T إيش منها الساوي Bil عوضنا عن قيمة F0 W sin α
+
+534
+00:40:20,140 --> 00:40:25,740
+W اللي هو ال width تبع العند طلعنا كويس على ال
+
+535
+00:40:25,740 --> 00:40:30,580
+loop رجعنا L في W إيش بمثل ليها ده ال area بتاعة
+
+536
+00:40:30,580 --> 00:40:34,720
+المستطيل ولا I في L ال area بتاعة ال loop
+
+537
+00:40:34,720 --> 00:40:40,980
+rectangular loop فعندي ال area بتاعته L في W إذا 
+
+538
+00:40:40,980 --> 00:40:46,180
+معناه T إيش بتساوي B في I بدل W أسفل أسميها S اللي 
+
+539
+00:40:46,180 --> 00:40:51,210
+هي ال area هي sin alpha كما في حاجة إضافة احنا
+
+540
+00:40:51,210 --> 00:40:54,810
+بنعرف أن حاصل ضرب ال current في ال area I في A أو
+
+541
+00:40:54,810 --> 00:40:59,410
+I في S بدّه اسميه ال moment ودايمًا احنا ال vector
+
+542
+00:40:59,410 --> 00:41:03,070
+تبع ال area قلنا أنه بيكون عمودي على ال area مش
+
+543
+00:41:03,070 --> 00:41:06,250
+احنا اللي قلنا ال area مالها مش scalar، اللي هي
+
+544
+00:41:06,250 --> 00:41:10,490
+vector وبيكون عمودي على ال area فانحنا نسمي ال
+
+545
+00:41:10,490 --> 00:41:15,940
+unit vector تبع ال area وهعرف ال moment ال
+
+546
+00:41:15,940 --> 00:41:20,600
+magnetic dipole moment اللي ال M بيساوي I في S في a
+
+547
+00:41:20,600 --> 00:41:23,320
+hat احنا كان في عندنا electric dipole moment 
+
+548
+00:41:23,320 --> 00:41:26,800
+ما تذكرينه؟ و two charges هنا ال magnetic dipole
+
+549
+00:41:26,800 --> 00:41:30,860
+moment اللي هو ناتج من أنه فيه دي تيارين متعاكسين
+
+550
+00:41:30,860 --> 00:41:34,160
+في اتجاه مجال المغناطيس هيتولد أن دي couple من ال
+
+551
+00:41:34,160 --> 00:41:38,810
+forces متساويين اتجاههم متعاكسين إذا ال magnetic
+
+552
+00:41:38,810 --> 00:41:43,490
+dipole moment بنعرفه هو عبارة عن حاصل ضرب ال 
+
+553
+00:41:43,490 --> 00:41:48,890
+current في ال area بتاعة ال loop تمام؟ واتجاهه
+
+554
+00:41:48,890 --> 00:41:53,970
+عمودي على ال area طيب ال units تعونه هيكون amps
+
+555
+00:41:53,970 --> 00:41:58,330
+per meter تربيع ال units تعونه amps per meter
+
+556
+00:41:58,330 --> 00:42:02,390
+تربيع تمام؟ هاذ ال magnetic dipole moment
+
+557
+00:42:12,400 --> 00:42:16,580
+طيب كمان لو بدرجة أكتب ال torque اللي احنا حسبنا
+
+558
+00:42:16,580 --> 00:42:21,080
+أن هو عبارة عن B في ال magnetic moment في sin α
+
+559
+00:42:21,080 --> 00:42:24,640
+حلوة أحس أن أنا بقدر احنا متذكرين قلنا ال sin α
+
+560
+00:42:24,640 --> 00:42:29,330
+هيبتمثل ليه؟ cross product بينما ال cosine بتمثل لي
+
+561
+00:42:29,330 --> 00:42:32,690
+dot product ف أنا عندي vector يوه ال moment وفيه
+
+562
+00:42:32,690 --> 00:42:36,950
+عندي sin alpha معناه أنه هاذ المقدار تبع ال vector
+
+563
+00:42:36,950 --> 00:42:40,590
+M في ال sin alpha معناه هدا فيه عندي cross product
+
+564
+00:42:40,590 --> 00:42:44,370
+بين حاجتين بال moment وحاجة ثانية اللي هي في هاذ
+
+565
+00:42:44,370 --> 00:42:46,470
+الحالة مين ال vector الثاني ال magnetic field
+
+566
+00:42:46,470 --> 00:42:51,430
+فعندي B وال moment و sin alpha إذا هذا عبارة عن 
+
+567
+00:42:51,430 --> 00:42:54,210
+ال magnitude of the cross product بين ال magnetic
+
+568
+00:42:54,210 --> 00:42:58,840
+field وال moment Torque هو عبارة عن ال magnetic
+
+569
+00:42:58,840 --> 00:43:02,320
+moment across ال magnetic field ال magnetic
+
+570
+00:43:02,320 --> 00:43:05,460
+moment كمان مرة هو عبارة عن حاصل ضرب ال current في
+
+571
+00:43:05,460 --> 00:43:12,900
+ال area وال vector بتاعه هو عمودي على ال area وال
+
+572
+00:43:12,900 --> 00:43:16,440
+sin α هي اللي أوحطلنا أن هي عبارة عن cross product
+
+573
+00:43:16,440 --> 00:43:19,860
+لأن اتفقنا أن ال sin هي بتمثل cross بين لو كان 
+
+574
+00:43:19,860 --> 00:43:22,920
+عندكو sin إيش بنقول؟ في عندي dot ال product دي وفي 
+
+575
+0
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/tlgyXNIYaB8_raw.srt b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/tlgyXNIYaB8_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..6b6d36615bfaa35c2864e820db468778a4315578
--- /dev/null
+++ b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/tlgyXNIYaB8_raw.srt
@@ -0,0 +1,2388 @@
+1
+00:00:22,580 --> 00:00:25,480
+السلام عليكم ورحمة الله وبركاته احنا اليوم هنتبع
+
+2
+00:00:25,480 --> 00:00:29,340
+موضوعنا على أنواع اللي هي القوة أسواق المناطسية أو
+
+3
+00:00:29,340 --> 00:00:33,320
+الكهربائية وكيف تأثيرهم على ال particles احنا
+
+4
+00:00:33,320 --> 00:00:36,340
+شوفنا في المحاضر الماضي ان يسهل كيف particle تحت
+
+5
+00:00:36,340 --> 00:00:39,960
+أثير القوة المناطسية انه بيصير في مدار دائري و ال
+
+6
+00:00:39,960 --> 00:00:44,280
+particle او يعني ال charge في مسار كهربا ..
+
+7
+00:00:44,280 --> 00:00:47,130
+electric fieldإنها بتسير في اتجاه ال electric
+
+8
+00:00:47,130 --> 00:00:49,310
+field حسب ال charge إذا ال positive معاه إذا ال
+
+9
+00:00:49,310 --> 00:00:54,610
+negative عكسه اليوم هنشوف لو كانت ال force الكلية
+
+10
+00:00:54,610 --> 00:00:56,770
+أسوأ جاي من ال magnetic أو ال electric field
+
+11
+00:00:56,770 --> 00:01:00,390
+تأثيرها على ال particle اللي بتحرك في المجالين
+
+12
+00:01:00,390 --> 00:01:04,170
+المثال اللي أمامنا بقول إن في عندي particle ال
+
+13
+00:01:04,170 --> 00:01:07,530
+charge particle اللي بتتحرك بسرعة منتظمة في نفس
+
+14
+00:01:07,530 --> 00:01:11,470
+سرعة Velocity متدارها أربعة X hat meter per second
+
+15
+00:01:11,470 --> 00:01:15,340
+يعني ال particle بتحرك اتجاه ال X hatفى ال region
+
+16
+00:01:15,340 --> 00:01:17,960
+فى المنطقة اللى فىها ال both electric and magnetic
+
+17
+00:01:17,960 --> 00:01:20,660
+field ال electric field اتجاهه في ال Y وال
+
+18
+00:01:20,660 --> 00:01:24,220
+magnetic في اتجاه ال Z يعني الفاردكر اتجه اتجاه ال
+
+19
+00:01:24,220 --> 00:01:28,020
+X مثلا طالع من الصفحة ال electric field في اتجاه
+
+20
+00:01:28,020 --> 00:01:34,230
+ال Yxyz المجنت في اتجاه z اكسس ان ال magnitude تبع
+
+21
+00:01:34,230 --> 00:01:37,090
+ال electric والمجنت ال constant يعني مايعتمدش على
+
+22
+00:01:37,090 --> 00:01:40,370
+الزمان ال electric field القابل يتبع عشرين واتجاه
+
+23
+00:01:40,370 --> 00:01:43,710
+y hat مافيش عشرين كوسين ولا سين ولا تي ولا ..
+
+24
+00:01:43,710 --> 00:01:46,390
+مافيش مايعتمدش على الزمان لأن احنا بناخد course
+
+25
+00:01:46,390 --> 00:01:49,710
+electrostatic مايعتمدش على .. مش electrodynamic
+
+26
+00:01:50,170 --> 00:01:53,570
+فإذا عندنا electric field مقدره عشرين y hat ال max
+
+27
+00:01:53,570 --> 00:01:57,470
+field some constant P0 z hat و بارد متر ترابين
+
+28
+00:01:57,470 --> 00:02:01,990
+طالب مننا أن نقرأ قداش قيمة P0 اللي ال velocity of
+
+29
+00:02:01,990 --> 00:02:05,090
+the particle remains constant يعني كم مرة احنا
+
+30
+00:02:05,090 --> 00:02:13,050
+عندنا هاي ال X Y Z هاي ال X Y Z ال particle اتحرك
+
+31
+00:02:13,050 --> 00:02:20,000
+بسرعة متظامة مقدارها أربع X hat متر ثانعندى فى ال
+
+32
+00:02:20,000 --> 00:02:23,640
+region electric field فى اتجاه ال Y hat هى ال E
+
+33
+00:02:23,640 --> 00:02:30,160
+ومفضله 20 Y hat فهى خطوط المجال الكهربائى والمجال
+
+34
+00:02:30,160 --> 00:02:32,980
+المعاطس فى خطوطه فى اتجاه ال Z axis
+
+35
+00:02:41,590 --> 00:02:44,390
+لنشوف ايش .. ايش اللي بيصير لهذا ال particle اللي
+
+36
+00:02:44,390 --> 00:02:49,050
+بيتجه بسرعة متظنة في اتجاه ال X-axis بمعنى اخر هو
+
+37
+00:02:49,050 --> 00:02:52,250
+صار السؤال بطريقة تانية قال لك دي قيمة P not هاي
+
+38
+00:02:52,250 --> 00:02:57,470
+اللي بتخليه يستمر في انه يكون يتحرك بهذه السرعة
+
+39
+00:02:57,470 --> 00:03:02,950
+اللي هي 4X hat قداش قيمة P not اللي بتخلي ال
+
+40
+00:03:02,950 --> 00:03:06,550
+particle يستمر بconstant velocity مقدارها 4X hat
+
+41
+00:03:06,550 --> 00:03:12,030
+متر per secondطبعا احنا عشان المجاليين عندنا
+
+42
+00:03:12,030 --> 00:03:17,350
+قُبتين بيأسروا على ال particle هذا قوة كهربائية و
+
+43
+00:03:17,350 --> 00:03:21,410
+قوة ماناطسية اتنتين بيأسروا على ال particle و
+
+44
+00:03:21,410 --> 00:03:25,030
+مجموعهم لازم يساوي قدرش او فئة ال acceleration
+
+45
+00:03:25,030 --> 00:03:29,650
+بتاعة ال object لكن هو اللي انا بدي اياها ال total
+
+46
+00:03:29,650 --> 00:03:32,650
+force بحيث ان ال particle remains in a constant
+
+47
+00:03:32,650 --> 00:03:35,430
+velocity constant velocity اشمعها ال acceleration
+
+48
+00:03:35,430 --> 00:03:42,240
+بتساوي zeroبأن ال acceleration شو بتساوي؟ دي V بقي
+
+49
+00:03:42,240 --> 00:03:45,920
+80 إذا V كونستانت إذا ال acceleration بتكون Zero
+
+50
+00:03:45,920 --> 00:03:49,480
+إذا هاي لازم تساوي سفر يعني مجموعة two forces
+
+51
+00:03:49,480 --> 00:03:52,320
+بديوا تساوي سفر هاي المعنى إن أنا بدي ال particle
+
+52
+00:03:52,320 --> 00:03:57,180
+اللي طالع مستمر فيه constant فلسطين إن ال electric
+
+53
+00:03:57,180 --> 00:04:01,800
+force شو بتساوي؟ ال charge في ال electric field و
+
+54
+00:04:01,800 --> 00:04:06,120
+هي ال magnetic force هو QV cross P إذا هتكون V
+
+55
+00:04:06,120 --> 00:04:12,000
+cross Pهذا هو قوتنا طبعاً كيولها تساوي zero وبقدر
+
+56
+00:04:12,000 --> 00:04:14,900
+أقسم عليها لأنه chart particle لو صمم ال chart
+
+57
+00:04:14,900 --> 00:04:20,460
+فهذا المعنى هذا الحكي أن E بالها تساوي سالب V
+
+58
+00:04:20,460 --> 00:04:25,520
+across B طب نعوض E إيش هي E ال electric field
+
+59
+00:04:25,520 --> 00:04:33,180
+المقدر 20Y hat minus V اللي هي 4X hat across B
+
+60
+00:04:33,180 --> 00:04:36,100
+اللي هي B not زدها
+
+61
+00:04:37,910 --> 00:04:44,490
+ايش ال cross product بين ال X و ال Z؟ X Z A Y بس
+
+62
+00:04:44,490 --> 00:04:53,830
+موجة ولا سالد؟ لإن موجة بقولنا X Y Z X Y Z هيك
+
+63
+00:04:53,830 --> 00:04:58,690
+موجة، لكن لو العكس بقولنا X Z إذا سالد Y، فهو
+
+64
+00:04:58,690 --> 00:05:03,490
+ستصبح ال plus أربع بي نقطة في اتجاه ال Y هذا، بين
+
+65
+00:05:03,490 --> 00:05:07,100
+بي سالد و سالد بيصبح ال plusطبعا بما انه من نفس
+
+66
+00:05:07,100 --> 00:05:11,100
+الاتجاه اذا ال amplitude لازم يكون متساوى تلف
+
+67
+00:05:11,100 --> 00:05:13,640
+اتجاه ال y hat معناه انه عند العشرين لازم تساوي
+
+68
+00:05:13,640 --> 00:05:16,480
+اربعة بي نوت او بي نوت اشهر سبعة اشهر اربعة هي
+
+69
+00:05:16,480 --> 00:05:20,920
+خمسة اذا عرفنا قيمة اللي هو ال بي نوت اللي بتخلي
+
+70
+00:05:20,920 --> 00:05:27,800
+هذا ال charge particle يظل مستمر في المسار تبعه ب
+
+71
+00:05:27,800 --> 00:05:32,250
+constant velocityواضح؟ هاد ال idea بتاعة إنه أنا
+
+72
+00:05:32,250 --> 00:05:34,350
+لما أحط electric field و magnet فيه ممكن أحصى و
+
+73
+00:05:34,350 --> 00:05:37,170
+أخلص من ال acceleration بيستخدموها أني ممكن أعمل
+
+74
+00:05:37,170 --> 00:05:40,330
+أنموع فلترة فلترة يعني عند particles اللي لهم
+
+75
+00:05:40,330 --> 00:05:44,030
+فلسطة معينة مثلا في هذا المثال ال particle بتحرك
+
+76
+00:05:44,030 --> 00:05:48,150
+باربع x hat بيسلهوش أي drift اي acceleration بيبقى
+
+77
+00:05:48,150 --> 00:05:51,670
+اللي ماشي بخط مستقيم بيبقى اللي ماشي بدون اي
+
+78
+00:05:51,670 --> 00:05:54,410
+trajectory لو في acceleration بيسلهو trajectory
+
+79
+00:05:54,410 --> 00:05:58,370
+بيسلهو ميلانزي أي جسم في ال gravitational force،
+
+80
+00:05:58,370 --> 00:06:02,090
+لو دلوا في constant velocity، بيمشي بمصارع ثابت،
+
+81
+00:06:02,090 --> 00:06:05,250
+لكن مع وجود ال acceleration أشبه له في ال X-axis
+
+82
+00:06:05,250 --> 00:06:10,170
+بيمشي بخط مستقيم، لكن في ال Y-axis أشبه له تسارع،
+
+83
+00:06:10,170 --> 00:06:14,650
+بيبدأ بسرعة عالية، وبعدين تطلع
+
+84
+00:06:14,650 --> 00:06:19,550
+لحدبسيلها ال de-acceleration لحد ما تصير سفر
+
+85
+00:06:19,550 --> 00:06:22,550
+وبعدين بسيلها acceleration مرة تانية في المجال
+
+86
+00:06:22,550 --> 00:06:25,990
+المناطسي اخدتوا هذا في المجال ال gravitational اذا
+
+87
+00:06:25,990 --> 00:06:30,490
+مادام هي بتتحرك ب constant velocity معناه انه هذا
+
+88
+00:06:30,490 --> 00:06:33,790
+ال particle او هم بيستغلوها ان particles معينين
+
+89
+00:06:33,790 --> 00:06:38,300
+اللي هم بسرعة معينةبيحطوه في مجال كهربا وماناطيسي
+
+90
+00:06:38,300 --> 00:06:41,660
+بحيث ان هدول الاتنين يحافظوا على هاي ال constant
+
+91
+00:06:41,660 --> 00:06:44,720
+velocity فبيظلوا في مصار مستقيم البقى ايش
+
+92
+00:06:44,720 --> 00:06:47,740
+بيصيرلهم؟ بيصيرلهم drift فانهم مش ماشيين في هاي ال
+
+93
+00:06:47,740 --> 00:06:52,520
+velocity هيتأثروا في هاي القوة، هيصير في عندهم
+
+94
+00:06:52,520 --> 00:06:55,680
+acceleration، هيتصارعوا فهذا بتسمونه من ألواء
+
+95
+00:06:55,680 --> 00:06:58,380
+filters هفرشيكوا الصورة اللي بتقوم بهذا الشكل
+
+96
+00:06:58,380 --> 00:07:01,160
+عندنا طبعا ال electric field دايما بيودوهم من خلال
+
+97
+00:07:01,160 --> 00:07:05,280
+capacitorsهي في عندنا مثلا capacitor و في عندنا
+
+98
+00:07:05,280 --> 00:07:08,000
+اللي هو مثلا فبكون تجاه ال electric field هي تجاه
+
+99
+00:07:08,000 --> 00:07:11,360
+مصر ال electric field و في عندنا المجال المناطيسي
+
+100
+00:07:11,360 --> 00:07:14,660
+اللي هي طالع من الصفحة ال dot متعمدين على بعض زي
+
+101
+00:07:14,660 --> 00:07:17,420
+المثال تبعنا بالتمام عندنا electric field و magnet
+
+102
+00:07:17,420 --> 00:07:21,800
+field متعمدين على بعض و ال particle مصار عمودي على
+
+103
+00:07:21,800 --> 00:07:25,940
+التانيةالبارتكال اللى له ال constant او ال
+
+104
+00:07:25,940 --> 00:07:29,620
+velocity المحددة هو اللى بيبقى ماشى في خط مستقيم
+
+105
+00:07:29,620 --> 00:07:33,520
+اللى بيسلمهش اى تسارة البقى بيسلمهش تسارة فتشوفوا
+
+106
+00:07:33,520 --> 00:07:37,840
+ال trajectory اللى هو ال object في مجال الجاذبى
+
+107
+00:07:37,840 --> 00:07:41,120
+العربيه هنا الفرق ان ال charge تخلق ممكن كموجة او
+
+108
+00:07:41,120 --> 00:07:46,000
+سالبة عشان هيك ممكن نلاقيها مرة فوق و مرة تحت طبعا
+
+109
+00:07:46,000 --> 00:07:48,840
+عشان نحدد اشيه هذه ال velocity احنا لو أخدنا ال
+
+110
+00:07:48,840 --> 00:07:51,400
+magnitude تبع ال two forces احنا ال magnitude تبع
+
+111
+00:07:51,400 --> 00:07:55,000
+هدولهيعني ال magnet تبقى هال force و force هذه
+
+112
+00:07:55,000 --> 00:08:00,220
+حياتنا ال E بديها تسوى بس كمagnitude ال volume 6
+
+113
+00:08:00,220 --> 00:08:03,920
+في B إذا ال volume بتاعة ال particle اللي بيسرهوش
+
+114
+00:08:03,920 --> 00:08:07,600
+اي drift بيساوي E على B اللي ال acceleration
+
+115
+00:08:07,600 --> 00:08:11,450
+بتاعته بال saucerإذا ال particle بتروحش أي drift
+
+116
+00:08:11,450 --> 00:08:15,190
+أو بتبقى instant velocity هذي من الأشياء اللي ممكن
+
+117
+00:08:15,190 --> 00:08:17,650
+تكون فيها ال multiple choice إن ال velocity بتاعة
+
+118
+00:08:17,650 --> 00:08:19,830
+ال particle اللي بيعنيش من أي drift أو اللي بيسله
+
+119
+00:08:19,830 --> 00:08:23,190
+filtering بيبقى ماشي في مساره، بيكون فيه هنا حرق
+
+120
+00:08:23,190 --> 00:08:26,810
+في ال aperture يعني فيه هنا هذي زي wall زي حاجز
+
+121
+00:08:26,810 --> 00:08:29,970
+وفيه بيكون هول ال particles اللي بتكون constant
+
+122
+00:08:29,970 --> 00:08:33,680
+velocity هي اللي بتطلع من خلال ال hallهي بتسميها
+
+123
+00:08:33,680 --> 00:08:38,060
+ال critical speed اللي لازم عشان هذا ال object يظل
+
+124
+00:08:38,060 --> 00:08:44,200
+ماشي constant بواسطة واضح طب كده مثال لو احنا
+
+125
+00:08:44,200 --> 00:08:48,540
+لدينا two filaments
+
+126
+00:08:48,540 --> 00:08:51,820
+واحدة منهم على شكل infinite line بمور فيها current
+
+127
+00:08:51,820 --> 00:08:55,960
+أي واحد والتاني على شكل loop بمور فيها current أي
+
+128
+00:08:55,960 --> 00:09:00,820
+تانين وبدنا نسبة هي واحدة اللي هي long filamentary
+
+129
+00:09:00,820 --> 00:09:04,930
+Ywhere currying current I1 والتاني اللي هو
+
+130
+00:09:04,930 --> 00:09:09,470
+rectangular loop بحمل current I2 بدنا ان القوة
+
+131
+00:09:09,470 --> 00:09:12,790
+اللي experienced by the loop is given by القوة
+
+132
+00:09:12,790 --> 00:09:17,970
+اللي على ال loop given by F equal minus mu0 I1 I2
+
+133
+00:09:17,970 --> 00:09:22,290
+B على 2π ف1 على rho0 minus 1 على النوت زا اد اين
+
+134
+00:09:22,290 --> 00:09:27,090
+اتجاه روهات الميوترتجاهة في روحات الـinfinite يعني
+
+135
+00:09:27,090 --> 00:09:30,350
+مين هي ال رنود و روحه والإيه ال رنود هي المسافة
+
+136
+00:09:30,350 --> 00:09:33,590
+يعني لو حطينا ال first filament اللي هي ال
+
+137
+00:09:33,590 --> 00:09:38,350
+infinite where عند ال origin رنود هي المسافة ما
+
+138
+00:09:38,350 --> 00:09:44,610
+بين ال infinite line و أول ضلع من أضلع المستطيل هي
+
+139
+00:09:44,610 --> 00:09:50,170
+رنود هذه المسافة أو بعد ال loop القريب عن مين عن
+
+140
+00:09:50,170 --> 00:09:54,530
+ال filament ال infinite lineالـ A هي عبارة عن ميل
+
+141
+00:09:54,530 --> 00:09:59,870
+ال width تبع ال rectangular loop فبيكون الدلع
+
+142
+00:09:59,870 --> 00:10:05,130
+البعيد بعضه عن ال wire مقدار raw node زايد يعني
+
+143
+00:10:05,130 --> 00:10:11,990
+واضح I1 هو التيار الممر في ال infinite line I2 هو
+
+144
+00:10:11,990 --> 00:10:15,390
+ال current الممر في ال rectangular wire اذا احنا
+
+145
+00:10:15,390 --> 00:10:20,090
+طلبين القوة اللي على ميل على ال rectangular loop
+
+146
+00:10:20,090 --> 00:10:20,570
+اللي
+
+147
+00:10:23,420 --> 00:10:26,900
+by the loop is given by .. for experience by the
+
+148
+00:10:26,900 --> 00:10:30,740
+loop is given by بالنسبة هي العلاقة اللي اتأثر
+
+149
+00:10:30,740 --> 00:10:35,790
+فيها ال loopطبعا احنا هلاحظ ان في عندى اكم ويرع في
+
+150
+00:10:35,790 --> 00:10:41,150
+ال loop واحد اتنين تلاتة اربعة كل واحد منهم هيتأثر
+
+151
+00:10:41,150 --> 00:10:45,290
+عليه المجال المناطيسي اللى جاي من ال current اللى
+
+152
+00:10:45,290 --> 00:10:48,750
+مارق في ال loop الفائض اللى ال infinite line اللى
+
+153
+00:10:48,750 --> 00:10:53,610
+هو مورفي I واحد هيأثر على كل واحد بقوة هنسميهم F
+
+154
+00:10:53,610 --> 00:10:58,490
+واحد F تنين F تلاتة F اربعة احنا أخدنا قبل هيك
+
+155
+00:10:58,490 --> 00:11:02,110
+اللى هو القوة بين two lines بتذكرينهاهنشوفها من
+
+156
+00:11:02,110 --> 00:11:07,650
+هذا المثال هنشوفها
+
+157
+00:11:07,650 --> 00:11:12,650
+من هذا المثال هنشوفها من هذا المثال هنشوفها من هذا
+
+158
+00:11:12,650 --> 00:11:12,710
+المثال هنشوفها من هذا المثال هنشوفها من هذا المثال
+
+159
+00:11:12,710 --> 00:11:12,710
+هنشوفها من هذا المثال هنشوفها من هذا المثال
+
+160
+00:11:12,710 --> 00:11:12,890
+هنشوفها من هذا المثال هنشوفها من هذا المثال
+
+161
+00:11:12,890 --> 00:11:12,910
+هنشوفها من هذا المثال هنشوفها من هذا المثال
+
+162
+00:11:12,910 --> 00:11:12,910
+هنشوفها من هذا المثال هنشوفها من هذا المثال
+
+163
+00:11:12,910 --> 00:11:12,910
+هنشوفها من هذا المثال هنشوفها من هذا المثال
+
+164
+00:11:12,910 --> 00:11:12,910
+هنشوفها من هذا المثال هنشوفها من هذا المثال
+
+165
+00:11:12,910 --> 00:11:12,990
+هنشوفها من هذا المثال هنشوفها من هذا المثال
+
+166
+00:11:12,990 --> 00:11:31,230
+هنشوفها من هذا المثال هنشوفها من هذا المثال هنشوف
+
+167
+00:11:38,400 --> 00:11:45,940
+لو كان عندنا هذه القوة ما بين اللي بيأثر فيها مجال
+
+168
+00:11:45,940 --> 00:11:50,220
+معناطيسي مثلا اللي هو ال wire 2 هذا على ال wire 1
+
+169
+00:11:50,220 --> 00:11:58,400
+I D L cross B احنا كانت QV cross B لتشارج لو صرت
+
+170
+00:11:58,400 --> 00:12:04,110
+lines لو بحكي ع ال lines هيصير بقل QV I D LIDL
+
+171
+00:12:04,110 --> 00:12:07,310
+cross B هو مين المجال المناطيسي اللي ناتج من
+
+172
+00:12:07,310 --> 00:12:11,090
+التيار الآخر يعني لما يكون عندى two lines مذكرين
+
+173
+00:12:11,090 --> 00:12:15,110
+الحكاية ده الحكاية بيمور فيهم currents بس بيفرق
+
+174
+00:12:15,110 --> 00:12:19,350
+اتجاه او يعني إيش هي القوة تجازب أو تنافر هيكون
+
+175
+00:12:19,350 --> 00:12:22,330
+القوة اللى بأثر فيها مثلا في هالحالة اتنين على
+
+176
+00:12:22,330 --> 00:12:27,290
+واحد هي ال current بيمور في واحد بذكركم فيها ال
+
+177
+00:12:27,290 --> 00:12:30,990
+current بيمور في واحد IDL cross مين المجال
+
+178
+00:12:30,990 --> 00:12:35,710
+المناطيسي اللي ناتج من اتنينواضح؟ احنا لأنه كنا
+
+179
+00:12:35,710 --> 00:12:39,610
+باخدنا elements فقلنا بكون في double integral على
+
+180
+00:12:39,610 --> 00:12:42,830
+اللي هو عشان احصل على كل القوة اللي بأثر فيها ال
+
+181
+00:12:42,830 --> 00:12:48,110
+current مش بس ال element I2DI2 كل اللوب I2 اللي
+
+182
+00:12:48,110 --> 00:12:53,770
+مورفي I2 على اللوب المورفي I1 فبكمل مرة كاملا على
+
+183
+00:12:53,770 --> 00:12:57,780
+اللوب الأول عشان يعطينا كل ال elementsمرة تانية
+
+184
+00:12:57,780 --> 00:13:01,300
+بكامل عادي الواحد عشان تعطيني كل القوة اللى على
+
+185
+00:13:01,300 --> 00:13:04,840
+النقل اول اذا بس تذكيرها على السريع ان هي عبارة عن
+
+186
+00:13:04,840 --> 00:13:11,040
+mean of force I dl cross P هذا
+
+187
+00:13:11,040 --> 00:13:16,840
+اللى احنا هنستخدمه فى المثال تبعنا ان
+
+188
+00:13:16,840 --> 00:13:19,780
+اذا بدى اشوف القوة مثلا اللى على الاولانى لازم
+
+189
+00:13:19,780 --> 00:13:23,900
+اجيب ال magnetic field اللى بيأثر فيه I واحد على
+
+190
+00:13:23,900 --> 00:13:31,480
+الدلع الاولو بعمل ان i dl across b بقدر اجيب F1
+
+191
+00:13:31,480 --> 00:13:36,300
+على كل التحالي كل القوة هتكون مجموعة يعني انا
+
+192
+00:13:36,300 --> 00:13:39,120
+هجيبهم واحد واحد بس القوة الكلية اللي على ال
+
+193
+00:13:39,120 --> 00:13:43,900
+rectangular loop اللي هو طلبها هتكون F1 زاد F2 زاد
+
+194
+00:13:43,900 --> 00:13:49,330
+F3 زاد F4 مجموعة القوة الأربعةبزم حكيت لازم اجي
+
+195
+00:13:49,330 --> 00:13:55,030
+بالمجال المعطيسى على كل واحد و اقول انه I I DL X B
+
+196
+00:13:55,030 --> 00:13:58,530
+او I L X B لانه قال احنا واضحين بتاعنا او باخد ال
+
+197
+00:13:58,530 --> 00:14:03,210
+element DL و بكامل من مثلا هنا من سفر لاتول تبعه
+
+198
+00:14:03,210 --> 00:14:07,670
+اللي هو B و هكذا نبدأ في ال site الأولى يعني واحد
+
+199
+00:14:07,670 --> 00:14:12,310
+طبعا مشكلة عامة هي ايش هتكون I2 I1
+
+200
+00:14:14,850 --> 00:14:18,530
+هذا هو الواحد والاتنين هذا هو الاتنين الممر فيه ف
+
+201
+00:14:18,530 --> 00:14:24,950
+I تنين DL تنين cross P واحد I تنين DL تنين cross P
+
+202
+00:14:24,950 --> 00:14:27,770
+واحد بكامل على DL تنين و بعدين انا معودة على P
+
+203
+00:14:27,770 --> 00:14:30,410
+واحد بشوف ان انا محتاجة اكامل ولا لا بس احنا
+
+204
+00:14:30,410 --> 00:14:33,850
+حلناها باستخدام ambers law متذكرين مجلة مالاطيسي
+
+205
+00:14:33,850 --> 00:14:37,310
+الجامعه ال infinite line قلنا هذا symmetric بستخدم
+
+206
+00:14:37,310 --> 00:14:43,150
+ambers law اللي هو close integral لب أو h dot dl
+
+207
+00:14:43,150 --> 00:14:48,730
+بتساوي ال enclosed current اتذكرين؟ و dl اللي هو
+
+208
+00:14:48,730 --> 00:14:53,770
+أخدناه بال unit lengths فإيش طلع عندنا كله؟ ال
+
+209
+00:14:53,770 --> 00:14:58,930
+magnetic field الناتج من infinite line mu not I
+
+210
+00:14:58,930 --> 00:15:05,530
+على 2pi rho واضح؟ اتذكرينه؟ في اتجاه Phi hat فال
+
+211
+00:15:05,530 --> 00:15:08,870
+current في هذا الاتجاه دلوقتي هيكون في اتجاه Phi
+
+212
+00:15:08,870 --> 00:15:13,660
+hatبتذكرين؟ حسب ده امبرز لوي يعني ال infinite line
+
+213
+00:15:13,660 --> 00:15:16,320
+حلتها حتى الطريقة التالية و أكتر من طريقة حلنا
+
+214
+00:15:16,320 --> 00:15:19,720
+نذكرها infinite line اذا ال infinite line بس هو
+
+215
+00:15:19,720 --> 00:15:22,200
+أسوأ أسخنان ال closed integral اكشن و TR بتساوي ال
+
+216
+00:15:22,200 --> 00:15:25,880
+enclosed current اللي هو I enclosed هنا في الحالة
+
+217
+00:15:25,880 --> 00:15:28,960
+يعني I enclosed أي واحد فهيكون ايش هو المسار تبع
+
+218
+00:15:28,960 --> 00:15:31,140
+ال اكشن؟ اللي هو ال circle
+
+219
+00:15:34,320 --> 00:15:38,220
+H في اتجاه الـ 5 متأكدين ان دي ال mean هي 2pi لو
+
+220
+00:15:38,220 --> 00:15:44,300
+أخدنا انه مثلا R نصف القطر تبع الدائرة هيكون H 2pi
+
+221
+00:15:44,300 --> 00:15:50,560
+R بتساوي I enclosed فH هتساوي I على 2pi R وH
+
+222
+00:15:50,560 --> 00:15:55,560
+شلقتها B بي على Mu node فهيكون بي بتساوي Mu node I
+
+223
+00:15:55,560 --> 00:15:58,660
+على 2pi R سهلة أحلى على اللوح ولا واضح من ذاكرينها
+
+224
+00:15:59,810 --> 00:16:03,030
+هلاد احنا قداش ال radius بتاع ال circle هناخده
+
+225
+00:16:03,030 --> 00:16:05,130
+هناخده بالطبع ال raw node فانا بدي المجال
+
+226
+00:16:05,130 --> 00:16:11,070
+المناطيسي و المكانه عند الضلع واحد فإيش هيكون مجلة
+
+227
+00:16:11,070 --> 00:16:15,570
+ال field عند هذه النقطة؟ و عبارة عن P بتساوي Mu
+
+228
+00:16:15,570 --> 00:16:19,990
+node I اللي هي المور في هذا ال wire و I واحد على
+
+229
+00:16:19,990 --> 00:16:26,700
+2Pi في ال raw node باضح؟واتجاههم فيهات يعني هو في
+
+230
+00:16:26,700 --> 00:16:29,200
+هذه الحالة في هذه الجهة اللي هو أنا النقطة اللي
+
+231
+00:16:29,200 --> 00:16:33,720
+أنا بتدقيس فيها القوة من اتجاههم ده اتدقيس القوة
+
+232
+00:16:33,720 --> 00:16:33,840
+من اتجاههم ده اتدقيس القوة من اتجاههم ده اتدقيس
+
+233
+00:16:33,840 --> 00:16:35,660
+القوة من اتجاههم ده اتدقيس القوة من اتجاههم ده
+
+234
+00:16:35,660 --> 00:16:41,760
+اتدقيس القوة
+
+235
+00:16:41,760 --> 00:16:48,440
+من اتجاههم
+
+236
+00:16:48,440 --> 00:16:50,960
+ده اتدقيس القوة من اتجاههم ده اتدقيس القوة من
+
+237
+00:16:50,960 --> 00:16:50,960
+اتجاههم ده اتدقيس القوة من اتجاههم ده اتدقيس القوة
+
+238
+00:16:50,960 --> 00:16:50,960
+من اتجاههم ده اتدقيس القوة من اتدقيس القوة من
+
+239
+00:16:50,960 --> 00:16:56,000
+اتدقيس القوة من اتدقيسمش هنأجيب انبرسلو احنا
+
+240
+00:16:56,000 --> 00:17:00,940
+عارفين انه هيك اتجاه الماقنة كتير I هي ال H اللي
+
+241
+00:17:00,940 --> 00:17:06,960
+ال plus بتكراه ال H ال TL تساوي I ال plus قولنا
+
+242
+00:17:06,960 --> 00:17:14,700
+التاني H بتساوي I على 2YR اللي هي R الماقنة كتير
+
+243
+00:17:14,700 --> 00:17:20,640
+اللي احنا عارفين انها اتجاهها هو I بيه هتساوي U
+
+244
+00:17:20,640 --> 00:17:27,680
+non I علىطبعا لو طلعنا على الرسم بتاعتنا احنا هاي
+
+245
+00:17:27,680 --> 00:17:31,200
+المجال معاكس انتجاه الانتمي الكوية اشهرنا اتجاهه
+
+246
+00:17:31,200 --> 00:17:35,460
+هكذا داخل فعند هاي النقطة اللي بيكون اتجاهه ده جوا
+
+247
+00:17:35,460 --> 00:17:45,010
+هاي ال current وهي انجام داخل وطالب واضر هنا داخلو
+
+248
+00:17:45,010 --> 00:17:48,390
+من الجهة التانية اش هيكون طرف انا لو بدأ اخط لو
+
+249
+00:17:48,390 --> 00:17:51,550
+لازم يبص مش لازم هنا هبكون نقاطي هنا هيكون داخل
+
+250
+00:17:51,550 --> 00:17:54,990
+هيكون هو الطرف منها الى الساعة لما فى سنة احنا
+
+251
+00:17:54,990 --> 00:17:58,250
+عرفنا ان مجرد ما انا قاعدة يسي هنا اش هيكون B knot
+
+252
+00:17:58,250 --> 00:18:03,430
+يعني شهية كتير من الوقت بس هعوض عن R بقى ايه اش ال
+
+253
+00:18:03,430 --> 00:18:10,390
+raw raw knot و Psychic يعني الحمد لله اشتغلت عليكم
+
+254
+00:18:10,390 --> 00:18:11,970
+هيكون B
+
+255
+00:18:15,390 --> 00:18:23,210
+ميو نوت في اي واحد على two by رو نوت اهنا بالتمام
+
+256
+00:18:23,210 --> 00:18:26,590
+هنا المجال المعناطيسي هنا في اتجاهه اللي هو الواحد
+
+257
+00:18:26,590 --> 00:18:31,550
+تمام في اس سبحت هنا اذا هذا المجال المعناطيسي اللي
+
+258
+00:18:31,550 --> 00:18:34,910
+بأثر فيه القرع باي واحد على هذا الدلال لو على
+
+259
+00:18:34,910 --> 00:18:39,430
+الدلال ال بعيد مش هيكون رو نوت زائد ايه نفس
+
+260
+00:18:39,430 --> 00:18:40,870
+الاتجاه رهاد
+
+261
+00:18:44,620 --> 00:18:48,420
+هو في كل نتفة داخل بس انا بدي على هذه النقطة وعلى
+
+262
+00:18:48,420 --> 00:18:50,720
+هذه النقطة انا بدي ال current ال force اللي بيأثر
+
+263
+00:18:50,720 --> 00:18:54,820
+فيها المجاري المناطيسي المتولد من التيار المر في
+
+264
+00:18:54,820 --> 00:18:58,600
+ال filement الأولى على الدلع الأول و مرة تانية على
+
+265
+00:18:58,600 --> 00:19:05,660
+الدلع التالت نفس الحكاية اللي هيكون المجاري
+
+266
+00:19:05,660 --> 00:19:09,920
+المناطيسي المتولد في كل نقطة هيكون ده بس هنا هيكون
+
+267
+00:19:09,920 --> 00:19:13,610
+على بعد raw node هنا هيكون على بعداللي هو Ronald
+
+268
+00:19:13,610 --> 00:19:18,850
+plus A هنا متغير البعد ما بين رونالد لرونالد plus
+
+269
+00:19:18,850 --> 00:19:23,070
+A صحيح؟
+
+270
+00:19:23,070 --> 00:19:29,830
+هنشوف
+
+271
+00:19:29,830 --> 00:19:34,470
+القورة هنضغط مسحها داكي عشان ما يدخلش على الواحد
+
+272
+00:19:35,260 --> 00:19:39,180
+نبدأ فى الأولى الفرصة الأولى أنها I تنين DL تنين
+
+273
+00:19:39,180 --> 00:19:42,740
+اللى هو هدا ال line الأولانى اللى طوله بتغير من
+
+274
+00:19:42,740 --> 00:19:49,020
+سفر لمين ل B من سفر ل B يعني إيش ال DL بتاعته DZ
+
+275
+00:19:49,020 --> 00:19:56,320
+DL هى DZ زدهات DL DZ زدهات across B اللى هنا
+
+276
+00:19:56,320 --> 00:20:00,800
+شفناها مع بعض هنكون تجاه قائهات قيمتها ميو نوت I
+
+277
+00:20:00,800 --> 00:20:06,050
+واحد على two by remoteاذا عندنا ال z هتطير من zero
+
+278
+00:20:06,050 --> 00:20:10,650
+ل b, z hat cross phi hat هتكون موجهه ولا سالفه نفس
+
+279
+00:20:10,650 --> 00:20:19,130
+القضية تذكر ان قلنا rho phi z, z cross phi hat
+
+280
+00:20:19,130 --> 00:20:22,850
+هتكون minus rho hatفزا ما هيكون الاتجاه في السالب
+
+281
+00:20:22,850 --> 00:20:27,130
+رو هات هي أول حاجة التكمل طبعا زاد سهل هيكون من
+
+282
+00:20:27,130 --> 00:20:31,670
+صفر ل بيه نحط بينا بيه فزا نهاش هيكون ناتج I تنين
+
+283
+00:20:31,670 --> 00:20:34,630
+في I واحد في ميو نوت في بيه على طول by رو نوت
+
+284
+00:20:34,630 --> 00:20:38,530
+واتجاهه minus رو هات هذه ال F على الواحد نفس
+
+285
+00:20:38,530 --> 00:20:42,850
+الكلام بنعيده على F اللي هي قلنا الاطلاع البعيد
+
+286
+00:20:42,850 --> 00:20:45,970
+تلاتة سمناها تلاتة
+
+287
+00:20:50,960 --> 00:20:59,020
+بس الفرقية انه هنغير قيمة ال رو هتكون رو نود زائد
+
+288
+00:20:59,020 --> 00:21:03,020
+اه تمام؟ و ال integration هيكون من مين بدل من zero
+
+289
+00:21:03,020 --> 00:21:07,660
+ل بي هيكون من بي ل zero عن اتجاه ال current جاي من
+
+290
+00:21:07,660 --> 00:21:11,460
+فوق لتحت هيكون من بي ل zero يعني في تغيرون بسطين
+
+291
+00:21:11,460 --> 00:21:15,760
+ان بدل رو هتكون رو نود زائد اه و ال current بتغير
+
+292
+00:21:15,760 --> 00:21:20,950
+من اللي هي بي ل zeroz hat cross phi hat minus rho
+
+293
+00:21:20,950 --> 00:21:25,230
+hat وعندي كمان minus v جي من تكمل ال z هتعطينا z
+
+294
+00:21:25,230 --> 00:21:28,830
+من zero بيه هتعطينا minus v فبتصير plus rho hat و
+
+295
+00:21:28,830 --> 00:21:32,550
+الباقى هيكون نفس الشيء u naught I1 I2 على two pi
+
+296
+00:21:32,550 --> 00:21:39,410
+rho naught plus a تمام؟ اذا القوة اللى ناجح من ال
+
+297
+00:21:39,410 --> 00:21:46,640
+current المورفي ال line علىالصيد الأول سالب رو هات
+
+298
+00:21:46,640 --> 00:21:51,720
+اتجاهها سالب رو هات هذه رو هات لأنه لو أخدناها
+
+299
+00:21:51,720 --> 00:21:58,240
+سليندركا اتجاه الفاية هذه رو هات صح؟ أخ واحد سالب
+
+300
+00:21:58,240 --> 00:22:03,780
+رو هات إيش نوع رو هات إتجازه 8 مرة هذا سليندركا
+
+301
+00:22:03,780 --> 00:22:07,820
+يعني احنا أخدناها هيك المجال المناطسي وهذه الرو
+
+302
+00:22:07,820 --> 00:22:10,500
+هات يعني احنا ماخدين إيش اتجاهها وهذا الفاية
+
+303
+00:22:10,500 --> 00:22:17,510
+سليندركا الكوربينة ديصح؟ إذا هذا هو اتجاه الروهات
+
+304
+00:22:17,510 --> 00:22:22,450
+و هذا ال minus روهات إذا بنطلع على التاني في ال
+
+305
+00:22:22,450 --> 00:22:26,950
+currents لما يكونوا بنفس الاتجاه عكس المعنى ال
+
+306
+00:22:26,950 --> 00:22:29,910
+currents بتتفق في نفس اتجاه نوع القوة إيش بتكون
+
+307
+00:22:29,910 --> 00:22:34,670
+تجاذب هذه أنا بتجذب هذا ال current أنا بيزف هذا ال
+
+308
+00:22:34,670 --> 00:22:38,230
+current معاه عكس ال charges لما نقول نجد .. بصي في
+
+309
+00:22:38,230 --> 00:22:41,330
+نجد في ال charge بالساعة و بتجاذبه يعني عندي تيرين
+
+310
+00:22:41,330 --> 00:22:46,670
+بنفس الاتجاه جاذبوا عنيإذا لاحظت إنه ال line اللي
+
+311
+00:22:46,670 --> 00:22:51,290
+مور في ال current أي واحد، إيش بيسويه؟ بالزب،
+
+312
+00:22:51,290 --> 00:22:56,150
+بالزب بيعمل عملية جاذب ل ال current اللي بتدفق في
+
+313
+00:22:56,150 --> 00:22:59,550
+ال line اللي نفس الاتجاه، بيطلع على ال bait، ال
+
+314
+00:22:59,550 --> 00:23:02,910
+side of ال bait، ال current ماله معاكس الاتجاه إذا
+
+315
+00:23:02,910 --> 00:23:07,570
+انه revulsive، plus rho hat، واضح؟ إذا هذه كنت
+
+316
+00:23:07,570 --> 00:23:10,730
+تذكروها، لما ال current مور في ال two wires، اللي
+
+317
+00:23:10,730 --> 00:23:13,710
+نفس الاتجاه، تجازب، واحد عكس، تنفر
+
+318
+00:23:18,530 --> 00:23:21,390
+مثبتة experimentally و احنا كمان هينا شفناها
+
+319
+00:23:21,390 --> 00:23:24,570
+theoretical نظرية لما يكونوا التيارين في نفس
+
+320
+00:23:24,570 --> 00:23:29,450
+الاتجاه هيكون في عملية تجاذب متعاكسين بيكون عملية
+
+321
+00:23:29,450 --> 00:23:34,210
+تناقص و مين ضال عندنا F2 و F4 هنا DL ايش اللي
+
+322
+00:23:34,210 --> 00:23:39,570
+هتكون DL2؟ اللي دي raw هنا هتكون دي raw و بتروح من
+
+323
+00:23:39,570 --> 00:23:45,000
+raw node ل non-rod plus Aنجي نعمل اللي هي
+
+324
+00:23:45,000 --> 00:23:48,620
+afternoon هيكون عندنا التكامل من row node ل row
+
+325
+00:23:48,620 --> 00:23:52,140
+node plus ا و بدل دي زد ايش هيكون دي row row her
+
+326
+00:23:52,140 --> 00:23:55,940
+across بيقلي نفسها قولنا نفسها و كلهم داخلين في
+
+327
+00:23:55,940 --> 00:24:00,240
+هالجهة row node اي واحد اتوه by row فايهاد row
+
+328
+00:24:00,240 --> 00:24:05,900
+cross five ايش بيكون ايها row cross across five
+
+329
+00:24:05,900 --> 00:24:11,660
+ايش هتكون زدهاد row cross five زدهادرو هنكملها من
+
+330
+00:24:11,660 --> 00:24:16,920
+رو نود لرو نود plus A لكن هنلاحظ أنه في عند دي رو
+
+331
+00:24:16,920 --> 00:24:21,140
+على رو كله بيطلع برا ال integral هي I تنين و I
+
+332
+00:24:21,140 --> 00:24:27,960
+واحد و مي نود و ال .. ال .. ال .. هي ال unit
+
+333
+00:24:27,960 --> 00:24:31,720
+vector زدها على two pi كله بيطلع بضم عند دي رو على
+
+334
+00:24:31,720 --> 00:24:34,900
+رو ال integration من رو زيرو لرو زيرو plus A دي رو
+
+335
+00:24:34,900 --> 00:24:38,800
+على رو اللي هي اللان دي رو على رو حيث أن اللي بيضل
+
+336
+00:24:38,800 --> 00:24:43,820
+جوا ال integralمن رو نود لرو نود plus a كله بيطلع
+
+337
+00:24:43,820 --> 00:24:47,940
+في ال integer بال D رو على رو يبقى تكون len ال raw
+
+338
+00:24:47,940 --> 00:24:53,800
+من رو نود لرو نود plus a هتكون len ال raw نود plus
+
+339
+00:24:53,800 --> 00:24:59,040
+a minus len ال raw نود اللي هي عبارة عن len ال raw
+
+340
+00:24:59,040 --> 00:25:00,760
+نود plus a على
+
+341
+00:25:08,870 --> 00:25:13,770
+القضيب او على الجزء من ال rectangle ان هي في تجاه
+
+342
+00:25:13,770 --> 00:25:17,370
+ال raw hat ال current في تجاه ال raw hat كانت
+
+343
+00:25:17,370 --> 00:25:20,790
+القوة على تجاه positive z hat افتنين في تجاه
+
+344
+00:25:20,790 --> 00:25:25,030
+positive z hat دال من عندنا اللي هو الدلع الأخير
+
+345
+00:25:25,030 --> 00:25:28,890
+اللي هو الرابع نفس الحاجة هتكون mean ان دي raw دي
+
+346
+00:25:28,890 --> 00:25:32,850
+z هي دي raw raw hat والتكامل هيكون من raw node
+
+347
+00:25:32,850 --> 00:25:34,830
+plus a ل raw node
+
+348
+00:25:37,600 --> 00:25:40,780
+إذن التكامل عندنا من raw node plus a ل raw node و
+
+349
+00:25:40,780 --> 00:25:45,100
+دي z هي دي raw raw hat دي ال .. دي raw raw hat
+
+350
+00:25:45,100 --> 00:25:48,460
+cross mu node أي واحد phi hat ع two by raw إن ال
+
+351
+00:25:48,460 --> 00:25:53,000
+raw hat cross phi hat إيش هتكون؟ raw hat cross phi
+
+352
+00:25:53,000 --> 00:25:57,580
+hat برضه ال z hat لكن لما نيجي نعمل ال integration
+
+353
+00:25:57,580 --> 00:26:05,370
+إيش هيكون عندى؟ raw hat cross phi hatرو فاتر وزدها
+
+354
+00:26:05,370 --> 00:26:08,770
+اتنان لما نيش نكمل برضه نفس الحاجة ماننساش ان في
+
+355
+00:26:08,770 --> 00:26:12,730
+عند D رو على رو بس من وين من رو ند plus A لرو رو
+
+356
+00:26:12,730 --> 00:26:18,590
+ند يعني هيكون عند التكامل D رو على رو من وين من رو
+
+357
+00:26:18,590 --> 00:26:21,810
+ند plus A لرو الفرقية بينها أي حيكون في إشارة
+
+358
+00:26:21,810 --> 00:26:25,890
+سالفة عشان أخليها تبين زي هيك هتكون minus length
+
+359
+00:26:25,890 --> 00:26:33,520
+رو plus A على رو ند صح هتكون length رو ندعلى
+
+360
+00:26:33,520 --> 00:26:38,160
+Ronald plus A يعني هي تسوى سالق لان ال Ronald plus
+
+361
+00:26:38,160 --> 00:26:43,560
+A معايا هاي نجلة من الإشهار السالق إذا ماحيكون F4
+
+362
+00:26:43,560 --> 00:26:48,700
+بتسوى minus Mu null I1 فI2 على 2I لان Ronald plus
+
+363
+00:26:48,700 --> 00:26:54,390
+A على 0 اتجاه is it thatوحدة في اتجاه الـ boost في
+
+364
+00:26:54,390 --> 00:27:00,170
+زدها والتانية في السانر في زدها يعني اذا طلعت
+
+365
+00:27:00,170 --> 00:27:04,010
+بلاحظ اذا كان في عندي قضيب في اتجاه ال current
+
+366
+00:27:04,010 --> 00:27:08,410
+تبعه عمودي على ال current اللي بمر فيه السبب
+
+367
+00:27:08,410 --> 00:27:11,610
+المسبب ل magnetic field اللي بيحدث في القوة هتكون
+
+368
+00:27:11,610 --> 00:27:17,030
+القوة مالها موازية بسميها قوة موازية يعني افعل هذا
+
+369
+00:27:17,030 --> 00:27:23,030
+القضي مالها موازية لاتجاه التيارو F4 موازي يعني
+
+370
+00:27:23,030 --> 00:27:26,170
+anti-parallel يعني هذه بالاتجاه الزدها ت الاتجاه
+
+371
+00:27:26,170 --> 00:27:30,750
+السالب زدها بس مالها parallel إذا لو كان الطيار
+
+372
+00:27:30,750 --> 00:27:34,550
+الطيارين في نفس الاتجاه هتكون attractive واحد
+
+373
+00:27:34,550 --> 00:27:38,490
+معاكس هتكون repulsive لو كان اتجاه الطيار ماله
+
+374
+00:27:38,490 --> 00:27:42,110
+عمودي على اتجاه المجال مع ناطيسيا أو يعني عمودي
+
+375
+00:27:42,110 --> 00:27:47,870
+على اتجاه الطيار هيكون إيش نوع القوة موازيةبعتمد
+
+376
+00:27:47,870 --> 00:27:52,590
+ازا بعيدة ولا قريبة، اذا بعيد التيار هتكون في نفس
+
+377
+00:27:52,590 --> 00:27:56,770
+الاتجاه، اذا التيار بقترب بتكون في عكس الاتجاه، زي
+
+378
+00:27:56,770 --> 00:28:00,470
+ما انتوا شايفينه، التيار بتاعت معناه انها القوة
+
+379
+00:28:00,470 --> 00:28:07,050
+لفوق، التيار جايب في ناحيته هيكوننفس المقدار إذا
+
+380
+00:28:07,050 --> 00:28:12,990
+طلعنا على F3 و F4 فهو نفس المقدار بس الاتجاه ماله
+
+381
+00:28:12,990 --> 00:28:16,510
+معاكس واحد في اتجاه الزدهات والثاني في اتجاه السلب
+
+382
+00:28:16,510 --> 00:28:19,350
+زدهات لو جمعناها مع بعضاش برضه اعطونا سفر يعني
+
+383
+00:28:19,350 --> 00:28:23,130
+احنا على كل القوة مانها مجموعة هذه القوةالقوة
+
+384
+00:28:23,130 --> 00:28:27,210
+الكلية مجموعة القوة على الدلع الأول زي الدلع
+
+385
+00:28:27,210 --> 00:28:30,270
+التاني زي الدلع التاني زي الدلع الرابع هنلاحظ أنه
+
+386
+00:28:30,270 --> 00:28:32,930
+لما نجمع هدولة مع بعض حياتهم نصفر مية بيظل لنا
+
+387
+00:28:32,930 --> 00:28:39,670
+القوة اللي مأسرة على واحد و تلاتة لما نجمعهم لو
+
+388
+00:28:39,670 --> 00:28:44,330
+أخدنا السالب ع المشترك هيكون عند ميو نود I1I2 بي
+
+389
+00:28:44,330 --> 00:28:49,370
+على two by رو نود وهذا بيصير سالب ميو نود I1I2 بي
+
+390
+00:28:49,370 --> 00:28:54,150
+على اتنين by رو نود زي ات او روهاد لبرا بيطلع من
+
+391
+00:28:54,150 --> 00:28:58,330
+كل شي لو طلعنا برا ال mu node اي واحد اي اتنين بي
+
+392
+00:28:58,330 --> 00:29:01,130
+على اتنين باي بيطلع عندي واحد على ال raw node
+
+393
+00:29:01,130 --> 00:29:04,210
+minus واحد على ال node plus ايه اللي هو الحاجة
+
+394
+00:29:04,210 --> 00:29:09,450
+المطلوبة مني اكتب فياها
+
+395
+00:29:09,450 --> 00:29:14,570
+لو جمعنا هدول القواتين اللي ضالوا اللي مش هيكون
+
+396
+00:29:14,570 --> 00:29:24,250
+مجموعهم سفر هيكون F total minus ال mu nodeI1 I2 بي
+
+397
+00:29:24,250 --> 00:29:27,690
+على 2 بقى ايش بتبقى من هنا I1 I2 بي على 2 بقى ايش
+
+398
+00:29:27,690 --> 00:29:28,710
+بتبقى من هنا I1 I2 بي على 2 بقى ايش بتبقى من هنا
+
+399
+00:29:28,710 --> 00:29:31,010
+I1 I2 بي على 2 بقى ايش بتبقى من هنا I1 I2 بي على 2
+
+400
+00:29:31,010 --> 00:29:31,690
+بقى ايش بتبقى من هنا I1 I2 بي على 2 بقى ايش بتبقى
+
+401
+00:29:31,690 --> 00:29:31,950
+من هنا I1 I2 بي على 2 بقى ايش بتبقى من هنا I1 I2
+
+402
+00:29:31,950 --> 00:29:33,250
+بي على 2 بقى ايش بتبقى من هنا I1 I2 بي على 2 بقى
+
+403
+00:29:33,250 --> 00:29:34,890
+ايش بتبقى من هنا I1 I2 بي على 2 بقى ايش بتبقى من
+
+404
+00:29:34,890 --> 00:29:41,490
+هنا I1 I2 بي على 2 بقى ايش بتبقى من هنا I1
+
+405
+00:29:41,490 --> 00:29:43,690
+I2
+
+406
+00:29:49,510 --> 00:29:52,670
+المقام أكبر، هذا رنود، هذا رنود بصير، فالمقام
+
+407
+00:29:52,670 --> 00:29:55,930
+أكبر، يعني هذا رنود ماله أقل من هذا، يعني هذا كله
+
+408
+00:29:55,930 --> 00:30:01,010
+على بعض ماله مجد، بس كذا الإشارة السالبة و الضهر
+
+409
+00:30:01,010 --> 00:30:06,450
+السالب، إذا إيش نقولته؟ attractive، بالظبط قعدت،
+
+410
+00:30:06,450 --> 00:30:11,110
+ما نصرها، attractive،
+
+411
+00:30:11,110 --> 00:30:14,490
+attractive، قعدت بالظبط، كله قعدت بالظبط، كله
+
+412
+00:30:14,490 --> 00:30:18,200
+نحيته، ال total force مالها attractiveهي ال total
+
+413
+00:30:18,200 --> 00:30:22,560
+force of total اللي هي مجموهم كلهم واحد و اتنين و
+
+414
+00:30:22,560 --> 00:30:26,160
+تلاتة و اربع لقينا ان تلاتة و اربع cancel مع بعض
+
+415
+00:30:26,160 --> 00:30:29,280
+بيساوي بعض في المقدار و الإشارة سالبة ضال عندي
+
+416
+00:30:29,280 --> 00:30:34,980
+واحد ويه اللي هو اربع اتنين واحد و تلاتة مجموهم
+
+417
+00:30:34,980 --> 00:30:39,280
+كلهم attractive ايش طبيعي هذه ال robots مالها أبعد
+
+418
+00:30:39,280 --> 00:30:43,700
+المسافة أبعدلكن هذه أقرب فإيش طبيعي أن يكون ال
+
+419
+00:30:43,700 --> 00:30:47,120
+attractive أقوى من ال passive فمجموحهم هيكون ال
+
+420
+00:30:47,120 --> 00:30:51,340
+total force هي attractive تجاهها minus rho hat
+
+421
+00:30:51,340 --> 00:30:56,820
+واضحة؟ طب أخر حاجة اللي هي ال magnetic torque and
+
+422
+00:30:56,820 --> 00:31:01,060
+moment تعريف
+
+423
+00:31:01,060 --> 00:31:04,360
+أول حاجة ال torque أنتم متذكرين ال torque هي R
+
+424
+00:31:04,360 --> 00:31:09,100
+cross F متذكرينه أحطته العزوم؟torque or mechanical
+
+425
+00:31:09,100 --> 00:31:12,300
+moment of force on a loop is the vector product of
+
+426
+00:31:12,300 --> 00:31:16,480
+the force and the moment arm اللي هو زراع العزم
+
+427
+00:31:16,480 --> 00:31:20,460
+بنسميه، ذاكرين كنتوا يسموه زراع العزم و العزم و
+
+428
+00:31:20,460 --> 00:31:24,880
+القوة، طب إذا عندنا ال torque هو حاصل أو ال cross
+
+429
+00:31:24,880 --> 00:31:29,580
+product لزراع العزم R cross F اللي هي القوة
+
+430
+00:31:29,580 --> 00:31:30,880
+المؤثرة
+
+431
+00:31:34,790 --> 00:31:41,330
+لو احنا بنطبق هذا الحكيم على sliding يعني تقريبا
+
+432
+00:31:41,330 --> 00:31:44,450
+نفس الشكل اللي احنا شوفناه بس هنغير اتجاهات ال
+
+433
+00:31:44,450 --> 00:31:50,650
+loop و القوة مش التوح اللي هنا عليه القوة بس هذا
+
+434
+00:31:50,650 --> 00:31:55,470
+ال rectangular loop هيكون له طول L و عرضه Wوبدنا
+
+435
+00:31:55,470 --> 00:31:57,590
+نحطه في reform magnetic field ما هو المثال اللي
+
+436
+00:31:57,590 --> 00:32:00,570
+طبعا جيبنا القوة عليه كان loop في مجال معناطيسي
+
+437
+00:32:00,570 --> 00:32:04,210
+متظن، من وين جاي؟ عارفين احنا من وين جاي، جاي من
+
+438
+00:32:04,210 --> 00:32:07,470
+select morphic karate فكان loop موجود في مجال
+
+439
+00:32:07,470 --> 00:32:11,150
+معناطيسي متظن داخل في قلب الصفحة صح؟ نفس ال loop
+
+440
+00:32:11,150 --> 00:32:13,670
+بس احنا هنغير ال coordinates، loop موجود في مجال
+
+441
+00:32:13,670 --> 00:32:17,600
+معناطيسيطوله L و عرضه W in order for magnetic
+
+442
+00:32:17,600 --> 00:32:21,240
+field B from this figure ويتنقل .. طبعا خلنا نشوف
+
+443
+00:32:21,240 --> 00:32:24,340
+إيش الوضع تبعنا إيش شكل ال force و إيش شكل ال
+
+444
+00:32:24,340 --> 00:32:27,060
+magnetic field هنا ال magnetic field مش طالع من
+
+445
+00:32:27,060 --> 00:32:32,500
+برا الصفحة في نفس الصفحة يعني مش عمودي على كل أطلع
+
+446
+00:32:32,500 --> 00:32:37,980
+المستطيل كان المثل اللي أخدناه قبل قليل ال loop
+
+447
+00:32:37,980 --> 00:32:42,000
+هيكي و المجال المناطيسي ماله عمودي على كل أطلع ال
+
+448
+00:32:42,000 --> 00:32:47,100
+loopهنا ال magnetic field بهذا الاتجاه عمودي فقط
+
+449
+00:32:47,100 --> 00:32:50,960
+على الدلعين اللي هنا لكن في نفس اتجاه التيار اللي
+
+450
+00:32:50,960 --> 00:32:55,580
+في ال .. او يعني في نفس اللي هو اتجاه او يعني اللي
+
+451
+00:32:55,580 --> 00:32:59,640
+تبع الدلعين اللي فوق و تحت طبعا؟ طبعا التيار
+
+452
+00:32:59,640 --> 00:33:02,520
+يعطينا اتجاه التيار يعني هنا بيكون ال magnetic في
+
+453
+00:33:02,520 --> 00:33:05,960
+اتجاه التيار هنا بس في عكس اتجاه التيار هي التيار
+
+454
+00:33:05,960 --> 00:33:11,660
+اتجاه السهم هذا اللي ممر في اللوغ طوله L عرضه W
+
+455
+00:33:15,490 --> 00:33:20,050
+القوة اللى على CD وAB إحنا إيش تعرف القوة قلنا؟
+
+456
+00:33:20,050 --> 00:33:25,790
+عبارة عن IL IL اللى هو ال current بور في cross B
+
+457
+00:33:25,790 --> 00:33:28,990
+في نماذجهم في نفس الاتجاه ال cross product بتاعهم
+
+458
+00:33:28,990 --> 00:33:33,550
+zeroصح؟ مافيش زاوية و تسعين درجة بينهم سفر الزاوية
+
+459
+00:33:33,550 --> 00:33:38,490
+بينهم sin 00 نفس الاشي هنا الزاوية بينهم 180 هيكل
+
+460
+00:33:38,490 --> 00:33:41,790
+cross product سفر إذا القوة اللي بيأثرها المجال
+
+461
+00:33:41,790 --> 00:33:48,110
+المناطيسي على ضلع CD على ضلع AB ماله سفر لكن القوة
+
+462
+00:33:48,110 --> 00:33:53,850
+اللي على ال BC و DA معلها لا تساو سفر لأن ال I و
+
+463
+00:33:53,850 --> 00:33:56,970
+ال B في بينهم زاوية تسعين درجة ف I cross B في
+
+464
+00:33:56,970 --> 00:34:02,170
+زاوية بينهم لا تساو سفرأو يعني أنه فيه زاوية فهو
+
+465
+00:34:02,170 --> 00:34:06,530
+فيه زاوية بس يعني أنه مش سفر أوي بتبقى اذا ال
+
+466
+00:34:06,530 --> 00:34:09,550
+total force هتكون لو أنا بتحسب ال total force زي
+
+467
+00:34:09,550 --> 00:34:14,990
+ما عملنا هيكون فينا two sides اللي هي ال force two
+
+468
+00:34:14,990 --> 00:34:19,230
+sides قلنا ال force فيهم سفر بتلقى اللي هو ال two
+
+469
+00:34:19,230 --> 00:34:23,090
+loops اللي عندنا هو بسميهم zero واحد اتنين تلاتة
+
+470
+00:34:23,090 --> 00:34:25,390
+اربعة يعني فعندنا ال woman's side
+
+471
+00:34:29,280 --> 00:34:32,500
+هيكون عندها ال loop الأولاني اللي هو I DL cross B
+
+472
+00:34:32,500 --> 00:34:37,000
+أو ال side الأولاني ذات I ال integral من 4 على 1
+
+473
+00:34:37,000 --> 00:34:42,220
+DL cross B هنا هيكون من 0 لأقل، مش من 0 لأقل،
+
+474
+00:34:42,220 --> 00:34:46,160
+لأنها من 0 لأقل لاتجاه التيار وهذا الاتجاه، هنا
+
+475
+00:34:46,160 --> 00:34:52,260
+هيكون من أقل ل0 اذا
+
+476
+00:34:52,260 --> 00:34:56,540
+ال integral الأولاني هيكون I ال integral من 0
+
+477
+00:34:56,540 --> 00:35:06,120
+لأقل، واش تجاهه؟دى زد دى
+
+478
+00:35:06,120 --> 00:35:10,620
+زد زد هات cross P دى زد زد هات cross P فدى زد اش
+
+479
+00:35:10,620 --> 00:35:14,940
+حاططينا فى هالحالة L وضل ال cross product بين اللى
+
+480
+00:35:14,940 --> 00:35:19,240
+هى زد و بيه هنا نيجي كام مرة I ال integral من L ل
+
+481
+00:35:19,240 --> 00:35:25,420
+Zero اتجاه القرن من L ل Zero واتجاهه زد هات
+
+482
+00:35:29,220 --> 00:35:34,600
+ز من ال لزيرو ز هتكروس بي بضوء ز هتعطينا هنا سالب
+
+483
+00:35:34,600 --> 00:35:37,760
+ال يعني هنا هتعطينا ال و هنا سالب ال و هنا ز
+
+484
+00:35:37,760 --> 00:35:41,700
+هتكروس بي و هنا ز هتكروس بي نفس القيام تبهين معايا
+
+485
+00:35:41,700 --> 00:35:49,180
+عندي I I ز اللي هي من زرو لأل هتعطينا I L إيش بضلع
+
+486
+00:35:49,180 --> 00:35:55,480
+هنا ز هتكروس بي و هنا هيكون minus I L ز هتكروس بي
+
+487
+00:35:55,480 --> 00:35:58,720
+نفس المقدار ولتجاه ماله مخالف
+
+488
+00:36:02,490 --> 00:36:06,130
+القوة الأولى ايش هتعطينا اي او ال term الأولاني
+
+489
+00:36:06,130 --> 00:36:11,410
+هتعطينا I L زي ذات cross P والterm التاني هتعطينا
+
+490
+00:36:11,410 --> 00:36:20,030
+minus I L زي ذات cross P ما هو ب cross my total
+
+491
+00:36:20,030 --> 00:36:26,070
+force صفر لكن لو طلعنا الدقة مش هلاحظ أن ال object
+
+492
+00:36:26,070 --> 00:36:30,330
+هذا ساكنمش هيكون في حالة سكون، القوة لو تكون
+
+493
+00:36:30,330 --> 00:36:34,030
+ساكنة، المفروض يا بيكون في .. بيمشي بسرعة منتظمة
+
+494
+00:36:34,030 --> 00:36:36,310
+يا ساكن، هنا مش قيلنا إنه قاعد بيتحرك بسرعة
+
+495
+00:36:36,310 --> 00:36:41,490
+منتظمة، إيش بسله؟ بلوف، ليش بلوف؟ لإن النقاطين
+
+496
+00:36:41,490 --> 00:36:44,370
+هدولة مش قاعدين على نفس العمود، يعني لو قاعدين على
+
+497
+00:36:44,370 --> 00:36:48,070
+نفس ..النقطة بيأثروا على نفس النقطة، هيكون في
+
+498
+00:36:48,070 --> 00:36:52,210
+توازن، هي cancelوا بعض و مش هيصير أي دوران لأقله،
+
+499
+00:36:52,210 --> 00:36:55,970
+لكن الواضح أن واحدة و التانية في بينهم مسافة،
+
+500
+00:36:55,970 --> 00:37:01,990
+واحدة اتجاهها، اللي هي عكس اتجاه التاني، اتعكس B،
+
+501
+00:37:01,990 --> 00:37:05,030
+والتانية في اتجاه المعكس، ال magnitude تبعهم اذا
+
+502
+00:37:05,030 --> 00:37:08,190
+معلوم متساوي، لو بدأت طالع على ال magnitude، لو
+
+503
+00:37:08,190 --> 00:37:15,520
+سميتها هذه F modالـ magnitude بتاع التنتين هي ساوي
+
+504
+00:37:15,520 --> 00:37:21,020
+I ألف ال magnitude بتاع بي و الـ z هت cross
+
+505
+00:37:21,020 --> 00:37:27,380
+الاتجاه بتاع بي هو اللي هيعطينا الاتجاه تبع ال F0
+
+506
+00:37:27,380 --> 00:37:33,480
+تمام؟ اذا عندنا ال magnitude يعني هو اسمها F0
+
+507
+00:37:33,480 --> 00:37:39,880
+vector minus F0 فدي كلها اسمها F0 vectorمينوس
+
+508
+00:37:39,880 --> 00:37:44,600
+أفنود فإذا المقدار تبع أفنود هو I أقل في مين في
+
+509
+00:37:44,600 --> 00:37:47,460
+المجموعة تبع بيه فانحنا هيتولد Z hat cross اتجاه
+
+510
+00:37:47,460 --> 00:37:51,180
+ال بيه لهم مثلا X hat او احنا متبع الاتجاه المحلي
+
+511
+00:37:51,180 --> 00:37:55,640
+المواضر اذا أفنود لهم نفس المقدار مش هو عيين على
+
+512
+00:37:55,640 --> 00:38:00,220
+نفس الأسروشة نفس النقطة هو حط القوة مش نفس الحط
+
+513
+00:38:00,220 --> 00:38:04,260
+فبالتالي فيه هيتولد torque واحدة منهم أفنود واحدة
+
+514
+00:38:04,260 --> 00:38:07,820
+minus أفنود في إشارة سلمة بينهم تاني
+
+515
+00:38:10,290 --> 00:38:14,670
+عشان هيك قولنا هذا بيسببلنا ازدواج و بيعملنا عزم
+
+516
+00:38:14,670 --> 00:38:18,570
+ازدواج و هيلف ال loop في وجود المجال المعناطي لسه
+
+517
+00:38:18,570 --> 00:38:24,510
+ال torque احنا بنعرف ايش هو F knot في اللي هو
+
+518
+00:38:24,510 --> 00:38:27,390
+الزراع ال arm ال magnitude دي دي بالكم احنا قولنا
+
+519
+00:38:27,390 --> 00:38:32,430
+هو R cross F يعني ال magnitude تبع R في F F اللي
+
+520
+00:38:32,430 --> 00:38:37,890
+هي انا F knot سمناها و الزراع تبعنا هيكون ال بالة
+
+521
+00:38:37,890 --> 00:38:42,770
+التنتين لو مدينا هذا على طولههي هتكون الزراع اش
+
+522
+00:38:42,770 --> 00:38:47,530
+بيساوي هاي الزاوية هتكون نفسها Alpha هيكون الزراع
+
+523
+00:38:47,530 --> 00:38:53,950
+أو هذا العمود بينهم اش بيساوي W Sin Alpha واضر W
+
+524
+00:38:53,950 --> 00:38:56,530
+Sin Alpha مش هذا اللي على فول هذا اللي هو الزراع
+
+525
+00:38:56,530 --> 00:39:01,390
+اللي بينهم هيكون ايش W Sin Alpha هاي الزاوية
+
+526
+00:39:01,390 --> 00:39:05,290
+بتساوي نفس الزاوية اللي هنا معايا ألسمها ولا
+
+527
+00:39:05,290 --> 00:39:05,990
+بأضحك؟
+
+528
+00:39:15,340 --> 00:39:23,280
+هذه تكمل هذه وهذه تكمل هذه فهذه Alpha هذه
+
+529
+00:39:23,280 --> 00:39:28,700
+تكمل هذه وهذه تكمل هذه فهذه Alpha وهذا اللي انا
+
+530
+00:39:28,700 --> 00:39:34,100
+بديه ايش هيكون Sine Alpha ايش بالساوية تظهر اللي
+
+531
+00:39:34,100 --> 00:39:40,920
+انا بديه مثلا X على W ف X بالساوية W Sine Alpha
+
+532
+00:39:40,920 --> 00:39:43,000
+واضح؟ هاي ال R تبعه هو
+
+533
+00:39:46,650 --> 00:39:51,470
+التوك بيساوي قيمة if not اللي هو الشي اللي بتساوي
+
+534
+00:39:51,470 --> 00:40:00,180
+IL في B في BT Wsin α اللي هو الذراع القوة فإيش لو
+
+535
+00:40:00,180 --> 00:40:03,940
+انا بدي أجيب الترتيب تبع T او ال magnitude بدي
+
+536
+00:40:03,940 --> 00:40:06,480
+أخطه بدون bold احنا قولنا بدون bold هذا magnitude
+
+537
+00:40:06,480 --> 00:40:10,520
+ال bold بتكون vector او ان اخطه بين اللي هي ال
+
+538
+00:40:10,520 --> 00:40:13,660
+absolute هاد اللي باليه فهي magnitude يعني هاي نفس
+
+539
+00:40:13,660 --> 00:40:20,140
+هاي فT إيش منها الساوة Bil عوضنا عن قيمة F0 Wsin α
+
+540
+00:40:20,140 --> 00:40:25,740
+W اللي هو ال width تبع العند طلعنا كويس على ال
+
+541
+00:40:25,740 --> 00:40:30,580
+loop رجعنا L في W إيش بمثل ليها ده ال area بتاعة
+
+542
+00:40:30,580 --> 00:40:34,720
+المستطيل ولا I في L ال area بتاعة ال loop
+
+543
+00:40:34,720 --> 00:40:40,980
+rectangular loop فعندي ال area بتاعته L في W إذا
+
+544
+00:40:40,980 --> 00:40:46,180
+معناه T إيش بتساوي B في I بدل W أسفل أسميها S اللي
+
+545
+00:40:46,180 --> 00:40:51,210
+هي ال area هي sin alphaكما في حاجة اضافة احنا
+
+546
+00:40:51,210 --> 00:40:54,810
+بنعرف ان حاصل ضغط ال current في ال area I في A او
+
+547
+00:40:54,810 --> 00:40:59,410
+I في S بده اسميه ال moment و دايما احنا ال vector
+
+548
+00:40:59,410 --> 00:41:03,070
+تبع ال area قولنا انه بيكون عمودي على ال area مش
+
+549
+00:41:03,070 --> 00:41:06,250
+احنا اللي قولنا ال area مالها مش scalar، اللي هي
+
+550
+00:41:06,250 --> 00:41:10,490
+vector و بيكون عمودي على ال area فانحن نسمي ال
+
+551
+00:41:10,490 --> 00:41:15,940
+unit vector تبع ال areaو هعرف ال moment ال
+
+552
+00:41:15,940 --> 00:41:20,600
+magnetic dipole moment اللي ال M بسوء I في S في A
+
+553
+00:41:20,600 --> 00:41:23,320
+and Hat احنا كان في عندنا electric dipole moment
+
+554
+00:41:23,320 --> 00:41:26,800
+ما تذكرينه و two charges هنا ال magnetic dipole
+
+555
+00:41:26,800 --> 00:41:30,860
+moment اللي هو نتاج من انه فيه دي تيارين متعاكسين
+
+556
+00:41:30,860 --> 00:41:34,160
+في اتجاه مجال المناطيس هيتولد ان دي couple من ال
+
+557
+00:41:34,160 --> 00:41:38,810
+forces متساوين اتجاههم متعاكسينإذا الـ magnetic
+
+558
+00:41:38,810 --> 00:41:43,490
+dipole moment بنعرفه هو عبارة عن حاصل ضرب ال
+
+559
+00:41:43,490 --> 00:41:48,890
+current في ال area بتاعة ال loop تمام؟ و اتجاهه
+
+560
+00:41:48,890 --> 00:41:53,970
+عمودي على ال area طيب ال units تعونه هيكون amps
+
+561
+00:41:53,970 --> 00:41:58,330
+per meter تربية ال units تعونه amps per meter
+
+562
+00:41:58,330 --> 00:42:02,390
+تربية تمام؟ هاي ال magnetic dipole moment
+
+563
+00:42:12,400 --> 00:42:16,580
+طيب كمان لو بدرجة اكتوب ال torque اللي احنا حسبنا
+
+564
+00:42:16,580 --> 00:42:21,080
+ان هو عبارة عن P في ال magnetic moment في sin α
+
+565
+00:42:21,080 --> 00:42:24,640
+حلوة أحس ان انا بقدر احنا متذكرين نقولنا ال sin α
+
+566
+00:42:24,640 --> 00:42:29,330
+هيبتمثل ليه؟cross product بينما ال cosine بتمثلني
+
+567
+00:42:29,330 --> 00:42:32,690
+dot product فانا عندى vector يوه ال moment وفيه
+
+568
+00:42:32,690 --> 00:42:36,950
+عندى sin alpha معناه انه هاد المقدار تبع ال vector
+
+569
+00:42:36,950 --> 00:42:40,590
+M في ال sin alpha معناه هدا فيه عندى cross product
+
+570
+00:42:40,590 --> 00:42:44,370
+بين حاشتين بال moment وحاجة تانية اللى هى في هاي
+
+571
+00:42:44,370 --> 00:42:46,470
+الحالة مين ال vector التانى ال magnetic field
+
+572
+00:42:46,470 --> 00:42:51,430
+فعندى بيه و ال moment و sin alpha اذا هذا عبارة عن
+
+573
+00:42:51,430 --> 00:42:54,210
+ال magnitude of the cross product بين ال magnetic
+
+574
+00:42:54,210 --> 00:42:58,840
+field و ال momentTorque هو عبارة عن الـ magnetic
+
+575
+00:42:58,840 --> 00:43:02,320
+moment across الـ magnetic field الـ magnetic
+
+576
+00:43:02,320 --> 00:43:05,460
+moment كمان مرة هو عبارة عن حصل ضرب ال current في
+
+577
+00:43:05,460 --> 00:43:12,900
+ال area و ال vector بتاعه هو عمودي على ال areaو ال
+
+578
+00:43:12,900 --> 00:43:16,440
+sin α هي اللي أوحطلنا ان هي عبارة عن cross product
+
+579
+00:43:16,440 --> 00:43:19,860
+لان اتفقنا ان ال sin هي بتمثل cross بين لو كان
+
+580
+00:43:19,860 --> 00:43:22,920
+عندكو sin ايش بنقول في عندي dot ال product دي و في
+
+581
+00:43:22,920 --> 00:43:25,740
+ال torque ثانوي اللي هو ال magnetic dipole moment
+
+582
+00:43:25,740 --> 00:43:33,020
+والmagnetic torque هو عبارة عن m cross d تمام؟
+
+583
+00:43:33,020 --> 00:43:36,100
+اذا عرفنا اشهر تعريف ال torque عرفنا اشهر ما تعريف
+
+584
+00:43:36,100 --> 00:43:40,460
+ال magnetic dipole moment عرفناكيف نجيب ال forces
+
+585
+00:43:40,460 --> 00:43:44,840
+الناتجة من المجال المناطيسي أسوأ متولد احنا عارفين
+
+586
+00:43:44,840 --> 00:43:47,820
+مصدره أو مش عارفين مصدره، احنا في الحالتين جيبنا
+
+587
+00:43:47,820 --> 00:43:52,180
+ال forcesالحالة الأولى كنا عارفين مصدر ال force او
+
+588
+00:43:52,180 --> 00:43:54,980
+ال magnet field اللى هو infinite line جبنا ال
+
+589
+00:43:54,980 --> 00:43:58,480
+forces على كل ضلع من أضلع ال loop و في الحالة
+
+590
+00:43:58,480 --> 00:44:01,600
+التانية ماهتمناش اش مصدر ال magnet field كان
+
+591
+00:44:01,600 --> 00:44:05,020
+معطقلنا و جبنا ال force على أضلع اللى هو ال loop
+
+592
+00:44:05,020 --> 00:44:09,880
+اللى قدامنا و حسبنا ال torque الناتج من القوتين F0
+
+593
+00:44:10,420 --> 00:44:14,420
+اللي موجودين على الضغايا المتقابلين انه في عندى
+
+594
+00:44:14,420 --> 00:44:19,640
+هتولد torque و هيصير لف لل loop وهدى هى فكرة اللى
+
+595
+00:44:19,640 --> 00:44:27,420
+هو عمل ال motor تمام؟ يعطيكوا العفو، في اي سفسار
+
+596
+00:44:27,420 --> 00:44:32,920
+قبل ما ننهي المحاضرة بتاعتنا؟ في اي سفسار؟ يلا
+
+597
+00:44:32,920 --> 00:44:33,560
+يعطيكوا العفو
+
diff --git a/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/wO3oYIFvFRw_raw.json b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/wO3oYIFvFRw_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..a12e1ded08b59acae01bd8dcd8eca116a7ed29fb
--- /dev/null
+++ b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/wO3oYIFvFRw_raw.json
@@ -0,0 +1 @@
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0.8338216145833334}, {"start": 510.8, "end": 511.84, "word": " الفكتور", "probability": 0.9151611328125}, {"start": 511.84, "end": 512.1, "word": " له", "probability": 0.401611328125}, {"start": 512.1, "end": 512.58, "word": " magnitude", "probability": 0.86669921875}, {"start": 512.58, "end": 513.84, "word": " له", "probability": 0.358154296875}, {"start": 513.84, "end": 514.18, "word": " هاكي", "probability": 0.72662353515625}, {"start": 514.18, "end": 514.38, "word": " بهذا", "probability": 0.755615234375}, {"start": 514.38, "end": 514.76, "word": " الشكل", "probability": 0.99072265625}, {"start": 514.76, "end": 515.18, "word": " و", "probability": 0.6298828125}, {"start": 515.18, "end": 515.6, "word": " احيانا", "probability": 0.907421875}, {"start": 515.6, "end": 516.18, "word": " نكتبه", "probability": 0.78515625}, {"start": 516.18, "end": 516.5, "word": " بهذا", "probability": 0.807861328125}, {"start": 516.5, "end": 516.82, "word": " الشكل", "probability": 0.96337890625}, {"start": 516.82, "end": 518.84, "word": " ايه", "probability": 0.4879150390625}, {"start": 518.84, "end": 519.8, "word": " الفكتور", "probability": 0.8115234375}, {"start": 519.8, "end": 520.12, "word": " و", "probability": 0.63818359375}, {"start": 520.12, "end": 520.34, "word": " بين", "probability": 0.54833984375}, {"start": 520.34, "end": 520.56, "word": " هذه", "probability": 0.2352294921875}, {"start": 520.56, "end": 521.18, "word": " الرمزات", "probability": 0.80987548828125}, {"start": 521.18, "end": 521.54, "word": " و", "probability": 0.80224609375}, {"start": 521.54, "end": 521.72, "word": " له", "probability": 0.184814453125}, {"start": 521.72, "end": 522.72, "word": " اتجارة", "probability": 0.86435546875}, {"start": 522.72, "end": 525.2, "word": " طبعا", "probability": 0.7705078125}, {"start": 525.2, "end": 525.44, "word": " اذا", "probability": 0.76708984375}, {"start": 525.44, "end": 525.98, "word": " هاكي", "probability": 0.9010009765625}, {"start": 525.98, "end": 526.72, "word": " بنعرف", "probability": 0.8904622395833334}, {"start": 526.72, "end": 527.04, "word": " هو", "probability": 0.1544189453125}, {"start": 527.04, "end": 527.6, "word": " الفكتور", "probability": 0.9737548828125}], "temperature": 1.0}, {"id": 21, "seek": 55672, "start": 528.52, "end": 556.72, "text": "قلنا إله quantity إله magnitude وإله اتجار ال quantity بتاعته عرفناها بهذا الشكل أو بهذا الشكل عشان أعرف ال a hat اللي هو اتجارنا الاتجار a hat a hat معناه هو unit vector إيش معناه unit vector إنه ال magnitude تبعه واحد لكن إله اتجار عشان أعرف اتجاره بقول", "tokens": [4587, 1211, 8315, 11933, 43761, 11275, 11933, 43761, 15668, 4032, 28814, 43761, 1975, 2655, 7435, 9640, 2423, 11275, 39894, 995, 34268, 3224, 6225, 28480, 8315, 11296, 39627, 15730, 25124, 28820, 34051, 39627, 15730, 25124, 28820, 6225, 8592, 7649, 5551, 3615, 28480, 2423, 257, 2385, 13672, 1829, 31439, 1975, 2655, 7435, 9640, 8315, 2423, 9307, 7435, 9640, 257, 2385, 257, 2385, 20449, 8315, 3224, 31439, 4985, 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"probability": 0.697265625}, {"start": 533.18, "end": 533.6, "word": " quantity", "probability": 0.85009765625}, {"start": 533.6, "end": 534.24, "word": " بتاعته", "probability": 0.93212890625}, {"start": 534.24, "end": 536.12, "word": " عرفناها", "probability": 0.94482421875}, {"start": 536.12, "end": 536.36, "word": " بهذا", "probability": 0.939453125}, {"start": 536.36, "end": 536.8, "word": " الشكل", "probability": 0.992431640625}, {"start": 536.8, "end": 537.5, "word": " أو", "probability": 0.81103515625}, {"start": 537.5, "end": 537.76, "word": " بهذا", "probability": 0.962646484375}, {"start": 537.76, "end": 538.24, "word": " الشكل", "probability": 0.98828125}, {"start": 538.24, "end": 539.84, "word": " عشان", "probability": 0.9773763020833334}, {"start": 539.84, "end": 540.18, "word": " أعرف", "probability": 0.93994140625}, {"start": 540.18, "end": 540.42, "word": " ال", "probability": 0.9326171875}, {"start": 540.42, "end": 540.6, "word": " a", "probability": 0.41650390625}, 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vector", "probability": 0.97216796875}, {"start": 549.48, "end": 549.76, "word": " إيش", "probability": 0.8214518229166666}, {"start": 549.76, "end": 550.0, "word": " معناه", "probability": 0.9239908854166666}, {"start": 550.0, "end": 550.18, "word": " unit", "probability": 0.95263671875}, {"start": 550.18, "end": 550.58, "word": " vector", "probability": 0.98193359375}, {"start": 550.58, "end": 551.36, "word": " إنه", "probability": 0.4515380859375}, {"start": 551.36, "end": 551.44, "word": " ال", "probability": 0.60693359375}, {"start": 551.44, "end": 551.78, "word": " magnitude", "probability": 0.947265625}, {"start": 551.78, "end": 552.26, "word": " تبعه", "probability": 0.9149169921875}, {"start": 552.26, "end": 552.84, "word": " واحد", "probability": 0.937255859375}, {"start": 552.84, "end": 553.8, "word": " لكن", "probability": 0.86474609375}, {"start": 553.8, "end": 554.04, "word": " إله", "probability": 0.90673828125}, {"start": 554.04, "end": 554.56, "word": " اتجار", "probability": 0.980712890625}, {"start": 554.56, "end": 555.28, "word": " عشان", "probability": 0.9899088541666666}, {"start": 555.28, "end": 555.56, "word": " أعرف", "probability": 0.9840494791666666}, {"start": 555.56, "end": 556.18, "word": " اتجاره", "probability": 0.968359375}, {"start": 556.18, "end": 556.72, "word": " بقول", "probability": 0.96142578125}], "temperature": 1.0}, {"id": 22, "seek": 58144, "start": 557.08, "end": 581.44, "text": "هو ال vector a على ال magnitude تبع ال vector a أي unit vector في الدنيا بدي أحصل عليه لأي vector quantity لو ماكنتش a لو كانت b بي حيكونها magnitude بي و بي hat ايش هي ال b hat unit vector ايش بيساوي ال vector نفسه على ال magnitude تبع ال vector", "tokens": [3224, 2407, 2423, 8062, 257, 15844, 2423, 15668, 6055, 3555, 3615, 2423, 8062, 257, 36632, 4985, 8062, 8978, 32748, 22653, 995, 4724, 16254, 5551, 5016, 36520, 47356, 5296, 10721, 1829, 8062, 11275, 45164, 19446, 19452, 2655, 8592, 257, 45164, 25961, 2655, 272, 4724, 1829, 11331, 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564.38, "end": 564.98, "word": " vector", "probability": 0.97509765625}, {"start": 564.98, "end": 565.6, "word": " quantity", "probability": 0.96826171875}, {"start": 565.6, "end": 566.26, "word": " لو", "probability": 0.57373046875}, {"start": 566.26, "end": 566.74, "word": " ماكنتش", "probability": 0.924560546875}, {"start": 566.74, "end": 567.18, "word": " a", "probability": 0.74755859375}, {"start": 567.18, "end": 567.4, "word": " لو", "probability": 0.96923828125}, {"start": 567.4, "end": 567.72, "word": " كانت", "probability": 0.923828125}, {"start": 567.72, "end": 567.98, "word": " b", "probability": 0.5869140625}, {"start": 567.98, "end": 570.0, "word": " بي", "probability": 0.608154296875}, {"start": 570.0, "end": 570.66, "word": " حيكونها", "probability": 0.695556640625}, {"start": 570.66, "end": 571.2, "word": " magnitude", "probability": 0.85107421875}, {"start": 571.2, "end": 571.86, "word": " بي", "probability": 0.62646484375}, {"start": 571.86, "end": 572.66, "word": " و", "probability": 0.19140625}, {"start": 572.66, "end": 573.28, "word": " بي", "probability": 0.715087890625}, {"start": 573.28, "end": 573.62, "word": " hat", "probability": 0.63916015625}, {"start": 573.62, "end": 574.32, "word": " ايش", "probability": 0.641357421875}, {"start": 574.32, "end": 574.46, "word": " هي", "probability": 0.55712890625}, {"start": 574.46, "end": 574.58, "word": " ال", "probability": 0.93359375}, {"start": 574.58, "end": 574.74, "word": " b", "probability": 0.430908203125}, {"start": 574.74, "end": 575.16, "word": " hat", "probability": 0.95068359375}, {"start": 575.16, "end": 576.08, "word": " unit", "probability": 0.74658203125}, {"start": 576.08, "end": 576.58, "word": " vector", "probability": 0.97607421875}, {"start": 576.58, "end": 576.8, "word": " ايش", "probability": 0.8271484375}, {"start": 576.8, "end": 577.34, "word": " بيساوي", "probability": 0.80791015625}, {"start": 577.34, "end": 577.92, "word": " ال", "probability": 0.85107421875}, {"start": 577.92, "end": 578.28, "word": " vector", "probability": 0.98291015625}, {"start": 578.28, "end": 578.98, "word": " نفسه", "probability": 0.9964192708333334}, {"start": 578.98, "end": 579.46, "word": " على", "probability": 0.8271484375}, {"start": 579.46, "end": 579.62, "word": " ال", "probability": 0.84228515625}, {"start": 579.62, "end": 580.1, "word": " magnitude", "probability": 0.96875}, {"start": 580.1, "end": 580.92, "word": " تبع", "probability": 0.9270833333333334}, {"start": 580.92, "end": 581.16, "word": " ال", "probability": 0.92578125}, {"start": 581.16, "end": 581.44, "word": " vector", "probability": 0.9814453125}], "temperature": 1.0}, {"id": 23, "seek": 59676, "start": 582.24, "end": 596.76, "text": "إذا ال unit vector بقدر أجيبه أو اتجاه أي vector بإني أسم Pنة ال vector على ال magnitude تبع هذا ال vector طب ال vector كيف أنا بعبر عنه؟ ال vector غالبا اللي هو components", "tokens": [28814, 15730, 2423, 4985, 8062, 4724, 28543, 2288, 5551, 7435, 1829, 3555, 3224, 34051, 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R لمة و R حنان هيكون ليه موضوع حنان بالنسبالي ال origin RH ال displacement هي المسافة بين لمة و حنان، واضحة؟ هاي الفرق بين position و displacement طب نتفق على ال notation، يعني ال RBQ هي عبارة عن RBQ minus RB", "tokens": [40228, 22653, 50113, 15040, 41850, 39894, 3615, 28480, 9673, 3794, 31845, 3660, 13672, 1829, 49374, 11331, 1863, 7649, 4032, 19528, 3660, 12399, 11933, 1829, 8592, 31439, 21542, 26108, 3660, 4724, 25957, 1211, 11296, 22807, 4724, 3615, 28480, 3714, 2407, 11242, 45367, 32767, 3660, 20666, 1863, 35457, 6027, 1829, 2423, 4957, 8032, 2304, 9957, 497, 2423, 4386, 497, 32767, 3660, 4032, 497, 11331, 1863, 7649, 39896, 30544, 32239, 3224, 3714, 2407, 11242, 45367, 11331, 1863, 7649, 20666, 1863, 35457, 6027, 1829, 2423, 4957, 50209, 2423, 21899, 39896, 9673, 3794, 31845, 3660, 49374, 32767, 3660, 4032, 11331, 1863, 7649, 12399, 4032, 46958, 5016, 3660, 22807, 8032, 47302, 27188, 2288, 4587, 49374, 2535, 4032, 21899, 23032, 3555, 8717, 2655, 5172, 4587, 15844, 2423, 24657, 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إحنا", "probability": 0.6167805989583334}, {"start": 1535.45, "end": 1535.87, "word": " اتفقنا", "probability": 0.838671875}, {"start": 1535.87, "end": 1535.99, "word": " إن", "probability": 0.79052734375}, {"start": 1535.99, "end": 1536.45, "word": " هذا", "probability": 0.931640625}, {"start": 1536.45, "end": 1537.13, "word": " مع", "probability": 0.994140625}, {"start": 1537.13, "end": 1537.39, "word": " هذا", "probability": 0.90087890625}, {"start": 1537.39, "end": 1537.75, "word": " معناه", "probability": 0.78759765625}, {"start": 1537.75, "end": 1538.45, "word": " جامع،", "probability": 0.649810791015625}, {"start": 1538.45, "end": 1539.53, "word": " يعني", "probability": 0.942626953125}, {"start": 1539.53, "end": 1540.31, "word": " RB", "probability": 0.92626953125}, {"start": 1540.31, "end": 1540.91, "word": " زاد", "probability": 0.3345947265625}, {"start": 1540.91, "end": 1541.69, "word": " RBQ", "probability": 0.947265625}, {"start": 1541.69, "end": 1542.15, "word": " بيبقى", "probability": 0.5972412109375}, {"start": 1542.15, "end": 1542.41, "word": " تسوى", "probability": 0.75439453125}, {"start": 1542.41, "end": 1542.89, "word": " RQ", "probability": 0.9501953125}], "temperature": 1.0}, {"id": 59, "seek": 157318, "start": 1543.88, "end": 1573.18, "text": "صح؟ إيش طبعا شفنا ال Gemini؟ إنها هذي إذا حطيت ال tail تبع ال vector على رأسي الأولاني، هيكون هذا مجموع مع هذا بساوي اللي هو ال vector اللي واصل من هنا لهنا، اللي هو متوازن الأرضاء، يعني عندي RB ثائق RPQ بتساوي RQ معناه إن RBQ إيش بتساوي؟ IRQ minus RB، دولة طبعا ال vector كانت أفضل من النقطة اللي بحط في السنة، مش هبعيز من هذا السيئة", "tokens": [9381, 5016, 22807, 11933, 1829, 8592, 23032, 3555, 3615, 995, 13412, 5172, 8315, 2423, 22894, 3812, 22807, 36145, 11296, 8032, 8848, 1829, 11933, 15730, 11331, 9566, 36081, 2423, 6838, 6055, 3555, 3615, 2423, 8062, 15844, 12602, 10721, 3794, 1829, 16247, 12610, 7649, 1829, 12399, 39896, 30544, 23758, 3714, 7435, 2304, 45367, 20449, 23758, 4724, 3794, 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"word": " ال", "probability": 0.98681640625}, {"start": 1553.14, "end": 1553.36, "word": " vector", "probability": 0.9794921875}, {"start": 1553.36, "end": 1553.58, "word": " اللي", "probability": 0.824462890625}, {"start": 1553.58, "end": 1553.98, "word": " واصل", "probability": 0.89697265625}, {"start": 1553.98, "end": 1554.22, "word": " من", "probability": 0.98876953125}, {"start": 1554.22, "end": 1554.74, "word": " هنا", "probability": 0.9912109375}, {"start": 1554.74, "end": 1555.38, "word": " لهنا،", "probability": 0.77978515625}, {"start": 1555.38, "end": 1555.46, "word": " اللي", "probability": 0.99365234375}, {"start": 1555.46, "end": 1555.54, "word": " هو", "probability": 0.9521484375}, {"start": 1555.54, "end": 1555.9, "word": " متوازن", "probability": 0.9149169921875}, {"start": 1555.9, "end": 1556.76, "word": " الأرضاء،", "probability": 0.759521484375}, {"start": 1556.76, "end": 1556.98, "word": " يعني", "probability": 0.9609375}, {"start": 1556.98, "end": 1557.24, "word": " عندي", "probability": 0.689453125}, {"start": 1557.24, "end": 1557.66, "word": " RB", "probability": 0.505859375}, {"start": 1557.66, "end": 1559.52, "word": " ثائق", "probability": 0.4433186848958333}, {"start": 1559.52, "end": 1560.96, "word": " RPQ", "probability": 0.4899495442708333}, {"start": 1560.96, "end": 1561.96, "word": " بتساوي", "probability": 0.8741455078125}, {"start": 1561.96, "end": 1562.6, "word": " RQ", "probability": 0.9296875}, {"start": 1562.6, "end": 1565.2, "word": " معناه", "probability": 0.8245442708333334}, {"start": 1565.2, "end": 1565.42, "word": " إن", "probability": 0.638671875}, {"start": 1565.42, "end": 1566.02, "word": " RBQ", "probability": 0.845947265625}, {"start": 1566.02, "end": 1566.12, "word": " إيش", "probability": 0.8478190104166666}, {"start": 1566.12, "end": 1566.98, "word": " بتساوي؟", "probability": 0.88984375}, {"start": 1566.98, "end": 1567.44, "word": " IRQ", "probability": 0.65234375}, {"start": 1567.44, "end": 1567.74, "word": " minus", "probability": 0.1959228515625}, {"start": 1567.74, "end": 1569.28, "word": " RB،", "probability": 0.6671142578125}, {"start": 1569.28, "end": 1569.58, "word": " دولة", "probability": 0.8058268229166666}, {"start": 1569.58, "end": 1569.78, "word": " طبعا", "probability": 0.9278564453125}, {"start": 1569.78, "end": 1569.92, "word": " ال", "probability": 0.83837890625}, {"start": 1569.92, "end": 1570.18, "word": " vector", "probability": 0.9560546875}, {"start": 1570.18, "end": 1570.56, "word": " كانت", "probability": 0.7215576171875}, {"start": 1570.56, "end": 1570.74, "word": " أفضل", "probability": 0.64202880859375}, {"start": 1570.74, "end": 1570.9, "word": " من", "probability": 0.60986328125}, {"start": 1570.9, "end": 1571.18, "word": " النقطة", "probability": 0.72998046875}, {"start": 1571.18, "end": 1571.28, "word": " اللي", "probability": 0.91015625}, {"start": 1571.28, "end": 1571.52, "word": " بحط", "probability": 0.4737955729166667}, {"start": 1571.52, "end": 1571.64, "word": " في", "probability": 0.33349609375}, {"start": 1571.64, "end": 1572.16, "word": " السنة،", "probability": 0.56585693359375}, {"start": 1572.16, "end": 1572.3, "word": " مش", "probability": 0.57421875}, {"start": 1572.3, "end": 1572.58, "word": " هبعيز", "probability": 0.6591796875}, {"start": 1572.58, "end": 1572.68, "word": " من", "probability": 0.443115234375}, {"start": 1572.68, "end": 1572.82, "word": " هذا", "probability": 0.732421875}, {"start": 1572.82, "end": 1573.18, "word": " السيئة", "probability": 0.49951171875}], "temperature": 1.0}, {"id": 60, "seek": 159885, "start": 1574.03, "end": 1598.85, "text": "مش حاجة بتعرف اوضحها بالبوابة كل واحد منهم يبقى له component RQ XQ YQ ZQ يعني RQ في ال space يعبارة عن XQ YQ ZQ و RB يعبارة عن XP YP ZP", "tokens": [2304, 8592, 11331, 26108, 3660, 39894, 3615, 28480, 1975, 2407, 11242, 5016, 11296, 20666, 3555, 14407, 49401, 28242, 36764, 24401, 9154, 16095, 7251, 3555, 4587, 7578, 46740, 6542, 497, 48, 1783, 48, 398, 48, 1176, 48, 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1577.47, "end": 1577.63, "word": " يبقى", "probability": 0.597076416015625}, {"start": 1577.63, "end": 1577.75, "word": " له", "probability": 0.30419921875}, {"start": 1577.75, "end": 1578.23, "word": " component", "probability": 0.85986328125}, {"start": 1578.23, "end": 1579.57, "word": " RQ", "probability": 0.6661376953125}, {"start": 1579.57, "end": 1580.85, "word": " XQ", "probability": 0.5082244873046875}, {"start": 1580.85, "end": 1582.29, "word": " YQ", "probability": 0.87060546875}, {"start": 1582.29, "end": 1583.19, "word": " ZQ", "probability": 0.818115234375}, {"start": 1583.19, "end": 1583.81, "word": " يعني", "probability": 0.8037109375}, {"start": 1583.81, "end": 1584.57, "word": " RQ", "probability": 0.89013671875}, {"start": 1584.57, "end": 1584.99, "word": " في", "probability": 0.81298828125}, {"start": 1584.99, "end": 1585.07, "word": " ال", "probability": 0.966796875}, {"start": 1585.07, "end": 1585.51, "word": " space", "probability": 0.7158203125}, {"start": 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"seek": 162472, "start": 1600.24, "end": 1624.72, "text": "و احنا اتعلمنا كيف نطرح يعني RQ-RB ايش هي مشغولنا يعني عبارة عن RQ plus minus RB يعني بضرب RB بسالب و بجمعهم هتكون XQ-XB Xها YQ-YB Yها زي ZQ-ZB Zها في اي سؤال لحد هنا صار واضح ايش الفرق بين ال position و ال displacement", "tokens": [2407, 1975, 5016, 8315, 1975, 2655, 3615, 19528, 8315, 9122, 33911, 8717, 9566, 2288, 5016, 37495, 22653, 497, 48, 12, 49, 33, 1975, 1829, 8592, 39896, 37893, 17082, 12610, 8315, 37495, 22653, 6225, 3555, 9640, 3660, 18871, 497, 48, 1804, 3175, 40302, 37495, 22653, 4724, 11242, 25513, 40302, 4724, 3794, 6027, 3555, 4032, 4724, 7435, 2304, 3615, 16095, 8032, 2655, 30544, 1783, 48, 12, 55, 33, 1783, 11296, 398, 48, 12, 56, 33, 398, 11296, 30767, 1829, 1176, 48, 12, 57, 33, 1176, 11296, 8978, 1975, 1829, 8608, 33604, 6027, 5296, 24401, 34105, 20328, 9640, 4032, 46958, 5016, 1975, 1829, 8592, 27188, 2288, 4587, 49374, 2423, 2535, 4032, 2423, 21899], "avg_logprob": -0.2874437001374391, "compression_ratio": 1.462882096069869, "no_speech_prob": 0.0, "words": [{"start": 1600.24, "end": 1600.42, "word": "و", "probability": 0.426513671875}, {"start": 1600.42, "end": 1600.56, "word": " احنا", "probability": 0.71337890625}, {"start": 1600.56, "end": 1601.16, "word": " اتعلمنا", "probability": 0.898046875}, {"start": 1601.16, "end": 1601.4, "word": " كيف", "probability": 0.888427734375}, {"start": 1601.4, "end": 1601.8, "word": " نطرح", "probability": 0.8822021484375}, {"start": 1601.8, "end": 1602.02, "word": " يعني", "probability": 0.771484375}, {"start": 1602.02, "end": 1602.54, "word": " RQ", "probability": 0.5648193359375}, {"start": 1602.54, "end": 1603.14, "word": "-RB", "probability": 0.6068522135416666}, {"start": 1603.14, "end": 1603.32, "word": " ايش", "probability": 0.5486653645833334}, {"start": 1603.32, "end": 1603.5, "word": " هي", "probability": 0.92919921875}, {"start": 1603.5, "end": 1604.1, "word": " مشغولنا", "probability": 0.72052001953125}, {"start": 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"end": 2203.49, "word": " الفلوس", "probability": 0.7937825520833334}, {"start": 2203.49, "end": 2203.73, "word": " بتاع", "probability": 0.77685546875}, {"start": 2203.73, "end": 2203.97, "word": " ال", "probability": 0.685546875}, {"start": 2203.97, "end": 2204.01, "word": " ..", "probability": 0.73681640625}, {"start": 2204.01, "end": 2204.55, "word": " القاع", "probability": 0.564208984375}, {"start": 2204.55, "end": 2204.69, "word": " ال", "probability": 0.7177734375}, {"start": 2204.69, "end": 2205.03, "word": " boat", "probability": 0.94140625}, {"start": 2205.03, "end": 2205.47, "word": " إذا", "probability": 0.6112060546875}, {"start": 2205.47, "end": 2205.71, "word": " انهي", "probability": 0.487548828125}, {"start": 2205.71, "end": 2206.05, "word": " اتجاه", "probability": 0.9561767578125}, {"start": 2206.05, "end": 2206.23, "word": " ال", "probability": 0.86181640625}, {"start": 2206.23, "end": 2206.49, "word": " man", "probability": 0.8603515625}, {"start": 2206.49, "end": 2206.77, "word": " اللي", "probability": 0.91650390625}, {"start": 2206.77, "end": 2207.05, "word": " برضه", "probability": 0.9903971354166666}, {"start": 2207.05, "end": 2207.37, "word": " خمسة", "probability": 0.9144287109375}, {"start": 2207.37, "end": 2207.67, "word": " واربعين", "probability": 0.83134765625}, {"start": 2207.67, "end": 2208.07, "word": " درجة", "probability": 0.9928385416666666}, {"start": 2208.07, "end": 2208.59, "word": " بالنسبة", "probability": 0.9920654296875}, {"start": 2208.59, "end": 2209.01, "word": " لمين", "probability": 0.74853515625}, {"start": 2209.01, "end": 2209.51, "word": " ل", "probability": 0.50048828125}, {"start": 2209.51, "end": 2209.75, "word": " ال", "probability": 0.5458984375}, {"start": 2209.75, "end": 2210.09, "word": " west", "probability": 0.8896484375}, {"start": 2210.09, "end": 2210.41, "word": " و", "probability": 0.87939453125}, {"start": 2210.41, "end": 2210.67, "word": " ال", "probability": 0.64892578125}, {"start": 2210.67, 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"probability": 0.9814453125}, {"start": 2226.31, "end": 2226.73, "word": " تاني", "probability": 0.9716796875}, {"start": 2226.73, "end": 2226.87, "word": " اللي", "probability": 0.95849609375}, {"start": 2226.87, "end": 2227.09, "word": " هي", "probability": 0.95751953125}, {"start": 2227.09, "end": 2227.69, "word": " human", "probability": 0.9189453125}, {"start": 2227.69, "end": 2228.27, "word": " sin", "probability": 0.80615234375}, {"start": 2228.27, "end": 2229.21, "word": " 45", "probability": 0.91552734375}, {"start": 2229.21, "end": 2229.45, "word": " في", "probability": 0.96435546875}, {"start": 2229.45, "end": 2229.87, "word": " اتجاه", "probability": 0.9556884765625}, {"start": 2229.87, "end": 2230.55, "word": " السالب", "probability": 0.8601888020833334}, {"start": 2230.55, "end": 2230.95, "word": " Y", "probability": 0.98974609375}], "temperature": 1.0}, {"id": 85, "seek": 225315, "start": 2231.43, "end": 2253.15, "text": "هيعرفنا ال UB ال component استعونها و UMAN ال component استعونها as vectors اتجمع بصير تبعهم عشان اجيب ال relative UB زائد UR هي بتعطيني ال relative اللي هي UAB اللي هي ال value بتاعة ال man بالنسبة لل R اللي هي UMAN زائد UB", "tokens": [3224, 40228, 28480, 8315, 2423, 624, 33, 2423, 6542, 44713, 3615, 11536, 11296, 4032, 624, 11866, 2423, 6542, 44713, 3615, 11536, 11296, 382, 18875, 1975, 2655, 7435, 2304, 3615, 4724, 9381, 13546, 6055, 3555, 3615, 16095, 6225, 8592, 7649, 1975, 7435, 1829, 3555, 2423, 4972, 624, 33, 30767, 16373, 3215, 624, 49, 39896, 39894, 3615, 9566, 9957, 1829, 2423, 4972, 13672, 1829, 39896, 624, 13868, 13672, 1829, 39896, 2423, 2158, 39894, 995, 27884, 2423, 587, 20666, 1863, 35457, 3660, 24976, 497, 13672, 1829, 39896, 624, 11866, 30767, 16373, 3215, 624, 33], "avg_logprob": -0.30842390202957654, "compression_ratio": 1.6989795918367347, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2231.43, "end": 2232.15, "word": "هيعرفنا", "probability": 0.8658447265625}, {"start": 2232.15, "end": 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new file mode 100644
index 0000000000000000000000000000000000000000..c53ed90aba3899c7044b89a890eecfa269e51938
--- /dev/null
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"probability": 0.9482421875}, {"start": 3003.8, "end": 3004.54, "word": " تجيبوها؟", "probability": 0.9335239955357143}], "temperature": 1.0}, {"id": 115, "seek": 303442, "start": 3005.5, "end": 3034.42, "text": "من اللى اتعلمناه اليوم طب بدي unit vector عمودي عليه من اللى اتعلمناه اليوم بدي unit vector عمودي على ال field يعني انا عندى ال field دى هى ال field و بدي ال unit vector عمودي عليه من اللى اتعلمناه اليوم اخر حاجة", "tokens": [27842, 13672, 7578, 1975, 2655, 3615, 19528, 8315, 3224, 45595, 20498, 23032, 3555, 4724, 16254, 4985, 8062, 6225, 2304, 2407, 16254, 25894, 3224, 9154, 13672, 7578, 1975, 2655, 3615, 19528, 8315, 3224, 45595, 20498, 4724, 16254, 4985, 8062, 6225, 2304, 2407, 16254, 15844, 2423, 2519, 37495, 22653, 1975, 8315, 43242, 7578, 2423, 2519, 11778, 7578, 8032, 7578, 2423, 2519, 4032, 4724, 16254, 2423, 4985, 8062, 6225, 2304, 2407, 16254, 25894, 3224, 9154, 13672, 7578, 1975, 2655, 3615, 19528, 8315, 3224, 45595, 20498, 1975, 34740, 11331, 26108, 3660], "avg_logprob": -0.27929687229069794, "compression_ratio": 2.4962962962962965, "no_speech_prob": 6.556510925292969e-07, "words": [{"start": 3005.5, "end": 3005.74, "word": "من", "probability": 0.320556640625}, {"start": 3005.74, "end": 3005.86, "word": " اللى", "probability": 0.49365234375}, {"start": 3005.86, "end": 3006.36, "word": " اتعلمناه", "probability": 0.8026529947916666}, {"start": 3006.36, "end": 3006.68, "word": " اليوم", "probability": 0.942626953125}, {"start": 3006.68, "end": 3008.86, "word": " طب", "probability": 0.81298828125}, {"start": 3008.86, "end": 3009.0, "word": " بدي", "probability": 0.64599609375}, {"start": 3009.0, "end": 3009.24, "word": " unit", "probability": 0.9482421875}, {"start": 3009.24, "end": 3009.52, "word": " vector", "probability": 0.97607421875}, {"start": 3009.52, "end": 3009.9, "word": " عمودي", "probability": 0.9632568359375}, {"start": 3009.9, "end": 3010.38, "word": " عليه", "probability": 0.549072265625}, {"start": 3010.38, "end": 3011.24, "word": " من", "probability": 0.57470703125}, {"start": 3011.24, "end": 3011.34, "word": " اللى", "probability": 0.9873046875}, {"start": 3011.34, "end": 3011.82, "word": " اتعلمناه", "probability": 0.949462890625}, {"start": 3011.82, "end": 3012.4, "word": " اليوم", "probability": 0.86865234375}, {"start": 3012.4, "end": 3012.96, "word": " بدي", "probability": 0.6988525390625}, {"start": 3012.96, "end": 3013.14, "word": " unit", "probability": 0.9794921875}, {"start": 3013.14, "end": 3013.54, "word": " vector", "probability": 0.9853515625}, {"start": 3013.54, "end": 3014.1, "word": " عمودي", "probability": 0.987548828125}, {"start": 3014.1, "end": 3014.6, "word": " على", "probability": 0.47998046875}, {"start": 3014.6, "end": 3014.84, "word": " ال", "probability": 0.8408203125}, {"start": 3014.84, "end": 3015.02, "word": " field", "probability": 0.841796875}, {"start": 3015.02, "end": 3015.26, "word": " يعني", "probability": 0.906982421875}, {"start": 3015.26, "end": 3015.38, "word": " انا", "probability": 0.7052001953125}, {"start": 3015.38, "end": 3015.62, "word": " عندى", "probability": 0.797607421875}, {"start": 3015.62, "end": 3015.72, "word": " ال", "probability": 0.89453125}, {"start": 3015.72, "end": 3015.96, "word": " field", "probability": 0.9521484375}, {"start": 3015.96, "end": 3019.68, "word": " دى", "probability": 0.6884765625}, {"start": 3019.68, "end": 3021.26, "word": " هى", "probability": 0.601318359375}, {"start": 3021.26, "end": 3021.7, "word": " ال", "probability": 0.397705078125}, {"start": 3021.7, "end": 3022.02, "word": " field", "probability": 0.88427734375}, {"start": 3022.02, "end": 3022.38, "word": " و", "probability": 0.42041015625}, {"start": 3022.38, "end": 3022.82, "word": " بدي", "probability": 0.82763671875}, {"start": 3022.82, "end": 3024.34, "word": " ال", "probability": 0.110595703125}, {"start": 3024.34, "end": 3026.34, "word": " unit", "probability": 0.9697265625}, {"start": 3026.34, "end": 3026.72, "word": " vector", "probability": 0.98583984375}, {"start": 3026.72, "end": 3027.14, "word": " عمودي", "probability": 0.8900146484375}, {"start": 3027.14, "end": 3027.48, "word": " عليه", "probability": 0.5714111328125}, {"start": 3027.48, "end": 3029.32, "word": " من", "probability": 0.51416015625}, {"start": 3029.32, "end": 3031.72, "word": " اللى", "probability": 0.61773681640625}, {"start": 3031.72, "end": 3032.8, "word": " اتعلمناه", "probability": 0.9580078125}, {"start": 3032.8, "end": 3033.1, "word": " اليوم", "probability": 0.99365234375}, {"start": 3033.1, "end": 3033.98, "word": " اخر", "probability": 0.7958984375}, {"start": 3033.98, "end": 3034.42, "word": " حاجة", "probability": 0.9671223958333334}], "temperature": 1.0}, {"id": 116, "seek": 305903, "start": 3034.71, "end": 3059.03, "text": "ماذا نسميه Gradient؟ انه عمودي علي Grad V بس هذا مش unit vector عشان اجيب unit vector مش بس انا بجيب Grad V و اسمع ال magnitude تبعه فبعطيني unit vector في اتجاهه بدأ اجيب product او يعني vector اللي عمودي علي هذا", "tokens": [2304, 45636, 995, 8717, 38251, 1829, 3224, 16710, 1196, 22807, 16472, 3224, 6225, 2304, 2407, 16254, 25894, 16710, 691, 4724, 3794, 23758, 37893, 4985, 8062, 6225, 8592, 7649, 1975, 7435, 1829, 3555, 4985, 8062, 37893, 4724, 3794, 1975, 8315, 4724, 7435, 1829, 3555, 16710, 691, 4032, 1975, 38251, 3615, 2423, 15668, 6055, 3555, 3615, 3224, 6156, 3555, 3615, 9566, 9957, 1829, 4985, 8062, 8978, 1975, 2655, 7435, 40294, 3224, 47525, 10721, 1975, 7435, 1829, 3555, 1674, 1975, 2407, 37495, 22653, 8062, 13672, 1829, 6225, 2304, 2407, 16254, 25894, 23758], "avg_logprob": -0.5027777757909563, "compression_ratio": 1.6613756613756614, "no_speech_prob": 2.980232238769531e-07, "words": [{"start": 3034.71, "end": 3034.95, "word": "ماذا", "probability": 0.5494791666666666}, {"start": 3034.95, "end": 3035.33, "word": " نسميه", "probability": 0.48095703125}, {"start": 3035.33, "end": 3036.33, "word": " Gradient؟", "probability": 0.6184488932291666}, {"start": 3036.33, "end": 3036.69, "word": " انه", "probability": 0.236358642578125}, {"start": 3036.69, "end": 3037.09, "word": " عمودي", "probability": 0.89111328125}, {"start": 3037.09, "end": 3037.29, "word": " علي", "probability": 0.21337890625}, {"start": 3037.29, "end": 3038.77, "word": " Grad", "probability": 0.2744140625}, {"start": 3038.77, "end": 3039.61, "word": " V", "probability": 0.247314453125}, {"start": 3039.61, "end": 3039.93, "word": " بس", "probability": 0.5679931640625}, {"start": 3039.93, "end": 3040.07, "word": " هذا", "probability": 0.69677734375}, {"start": 3040.07, "end": 3040.27, "word": " مش", "probability": 0.470703125}, {"start": 3040.27, "end": 3040.47, "word": " unit", "probability": 0.78466796875}, {"start": 3040.47, "end": 3040.75, "word": " vector", "probability": 0.962890625}, {"start": 3040.75, "end": 3041.05, "word": " عشان", "probability": 0.8836263020833334}, {"start": 3041.05, "end": 3041.29, "word": " اجيب", "probability": 0.7781982421875}, {"start": 3041.29, "end": 3041.53, "word": " unit", "probability": 0.59375}, {"start": 3041.53, "end": 3041.75, "word": " vector", "probability": 0.888671875}, {"start": 3041.75, "end": 3042.05, "word": " مش", "probability": 0.28369140625}, {"start": 3042.05, "end": 3042.27, "word": " بس", "probability": 0.7978515625}, {"start": 3042.27, "end": 3042.41, "word": " انا", "probability": 0.27362060546875}, {"start": 3042.41, "end": 3042.69, "word": " بجيب", "probability": 0.9161376953125}, {"start": 3042.69, "end": 3043.07, "word": " Grad", "probability": 0.59033203125}, {"start": 3043.07, "end": 3043.31, "word": " V", "probability": 0.96728515625}, {"start": 3043.31, "end": 3043.49, "word": " و", "probability": 0.76708984375}, {"start": 3043.49, "end": 3043.89, "word": " اسمع", "probability": 0.7577311197916666}, {"start": 3043.89, "end": 3044.03, "word": " ال", "probability": 0.1513671875}, {"start": 3044.03, "end": 3044.47, "word": " magnitude", "probability": 0.97412109375}, {"start": 3044.47, "end": 3045.25, "word": " تبعه", "probability": 0.81878662109375}, {"start": 3045.25, "end": 3045.89, "word": " فبعطيني", "probability": 0.6261189778645834}, {"start": 3045.89, "end": 3046.13, "word": " unit", "probability": 0.7841796875}, {"start": 3046.13, "end": 3046.59, "word": " vector", "probability": 0.97802734375}, {"start": 3046.59, "end": 3051.57, "word": " في", "probability": 0.578125}, {"start": 3051.57, "end": 3053.51, "word": " اتجاهه", "probability": 0.7888671875}, {"start": 3053.51, "end": 3054.25, "word": " بدأ", "probability": 0.599365234375}, {"start": 3054.25, "end": 3054.61, "word": " اجيب", "probability": 0.9307861328125}, {"start": 3054.61, "end": 3054.95, "word": " product", "probability": 0.360595703125}, {"start": 3054.95, "end": 3055.65, "word": " او", "probability": 0.681884765625}, {"start": 3055.65, "end": 3055.97, "word": " يعني", "probability": 0.87841796875}, {"start": 3055.97, "end": 3057.89, "word": " vector", "probability": 0.5869140625}, {"start": 3057.89, "end": 3058.19, "word": " اللي", "probability": 0.7607421875}, {"start": 3058.19, "end": 3058.67, "word": " عمودي", "probability": 0.9879150390625}, {"start": 3058.67, "end": 3058.83, "word": " علي", "probability": 0.7060546875}, {"start": 3058.83, "end": 3059.03, "word": " هذا", "probability": 0.4580078125}], "temperature": 1.0}, {"id": 117, "seek": 308034, "start": 3060.06, "end": 3080.34, "text": "ال vector ال minus vector اللي عمودي و انا اخدته اكيد بالفضل الله احنا لما هيك ما اخدناها بالخلاص بلاص يعني هذا كله جزء الاول من ال electromagnet هى ايه السرعال اللى حدناها؟ اه خلاص احنا هتا", "tokens": [6027, 8062, 2423, 3175, 8062, 13672, 1829, 6225, 2304, 2407, 16254, 4032, 1975, 8315, 1975, 9778, 3215, 47395, 1975, 4117, 25708, 20666, 5172, 11242, 1211, 21984, 1975, 5016, 8315, 5296, 15042, 39896, 4117, 19446, 1975, 9778, 3215, 8315, 11296, 20666, 9778, 1211, 33546, 4724, 1211, 33546, 37495, 22653, 23758, 28242, 3224, 10874, 11622, 38207, 42963, 12610, 9154, 2423, 27528, 302, 8032, 7578, 1975, 1829, 3224, 21136, 2288, 3615, 6027, 13672, 7578, 11331, 3215, 8315, 11296, 22807, 1975, 3224, 16490, 1211, 33546, 1975, 5016, 8315, 8032, 2655, 995], "avg_logprob": -0.5319602462378415, "compression_ratio": 1.6972972972972973, "no_speech_prob": 3.5762786865234375e-07, "words": [{"start": 3060.06, "end": 3060.32, "word": "ال", "probability": 0.68505859375}, {"start": 3060.32, "end": 3060.72, "word": " vector", "probability": 0.05279541015625}, {"start": 3060.72, "end": 3061.02, "word": " ال", "probability": 0.65185546875}, {"start": 3061.02, "end": 3061.2, "word": " minus", "probability": 0.1409912109375}, {"start": 3061.2, "end": 3061.6, "word": " vector", "probability": 0.98291015625}, {"start": 3061.6, "end": 3061.76, "word": " اللي", "probability": 0.673095703125}, {"start": 3061.76, "end": 3062.1, "word": " عمودي", "probability": 0.9013671875}, {"start": 3062.1, "end": 3063.04, "word": " و", "probability": 0.09478759765625}, {"start": 3063.04, "end": 3063.28, "word": " انا", "probability": 0.297607421875}, {"start": 3063.28, "end": 3063.62, "word": " اخدته", "probability": 0.70062255859375}, {"start": 3063.62, "end": 3063.9, "word": " اكيد", "probability": 0.9065755208333334}, {"start": 3063.9, "end": 3064.32, "word": " بالفضل", "probability": 0.615142822265625}, {"start": 3064.32, "end": 3064.56, "word": " الله", "probability": 0.1871337890625}, {"start": 3064.56, "end": 3068.98, "word": " احنا", "probability": 0.7403971354166666}, {"start": 3068.98, "end": 3069.18, "word": " لما", "probability": 0.5560302734375}, {"start": 3069.18, "end": 3069.44, "word": " هيك", "probability": 0.5902099609375}, {"start": 3069.44, "end": 3069.52, "word": " ما", "probability": 0.86279296875}, {"start": 3069.52, "end": 3069.9, "word": " اخدناها", "probability": 0.83056640625}, {"start": 3069.9, "end": 3070.24, "word": " بالخلاص", "probability": 0.488800048828125}, {"start": 3070.24, "end": 3070.54, "word": " بلاص", "probability": 0.496337890625}, {"start": 3070.54, "end": 3071.36, "word": " يعني", "probability": 0.8330078125}, {"start": 3071.36, "end": 3073.06, "word": " هذا", "probability": 0.6748046875}, {"start": 3073.06, "end": 3073.44, "word": " كله", "probability": 0.92333984375}, {"start": 3073.44, "end": 3073.66, "word": " جزء", "probability": 0.982421875}, {"start": 3073.66, "end": 3074.02, "word": " الاول", "probability": 0.862060546875}, {"start": 3074.02, "end": 3074.24, "word": " من", "probability": 0.978515625}, {"start": 3074.24, "end": 3074.5, "word": " ال", "probability": 0.90771484375}, {"start": 3074.5, "end": 3075.5, "word": " electromagnet", "probability": 0.6295166015625}, {"start": 3075.5, "end": 3077.38, "word": " هى", "probability": 0.61083984375}, {"start": 3077.38, "end": 3077.6, "word": " ايه", "probability": 0.6392415364583334}, {"start": 3077.6, "end": 3077.9, "word": " السرعال", "probability": 0.69970703125}, {"start": 3077.9, "end": 3078.0, "word": " اللى", "probability": 0.907958984375}, {"start": 3078.0, "end": 3078.44, "word": " حدناها؟", "probability": 0.6388671875}, {"start": 3078.44, "end": 3078.48, "word": " اه", "probability": 0.70263671875}, {"start": 3078.48, "end": 3078.7, "word": " خلاص", "probability": 0.9464518229166666}, {"start": 3078.7, "end": 3078.9, "word": " احنا", "probability": 0.6433919270833334}, {"start": 3078.9, "end": 3080.34, "word": " هتا", "probability": 0.3612467447916667}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 3082.031, "duration_after_vad": 2918.3124999999864}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/xHy5zWBD8Gs_raw.srt b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/xHy5zWBD8Gs_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..8e0ea48de144bef1011e099c8d36d4f43e152f64
--- /dev/null
+++ b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/xHy5zWBD8Gs_raw.srt
@@ -0,0 +1,2532 @@
+1
+00:00:21,060 --> 00:00:23,720
+بسم الله الرحمن الرحيم السلام عليكم ورحمة الله
+
+2
+00:00:23,720 --> 00:00:27,480
+وبركاته احنا بعد ما شوفنا ال vector كيف احنا
+
+3
+00:00:27,480 --> 00:00:30,620
+نتعامل مع ال differential links فيه spherical و
+
+4
+00:00:30,620 --> 00:00:32,880
+cylindrical و partition coordinate و differential
+
+5
+00:00:32,880 --> 00:00:35,760
+surfaceالـ cartesian و ال cylindrical و ال
+
+6
+00:00:35,760 --> 00:00:38,640
+spherical coordinates و كيف حساب ال volume برضه في
+
+7
+00:00:38,640 --> 00:00:40,900
+ال three coordinates ال cartesian و ال cylindrical
+
+8
+00:00:40,900 --> 00:00:45,880
+و ال spherical اليوم هنشوف كيف نتعامل مع ال
+
+9
+00:00:45,880 --> 00:00:50,300
+contour integral و ال surface integral و كمان حتى
+
+10
+00:00:50,300 --> 00:00:58,560
+هنتعامل مع الدلول و ال vector ال
+
+11
+00:00:58,560 --> 00:01:05,890
+cross product و ال product و الدل تربيهفنبدأ أولا
+
+12
+00:01:05,890 --> 00:01:11,410
+في ال line أو ال surface سنبدأ بال line ثم ال
+
+13
+00:01:11,410 --> 00:01:14,410
+surface ثم ال volume integral فنبدأ بال line
+
+14
+00:01:14,410 --> 00:01:17,430
+integral line integral برضه بقدر اقول عنه ال curve
+
+15
+00:01:17,430 --> 00:01:22,190
+او ال contour integral line integral غالبا معناها
+
+16
+00:01:22,190 --> 00:01:25,250
+ان بقول integral حوالين line ال هى بتقولي ان انا
+
+17
+00:01:25,250 --> 00:01:30,450
+بعمل integral حوالين ال ل vector dot dlالـDL
+
+18
+00:01:30,450 --> 00:01:33,090
+ماعرفنش يا الـDL الـDL اللى هى ال differential
+
+19
+00:01:33,090 --> 00:01:35,730
+displacement سواء فى ال kartesian او فى ال
+
+20
+00:01:35,730 --> 00:01:37,550
+cylindrical او فى ال spherical ال A اللى هو ال
+
+21
+00:01:37,550 --> 00:01:39,830
+vector اللى احنا بمساعدنا اللى هو ال
+
+22
+00:01:39,830 --> 00:01:42,270
+electromagnetic ال vector هذا هيكون دائما field
+
+23
+00:01:42,270 --> 00:01:45,990
+بالنسبالنا يعنى انها فى المستقبل هستبدلها دى ايه
+
+24
+00:01:45,990 --> 00:01:49,330
+ال E او H E اللى هى ال electric field او H اللى هى
+
+25
+00:01:49,330 --> 00:01:52,010
+ال magnetic field فبس هى اللى هيكون فرقية بين
+
+26
+00:01:52,010 --> 00:01:55,360
+الجزء الاول والثالث لما أنا بحكي بشكل عامالـ A هو
+
+27
+00:01:55,360 --> 00:02:00,380
+vector, I vector, vector field وDL هو الـ contour
+
+28
+00:02:00,380 --> 00:02:05,840
+أو الـ line أو الـ curve integral over a line للـ
+
+29
+00:02:05,840 --> 00:02:10,400
+field dot DL لو
+
+30
+00:02:10,400 --> 00:02:15,180
+أنا بحكي عن اللي هو integral حوالي ال contour يعني
+
+31
+00:02:15,180 --> 00:02:20,060
+مثلا زي هذا ال line اللي حوالين هذا اللي هو ال
+
+32
+00:02:20,060 --> 00:02:22,860
+line اللي موجود بالأسود يعني زي هيك الجسم وعمله
+
+33
+00:02:22,860 --> 00:02:28,090
+more منه fieldهيكون الـ integral مثلا من النقطة A
+
+34
+00:02:28,090 --> 00:02:31,930
+لنقطة B اللي هو الـ path أو ال line integral هنا
+
+35
+00:02:31,930 --> 00:02:35,710
+في هذه الحالة أنا باخد path من نقطة A لنقطة B
+
+36
+00:02:35,710 --> 00:02:41,050
+هيكون A dot DL أيش بتساوي؟ احنا قولنا A dot B هي A
+
+37
+00:02:41,050 --> 00:02:44,670
+المجموعة و B المجموعة فاكساينزروا بينهم نفس الحالة
+
+38
+00:02:44,670 --> 00:02:47,830
+دولة و vectors و dot product بينهم A dot DL
+
+39
+00:02:47,830 --> 00:02:49,350
+هتعطينا مجموعة A
+
+40
+00:03:07,430 --> 00:03:12,350
+هذا هو الـ Line Integral
+
+41
+00:03:19,780 --> 00:03:24,880
+الـ Line Integral هو اني باخد باص باص على Line هي
+
+42
+00:03:24,880 --> 00:03:27,640
+هذا Line اللى هو زى ما قولنا محيط دائرة ممكن او
+
+43
+00:03:27,640 --> 00:03:33,240
+محيط سفير او اى curve و انا باخد عنها ال Integral
+
+44
+00:03:33,240 --> 00:03:38,360
+ما بين نقطتين من A ل B و ال A دل DL يعنى هيكون
+
+45
+00:03:38,360 --> 00:03:41,680
+اللى هي ال component او ال projection تبع ال field
+
+46
+00:03:41,680 --> 00:03:47,670
+A تتجاه اللى هو ال Line يعني A Cosθ DLطب احنا كمان
+
+47
+00:03:47,670 --> 00:03:50,630
+بتبقى على طول ال line integral و في حاجة اسمها
+
+48
+00:03:50,630 --> 00:03:54,830
+closed contour integral الدوارة اللى بنصها دى
+
+49
+00:03:54,830 --> 00:03:58,810
+بستعمل فيها عشان تقولنا انها closed path احنا هنا
+
+50
+00:03:58,810 --> 00:04:03,510
+فى ال path من نقطة لنقطة ماحتناش الدوارة على ال
+
+51
+00:04:03,510 --> 00:04:07,560
+integralقلنا هذه النقطة لنقطة من A ل B بال
+
+52
+00:04:07,560 --> 00:04:11,180
+Integral A to DL هذا Contour أو Line Integral ما
+
+53
+00:04:11,180 --> 00:04:15,120
+بين نقطتي من A ل B لما أحط الدوارة على ال Integral
+
+54
+00:04:15,120 --> 00:04:18,540
+هذا معناه ان closed path يعني مثلا في هذه الرسمة
+
+55
+00:04:18,540 --> 00:04:22,800
+معناه اني بروح من A و برجع ل A هي closed path مصار
+
+56
+00:04:22,800 --> 00:04:27,950
+مغلق بالنفس النقطة و برجع لهالذن هذا هو ال clause
+
+57
+00:04:27,950 --> 00:04:31,410
+integral ل a dot dl كمان مرة a هو vector قد يكون
+
+58
+00:04:31,410 --> 00:04:35,450
+ال electric field دي ال اللي تعلمنا كيف احنا نطوله
+
+59
+00:04:35,450 --> 00:04:37,550
+أسواق ال Cartesian أو ال spherical أو ال
+
+60
+00:04:37,550 --> 00:04:42,890
+cylindrical coordinate هلت
+
+61
+00:04:42,890 --> 00:04:45,590
+لو أنا بحكي على ال surface integral لذن هك اتعرفنا
+
+62
+00:04:45,590 --> 00:04:49,230
+احنا ال line integral او ال clause plus integral
+
+63
+00:04:49,230 --> 00:04:56,730
+ال line integral هو ال vector dot dlclosed box لما
+
+64
+00:04:56,730 --> 00:05:03,610
+بحط الدوارة هذا يعني ال line integral او ال curve
+
+65
+00:05:03,610 --> 00:05:07,310
+integral او ال contour integral التلاتة بالنص
+
+66
+00:05:07,310 --> 00:05:12,110
+المعناه ليش لمين لأ ال surface integral ال surface
+
+67
+00:05:12,110 --> 00:05:15,210
+integral is a kind of vector a continuous region
+
+68
+00:05:15,210 --> 00:05:19,390
+اللي تحوي ال surface we define ال surface integral
+
+69
+00:05:19,390 --> 00:05:26,470
+انه عبارة عن integral of Sهذه المعناه لـprojection
+
+70
+00:05:26,470 --> 00:05:31,030
+لـA على S لـA كسانسية الـDS كيف بحددها أن دائما
+
+71
+00:05:31,030 --> 00:05:36,090
+الـDS هنا شبه عرف الـVector الـVector هو المجموعة
+
+72
+00:05:36,090 --> 00:05:41,090
+الـDS في أنها متمارضةهو ال unit vector العمودي على
+
+73
+00:05:41,090 --> 00:05:43,610
+ال surface يعني إذا ال surface تبع هو الطاولة
+
+74
+00:05:43,610 --> 00:05:47,410
+هيكون ال unit vector عمودي عليها إذا هي الطاولة
+
+75
+00:05:47,410 --> 00:05:51,390
+بتحتوي جسم أو object يعني volume دايما الانهات
+
+76
+00:05:51,390 --> 00:05:55,010
+بيكون برا ال object ماحطوش لجهة لبرا يعني ال
+
+77
+00:05:55,010 --> 00:05:59,090
+surface حوالين طبع بيكون الانهات لبرا تجاه ال R
+
+78
+00:05:59,090 --> 00:06:05,990
+hat طالع من ال surface طبعا إذا هذه عبارة عن مين A
+
+79
+00:06:05,990 --> 00:06:12,490
+dot S هي عبارة عن A dotانها باسم water الانها تنية
+
+80
+00:06:12,490 --> 00:06:15,470
+المجلة تبقى a المجلة تبقى انها تنية واحدة في خان
+
+81
+00:06:15,470 --> 00:06:23,910
+الزاوية الاباني هذا هو ال surface انتجرة مثل
+
+82
+00:06:23,910 --> 00:06:27,410
+هذه الرسمة، هذه الرسمة عندنا surface وفيه field
+
+83
+00:06:27,410 --> 00:06:31,190
+طالع منه هذا ال field مارق هذا ال field هذا ال
+
+84
+00:06:31,190 --> 00:06:33,790
+surface هذا ال control اللي حوالي ال surface و ال
+
+85
+00:06:33,790 --> 00:06:37,610
+field مارق هذا الشكل عندنا ان هو عمودي على ال
+
+86
+00:06:37,610 --> 00:06:41,780
+surfaceوهي ال field دي اس دوت انهارد هيتزوّر بيهم
+
+87
+00:06:41,780 --> 00:06:45,700
+ال data هيكون ال projection تبع ال field تجاه
+
+88
+00:06:45,700 --> 00:06:53,680
+الانهارد طبعا
+
+89
+00:06:53,680 --> 00:06:56,420
+ال DS احنا دائما بنقول انه جزء من ال surface اننا
+
+90
+00:06:56,420 --> 00:07:00,260
+اتعلمناه في المحاضرات السابقةأذا هذا surface زي
+
+91
+00:07:00,260 --> 00:07:04,020
+surface الطاولة وإن ال field بخترقه عادي من ناحية
+
+92
+00:07:04,020 --> 00:07:10,000
+لفوق فالfield و العمود اللي هو normal الشكل فال
+
+93
+00:07:10,000 --> 00:07:15,520
+field A dot and hat تدي أسلوية element صغير من ال
+
+94
+00:07:15,520 --> 00:07:20,780
+surface واضح؟
+
+95
+00:07:20,780 --> 00:07:25,640
+for a closed surface ده نفسنا متعلمين إن الدائرة
+
+96
+00:07:25,640 --> 00:07:33,790
+إذا إن ال surface انتجرةهو a.ds لو انا حطيت closed
+
+97
+00:07:33,790 --> 00:07:37,570
+معناه انه closed service نتيجة يعني بوحتي كل ال
+
+98
+00:07:37,570 --> 00:07:39,850
+service على closed
+
+99
+00:07:48,800 --> 00:07:52,060
+طبعا هذا هو بالنسباله ال service integral نجي لل
+
+100
+00:07:52,060 --> 00:07:54,820
+volume integral volume ماله احنا قلنا DV ماله
+
+101
+00:07:54,820 --> 00:07:58,140
+scalar يعني مافيش فيها dot ال product ولا cross
+
+102
+00:07:58,140 --> 00:08:02,340
+product DV scalar هذا ال dot هنلاحظها فقط في ال
+
+103
+00:08:02,340 --> 00:08:07,800
+line integral و في ال surface integral لكن
+
+104
+00:08:07,800 --> 00:08:10,700
+ال volume integral DV احنا اتفقدها من محاضرة
+
+105
+00:08:10,700 --> 00:08:14,640
+الماضية انها scalar فزم حيكون اندي مثلا ال volume
+
+106
+00:08:14,640 --> 00:08:18,770
+integral هو غضب integral على ال volumeمثلًا scalar
+
+107
+00:08:18,770 --> 00:08:27,290
+ρو V في DD هذا متنصب لـ scalar field زي الوفعي و
+
+108
+00:08:27,290 --> 00:08:33,750
+سنحكي عن الفيلز ال volume integral of a scalar ρو
+
+109
+00:08:33,750 --> 00:08:37,650
+V على ال volume V هي هذا الintegral او V رو V
+
+110
+00:08:37,650 --> 00:08:43,570
+مثلًا على طول هذه الفقطة اللي بحكي عنها انها
+
+111
+00:08:43,570 --> 00:08:48,130
+الانتيجرة لوثبت الانتيجرة وال volumeلو كنتي برقص
+
+112
+00:08:48,130 --> 00:08:53,770
+مضيق دي مثلا روحي دي خدمية هذا ال line هذا ال
+
+113
+00:08:53,770 --> 00:09:02,830
+surface هذا ال ball ناخد
+
+114
+00:09:02,830 --> 00:09:10,490
+أمثلة المثل أمامنا ball نائق تالي دول عندى field F
+
+115
+00:09:10,490 --> 00:09:15,290
+vector field اللي له three components في ال X و Y
+
+116
+00:09:15,290 --> 00:09:15,770
+و Z
+
+117
+00:09:22,100 --> 00:09:25,280
+بنحسب الـcirculation نحنا إيش الcirculation معناه
+
+118
+00:09:25,280 --> 00:09:31,640
+line integral curve contour line circulation of f
+
+119
+00:09:31,640 --> 00:09:36,900
+around closed path بده مصار مغلق اللي هو موضح
+
+120
+00:09:36,900 --> 00:09:41,150
+اللياة في الرسم اللي هو بده من نقطة واحدةأو يعني
+
+121
+00:09:41,150 --> 00:09:44,170
+هذه واحدة هي الطول هذا يعني من نقطة high إلى ال x
+
+122
+00:09:44,170 --> 00:09:47,530
+-axis على ال bus واحد ال bus تاني ال bus ثانية ال
+
+123
+00:09:47,530 --> 00:09:50,430
+bus أربعة ورجع نقطة نقطة نفس النقطة إذا هو a
+
+124
+00:09:50,430 --> 00:09:54,170
+closed bus طبعا كيف أول حاجة بدنا نعملها ده ال
+
+125
+00:09:54,170 --> 00:09:56,610
+integer طبعا هو مطلوب بالنيه closed bus يعني
+
+126
+00:09:56,610 --> 00:10:03,430
+هستخدم نيه اللي هي عيب closed bus closed bus لل
+
+127
+00:10:03,430 --> 00:10:10,010
+field up dot dl عيبفي حد بيحب يطلع عليه يحل على
+
+128
+00:10:10,010 --> 00:10:17,830
+الصدورة و أنا أساعده؟ عامحه؟ بسيط، ممتاز، اطلعي
+
+129
+00:10:17,830 --> 00:10:22,430
+لنا، مش مشكلة، أنا هساعدكم ده، أنا محدش لحالي، مش
+
+130
+00:10:22,430 --> 00:10:28,370
+مشكلة اذا احنا بنا ال line integral، اللي هو ال
+
+131
+00:10:28,370 --> 00:10:31,430
+closed line integral، ال closed integral، ال
+
+132
+00:10:31,430 --> 00:10:32,750
+closed، لمن؟ لأ
+
+133
+00:10:39,610 --> 00:10:53,710
+انتقل على ال bus الاول انتظر انتظر
+
+134
+00:10:53,710 --> 00:10:57,750
+انتظر انتظر انتظر انتظر انتظر
+
+135
+00:11:10,090 --> 00:11:15,090
+عشان أعمل close boss لازم أجمع ال integral كله بدأ
+
+136
+00:11:15,090 --> 00:11:17,210
+ال integral على أول ثم ال integral على التاني ثم
+
+137
+00:11:17,210 --> 00:11:19,550
+ال integral على تالته ثم ال integral على الرابعه
+
+138
+00:11:19,550 --> 00:11:24,590
+كل boss بقدرس إيش قيمة F وإيش قيمة DF نبدأ بال
+
+139
+00:11:24,590 --> 00:11:27,790
+boss الأول يعني نعمل ال integral على واحد
+
+140
+00:11:36,630 --> 00:11:39,510
+متذكرين احنا تفعل المحاضر الماضي انا بتطلع بشوف في
+
+141
+00:11:39,510 --> 00:11:47,450
+هذا ال bus مين بتغير فيه؟ قداش كيمة Y هنا؟ كتش
+
+142
+00:11:47,450 --> 00:11:50,710
+كيمة
+
+143
+00:11:50,710 --> 00:11:56,310
+Y هنا؟0 طب و Z قدش قيمتها؟ مين متغير هنا؟ مين
+
+144
+00:11:56,310 --> 00:12:02,010
+بتغير I؟ ال X بتغير من واحد لصفر ال X عارف تتغير
+
+145
+00:12:02,010 --> 00:12:06,070
+من واحد لصفر لذا هنا المتغير واحد مين D L يعني لو
+
+146
+00:12:06,070 --> 00:12:10,810
+احنا كتبنا ال D L بشكل عام فيه ال D L؟ D Alpha ال
+
+147
+00:12:10,810 --> 00:12:19,510
+Cartesian تساوي DX X hat زائد DY Y hat زائد DZ Z
+
+148
+00:12:19,510 --> 00:12:23,850
+hatزى الـ z أصلا صفر تتغيره شون و ال y تتغيره شون
+
+149
+00:12:23,850 --> 00:12:27,370
+هيبقى لعيننا dx except إذا ال dl هنا إحنا عارفينها
+
+150
+00:12:27,370 --> 00:12:33,850
+ال dl إيه هو ال partialings dl إيش بيساوي dx
+
+151
+00:12:33,850 --> 00:12:39,630
+except هاي ال bus الأولاني أبقى F لو طلعنا F ليه
+
+152
+00:12:39,630 --> 00:12:44,110
+هيكملها؟ إحنا عاملة بنقول إن ال z صفر و ال y صفر
+
+153
+00:12:44,110 --> 00:12:47,510
+إذا مين ضمن ال F؟ إذا أنا على ال bus الأولاني F و
+
+154
+00:12:47,510 --> 00:12:53,340
+تكملنا من ال Fعلى جانب السلسفة الأولى F بالبعص
+
+155
+00:12:53,340 --> 00:12:58,360
+الأولانى بيكون X تربيع X hat لأننا لدينا X تربيع X
+
+156
+00:12:58,360 --> 00:13:01,340
+hat بيكون على جانبي نفسى لأننا لدينا Y في هذا
+
+157
+00:13:01,340 --> 00:13:07,340
+البعص بتسوء Zero وY بتسوء Zero وY بتسوء Zero وZ
+
+158
+00:13:07,340 --> 00:13:12,120
+بتسوء Zero فإيش طبيعى هتكون Zero وY Zero معين؟ إذا
+
+159
+00:13:12,120 --> 00:13:17,180
+نأخدوا ال DL إيش هتكون X تربيع Antigual على واحد
+
+160
+00:13:17,180 --> 00:13:25,090
+واحدة Zero واحدة Zeroمن يمين X تربيع في DX من واحد
+
+161
+00:13:25,090 --> 00:13:33,750
+لسا ساوية من واحد لسا ساوية من واحد لسا ساوية من
+
+162
+00:13:33,750 --> 00:13:35,490
+واحد لسا ساوية من واحد لسا ساوية من واحد لسا ساوية
+
+163
+00:13:35,490 --> 00:13:35,810
+من واحد لسا ساوية من واحد لسا ساوية من واحد لسا
+
+164
+00:13:35,810 --> 00:13:36,490
+ساوية من واحد لسا ساوية من واحد لسا ساوية من واحد
+
+165
+00:13:36,490 --> 00:13:36,590
+لسا ساوية من واحد لسا ساوية من واحد لسا ساوية من
+
+166
+00:13:36,590 --> 00:13:38,150
+واحد لسا ساوية من واحد لسا ساوية من واحد لسا ساوية
+
+167
+00:13:38,150 --> 00:13:45,050
+من واحد لسا ساوية من واحد لسا ساوية من واحد لسا
+
+168
+00:13:45,050 --> 00:13:53,390
+ساوية من واحد لسا ساوية من واحدحد بده يجرب إسرارة
+
+169
+00:13:53,390 --> 00:13:58,190
+ال integration
+
+170
+00:13:58,190 --> 00:14:11,110
+التاني طبعا عليها خليها تكون DL أو Y دي وي
+
+171
+00:14:11,110 --> 00:14:15,950
+وي هت على هذا ال axis X صفر و Z صفر المتعير فقط
+
+172
+00:14:15,950 --> 00:14:18,230
+اللي هو Y بروح من Zero لواحد
+
+173
+00:14:21,320 --> 00:14:27,800
+فانتجر على الباص التاني الو F.DL هنقول ايش كيمة F
+
+174
+00:14:27,800 --> 00:14:33,140
+F ايش اللي انا سفر ال X سفر و ال Z سفر يعني الترم
+
+175
+00:14:33,140 --> 00:14:35,140
+الأول بروحها السفر و الترم الثاني بروحها السمين
+
+176
+00:14:35,140 --> 00:14:39,620
+بظهر لنا minus minus
+
+177
+00:14:39,620 --> 00:14:47,040
+Y تربيع Z hat ممتازة و DL ايش بها تساوي اكتب لنا
+
+178
+00:14:47,040 --> 00:14:47,580
+DL
+
+179
+00:14:51,630 --> 00:14:56,570
+D Y Y hat ايش ال dot product لهم على طول معايا
+
+180
+00:14:56,570 --> 00:14:59,430
+احكوا كلكم dot product ل F dot D F ماتحكيش في
+
+181
+00:14:59,430 --> 00:15:03,930
+أسرارك dot product ايش بيساوي ايش بيساوي احكوا في
+
+182
+00:15:03,930 --> 00:15:08,730
+حد جاوب صح zero dot product zero احنا Z hat dot Y
+
+183
+00:15:08,730 --> 00:15:14,850
+hat ده ايش بيساويx hat dot x hat واحد y hat dot y
+
+184
+00:15:14,850 --> 00:15:18,650
+hat واحد z hat dot z hat واحد اي dot product بين x
+
+185
+00:15:18,650 --> 00:15:22,310
+hat و y hat و y hat مع z hat كلهم هدولوا مع بعض
+
+186
+00:15:22,310 --> 00:15:25,590
+situation of the perpendicular of the x axis 90
+
+187
+00:15:25,590 --> 00:15:29,370
+درجة هيكون مجموعة الأول في التاني في الزهر اللي
+
+188
+00:15:29,370 --> 00:15:35,190
+بينهم جتر وزهر بينهم جتر و تسعين صفر اذا هدرقش ال
+
+189
+00:15:35,190 --> 00:15:39,550
+bus تبعه على الرأس اللي بيساوي صفر ممتاز فى حد جرب
+
+190
+00:15:39,550 --> 00:15:40,470
+ال bus التالت
+
+191
+00:15:43,020 --> 00:15:47,460
+هل حانت تجرب ال buff التالت؟
+
+192
+00:15:47,460 --> 00:15:55,180
+هل حانت تجربه؟ يللا نبدأ ال buff التالت بدنا ال
+
+193
+00:15:55,180 --> 00:15:58,520
+element ال element هنا ناله مين اللي ثابت في طول
+
+194
+00:15:58,520 --> 00:16:05,800
+هذا الطول؟ تمام ممتاز مين مضايق؟ او z اذا دي ال
+
+195
+00:16:05,800 --> 00:16:11,150
+ايش بيحن نساوي؟ ممتاز احنا دي اليقل بها تساوي dx x
+
+196
+00:16:11,150 --> 00:16:16,270
+hat زي dy y hat لأن ال y ثابت على هذا ال surface
+
+197
+00:16:16,270 --> 00:16:21,190
+من المفاعل ال y ثابت على قيمة واحد لكن ال x وزي ما
+
+198
+00:16:21,190 --> 00:16:25,570
+هم متغيرين طب قبل ايش هي تكون قيمتها ان ال y قدش
+
+199
+00:16:25,570 --> 00:16:29,930
+قيمتها فلل surface واحد طول واقع واحد فاحنا بس
+
+200
+00:16:29,930 --> 00:16:33,490
+اللي بيقولوا انه معروف ليه هو واحد بس هي طب تقف
+
+201
+00:16:42,450 --> 00:16:48,190
+DZDXDZ DX DX
+
+202
+00:16:48,190 --> 00:16:56,330
+DX DX DX DX DX DX DX DX DX DX
+
+203
+00:16:56,330 --> 00:16:56,330
+DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX
+
+204
+00:16:56,330 --> 00:16:56,330
+DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX
+
+205
+00:16:56,330 --> 00:16:56,330
+DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX
+
+206
+00:16:56,330 --> 00:16:57,530
+DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX
+
+207
+00:16:57,530 --> 00:16:57,530
+DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX
+
+208
+00:16:57,530 --> 00:16:57,910
+DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX
+
+209
+00:16:57,910 --> 00:16:57,910
+DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX
+
+210
+00:16:57,910 --> 00:16:57,910
+DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX
+
+211
+00:16:57,910 --> 00:16:57,910
+DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX
+
+212
+00:16:57,910 --> 00:16:57,910
+DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX
+
+213
+00:16:57,910 --> 00:16:57,910
+DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX
+
+214
+00:16:57,910 --> 00:16:57,910
+DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX DX
+
+215
+00:16:57,910 --> 00:16:59,070
+DX DX
+
+216
+00:17:23,380 --> 00:17:28,120
+بعدين الـ dy مش إلها y hat هتروحها السفر هتتقبل دي
+
+217
+00:17:28,120 --> 00:17:30,000
+minus d z
+
+218
+00:17:32,750 --> 00:17:35,630
+هذه dot ال product تبعها second dot مع X هتكون
+
+219
+00:17:35,630 --> 00:17:40,610
+zero dot مع Z هتكون zero لكن هيكون في عندي X dot X
+
+220
+00:17:40,610 --> 00:17:43,910
+هيكون في عندي X تبعي عندي X و في عندي Z dot Z
+
+221
+00:17:43,910 --> 00:17:47,570
+هيكون minus و هي زي نقطة 6000 اذا نعمل ال
+
+222
+00:17:47,570 --> 00:17:52,850
+integration على ال path تبعنا اللي هو F dot PL
+
+223
+00:17:52,850 --> 00:17:57,130
+بسبب ما اعمله في حاجة مهمة انا بدى الاحظها انه على
+
+224
+00:17:57,130 --> 00:18:01,530
+طول هذا المصال هيكون X و Z ممتساويينهو ده استغل
+
+225
+00:18:01,530 --> 00:18:05,290
+هذه الحاجة اقول ان X بتساوي Z يعني معناه DX اش
+
+226
+00:18:05,290 --> 00:18:09,130
+بتساوي DZ هو ده استغل هذا الاشي هنا يعني انا اقول
+
+227
+00:18:09,130 --> 00:18:14,410
+بس بمين DX بده DZ فخلنا نحط ان X على طول هذا
+
+228
+00:18:14,410 --> 00:18:22,910
+المصار بتساوي Z اذا DX بتساوي DZ اذا DX بتساوي DZ
+
+229
+00:18:22,910 --> 00:18:28,750
+فهيكون ال Integral هيكون
+
+230
+00:18:28,750 --> 00:18:37,110
+التكامليكون X تربية DX X hat DX X hat مافيش X hat
+
+231
+00:18:37,110 --> 00:18:40,190
+لان احنا ضبط بيحنا بتاسع سكيلة مش ممكن يال X hat
+
+232
+00:18:40,190 --> 00:18:42,890
+ضبط بيها مش ممكن يال X hat ضبط بيها مش ممكن يال X
+
+233
+00:18:42,890 --> 00:18:43,630
+hat ضبط بيها مش ممكن يال X hat ضبط بيها مش ممكن
+
+234
+00:18:43,630 --> 00:18:43,710
+يال X hat ضبط بيها مش ممكن يال X hat ضبط بيها مش
+
+235
+00:18:43,710 --> 00:18:43,750
+ممكن يال X hat ضبط بيها مش ممكن يال X hat ضبط بيها
+
+236
+00:18:43,750 --> 00:18:44,170
+مش ممكن يال X hat ضبط بيها مش ممكن يال X hat ضبط
+
+237
+00:18:44,170 --> 00:18:45,050
+بيها مش ممكن يال X hat ضبط بيها مش ممكن يال X hat
+
+238
+00:18:45,050 --> 00:18:51,970
+ضبط بيها مش ممكن يال X hat ضبط بيها مش ممكن يال X
+
+239
+00:18:51,970 --> 00:18:58,290
+hat ضبط بيها مش ممكن
+
+240
+00:18:58,290 --> 00:19:04,020
+يال Xل X تربية مانوس واحد DX يوم بتروح ال DX في
+
+241
+00:19:04,020 --> 00:19:11,820
+هالحالة ال DX بتروح من واحد صح من واحد من زيرو ل
+
+242
+00:19:11,820 --> 00:19:20,480
+واحد من زيرو ل واحد من زيرو ل واحد الكم هتزاوي X
+
+243
+00:19:20,480 --> 00:19:25,700
+كيوب على ثلاثة كمية من
+
+244
+00:19:25,700 --> 00:19:26,860
+زيرو ل واحد
+
+245
+00:19:29,490 --> 00:19:33,810
+-XE من 0 إلى 1 هيكون ثلث من ثلث من ثلث من ثلث من
+
+246
+00:19:33,810 --> 00:19:37,210
+ثلث من ثلث من ثلث من ثلث من ثلث من ثلث من ثلث من
+
+247
+00:19:37,210 --> 00:19:38,410
+ثلث من ثلث من ثلث من ثلث من ثلث من ثلث من ثلث من
+
+248
+00:19:38,410 --> 00:19:43,030
+ثلث من ثلث من ثلث من ثلث من ثلث من ثلث من ثلث من
+
+249
+00:19:43,030 --> 00:19:44,750
+ثلث من ثلث من ثلث من ثلث من ثلث من ثلث من ثلث من
+
+250
+00:19:44,750 --> 00:19:49,230
+ثلث من ثلث من ثلث من ثلث من ثلث من ثلث من ثلث من
+
+251
+00:19:49,230 --> 00:19:49,610
+ثلث من ثلث من ثلث من ثلث من ثلث من ثلث من ثلث من
+
+252
+00:19:49,610 --> 00:19:55,030
+ثلث من ثلث من ثلث من ثلث من ثلث من ثلث من ثلث من
+
+253
+00:19:55,030 --> 00:19:56,430
+ثلث
+
+254
+00:20:19,680 --> 00:20:24,740
+مين اللي سابت هنا مين سابت على هذا ال surface اكس
+
+255
+00:20:24,740 --> 00:20:26,460
+اكس اكس اكس اكس اكس اكس اكس اكس اكس اكس اكس اكس
+
+256
+00:20:26,460 --> 00:20:32,400
+اكس اكس اكس اكس اكس اكس اكس اكس اكس
+
+257
+00:20:33,530 --> 00:20:38,090
+خلّيني أقولها، إذا نسينا معاكين DL DL في هذا البعض
+
+258
+00:20:38,090 --> 00:20:45,210
+هي عبارة عن DX X hat دي Y Y hat زائد DZ Z hat
+
+259
+00:20:45,210 --> 00:20:51,070
+وعندنا F، إيش كيمة X فيها تقطع ال contour؟ هيكون
+
+260
+00:20:51,070 --> 00:20:56,570
+واحد، فخلّيني أضع F F بتاعة ثانوية X hat
+
+261
+00:21:01,790 --> 00:21:11,130
+-z y hat-y تلبية z hat بدنا ندبت ال product بينهم
+
+262
+00:21:11,130 --> 00:21:16,470
+F dot dl F
+
+263
+00:21:16,470 --> 00:21:22,530
+dot dl لإن ال x hat هتكون ستبقى x hat و y zero و x
+
+264
+00:21:22,530 --> 00:21:25,890
+hat و z hat zero لكن عندي component y hat y hat
+
+265
+00:21:25,890 --> 00:21:35,930
+هتكون-z dyعندي minus y تربية dy minus y تربية dz
+
+266
+00:21:35,930 --> 00:21:39,510
+نفس الحاجة هلاحظ ان ال y و ال z على هذا الكمتون
+
+267
+00:21:39,510 --> 00:21:43,450
+معناه متساوى و ال y بتساوي ال z إذا دي y بتساوي دي
+
+268
+00:21:43,450 --> 00:21:48,490
+z y تساوي ال z إذا دي y بتساوي دي z وهي إيش هتساوي
+
+269
+00:21:48,490 --> 00:21:59,980
+minus y dy minus y تربية dy يعني هتكون التكاملمن
+
+270
+00:21:59,980 --> 00:22:04,720
+اولى وين ال Y بتروح من اولى وين ال Y هتروح ال Y
+
+271
+00:22:04,720 --> 00:22:09,200
+هنا لقداش كمية ال Y عند هدفت النقطة كمية كمية هنا
+
+272
+00:22:09,200 --> 00:22:18,260
+واحد لزيرو اذا من واحد لزيرو ل minus Y dy minus Y
+
+273
+00:22:18,260 --> 00:22:26,180
+تربيع dy هسة minus Y تربيع على اثنين من واحد لستر
+
+274
+00:22:26,180 --> 00:22:29,300
+minus Y تربيع
+
+275
+00:22:34,190 --> 00:22:38,390
+الحالة الأولى ستكون plus نص والحالة الثانية plus
+
+276
+00:22:38,390 --> 00:22:43,190
+طول وهي كذا نكون حصلنا على الأربع باص اسم عليها
+
+277
+00:22:43,190 --> 00:22:44,290
+اللي أجمعهم مع بعض
+
+278
+00:22:47,900 --> 00:22:51,160
+في اي صعوبة لحد هنا؟ يعني احنا كل ما بنعمله لما
+
+279
+00:22:51,160 --> 00:22:53,800
+نجنا من ال boss integral او ال control integral
+
+280
+00:22:53,800 --> 00:22:57,060
+بروحه انا محددة اللي هو mean dl ال differential
+
+281
+00:22:57,060 --> 00:23:00,820
+links في هالحالة ابسط حالة هي mean ال Cartesian
+
+282
+00:23:00,820 --> 00:23:03,640
+اللي احنا متعودين عليه في ال cylindrical نفس الاشي
+
+283
+00:23:03,640 --> 00:23:07,860
+هنحدد ال control اللي بعمل عليه او ال باق ال dl ال
+
+284
+00:23:07,860 --> 00:23:10,440
+vector بكون موجود عندى و بعمل ال integration
+
+285
+00:23:24,790 --> 00:23:27,590
+نفس الفكرة لو كان عندي إيه اللي هو cylindrical
+
+286
+00:23:27,590 --> 00:23:29,630
+coordinate نحله مع بعض ولا نمشي
+
+287
+00:23:34,800 --> 00:23:38,380
+على أرضنا انت شايفين في عندنا contour بس هدف مين
+
+288
+00:23:38,380 --> 00:23:41,180
+في ال cylindrical coordinates بيعطينا قيمة رو
+
+289
+00:23:41,180 --> 00:23:46,660
+بتروح من 0 ل 2 فاي بتروح من 0 ل 60 و زي طبعا زيرو
+
+290
+00:23:46,660 --> 00:23:50,740
+لإن احنا في ال XY plane ومطلوب منها اننا نحسب ال
+
+291
+00:23:50,740 --> 00:23:52,960
+circulation لما نقول ال circulation مش معناه
+
+292
+00:23:52,960 --> 00:23:57,340
+closed path يعني نبدأ من السفر و نرجع لزيرو طب هنا
+
+293
+00:23:57,340 --> 00:24:02,980
+أحد بيقوللي إيش ال DL هنا؟DL DX ممتاز هنا او ال D
+
+294
+00:24:02,980 --> 00:24:05,220
+rho في الحلقة اللي ميلها بس ال D rho بتساوي بال
+
+295
+00:24:05,220 --> 00:24:09,140
+تمام DX هي في ال cylindrical coordinate هي D rho
+
+296
+00:24:09,140 --> 00:24:14,100
+rho hat عندها الفعيش بتساوي Zero فزي ما عملنا Phi
+
+297
+00:24:14,100 --> 00:24:16,900
+بتساوي Zero بنعوض عن Phi بتساوي Zero في هذا البعض
+
+298
+00:24:16,900 --> 00:24:23,680
+لل A وعندي اللي هو DL عبارة عن D rho rho hat واضح؟
+
+299
+00:24:24,190 --> 00:24:27,470
+لازم أكون عارفة قيمة الـ5 وإلا مش هقدر أحلها، إذا
+
+300
+00:24:27,470 --> 00:24:30,810
+ال integration هنا هيكون على d rho من 0 ل2، بس
+
+301
+00:24:30,810 --> 00:24:36,320
+عشان هي d rho بتسوى dx، مش معناه إن 5 تسوى 0لأن هي
+
+302
+00:24:36,320 --> 00:24:40,120
+الـPhi ما بين الـRow و الـX لما تنطق على الـX
+
+303
+00:24:40,120 --> 00:24:44,000
+الـPhi بتكون Zero لما تروح لأ الـY بتكون Phi على
+
+304
+00:24:44,000 --> 00:24:47,520
+اتنين فهي الحلقة بس مافينا وجه يعني مافينا جزء منه
+
+305
+00:24:47,520 --> 00:24:52,240
+اللي هي ما بين الـ0 و الـ60 فهي الـX Axis وهي اللي
+
+306
+00:24:52,240 --> 00:24:57,940
+هو ال element تبعنا ما بين الـ0 و الـ60 طبعا؟ طيب
+
+307
+00:24:57,940 --> 00:25:03,840
+فعلى هذا الباص إيش هتكون DRaw DRالـ DL من فاسفة
+
+308
+00:25:03,840 --> 00:25:08,540
+الـ DL مفروض دي رو رو هات، بس إيش هيكون عندي؟ الفا
+
+309
+00:25:08,540 --> 00:25:15,200
+ساعتها ستين، لكن هنا إيش هتكون؟ رو دي فاي فاي هات،
+
+310
+00:25:15,200 --> 00:25:18,680
+يعني بتقولنا لو أخدنا ال element الـ DL، إيش هيكون
+
+311
+00:25:18,680 --> 00:25:24,880
+المقابل للتغيير في D؟ فاي إنتوا مش داحسين أه؟
+
+312
+00:25:39,940 --> 00:25:44,200
+طبعا روحنا بالكون سالتة اللى هى قبلتها اتنين هم
+
+313
+00:25:44,200 --> 00:25:47,080
+عوض عنها اذا نفس ال procedure اللى طبقناها فى
+
+314
+00:25:47,080 --> 00:25:50,440
+partition coordinate اللى طبقها حتى لو كنا فى
+
+315
+00:25:50,440 --> 00:25:53,660
+cylindrical coordinate او في spherical coordinate
+
+316
+00:25:53,660 --> 00:25:58,940
+فى اي سؤال تتغلبوا ان كل حد اللى قاعد تجيبه ال DL
+
+317
+00:25:58,940 --> 00:25:59,540
+او ال
+
+318
+00:26:03,180 --> 00:26:09,040
+هي جلاء الدل ال operator الدل ال operator الدل هي
+
+319
+00:26:09,040 --> 00:26:12,260
+ال delta مشقلة يعني انت بتاعت دايما الدلتك اتشكلها
+
+320
+00:26:12,260 --> 00:26:15,600
+رمض
+
+321
+00:26:15,600 --> 00:26:25,740
+دلتا تحطيه في وياضياتك هم تبتدلوا صح؟ دل
+
+322
+00:26:25,740 --> 00:26:30,900
+الدل
+
+323
+00:26:30,900 --> 00:26:35,170
+هو المشقلة تبع الدلتعشان تتذكروا هذا بس ابدلوا
+
+324
+00:26:35,170 --> 00:26:38,210
+بهذا الشكل في ال Cartesian coordinate هو عبارة عن
+
+325
+00:26:38,210 --> 00:26:41,210
+differential operator يعني احنا بس أخدنا مثلا
+
+326
+00:26:41,210 --> 00:26:45,270
+تفاضهم بنقول d by dx ال differential يعني ماقلناش
+
+327
+00:26:45,270 --> 00:26:48,530
+أخدناها ك vector او d by dy يعني بتاخد ال
+
+328
+00:26:48,530 --> 00:26:53,010
+differential عيني ال function x,
+
+329
+00:26:53,350 --> 00:26:58,570
+y, z عشان أقول بقى أخد بس أحدنا يا d by dx يا d by
+
+330
+00:26:58,570 --> 00:27:02,610
+dy ده ال function هذا لإن ال function في x, y, zأو
+
+331
+00:27:02,610 --> 00:27:07,670
+باخد اللي هو D by DZ لهذا الـ Cartesian الـ del
+
+332
+00:27:07,670 --> 00:27:13,270
+operator هو vector مش scalar و بساوي ال Cartesian
+
+333
+00:27:13,270 --> 00:27:19,930
+coordinate D by DX X hat زي D by DY U hat زي D by
+
+334
+00:27:19,930 --> 00:27:25,150
+DZ Z hat هذا
+
+335
+00:27:25,150 --> 00:27:29,170
+ال del operator ممكن يجيب لي gradient أو scalar،
+
+336
+00:27:29,170 --> 00:27:33,480
+vectorV لو كان عندي ال vector V بيقول ال gradient
+
+337
+00:27:33,480 --> 00:27:39,720
+لما بقول دل أكتر دل أكتر لو كان Scalar او مثلا لو
+
+338
+00:27:39,720 --> 00:27:43,080
+كان عندي V بقول ال gradient دل أكتر دل أكتر دل
+
+339
+00:27:43,080 --> 00:27:44,600
+أكتر دل أكتر دل أكتر دل أكتر دل أكتر دل أكتر دل
+
+340
+00:27:44,600 --> 00:27:47,500
+أكتر دل أكتر دل أكتر دل أكتر دل أكتر دل أكتر دل
+
+341
+00:27:47,500 --> 00:27:48,220
+أكتر دل أكتر دل أكتر دل أكتر دل أكتر دل أكتر دل
+
+342
+00:27:48,220 --> 00:27:52,120
+أكتر دل أكتر دل أكتر دل أكتر دل أكتر دل أكتر دل
+
+343
+00:27:52,120 --> 00:27:59,910
+أكتر دل أكتر دل أكتر دل أكبما يكون الoperation تبع
+
+344
+00:27:59,910 --> 00:28:05,150
+تلك الارتكالة نسميه gradient of a field ال
+
+345
+00:28:05,150 --> 00:28:09,010
+diversion ل vector field لو كان vector field هيكون
+
+346
+00:28:09,010 --> 00:28:15,970
+تأثر في ال operator ممكن يكون ضد ال product لأنه
+
+347
+00:28:15,970 --> 00:28:19,210
+vector field يعني لو كان ال operation ضد ال
+
+348
+00:28:19,210 --> 00:28:23,110
+product بسميه divergence هذه العملية اسمها
+
+349
+00:28:23,110 --> 00:28:28,270
+divergence ال divergence ل vector Aلو كان cross
+
+350
+00:28:28,270 --> 00:28:33,170
+product او curl product نحن
+
+351
+00:28:33,170 --> 00:28:36,250
+نحفظها
+
+352
+00:28:36,250 --> 00:28:40,850
+يوم الصبحة يعني انا بقول اللي هي gradient لل field
+
+353
+00:28:40,850 --> 00:28:43,290
+معناه انا بحكي لما اقول gradient لل field بحكي ع
+
+354
+00:28:43,290 --> 00:28:46,870
+scalar field بحكي ب divergence ل field الناس بتعرف
+
+355
+00:28:46,870 --> 00:28:49,870
+اني بحكي ع vector field curl ال field بحكي ع
+
+356
+00:28:49,870 --> 00:28:57,240
+vector field ال class of a scalar Dهيكون هي دل
+
+357
+00:28:57,240 --> 00:29:10,920
+التربيه لبلاسين لسكيلر تير هو دل التربيه لبلاسين
+
+358
+00:29:10,920 --> 00:29:16,020
+لبلاسين فيه لليوم بيقولوها دل التربيه لإن هو دل
+
+359
+00:29:16,020 --> 00:29:21,900
+التربيه لبلاسين احنا
+
+360
+00:29:21,900 --> 00:29:28,120
+شفنا الدل تلالة ال XYZدلت الxy دلت الpartition
+
+361
+00:29:28,120 --> 00:29:34,520
+coordinates دي وي دي اكس اكسها زي دي وي ويها زي دي
+
+362
+00:29:34,520 --> 00:29:38,600
+وي دي زي اكسها طب ال cylindrical coordinates ده
+
+363
+00:29:38,600 --> 00:29:42,420
+كتبها دلت ال row و الفاية فالمعنى ان ال d by dx ده
+
+364
+00:29:42,420 --> 00:29:46,390
+كتبها دلت ال row و الفايةو الـ D by DZ تكون مضادة
+
+365
+00:29:46,390 --> 00:29:50,270
+رو و فاى و الـ DZ طبعا بتظل زى ما هي احنا قلنا فى
+
+366
+00:29:50,270 --> 00:29:51,770
+الـ cylindrical coordinate و ال Cartesian
+
+367
+00:29:51,770 --> 00:29:54,890
+coordinate زى ما هو مضاله مشترك اللى بتغير بدل ال
+
+368
+00:29:54,890 --> 00:29:58,830
+X و Y بيصيرين D رو و فاى فقمنا ببدأ لبنى ال D by
+
+369
+00:29:58,830 --> 00:30:03,090
+DX عشان أجيب ال D by DX مش بتستخدم ال chain rule
+
+370
+00:30:03,090 --> 00:30:11,870
+يعنى D by DX هدأجة من اين؟ D by D رو D رو by DX
+
+371
+00:30:13,120 --> 00:30:20,340
+زائر D by D Pi D Pi by D X احنا عارفين هاي
+
+372
+00:30:20,340 --> 00:30:24,360
+العلاقات شفناهم في محاضرات السابقة ان رو بساوية جت
+
+373
+00:30:24,360 --> 00:30:26,480
+تربيه على X تربيه على Y تربيه على Y تربيه على Y
+
+374
+00:30:26,480 --> 00:30:28,900
+تربيه على Y تربيه على Y تربيه على Y تربيه على X
+
+375
+00:30:28,900 --> 00:30:29,240
+تربيه على Y تربيه على Y تربيه على Y تربيه على Y
+
+376
+00:30:29,240 --> 00:30:29,240
+تربيه على Y تربيه على Y تربيه على Y تربيه على Y
+
+377
+00:30:29,240 --> 00:30:29,300
+تربيه على Y تربيه على Y تربيه على Y تربيه على Y
+
+378
+00:30:29,300 --> 00:30:30,660
+تربيه على Y تربيه على Y تربيه على Y تربيه على Y
+
+379
+00:30:30,660 --> 00:30:36,660
+تربيه على Y تربيه على Y تربيه على Y تربيه على Y
+
+380
+00:30:36,660 --> 00:30:42,380
+تربيه على Y ترRaw سوى جزر تربيه ل X تربيه زي Y
+
+381
+00:30:42,380 --> 00:30:52,500
+تربيه V Raw by V X شو تسوى 2X نص 2X على جزر X
+
+382
+00:30:52,500 --> 00:30:57,520
+تربيه ل Y تربيه مش هتبعش قبل غلط مش هدي يعني معناه
+
+383
+00:30:57,520 --> 00:31:00,140
+انا مش عارف ان انتوا عارفين و انا مش عارفين سكين و
+
+384
+00:31:00,140 --> 00:31:00,540
+عارفون
+
+385
+00:31:03,840 --> 00:31:09,980
+مش هيك يعني نص اللي هي الان او اشتغال
+
+386
+00:31:09,980 --> 00:31:17,100
+تجارب الجزر و تجارب اتنين اكس على اتنين الجثت اكس
+
+387
+00:31:17,100 --> 00:31:20,760
+على جثت اكس ترمية زي ال Y ترمية هذا في رو بقى في
+
+388
+00:31:20,760 --> 00:31:25,100
+اكس لو بطلعنا احنا على ال five احنا ال five زاوية
+
+389
+00:31:25,100 --> 00:31:29,980
+و بقولنا ثالثة بقى همين ليه Y و X صح وهذا ال roll
+
+390
+00:31:29,980 --> 00:31:32,940
+هي جثة ترمية ل X ترمية زي Y ترمية اللي هي ال roll
+
+391
+00:31:33,640 --> 00:31:39,260
+حنا طلعنا عنا X على روه داني بالهاتف من X على روه
+
+392
+00:31:39,260 --> 00:31:45,960
+جيبتها من الزاوية اذا هي عبارة عن cosine of I طبعا
+
+393
+00:31:45,960 --> 00:31:52,900
+فنسيت ال V0 by VX بدأ أرجع لل VX طبعا خلصنا بتضابط
+
+394
+00:31:52,900 --> 00:31:57,440
+VMD by V0 فإذا لو عوضت عن V by VX هذا ال term
+
+395
+00:31:57,440 --> 00:32:02,670
+عبارة عن مين؟ Cosine of I واضح كيف أجت؟نفس الحاجة
+
+396
+00:32:02,670 --> 00:32:05,630
+لهذه الجزئية دي five by دي اكس عاملكم اياها ولا
+
+397
+00:32:05,630 --> 00:32:11,890
+صارت واضحة اعملها خلاص تحط اذا ان هذا هو كيف احصل
+
+398
+00:32:11,890 --> 00:32:18,590
+على ال دي five by دي اكس عشان
+
+399
+00:32:18,590 --> 00:32:22,970
+اقل من اللي هو ال Cartesian للسيليندركال تاني نفس
+
+400
+00:32:22,970 --> 00:32:26,210
+الحاجة لل دي by دي واي نفس الخطوات اللي عملناها
+
+401
+00:32:26,210 --> 00:32:30,190
+باخد ال chain rule يعني هي تساوي دي دي واي دي رو
+
+402
+00:32:32,200 --> 00:32:40,940
+وهذه الجزئية بيجيب هدول الترمات و تطلع معايا علاقة
+
+403
+00:32:40,940 --> 00:32:45,780
+D by Dy بالنسبة للترمات ووصل D by Zero to D by Z
+
+404
+00:32:45,780 --> 00:32:52,100
+طبعا D by DZ يشملها D by DZ ويظهرها زي ما هي اذا
+
+405
+00:32:52,100 --> 00:32:57,560
+ندل ال operator مش هيكون بس ال cylindrical
+
+406
+00:32:57,560 --> 00:33:03,230
+coordinateدي باي دي رورو هات واحد على رورو دي باى
+
+407
+00:33:03,230 --> 00:33:06,950
+دي باى باى هات دي باى بيهات دي باى بيهات دي باى
+
+408
+00:33:06,950 --> 00:33:14,830
+بيهات دي باى بيهات دي باى بيهات
+
+409
+00:33:16,310 --> 00:33:19,270
+نفس الحاجة بقدر اعملها عشان احصل على اد ال
+
+410
+00:33:19,270 --> 00:33:23,210
+operator في ال spherical coordinate ان احنا علاقة
+
+411
+00:33:23,210 --> 00:33:29,250
+من r وθ وف وxyz معارضة انها جزر تربيع لx تربيع زي
+
+412
+00:33:29,250 --> 00:33:33,750
+y تربيع زي z تربيع ثم θ هي جزر تربيع لx تربيع زي y
+
+413
+00:33:33,750 --> 00:33:38,400
+تربيع زي z ثم فهي y على xإذا استخدمنا الـ chain
+
+414
+00:33:38,400 --> 00:33:42,000
+rule فبطلع معنا المقادير اللي أمامنا و بقدر أجيب
+
+415
+00:33:42,000 --> 00:33:48,260
+الموضّل ال operator هي بقرا روح Rها d by dr زائد θ
+
+416
+00:33:48,260 --> 00:33:54,320
+hat 1 على R d by d θ زائد φ hat 1 على R sin θ d by
+
+417
+00:33:54,320 --> 00:33:55,760
+dr واضح؟
+
+418
+00:34:01,600 --> 00:34:04,400
+gradient of scalar احنا قولنا لما يكون ال
+
+419
+00:34:04,400 --> 00:34:07,880
+operation للدل على scalar هيسميه gradient ال
+
+420
+00:34:07,880 --> 00:34:12,160
+gradient لل scalar فيه ده اسوأ اكتر في ولا في ولا
+
+421
+00:34:12,160 --> 00:34:15,540
+اكتر مهم لما اقول gradient بكون بحكي على scalar
+
+422
+00:34:17,870 --> 00:34:22,090
+issue يعني represent both the magnitude and
+
+423
+00:34:22,090 --> 00:34:26,230
+direction of a maximum space rate of increase of v
+
+424
+00:34:26,230 --> 00:34:30,870
+يعني ال gradient بتعطيني مقدار ال gradient of a
+
+425
+00:34:30,870 --> 00:34:36,310
+scalar field بتعطيني مقدار و اتجاه ال maximum rate
+
+426
+00:34:36,310 --> 00:34:41,230
+of change خلّيني أشوف إيش هذا بالرسمة أنا عندي هاي
+
+427
+00:34:41,230 --> 00:34:44,710
+ال control مثلاهذا ال control الأولاني وهذا ال
+
+428
+00:34:44,710 --> 00:34:48,110
+control التاني اللي يمثل اتجاه ال field وهذا ال
+
+429
+00:34:48,110 --> 00:34:52,830
+control التالف هذا الاتجاه اللي هو ال gradient عند
+
+430
+00:34:52,830 --> 00:34:57,270
+هذه النقطة مثلا يمثل اتجاه ال maximum change في ال
+
+431
+00:34:57,270 --> 00:35:04,950
+field يعني مثلا V2 هي V1 V2 هي V1 زي WV V3 هي V2
+
+432
+00:35:04,950 --> 00:35:10,690
+زي WV ال gradient هو عبارة عن اتجاهه غالبا يكون
+
+433
+00:35:10,690 --> 00:35:17,760
+norm علىبس مثلي اتجاه ال maximum increase ال
+
+434
+00:35:17,760 --> 00:35:22,420
+maximum increase ل ال scalar field V يعطينا
+
+435
+00:35:22,420 --> 00:35:26,400
+المقدار والاتجاه اذا ال gradient بيكون دايما عمودي
+
+436
+00:35:26,400 --> 00:35:30,180
+على اتجاه ال bus او ال field اللي هو V3 احنا
+
+437
+00:35:30,180 --> 00:35:34,480
+هيتجاه ال V3 اللي هو ال control الأزرق فال
+
+438
+00:35:34,480 --> 00:35:37,920
+gradient تبع ال V هيكون عمودي عليه
+
+439
+00:35:43,870 --> 00:35:47,370
+لذن لو انا بدى اجيب ال maximum او بدى افسره بطريقة
+
+440
+00:35:47,370 --> 00:35:52,910
+mathematical هقول انه DV لو انا بدى اروح من مقطة V
+
+441
+00:35:52,910 --> 00:35:59,310
+مثلا V2 ل V3 او من V1 ل V2 من V1 ل V2 زى ما انتوا
+
+442
+00:35:59,310 --> 00:36:02,810
+شايفينها على ال control هذا هقول انه DV ايش التغير
+
+443
+00:36:02,810 --> 00:36:07,390
+في DV هتكون DV by DX X DX عادي هذا ال partial
+
+444
+00:36:07,390 --> 00:36:11,530
+differentiationDV هي function of X,Y,Z في الـ
+
+445
+00:36:11,530 --> 00:36:16,410
+space هيكون DV اللي هو التغير في ال field عبارة عن
+
+446
+00:36:16,410 --> 00:36:20,570
+DV بي DX DX هحطوا هذا ال partial لإن V هي function
+
+447
+00:36:20,570 --> 00:36:27,630
+of X,Y,Z زي ال DV بي DY DY زي ال DV بي DZ DZ هاي
+
+448
+00:36:27,630 --> 00:36:31,350
+DV اللي هي إيش باله تساوي هذا ال product product
+
+449
+00:36:31,350 --> 00:36:36,810
+مع مين DV بي DX doted لو أنا حطيتها X hat
+
+450
+00:37:04,630 --> 00:37:08,070
+DVYDZDVYDZDVYDZDVYDZDVYDZالـ line element dx أو
+
+451
+00:37:08,070 --> 00:37:11,510
+تعيير فيه اللي هو ال line dx x hat زي dy y hat زي
+
+452
+00:37:11,510 --> 00:37:15,450
+z hat لو
+
+453
+00:37:15,450 --> 00:37:20,330
+أخدنا هذا سميته g vector اللي هو dv by dx x hat زي
+
+454
+00:37:20,330 --> 00:37:26,290
+dv by dy y hat زي dv by z سميته g فهيكون عندي ال
+
+455
+00:37:26,290 --> 00:37:30,530
+dv هي عبارة عن g dot dl ليه اسمها تساوي g cosine
+
+456
+00:37:30,530 --> 00:37:36,300
+thetaيعني معناه dv by dl أيش بتساوي جي كساين ساتر
+
+457
+00:37:36,300 --> 00:37:39,520
+وهي
+
+458
+00:37:39,520 --> 00:37:45,100
+ال DL زى ما نشاهده في الرسمة ال DL هي ال
+
+459
+00:37:45,100 --> 00:37:48,400
+differential base ما بين ال P1 و P2
+
+460
+00:38:00,100 --> 00:38:03,780
+DL بتوضح ليش الـ differential التغير اللي حصل في
+
+461
+00:38:03,780 --> 00:38:10,260
+اتجاه ال field بين
+
+462
+00:38:10,260 --> 00:38:14,080
+ال نقطتين D1 وD2 و θ هي ال angle between G ال
+
+463
+00:38:14,080 --> 00:38:18,820
+vector هذا field و بين ال DLلو انا بدأ اخد ال
+
+464
+00:38:18,820 --> 00:38:23,140
+maximum يعني dv by dl بسوة g cos θ هذي بتكون وقتش
+
+465
+00:38:23,140 --> 00:38:28,060
+ال maximum بتاعتها لما تكون θ بتسوى zero dv by dl
+
+466
+00:38:28,060 --> 00:38:31,220
+بتكون maximum value لما θ تكون zero يعني ال V
+
+467
+00:38:31,220 --> 00:38:34,860
+التغير يكون في اتجاه الباص بالتمام اتنا في اتجاه
+
+468
+00:38:34,860 --> 00:38:39,500
+البقى مع بعض اذا θ بتسوى zero معناه انه dv by dl
+
+469
+00:38:39,500 --> 00:38:44,800
+ال maximum value هي dv by dl بتسوى g اذا g اللي
+
+470
+00:38:44,800 --> 00:38:51,860
+يمين جي نرجع لجي اللي عبارة عندل دي by دي اكس
+
+471
+00:38:51,860 --> 00:38:57,500
+اكسها دي by دي واي وايها دي by دي زي زيها لمين؟
+
+472
+00:38:57,500 --> 00:39:06,700
+للأسكال عارفين لمين الـG هي عبارة عن حملي
+
+473
+00:39:06,700 --> 00:39:09,100
+سلطن نشيه تجاه الماكسما
+
+474
+00:39:13,070 --> 00:39:17,510
+إذا بيكون هذه ال maximum عندما θ تبت سواء zero في
+
+475
+00:39:17,510 --> 00:39:20,990
+هذه الحالة احنا بنقول ان G هي بتمثلني اللي هو ال
+
+476
+00:39:20,990 --> 00:39:25,630
+gradient تمثلني ال maximum direction او maximum
+
+477
+00:39:25,630 --> 00:39:28,870
+rate of change ل V واضح ليش هي ال maximum change
+
+478
+00:39:28,870 --> 00:39:34,530
+فأمروا عقلكم إياها ولا بضحكأحنا قلناها ال field
+
+479
+00:39:34,530 --> 00:39:44,070
+كان عندنا مقطة V1 وكانت مقطة V2 وكانت مقطة
+
+480
+00:39:44,070 --> 00:39:44,630
+V2 وكانت مقطة V2 وكانت مقطة V2 وكانت مقطة V2 وكانت
+
+481
+00:39:44,630 --> 00:39:44,630
+مقطة V2 وكانت مقطة V2 وكانت مقطة V2 وكانت مقطة V2
+
+482
+00:39:44,630 --> 00:39:44,670
+وكانت مقطة V2 وكانت مقطة V2 وكانت مقطة V2 وكانت
+
+483
+00:39:44,670 --> 00:39:44,670
+مقطة V2 وكانت مقطة V2 وكانت مقطة V2 وكانت مقطة V2
+
+484
+00:39:44,670 --> 00:39:44,670
+وكانت مقطة V2 وكانت مقطة V2 وكانت مقطة V2 وكانت
+
+485
+00:39:44,670 --> 00:39:48,290
+مقطة V2 وكانت مقطة V2 وكانت
+
+486
+00:39:48,290 --> 00:39:50,430
+مقطة V2 وكانت مقطة V
+
+487
+00:40:01,510 --> 00:40:05,730
+Dv by dx x hat Dv by dy y hat Dv by dz z hat doted
+
+488
+00:40:05,730 --> 00:40:12,150
+مع dx x hat dy y hat dz z hat واضح؟ لو قلنا هذا
+
+489
+00:40:12,150 --> 00:40:15,270
+كله بتسمي G اللي هي من الـ G بتاعتنا ال vector هذا
+
+490
+00:40:15,270 --> 00:40:21,330
+vector G هو ال gradient لل V صح؟ ربطه؟ هي عبارة عن
+
+491
+00:40:21,330 --> 00:40:24,630
+D by dx x hat زي ال D by dy y hat زي ال D by dz
+
+492
+00:40:24,630 --> 00:40:28,570
+أكتر على مين على D بعد ال gradient V لو سميتها G
+
+493
+00:40:28,570 --> 00:40:36,360
+dotted اللي هي DLماذا ستكون دي ال دي ال دي ال دي
+
+494
+00:40:36,360 --> 00:40:43,000
+ال دي ال دي ال دي ال دي ال دي ال دي ال دي ال دي ال
+
+495
+00:40:43,000 --> 00:40:46,460
+دي ال دي ال دي ال دي ال دي ال دي ال دي ال دي ال دي
+
+496
+00:40:46,460 --> 00:40:47,160
+ال دي ال دي ال دي ال دي ال دي ال دي ال دي ال دي ال
+
+497
+00:40:47,160 --> 00:40:47,820
+دي ال دي ال دي ال دي ال دي ال دي ال دي ال دي ال دي
+
+498
+00:40:47,820 --> 00:40:47,820
+ال دي ال دي ال دي ال دي ال دي ال دي ال دي ال دي ال
+
+499
+00:40:47,820 --> 00:40:47,820
+دي ال دي ال دي ال دي ال دي ال دي ال دي ال دي ال دي
+
+500
+00:40:47,820 --> 00:40:47,820
+ال دي ال دي ال دي ال دي ال دي ال دي ال دي ال دي ال
+
+501
+00:40:47,820 --> 00:40:49,880
+دي ال دي ال دي ال دي ال دي ال دي ال دي ال دي ال دي
+
+502
+00:40:49,880 --> 00:40:51,400
+ال دي
+
+503
+00:41:04,480 --> 00:41:07,740
+عشان هيك احنا بيقول ال gradient هو بيعطيني maximum
+
+504
+00:41:07,740 --> 00:41:11,380
+rate of change ل V نقدارا و اتجاها
+
+505
+00:41:16,940 --> 00:41:22,180
+هذا المعنى ال grade V اللي هي ال G تبعنا هي عبارة
+
+506
+00:41:22,180 --> 00:41:28,640
+عن D by DX X hat DV by DY Y hat DV by Z Z hatفي
+
+507
+00:41:28,640 --> 00:41:31,220
+الـ Cartesian Coordinate في الـ cylindrical
+
+508
+00:41:31,220 --> 00:41:34,380
+coordinate هتكون dv by d rho rho hat 1 على rho d
+
+509
+00:41:34,380 --> 00:41:39,000
+by d phi phi hat ل V زي dv by d z z hat في ال
+
+510
+00:41:39,000 --> 00:41:43,980
+spherical coordinate هتكون dv by dr r hat زي 1 على
+
+511
+00:41:43,980 --> 00:41:48,780
+r dv by d theta theta hat زي 1 على r theta dv by d
+
+512
+00:41:48,780 --> 00:41:53,050
+phi phi hatكلهم احنا بنقدر نشتقهم من بعض زي ما
+
+513
+00:41:53,050 --> 00:41:58,050
+احنا عملنا بالنسبة للانتقال من ال Cartesian ل ال
+
+514
+00:41:58,050 --> 00:42:02,430
+spherical من ال Cartesian ل ال cylindrical نقدر
+
+515
+00:42:02,430 --> 00:42:05,170
+برضه نروح من ال cylindrical ل ال spherical المنتهى
+
+516
+00:42:05,170 --> 00:42:12,450
+بالوساطة بعض ال identities اللي سهل اني اسمتها
+
+517
+00:42:12,450 --> 00:42:18,640
+عندي دلالـ D زي الـ U طبعا لما أقول Gradient او
+
+518
+00:42:18,640 --> 00:42:21,940
+دلق طبعا انا بحكي على scalar كتير Gradient ده D زي
+
+519
+00:42:21,940 --> 00:42:25,980
+الـ U هو عبارة عن Gradient الـ D زي الـ Gradient
+
+520
+00:42:25,980 --> 00:42:34,820
+يعني اش لو كان عندي D انه بساوي some quantity X
+
+521
+00:42:34,820 --> 00:42:41,880
+مثلا و الـ U بساوي مثلا Y فهيكون D زي الـ U بساوي
+
+522
+00:42:41,880 --> 00:42:49,270
+X زي الـ Yلو أخد الدل تبعهم أو أخد الدل تبع الـD و
+
+523
+00:42:49,270 --> 00:42:52,710
+الدل تبع الـU يعني لو أخدت أنميصات بسيطة زي ذلك
+
+524
+00:42:52,710 --> 00:42:57,010
+لازم تتساوى من التلاشق يعني هل هيكون الدل تبعها
+
+525
+00:42:57,010 --> 00:43:04,330
+إيش هيكون الدل لـD ذا الـU هتساوى D by DX والـD by
+
+526
+00:43:04,330 --> 00:43:11,270
+DY هيكون تانية إيشها ذا الـY فهي D by DX لـD ذا
+
+527
+00:43:11,270 --> 00:43:17,100
+الـU إيشها ذا الـD by DYلأ ال V زي ال U ويها فعندى
+
+528
+00:43:17,100 --> 00:43:21,400
+الاعتمادية على X وY يبقى يدي Z حت 5.1 لك لو انا
+
+529
+00:43:21,400 --> 00:43:26,380
+اشتت عملت دل لل V شفتني برضه Xها لان V بقى يدي X
+
+530
+00:43:26,380 --> 00:43:31,980
+وYها ودل لل U هتكون Yها فالمجموع هم هيكون Xها زي
+
+531
+00:43:31,980 --> 00:43:36,700
+Yها فإذا كنت حاولت السهل اسبحت ان دل ال V زي ال U
+
+532
+00:43:36,700 --> 00:43:37,380
+تساوي
+
+533
+00:43:40,150 --> 00:43:43,410
+معنى اول لو جمعت ال functions كانت functions اكبر
+
+534
+00:43:43,410 --> 00:43:47,830
+من هك مثلا X تربيعي او Y تربيعي و عملت جمعتهم مع
+
+535
+00:43:47,830 --> 00:43:51,490
+بعض او حتلهم الدل او ان انا عملت الدل لكل واحد
+
+536
+00:43:51,490 --> 00:43:55,850
+لحال و جمعته لازم يقين نفس النتاج هنا عند الدل ال
+
+537
+00:43:55,850 --> 00:44:03,350
+U و V بالتمام زي تفاضل دي باي بي اكس لمثل اك واحد
+
+538
+00:44:03,350 --> 00:44:08,480
+او اك ثانى اول في تفاضل التانىزائد التاني في تفاضل
+
+539
+00:44:08,480 --> 00:44:12,880
+الأول نفس الحاجة بس الفرقية ان هاد صار Vector يعني
+
+540
+00:44:12,880 --> 00:44:16,340
+ببطل ال D by DX البسيط بس ببطل ال D by DX اكساد
+
+541
+00:44:16,340 --> 00:44:19,680
+مثلا في ال Cartesian D by DY Y hat D by BZ Z hat
+
+542
+00:44:19,680 --> 00:44:23,220
+هيكون عند الأول في تفاضل التاني او ال gradient
+
+543
+00:44:23,220 --> 00:44:27,160
+التاني في هاي الحالة صار ببطل زائد التاني في
+
+544
+00:44:27,160 --> 00:44:32,660
+gradient الأول نفس الحاجة في gradient V على U ماشي
+
+545
+00:44:32,660 --> 00:44:36,400
+احنا نقول D by DX مثلا او واحد على اتناشرفقام
+
+546
+00:44:36,400 --> 00:44:43,240
+تربيه BYDX F1 على F2 هنا مثلًا بنقول مربع المقام
+
+547
+00:44:43,240 --> 00:44:49,540
+F2 تربيه تفاضل الأول في التاني ليديني F1 مثلًا
+
+548
+00:44:49,540 --> 00:44:57,100
+BYDX في F2 ناقص الأول تفاضل التاني صح؟ نعم نعم نعم
+
+549
+00:44:57,100 --> 00:45:00,140
+نفس الفكرة للـgradient بس هنا أثرنا لـgradient
+
+550
+00:45:00,140 --> 00:45:05,670
+vector Gradient V على U هيكون U تربيهتفاضل الأولي
+
+551
+00:45:05,670 --> 00:45:11,670
+Gradient الأول في U minus ما هو V Gradient V نفس
+
+552
+00:45:11,670 --> 00:45:15,810
+الحاجة Gradient V لقوة N هتكون N V لقوة N minus
+
+553
+00:45:15,810 --> 00:45:21,110
+واحد Gradient V واضح قد التشابه بينه وبين اللي هو
+
+554
+00:45:21,110 --> 00:45:27,210
+ال scalar differentiation طبعا ال N هو انتجار مجرد
+
+555
+00:45:27,210 --> 00:45:27,690
+انتجار
+
+556
+00:45:30,530 --> 00:45:33,510
+أشهر سنتاتنيتشنا أن الـ magnitude of a gradient in
+
+557
+00:45:33,510 --> 00:45:36,210
+the scalar field هو بساوة maximum rate of change
+
+558
+00:45:36,210 --> 00:45:39,950
+in V per unit distance. A grad V points in the
+
+559
+00:45:39,950 --> 00:45:42,330
+direction of the maximum rate of change تعطينا
+
+560
+00:45:42,330 --> 00:45:45,010
+برضه الاتجاه يعني تعطينا المقدار ال magnitude
+
+561
+00:45:45,010 --> 00:45:48,250
+والاتجاهنحكي نهاية الجملة واحدة نحكي تالتة جملة
+
+562
+00:45:48,250 --> 00:45:51,830
+المجنتيوت بيعطينا ال maximum rate of change اتجاهه
+
+563
+00:45:51,830 --> 00:45:55,070
+بيعطينا اتجاه ال maximum rate of change ال grade V
+
+564
+00:45:55,070 --> 00:45:57,770
+at any point is perpendicular to constant V ال
+
+565
+00:45:57,770 --> 00:46:01,070
+constant V surface احنا قولنا دايما ال gradient
+
+566
+00:46:01,070 --> 00:46:04,130
+بيكون عمودي على ال surface بيعطينا ال maximum rate
+
+567
+00:46:04,130 --> 00:46:04,730
+of change
+
+568
+00:46:10,000 --> 00:46:13,940
+الـ projection تبع ال gradient ل V في أي اتجاه لل
+
+569
+00:46:13,940 --> 00:46:19,420
+unit vector هو del V dot A hat and is called the
+
+570
+00:46:19,420 --> 00:46:23,740
+directional derivative of V along X أو X hat أو A
+
+571
+00:46:23,740 --> 00:46:27,440
+hat يعني انا بدي ال derivative بتاعة اي field في
+
+572
+00:46:27,440 --> 00:46:31,160
+اتجاه معين اش بعمله dot product ال component بتاعة
+
+573
+00:46:31,160 --> 00:46:36,010
+ال differential او ال directionalدريفتيف لانها
+
+574
+00:46:36,010 --> 00:46:38,790
+directional لانها vector ال gradient لل field انا
+
+575
+00:46:38,790 --> 00:46:41,190
+بديه في تجاه معين فعمله dot product زي اي vector
+
+576
+00:46:41,190 --> 00:46:44,510
+مثلا بدي انا ال component بتاعة ال vector field A
+
+577
+00:46:44,510 --> 00:46:48,650
+فتجاه X فعمله A dot X hat فهي نفس الحاجة اذا انا
+
+578
+00:46:48,650 --> 00:46:52,070
+بدي مثلا ال directional derivative ل V في تجاه
+
+579
+00:46:52,070 --> 00:46:57,990
+معين ايش بعمل؟ باخد ال product ال dot product لل
+
+580
+00:46:57,990 --> 00:47:00,590
+gradient لهذا ال field مع ال direction اللي انا
+
+581
+00:47:00,590 --> 00:47:04,390
+بدي ال component بتاعتهاهذه بتعطينا ال rate of
+
+582
+00:47:04,390 --> 00:47:08,910
+change ل V في direction of A for example احنا شفنا
+
+583
+00:47:08,910 --> 00:47:12,890
+ال derivative كلها واضحتنا ان DV by DL هي عبارة عن
+
+584
+00:47:12,890 --> 00:47:16,870
+ال derivative بتاعة ال field في اتجاه اللي هو بين
+
+585
+00:47:16,870 --> 00:47:23,310
+نقطة B1 و بنقطة B8 اذا كان عندي A طبعا vector لل V
+
+586
+00:47:23,310 --> 00:47:29,590
+هي A vector هذا بنسميها scalar set to B V V هي
+
+587
+00:47:29,590 --> 00:47:34,120
+scalar potential of A يعنيبشكل عربي احنا هشوفها ان
+
+588
+00:47:34,120 --> 00:47:37,600
+شاء الله لما ناخد ال fields لو كان عندى field مثلا
+
+589
+00:47:37,600 --> 00:47:43,960
+زى E و قلت انه بساوي del phi فبنقول هذا ال field
+
+590
+00:47:43,960 --> 00:47:47,580
+هذا ال field هو ال scalar potential لل vector
+
+591
+00:47:47,580 --> 00:47:52,660
+field E يعني تذكروا أشياء ان كل اللي هنعملوه احنا
+
+592
+00:47:52,660 --> 00:47:55,480
+عمالا ناخده ع شكل ال mathematics في الشباكة
+
+593
+00:47:55,480 --> 00:47:58,820
+القادمة هيصير بال تمام fields فلما أشوف انا عندى
+
+594
+00:47:58,820 --> 00:48:02,720
+هذه المعادلة A فهي vector طبعا لازم يكون vectorزي
+
+595
+00:48:02,720 --> 00:48:06,300
+طبعا في المثال بيقولنا G يساوي دلمة ثلاثة فيلد
+
+596
+00:48:06,300 --> 00:48:12,120
+تانية سنبيئة هنقول إن هذا ال field هو scalar field
+
+597
+00:48:12,120 --> 00:48:19,320
+ل vector field G لو
+
+598
+00:48:19,320 --> 00:48:24,960
+كان عندي أي دلمة field يساوي field تاني يقول إن
+
+599
+00:48:24,960 --> 00:48:28,640
+هذا ال scalar field ل vector field E
+
+600
+00:48:32,960 --> 00:48:35,520
+أحنا هنشوفهم إن شاء الله لما نبدأ نحكي باسمها
+
+601
+00:48:35,520 --> 00:48:40,140
+dollar field فبشكل عام A عندنا أي vector field V
+
+602
+00:48:40,140 --> 00:48:45,600
+أي scalar field تشوف
+
+603
+00:48:45,600 --> 00:48:51,640
+أمثلة معنوية؟ طب أكتبوا السؤال الأول A على الأقل
+
+604
+00:48:51,640 --> 00:48:54,420
+وتجيبوا ال .. ويعني إن شاء الله ازبط ال mood اللي
+
+605
+00:48:54,420 --> 00:48:59,940
+عليكم ترفيه كل ال exercise اللي حكينا عنه V بساوي
+
+606
+00:48:59,940 --> 00:49:07,910
+E to the minus ZSin 2XCos hyperbolic Y و إيش بدنا
+
+607
+00:49:07,910 --> 00:49:11,510
+نجيب ال gradient هدى هتكون مالها في ال Cartesian
+
+608
+00:49:11,510 --> 00:49:15,310
+coordinate ال U هتكون وين؟ في ال cylindrical
+
+609
+00:49:15,310 --> 00:49:21,610
+coordinate اللى هو تربيع Z Cos 2 Phi و W بالساوية
+
+610
+00:49:21,610 --> 00:49:26,030
+عشرة R Sin تربيع ستة Cos Phi إلى خاطر تعملوا تلتة
+
+611
+00:49:26,030 --> 00:49:28,050
+الواحدة في ال Cartesian والواحدة في ال cylindrical
+
+612
+00:49:28,050 --> 00:49:31,290
+والواحدة في ال spherical exercise جيبوا الدل تبعهم
+
+613
+00:49:31,290 --> 00:49:33,410
+ال gradient تبعهم يلما للتلتة
+
+614
+00:49:36,440 --> 00:49:38,700
+طبعا و ان شاء الله يمكنك ترفعه على ال model ان شاء
+
+615
+00:49:38,700 --> 00:49:42,320
+الله تكون حلت مشكلة ال model اليوم و تقدر ترفع كل
+
+616
+00:49:42,320 --> 00:49:51,340
+ال exercises في
+
+617
+00:49:51,340 --> 00:49:56,860
+اي سفسار لحد دلوقت طب
+
+618
+00:49:56,860 --> 00:50:01,740
+انا لو بدي اجيب unit vector في اتجاه ال control
+
+619
+00:50:01,740 --> 00:50:05,860
+تبعي او ال field تبعي بتعرفوا كيف تجيبوها؟من اللى
+
+620
+00:50:05,860 --> 00:50:11,240
+اتعلمناه اليوم طب بدي unit vector عمودي عليه من
+
+621
+00:50:11,240 --> 00:50:14,840
+اللى اتعلمناه اليوم بدي unit vector عمودي على ال
+
+622
+00:50:14,840 --> 00:50:19,680
+field يعني انا عندى ال field دى
+
+623
+00:50:19,680 --> 00:50:29,320
+هى ال field و بدي ال unit vector عمودي عليه من
+
+624
+00:50:29,320 --> 00:50:36,330
+اللى اتعلمناه اليوم اخر حاجةماذا نسميه Gradient؟
+
+625
+00:50:36,330 --> 00:50:41,050
+انه عمودي علي Grad V بس هذا مش unit vector عشان
+
+626
+00:50:41,050 --> 00:50:44,030
+اجيب unit vector مش بس انا بجيب Grad V و اسمع ال
+
+627
+00:50:44,030 --> 00:50:51,570
+magnitude تبعه فبعطيني unit vector في
+
+628
+00:50:51,570 --> 00:50:58,670
+اتجاهه بدأ اجيب product او يعني vector اللي عمودي
+
+629
+00:50:58,670 --> 00:51:03,280
+علي هذاال vector ال minus vector اللي عمودي و انا
+
+630
+00:51:03,280 --> 00:51:08,980
+اخدته اكيد بالفضل الله احنا
+
+631
+00:51:08,980 --> 00:51:13,660
+لما هيك ما اخدناها بالخلاص بلاص يعني هذا كله جزء
+
+632
+00:51:13,660 --> 00:51:18,000
+الاول من ال electromagnet هى ايه السرعال اللى
+
+633
+00:51:18,000 --> 00:51:20,340
+حدناها؟ اه خلاص احنا هتا
+
diff --git a/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/xQVL9n3FDqg_raw.srt b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/xQVL9n3FDqg_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..60959f42dc49f25f787e84a28178d10ef49c3e52
--- /dev/null
+++ b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/xQVL9n3FDqg_raw.srt
@@ -0,0 +1,1572 @@
+1
+00:00:20,650 --> 00:00:23,090
+بسم الله الرحمن الرحيم السلام عليكم ورحمة الله
+
+2
+00:00:23,090 --> 00:00:26,290
+وبركاته ان شاء الله اليوم هحكي عن ال electric
+
+3
+00:00:26,290 --> 00:00:30,490
+potential انتوا المحاضرات السابقة أخدتوا كيف حساب
+
+4
+00:00:30,490 --> 00:00:34,770
+ال electric field و ال electric field density و
+
+5
+00:00:34,770 --> 00:00:38,630
+اليوم هشوفوش هو ال electric potential زي اللي
+
+6
+00:00:38,630 --> 00:00:41,730
+أخدتوا في المحاضرات السابقة ان ال electric field
+
+7
+00:00:41,730 --> 00:00:45,710
+ممكن أحصل عليه بالطرق التالية ممكن أحصل عليها من
+
+8
+00:00:45,710 --> 00:00:48,710
+column block ولا لأ مش حدوني columns block حسبنا
+
+9
+00:00:49,780 --> 00:00:52,960
+لأي charge distribution أسوأ surface charge ولا
+
+10
+00:00:52,960 --> 00:00:55,380
+line of charge ولا volume of charge distribution
+
+11
+00:00:55,380 --> 00:01:00,440
+إذا كان في عندنا symmetry أولا بنستخدم مين؟ Gauss
+
+12
+00:01:00,440 --> 00:01:03,980
+law إذا ماقدر أجيب electric field يعني column law
+
+13
+00:01:03,980 --> 00:01:08,300
+إذا كان عندي charge distribution أسوأ كانت surface
+
+14
+00:01:08,300 --> 00:01:11,260
+ولا volume ولا line إذا كان في عندي نوم الأنواع
+
+15
+00:01:11,260 --> 00:01:16,080
+السيمتري بستخدم Gauss law كمان إحنا هنشوف إيه ممكن
+
+16
+00:01:16,080 --> 00:01:20,730
+نستخدمه لو كنا فيThe Scalar Potential V يعني لو
+
+17
+00:01:20,730 --> 00:01:24,330
+عرفنا Potential V بقدر برضه أجيب Electric Field
+
+18
+00:01:24,330 --> 00:01:30,010
+معناه أني لازم أعرف كيف أحسب Potential V وإيش هو
+
+19
+00:01:30,010 --> 00:01:34,970
+Potential V الفكرة إنه افترض إنه عندي هذا الخطوط
+
+20
+00:01:34,970 --> 00:01:38,730
+الزرقاء هي Electric Field جاي من أي مصدر ممكن جاي
+
+21
+00:01:38,730 --> 00:01:41,850
+من Pointed Charges، من Charge Distribution، عشان
+
+22
+00:01:41,850 --> 00:01:44,030
+ال line ولا عشان ال volume ولا عشان ال surface
+
+23
+00:01:44,030 --> 00:01:46,170
+فالمهم إنه عندي Electric Field اللي هو باللون
+
+24
+00:01:46,170 --> 00:01:51,900
+الأزرقبعدين انا بدى احرك ال charge من النقطة A
+
+25
+00:01:51,900 --> 00:01:57,200
+اللى تبعد RA عن ال origin للنقطة B اللى تبعد RB عن
+
+26
+00:01:57,200 --> 00:02:01,600
+ال origin اذا انا بدى اعمل ال moving لل charge Q
+
+27
+00:02:01,600 --> 00:02:07,040
+من النقطة A للنقطة B في وجود مين ال electric field
+
+28
+00:02:08,370 --> 00:02:11,290
+من column block احنا عارفين اذا انا عندى electric
+
+29
+00:02:11,290 --> 00:02:15,110
+field بقدر اقول ان ال force على ال charge بتساوي
+
+30
+00:02:15,110 --> 00:02:19,450
+قيمة ال charge فى ال electric field يعنى ال force
+
+31
+00:02:19,450 --> 00:02:22,230
+هتكون على ها ال charge اللى انا بعملها اذاها من
+
+32
+00:02:22,230 --> 00:02:26,690
+نقطة A لنقطة B ايش بتساوي Q فى Eلان عارفة ان في
+
+33
+00:02:26,690 --> 00:02:29,870
+عندي electric field و انا عمال بقول ال charge في
+
+34
+00:02:29,870 --> 00:02:32,170
+وجود ال electric field فقيمة ال force على هال
+
+35
+00:02:32,170 --> 00:02:36,390
+charge هيكون كل فيه، لما يكون عندي force عمال بعمل
+
+36
+00:02:36,390 --> 00:02:40,430
+اذا ها ايش بيصير عندي مانع في عندي work صح شغلتوا
+
+37
+00:02:40,430 --> 00:02:46,590
+هذا حتى في ال physics ممكن بيه اهأذا في عندي work
+
+38
+00:02:46,590 --> 00:02:51,150
+done ال work done عشان احرك ال charge من النقطة A
+
+39
+00:02:51,150 --> 00:02:55,910
+لنقطة B او خليني اخد لو انا بدى احركها بس جزئية DL
+
+40
+00:02:55,910 --> 00:02:59,910
+يعني هى ايش هتكون ال fraction of the work DW دلوقت
+
+41
+00:02:59,910 --> 00:03:05,210
+ايش هتساوي minus F dot DL الإشارة السالبة بس
+
+42
+00:03:05,210 --> 00:03:09,420
+بتقولى ان في عندي external agent هو اللى عملهامش
+
+43
+00:03:09,420 --> 00:03:12,060
+انه internal agent فيه ال external agent هو اللي
+
+44
+00:03:12,060 --> 00:03:16,920
+عملها بإذن dw بتساوي minus F dot dl و F اللي هي ال
+
+45
+00:03:16,920 --> 00:03:20,180
+force اللي على ال charge اللي موجودة في ال
+
+46
+00:03:20,180 --> 00:03:24,460
+electric field اللي بتساوي Q في E إذا ال work اللي
+
+47
+00:03:24,460 --> 00:03:29,560
+exerted عشان أحرك ال charge هي distance dl هيساوي
+
+48
+00:03:29,560 --> 00:03:35,780
+minus F dot dl و بمعنى آخر minus QE dot dlأذا ال
+
+49
+00:03:35,780 --> 00:03:38,460
+total work ايش بيسوي ال integration يعني انا بدي
+
+50
+00:03:38,460 --> 00:03:41,580
+ال total work اللي بدي احتاجه عشان احرق ال charge
+
+51
+00:03:41,580 --> 00:03:45,920
+من A ل B هيكون ال work بيسوي minus Q ال integral
+
+52
+00:03:45,920 --> 00:03:50,920
+من A ل B E هتكون function of L ضد L هدول هيكونوا
+
+53
+00:03:50,920 --> 00:03:54,760
+في قلب ال integration بدي اكمل على طول ال line من
+
+54
+00:03:54,760 --> 00:04:02,930
+النقطة A لنقطة Bلو قسمنا ال work و على Q بحصل على
+
+55
+00:04:02,930 --> 00:04:07,610
+ال potential energy per unit charge بسمي VAB
+
+56
+00:04:12,500 --> 00:04:16,060
+الـ minus لأنه معناه انه external agent اللي بيعمل
+
+57
+00:04:16,060 --> 00:04:19,460
+ال movement VAB اللي هو ال potential difference
+
+58
+00:04:19,460 --> 00:04:23,060
+بين النقطة A لنقطة B ال potential difference بين
+
+59
+00:04:23,060 --> 00:04:25,800
+نقطة A لنقطة B زي ال potential difference بين طرفي
+
+60
+00:04:25,800 --> 00:04:28,940
+المقامة ال potential difference بين نقطة A لنقطة B
+
+61
+00:04:28,940 --> 00:04:33,640
+هو عبارة عن minus ال integration من نقطة A لنقطة B
+
+62
+00:04:33,640 --> 00:04:36,720
+يعني ال position A ال position A اللي هو ر إيه
+
+63
+00:04:36,720 --> 00:04:40,350
+يعني لأ ال position B اللي هو ر بيهمن الـ position
+
+64
+00:04:40,350 --> 00:04:49,190
+A إلى الـ position B E.DL هى
+
+65
+00:04:49,190 --> 00:04:52,690
+هذا اللى حكيناه ان ال potential بيسوى W و ال work
+
+66
+00:04:52,690 --> 00:04:57,330
+على Q بيسواه minus integration من A إلى B E.DL اذا
+
+67
+00:04:57,330 --> 00:05:02,850
+ايش بنلاحظ اول حاجة و احنا بنقرر VAB لما نشوف AB
+
+68
+00:05:02,850 --> 00:05:06,690
+معناه ان A هي ال initial point و B هي ال final
+
+69
+00:05:06,690 --> 00:05:11,410
+pointلما أقول VAB معناه عندي A هي ال initial point
+
+70
+00:05:11,410 --> 00:05:15,590
+و B ال final point بيساوي minus integration ل A من
+
+71
+00:05:15,590 --> 00:05:20,270
+A ل B VAB قولنا negative ليش؟ لأنه هيكون في عندي
+
+72
+00:05:20,270 --> 00:05:22,370
+معناه احنا قولنا هو external agent بس هيكون في
+
+73
+00:05:22,370 --> 00:05:24,990
+عندي loss في potential energy أنا عندي charge
+
+74
+00:05:24,990 --> 00:05:28,730
+قاعدة و بحركها أيش معناه؟ تخسر potential energy
+
+75
+00:05:28,730 --> 00:05:32,850
+هذا ال negative تعني لي أنه في عندي loss في ال
+
+76
+00:05:32,850 --> 00:05:36,250
+energy لو positive معناه أنه قاعدة بعد الgen ل ال
+
+77
+00:05:36,250 --> 00:05:41,880
+energyكمان هدى انها VAB buff independent وحنشوفها
+
+78
+00:05:41,880 --> 00:05:45,540
+اللى قدام ليش هي buff independent بس احنا هذا ال
+
+79
+00:05:45,540 --> 00:05:50,220
+form بنعرف هذه خصائصه اقبل انه VAB هي ال emission
+
+80
+00:05:50,220 --> 00:05:52,720
+في ال final VAB is negative معناه بيلس في
+
+81
+00:05:52,720 --> 00:05:57,240
+potential energy VAB is buff independent بتعتمدش
+
+82
+00:05:57,240 --> 00:06:01,840
+على اتجاه ال buff و VAB is measured in joules per
+
+83
+00:06:01,840 --> 00:06:04,660
+column ليش في joules per column لأن ال work is
+
+84
+00:06:04,660 --> 00:06:12,500
+shell unit بتاعتهأيش ال unit بتاعة ال work؟
+
+85
+00:06:12,500 --> 00:06:17,760
+بصوت عالي تمام و ايش ال charge ال unit بتاعتها؟
+
+86
+00:06:17,760 --> 00:06:27,800
+volt إذا
+
+87
+00:06:27,800 --> 00:06:34,400
+ال unit volt بتكافر jewel بال columnبشخطنها في
+
+88
+00:06:34,400 --> 00:06:39,060
+الدوائر V بالفعل بتساوي ال work علقتها بال charge
+
+89
+00:06:39,060 --> 00:06:45,280
+work على Q فاصلة الشحنات أو بجمع الشحنات وبعطيني
+
+90
+00:06:45,280 --> 00:06:48,380
+ال potential difference بين أي element اللي بساوي
+
+91
+00:06:48,380 --> 00:06:53,340
+work على Q وبعملها هي Joule per Kole اللي هو ال
+
+92
+00:06:53,340 --> 00:07:00,080
+volt نفترض
+
+93
+00:07:00,080 --> 00:07:04,390
+إن أنا عادي electric fieldوهذا ال field ناتج من
+
+94
+00:07:04,390 --> 00:07:07,450
+point of charge وينوضع ال point of charge في ال
+
+95
+00:07:07,450 --> 00:07:10,210
+origin يعني انا عندى charge في ال origin ايش بديكن
+
+96
+00:07:10,210 --> 00:07:14,790
+شكل ال field يا طالع ع شكل spherical distribution
+
+97
+00:07:14,790 --> 00:07:20,530
+يا داخل صح ال line electric field line حسب الإشارة
+
+98
+00:07:20,530 --> 00:07:24,230
+تحت ال charge إذا موجبة هيكونوا طالعين من كل
+
+99
+00:07:24,230 --> 00:07:28,910
+الجهات حوالي المقطة إذا سالبة هيكون داخلين عليها
+
+100
+00:07:32,960 --> 00:07:35,120
+قيمة ال electric field الناتجة عن ال point of
+
+101
+00:07:35,120 --> 00:07:39,020
+charge شو تساوي؟ اكيو على four pipes ارثر بيه
+
+102
+00:07:39,020 --> 00:07:42,440
+ارهاد المفروض احطوه كيف تجيبوله ال point of charge
+
+103
+00:07:42,440 --> 00:07:47,770
+بال columns law و ال gauss law صحيح؟إذا الـ E
+
+104
+00:07:47,770 --> 00:07:50,970
+ستساوي Q على 4 بي إبسن أرثر بي أرهاد هذا الـ
+
+105
+00:07:50,970 --> 00:07:54,750
+electric field الناتج من ال point الـ charge إذا
+
+106
+00:07:54,750 --> 00:07:57,250
+ال potential لو بدي أن أنقل ال potential من أي
+
+107
+00:07:57,250 --> 00:08:02,430
+نقطة A ال charge من أي نقطة A لنقطة B لازم أحس ال
+
+108
+00:08:02,430 --> 00:08:05,170
+potential difference من نقطة A لنقطة B بإيه بيه مش
+
+109
+00:08:05,170 --> 00:08:10,890
+هتساوي minus ال integration من RA لRB ال Q على 4
+
+110
+00:08:10,890 --> 00:08:21,990
+by إبسن أرثر بي أرهاد.drr hat الـ
+
+111
+00:08:21,990 --> 00:08:27,270
+DL بتاعتي هي نقطة كالة نقطة A منتقلة لنقطة B أبعد
+
+112
+00:08:27,270 --> 00:08:29,210
+منها في اتجاه الريديا
+
+113
+00:08:31,950 --> 00:08:35,690
+هيكون النتيجة ال integration is an R hat هو اتجاه
+
+114
+00:08:35,690 --> 00:08:38,630
+ال electric field وانا عاملا بدنا نقول النقطة في
+
+115
+00:08:38,630 --> 00:08:43,290
+اتجاه ال dl اللي هي برضه في اتجاه ال radial فهيكون
+
+116
+00:08:43,290 --> 00:08:49,110
+Q على 4 by epsilon node R تربيه DR Q على 4 by
+
+117
+00:08:49,110 --> 00:08:51,230
+epsilon ماهي لها constant بقدر اطلعها برا ال
+
+118
+00:08:51,230 --> 00:08:55,540
+integrationQ على 4 بي إبسنون من ورد تخرج برا ال
+
+119
+00:08:55,540 --> 00:08:59,260
+integration و تكمل 1 على R تربيه دي R
+
+120
+00:09:09,330 --> 00:09:19,370
+VAB مفروض في الفيجور VAB مفروض
+
+121
+00:09:19,370 --> 00:09:30,330
+في الفيجور VAB مفروض
+
+122
+00:09:30,330 --> 00:09:34,010
+في الفيجور VAB مفروض في الفيجور VAB مفروض في
+
+123
+00:09:34,010 --> 00:09:37,570
+الفيجور VAB مفروض في الفيجور
+
+124
+00:09:46,690 --> 00:09:52,670
+بتبقى ممكن أنصر لهذا ال VAB انه عبارة عن ال
+
+125
+00:09:52,670 --> 00:09:58,430
+potential عند النقطة B with reference للنقطة A اذا
+
+126
+00:09:58,430 --> 00:10:01,810
+قلنا AQ على 4 by epsilon نقطة RB هي ال absolute
+
+127
+00:10:01,810 --> 00:10:03,190
+potential عند النقطة B
+
+128
+00:10:06,320 --> 00:10:10,780
+هي ال potential عند النقطة A يعني VAB بحسب VB
+
+129
+00:10:10,780 --> 00:10:13,300
+minus VA وهذا برضه يقول عنه ال potential
+
+130
+00:10:13,300 --> 00:10:16,240
+difference بين النقطة A وB ممكن أسميه هو ال
+
+131
+00:10:16,240 --> 00:10:21,280
+potential عند النقطة B ال reference للنقطة A واضح؟
+
+132
+00:10:21,280 --> 00:10:23,960
+بشكل عام ال potential الناتج عن ال point of charge
+
+133
+00:10:23,960 --> 00:10:28,480
+ايش بسوى Q على 4 by epsilon R ال absolute R
+
+134
+00:10:28,480 --> 00:10:31,820
+المسافر بالنقطة اللي بتحسب عندها ال potential عن
+
+135
+00:10:31,820 --> 00:10:35,820
+اللي هي النقطة ال charge وين ال charge موجودة؟بأسف
+
+136
+00:10:35,820 --> 00:10:38,920
+صلحت هنا احنا عرفنا هلقيت ايش هو ال potential
+
+137
+00:10:38,920 --> 00:10:42,140
+difference و ايش ال absolute potential ايش الفرق
+
+138
+00:10:42,140 --> 00:10:45,500
+بينهم ال absolute potential و ايش ال potential
+
+139
+00:10:45,500 --> 00:10:48,460
+difference potential difference ممكن ما بين نقطتين
+
+140
+00:10:48,460 --> 00:10:52,660
+من ظن نظر مواقعي مجالكها لكن absolute potential
+
+141
+00:10:52,660 --> 00:10:53,960
+ممكن من ال ..
+
+142
+00:10:57,160 --> 00:11:00,360
+ممتازة يعني انا ماحكيتهاش بس ما شاء الله ازملتكم
+
+143
+00:11:00,360 --> 00:11:03,500
+ممتازة انا لو بدأ اقول ايش هي ر بي يعني potential
+
+144
+00:11:03,500 --> 00:11:06,120
+عند النقطة ر بي اللي انا قولت q على four by
+
+145
+00:11:06,120 --> 00:11:09,320
+epsilon نقطة ر بي لو انا افترضت الـ ra عند ال
+
+146
+00:11:09,320 --> 00:11:12,440
+infinity هيكون ال potential عند هذه النقطة بساوة
+
+147
+00:11:12,440 --> 00:11:15,080
+صفر فال absolute potential في الواقع انا قولتلكم
+
+148
+00:11:15,080 --> 00:11:20,540
+هو قيمته four by على epsilon نقطة في Rاللي هي بعد
+
+149
+00:11:20,540 --> 00:11:25,160
+النقطة عن ال origin إذا كان عندى ال potential عند
+
+150
+00:11:25,160 --> 00:11:28,100
+ال infinity بساوة zero وهذا هي ال reference
+
+151
+00:11:28,100 --> 00:11:31,340
+بتاعتى، يعني أنا عمال بقى نقل ال charge بتاعتى من
+
+152
+00:11:31,340 --> 00:11:35,120
+ال infinity لنقطة اللى بدأي اسمها ال absolute
+
+153
+00:11:35,120 --> 00:11:40,340
+potentialممتازة باختصار اذا لو انا افترض ان ال
+
+154
+00:11:40,340 --> 00:11:43,420
+reference point بتاعتي هي ال infinity يعني عند ال
+
+155
+00:11:43,420 --> 00:11:46,800
+infinity واضح انه هيكون ال potential zero هيكون ال
+
+156
+00:11:46,800 --> 00:11:50,240
+potential عند النقطة مثلا RB ليه جاء من ال
+
+157
+00:11:50,240 --> 00:11:54,320
+infinity ل RB هي Q على four by epsilon node RB نفس
+
+158
+00:11:54,320 --> 00:11:56,900
+الحاجة لو انا بفكر على ال potential عند النقطة RA
+
+159
+00:11:56,900 --> 00:12:01,640
+انه انا بجيب من نقطة اد infinity لها نقطة هتكون Q
+
+160
+00:12:01,640 --> 00:12:07,540
+على four by epsilon node على RA تمامهذا الحكي
+
+161
+00:12:07,540 --> 00:12:11,720
+موجود هنا بس انا كنت حابه باختصار تقول ان هي Q فوق
+
+162
+00:12:11,720 --> 00:12:15,680
+Q على 4 by epsilon node R لكن اللي حكته قبلنا
+
+163
+00:12:15,680 --> 00:12:18,940
+وممتاز انه في حالة اللي انا بحكي عن ال absolute
+
+164
+00:12:18,940 --> 00:12:23,860
+potential انا بأفترض دائما انه انه ال potential at
+
+165
+00:12:23,860 --> 00:12:27,620
+infinity is 0 يعني مثلا اذا أخدنا RA بتروح ل
+
+166
+00:12:27,620 --> 00:12:31,160
+infinity اذا VA بتسوى 0 وبالتالي ال potential عند
+
+167
+00:12:31,160 --> 00:12:35,120
+النقطة B ايش بده يكون V بتسوى Q4 by epsilon node
+
+168
+00:12:35,120 --> 00:12:35,480
+في R
+
+169
+00:12:39,460 --> 00:12:41,520
+طب عاملنا ال electric field قولنا من point of
+
+170
+00:12:41,520 --> 00:12:44,100
+charge عند ال origin point of charge عند ال origin
+
+171
+00:12:44,100 --> 00:12:47,700
+ايش قولنا طالع radially يعني انت تخيل السفير
+
+172
+00:12:47,700 --> 00:12:50,300
+حوالين ال point of charge و ال electric field طالع
+
+173
+00:12:50,300 --> 00:12:55,180
+على شكل اللي هو radially اتجاه R معناه ان هنا
+
+174
+00:12:55,180 --> 00:12:59,020
+الاعتمادية اعلى ال theta و ال phi معلها لغيات مع
+
+175
+00:12:59,020 --> 00:13:06,380
+ال product يعني Eتجاه ال R وانا عمالي بعمل dot dl
+
+176
+00:13:06,380 --> 00:13:10,880
+حتى لو كان ال dot dl فيه component في التجاهات
+
+177
+00:13:10,880 --> 00:13:15,800
+الأخرى لما E R hat dot dl فببقى فقط ال radial
+
+178
+00:13:15,800 --> 00:13:19,340
+component فالاعتمادية على ال theta و ال phi ايش
+
+179
+00:13:19,340 --> 00:13:23,140
+بيصير لها cancellation يعني قيمة اللي هقولنا في
+
+180
+00:13:23,140 --> 00:13:27,640
+اتجاه ال radial فE R hat dot dl حتى لو ال dot dl
+
+181
+00:13:27,640 --> 00:13:30,440
+بتاعتى انا بيش على ال radial انا بنقولها من أي
+
+182
+00:13:30,440 --> 00:13:34,370
+نقطة لأي نقطةمش مضلولة على ال radial زي ما انا
+
+183
+00:13:34,370 --> 00:13:36,690
+حكيتلكم طوي قلت للتسجيل خم نفترضها على ال radial
+
+184
+00:13:36,690 --> 00:13:40,150
+لو كانت من أي نقطة لنقطة تانية مين هيظل عندى فقط
+
+185
+00:13:40,150 --> 00:13:43,410
+ال DL اللى في اتجاه ال component اللى في اتجاه ال
+
+186
+00:13:43,410 --> 00:13:51,410
+R هاتي طب اذا انا عندي E في DR هي عندي ال E ضد ال
+
+187
+00:13:51,410 --> 00:13:56,930
+DL تبصير بساطة E في ال DR هذا المجسنتش منه انه ال
+
+188
+00:13:56,930 --> 00:14:01,480
+potential ما بين نقطتينلا يعتمد على ال bus و كمان
+
+189
+00:14:01,480 --> 00:14:03,800
+ماراح نأكدها اول حاجة الاعتماد على ال theta و ال
+
+190
+00:14:03,800 --> 00:14:08,380
+phi انتهتها فإذا ما اعتمديه على ال bus مالهاش أي
+
+191
+00:14:08,380 --> 00:14:11,520
+قيمة في حساباتنا اللي بتنشر و كمان ماراح نشوف
+
+192
+00:14:11,520 --> 00:14:15,880
+أثباتها الطريقة أخرى انه انا لا اعتمد في حسابي على
+
+193
+00:14:15,880 --> 00:14:19,260
+ال V ما بين النقطة A و B على ال bus يعني انا عندي
+
+194
+00:14:19,260 --> 00:14:24,060
+نقطتين لو أخدت ال bus هيكي ال DL تعتي ولا ال DL
+
+195
+00:14:24,060 --> 00:14:25,520
+هيكده دايما هتكون DL
+
+196
+00:14:34,120 --> 00:14:37,200
+DL دائما تكون product of الـ DL مع الـ electric
+
+197
+00:14:37,200 --> 00:14:40,880
+field في اتجاه الارهاد فهي path independent
+
+198
+00:14:58,500 --> 00:15:03,320
+بشكل عام احنا قولنا غالبا بناخد النقطة اللى عند ال
+
+199
+00:15:03,320 --> 00:15:06,300
+infinity ال potential عندها zero لكن بشكل عام ال
+
+200
+00:15:06,300 --> 00:15:09,740
+potential ماقدر اقول عنه at any pointهو ال
+
+201
+00:15:09,740 --> 00:15:13,060
+potential difference between that point يعني ال
+
+202
+00:15:13,060 --> 00:15:15,760
+potential difference عند أي نقطة هي النقطة اللي
+
+203
+00:15:15,760 --> 00:15:18,840
+بحكي عنها هو ال potential عند هذه النقطة اللي
+
+204
+00:15:18,840 --> 00:15:22,340
+بتحسب عندها ال potential and and a chosen
+
+205
+00:15:22,340 --> 00:15:25,600
+difference يعني P أنا بدي عند النقطة ايه بقول هو
+
+206
+00:15:25,600 --> 00:15:29,580
+ال potential عند النقطة ايه ناقص اي potential عند
+
+207
+00:15:29,580 --> 00:15:31,860
+نقطة تانية بسميها ال reference اللي عندها ال
+
+208
+00:15:31,860 --> 00:15:32,800
+potential ساوة صفر
+
+209
+00:15:41,330 --> 00:15:44,770
+بشكل عام احنا اخدنا احد الحلقات الخاصة ال
+
+210
+00:15:44,770 --> 00:15:47,570
+potential difference او ال potential عند اي نقطة
+
+211
+00:15:47,570 --> 00:15:48,450
+ال absolute potential
+
+212
+00:15:53,100 --> 00:15:55,800
+وإذا أنا كان عند ال reference potential مثلا ال
+
+213
+00:15:55,800 --> 00:15:58,960
+infinity لكن المشكلة العامة هي أن ال potential عند
+
+214
+00:15:58,960 --> 00:16:01,780
+هذه النقطة مع reference لأي نقطة عندها potential
+
+215
+00:16:01,780 --> 00:16:04,820
+بساوة صفر ليس بالضرورة أن تكون infinity وزي ما قلت
+
+216
+00:16:04,820 --> 00:16:08,240
+سنشوف مثلان واحد لما أخد reference على طول هي ال
+
+217
+00:16:08,240 --> 00:16:10,900
+potential عند ال infinity بساوة zero واحدة ال
+
+218
+00:16:10,900 --> 00:16:13,360
+potential بساوة zero عن نقطة تانية غير ال infinity
+
+219
+00:16:13,360 --> 00:16:18,620
+هي ال reference بتاعتي مثلا
+
+220
+00:16:18,620 --> 00:16:21,000
+هاي هنا المثال اللي احنا شوفناه اللي هو عند ال
+
+221
+00:16:21,000 --> 00:16:23,420
+infinityأحنا قلنا إذا ال potential عند ال infinity
+
+222
+00:16:23,420 --> 00:16:27,020
+بساوة 0 فأقدر أحصل على ال absolute potential عند
+
+223
+00:16:27,020 --> 00:16:32,620
+النقطة اللى ببحث عنها على ال potential يعنى
+
+224
+00:16:32,620 --> 00:16:35,780
+V بساوة minus ال integral من ال infinity ل R E dot
+
+225
+00:16:35,780 --> 00:16:41,100
+DL طب if the Q is not هذا كله أنا بحكي وانفرضة ل
+
+226
+00:16:41,100 --> 00:16:46,180
+charge عند ال originيعني ال potential عند ال ra
+
+227
+00:16:46,180 --> 00:16:49,580
+بحسب بقشرة بالنسبة لل origin ال potential عند ال
+
+228
+00:16:49,580 --> 00:16:52,920
+rb بحسب بقشرة بالنسبة لل origin لأن عندي ال charge
+
+229
+00:16:52,920 --> 00:16:55,640
+عند ال origin طب لو كانت ال charge مش عند ال
+
+230
+00:16:55,640 --> 00:17:00,640
+origin عند أي نقطة تانية هيكون في عندي المسافة بين
+
+231
+00:17:00,640 --> 00:17:04,620
+ال distance بين النقطة اللى بتحسب عليها وموضوع ال
+
+232
+00:17:04,620 --> 00:17:09,220
+charge هذه هي اللى بتعطيلي ال potential absolute
+
+233
+00:17:09,220 --> 00:17:12,480
+potentialيعني لو كانت الـ charge مش عن الـ origin
+
+234
+00:17:12,480 --> 00:17:16,300
+بتقت a point whose position vector is R' إذا الـ
+
+235
+00:17:16,300 --> 00:17:19,820
+potential عند أي نقطة R إيش هيكون الـ Q على 4 by
+
+236
+00:17:19,820 --> 00:17:25,900
+Y0 في المسافة بين موضع الـ charge و النقطة اللي
+
+237
+00:17:25,900 --> 00:17:28,540
+بحسب عندها الـ potential هذا اللي أخدناه قبلها، لو
+
+238
+00:17:28,540 --> 00:17:32,280
+كانت عند الـ zero هتكون باشرة R اللي هي المسافة
+
+239
+00:17:32,280 --> 00:17:35,020
+بين الـ charge و الـ zero بين النقطة اللي بحسب
+
+240
+00:17:35,020 --> 00:17:37,260
+عندها الـ potential و الـ zero لكن لو كانت الـ
+
+241
+00:17:37,260 --> 00:17:40,870
+charge مش عند الـ originعند مسافة R' هتكون ال
+
+242
+00:17:40,870 --> 00:17:44,410
+potential على مين المسافة اللي بينهم، بين ال
+
+243
+00:17:44,410 --> 00:17:48,290
+charge بتشارج و النقطة اللي بتحسب عندها ال
+
+244
+00:17:48,290 --> 00:17:50,870
+potential واضح؟ فزان هتكون
+
+245
+00:17:58,260 --> 00:18:01,180
+موقع النقطة اللي بدأ يسيندها ال potential D of R
+
+246
+00:18:01,180 --> 00:18:05,120
+وR prime هو موقع التشارج في هذه الحالة لو كانت
+
+247
+00:18:05,120 --> 00:18:06,800
+ZERO أربع أربع أربع أربع أربع أربع أربع أربع أربع
+
+248
+00:18:06,800 --> 00:18:08,860
+أربع أربع أربع أربع أربع أربع أربع أربع أربع أربع
+
+249
+00:18:08,860 --> 00:18:10,720
+أربع أربع أربع أربع أربع أربع أربع أربع أربع أربع
+
+250
+00:18:10,720 --> 00:18:11,220
+أربع أربع أربع أربع أربع أربع أربع أربع أربع أربع
+
+251
+00:18:11,220 --> 00:18:12,340
+أربع أربع أربع أربع أربع أربع أربع أربع أربع أربع
+
+252
+00:18:12,340 --> 00:18:15,800
+أربع أربع أربع أربع أربع أربع أربع أربع أربع أربع
+
+253
+00:18:15,800 --> 00:18:16,260
+أربع أربع
+
+254
+00:18:34,330 --> 00:18:38,550
+بإمكاني اعمل عملية superposition و اجمع كل ال
+
+255
+00:18:38,550 --> 00:18:42,590
+potential متشين عن هدولة متشارجة هدلاحتها لاقيت ان
+
+256
+00:18:42,590 --> 00:18:45,950
+احنا اش مفترضين انه عند ال infinity ايش ال
+
+257
+00:18:45,950 --> 00:18:49,450
+potential بالساوة 0 فبيطلع عند ال position بيقيه
+
+258
+00:18:49,450 --> 00:18:55,290
+Qα0 في R هو absolute potentialكل ال potentials
+
+259
+00:18:55,290 --> 00:18:58,910
+هيكونوا مجموعة من ال superposition هذا scalar ولا
+
+260
+00:18:58,910 --> 00:19:02,390
+دي ايش راح يكون؟ scalar ولا مش scalar؟ scalar اكيد
+
+261
+00:19:02,390 --> 00:19:09,610
+scalar طب ليش scalar؟ المسافة اللي بيننا المضروبة
+
+262
+00:19:09,610 --> 00:19:18,310
+في ال R hat المتجهة هي المتجهة مين؟ مين المتجهة؟
+
+263
+00:19:18,310 --> 00:19:24,040
+هتنضرب المتجهة اللي هي ال .. هتنضرب AR مين؟هي
+
+264
+00:19:24,040 --> 00:19:26,380
+بتسوي ال work انت بتحكي بس انا ماكنت معاك كويسة
+
+265
+00:19:26,380 --> 00:19:29,380
+احكيها كويسة هو انا مش مجمعها هى كلها مضبوطة مش
+
+266
+00:19:29,380 --> 00:19:32,460
+حلقة ال potential ليش scalar؟ مين بقول ليش
+
+267
+00:19:32,460 --> 00:19:37,360
+potential scalar؟ المفروض انه ال work يعني مش هو
+
+268
+00:19:37,360 --> 00:19:40,900
+بتسوي ال work على شحط ال work كمية scalar ديش يعني
+
+269
+00:19:40,900 --> 00:19:42,900
+طب انا اعمل work كمية scalar اخد ليش ال work كمية
+
+270
+00:19:42,900 --> 00:19:48,160
+scalar؟ مارتعتبد
+
+271
+00:19:48,160 --> 00:19:50,300
+على التجمشات؟ طب احنا كتبناها يعني موجودين في
+
+272
+00:19:50,300 --> 00:19:52,600
+الأنكم في ال slide up ليش ال work scalar؟
+
+273
+00:19:56,220 --> 00:19:59,220
+الwork ليش scalar؟ ليش ال potential scalar؟ ال
+
+274
+00:19:59,220 --> 00:20:02,980
+potential اللي بيساوي إيه؟ دو ال DL؟ دو ال product
+
+275
+00:20:02,980 --> 00:20:08,560
+إيش معله؟ scalar ال potential اللي رجع على ال
+
+276
+00:20:08,560 --> 00:20:11,640
+potential عشان هي لما قالت لنا ال potential إيش ال
+
+277
+00:20:11,640 --> 00:20:17,980
+potential بيساوي؟ إيش F دو ال DL؟ إيش معله؟ scalar
+
+278
+00:20:17,980 --> 00:20:21,660
+لحد ده لقيته كله scalar product يعني غصب إنه بيطلع
+
+279
+00:20:21,660 --> 00:20:25,480
+على potential scalarصحيح جامن vector quantities بس
+
+280
+00:20:25,480 --> 00:20:29,020
+dot ال product اذا هو scalar quantity اذا ماقلتش
+
+281
+00:20:29,020 --> 00:20:32,780
+ايش نوعه؟ scalar quantity مينذكر اننا معرفنا امثلة
+
+282
+00:20:32,780 --> 00:20:36,220
+ال field ال vector field و ال scalar field؟فأول
+
+283
+00:20:36,220 --> 00:20:39,700
+المحاضرات قلنا ال potential هو نوع من ال scalar
+
+284
+00:20:39,700 --> 00:20:43,320
+quantities إذا لو كان عندى عدد من ال charges مش ال
+
+285
+00:20:43,320 --> 00:20:47,460
+charge واحدة عند q1 و q2 و q3 و qn هيكون ال
+
+286
+00:20:47,460 --> 00:20:51,320
+potential مجموعهم كلهم وهيدنقل الحالة العامة اللى
+
+287
+00:20:51,320 --> 00:20:54,680
+لو كان عند q1 and r1 و q2 and r2 يعني مش قاعدين
+
+288
+00:20:54,680 --> 00:20:58,590
+على ال originو Qn and Rn ممكن يكون واحد من هدول
+
+289
+00:20:58,590 --> 00:21:02,330
+الـR and الـorigin يعني بتكون 000 القرنين تبعها
+
+290
+00:21:02,330 --> 00:21:06,290
+فبشكل عام V at R بيساوي Q1 على 4 π إبسم نُط عارف
+
+291
+00:21:06,290 --> 00:21:10,050
+من نص عارف واحد زي Q2 على 4 بإبسم نُط عارف من نص
+
+292
+00:21:10,050 --> 00:21:14,780
+عارف تانين وهكذاأو بشكل عام اللي هو 1 الى 4 بإمس
+
+293
+00:21:14,780 --> 00:21:19,080
+النوت الـ summation من K equal 1 لأن QK على R
+
+294
+00:21:19,080 --> 00:21:22,920
+minus RK طبعا اللي هي ال magnitude اللي هي المسافة
+
+295
+00:21:22,920 --> 00:21:26,600
+من مين النقطة الباقية عندها ال potential و وضع ال
+
+296
+00:21:26,600 --> 00:21:27,060
+charge
+
+297
+00:21:31,010 --> 00:21:34,870
+هذا الحكي يتطبق مباشرة على اي distribution احنا
+
+298
+00:21:34,870 --> 00:21:37,470
+لاحقا قلت بنحكي عن مين على point of charge مرة
+
+299
+00:21:37,470 --> 00:21:39,610
+احطناها عند ال origin ومرة قلناها عند ال origin
+
+300
+00:21:39,610 --> 00:21:43,370
+ومرة قلنا مش واحدة عندنا call لو كان عندي line of
+
+301
+00:21:43,370 --> 00:21:45,730
+charge او surface of charge او volume of charge
+
+302
+00:21:45,730 --> 00:21:51,530
+تفرقية بدل من قول الهي Q علىR هيكون ال integration
+
+303
+00:21:51,530 --> 00:21:57,810
+القانون ال Q بس بدل ال Q إيش هتكون التكامل لل
+
+304
+00:21:57,810 --> 00:22:00,250
+charge distribution في طبيعة مثلا إذا كان ال line
+
+305
+00:22:00,250 --> 00:22:05,590
+distribution هيكون ال هو rho L DL prime طبعا وين
+
+306
+00:22:05,590 --> 00:22:08,030
+دي charge هتكون عند R prime احنا قولنا موضوع ال
+
+307
+00:22:08,030 --> 00:22:12,290
+charge عند R prime هتكون rho L at R prime DL prime
+
+308
+00:22:13,560 --> 00:22:17,940
+نجم ال surface charge distribution أسسة R' بيأسي
+
+309
+00:22:17,940 --> 00:22:24,260
+ال brine أو volume اتشارج رو V R' V ال brine تمام؟
+
+310
+00:22:24,260 --> 00:22:27,180
+طيب اذا كمان مرة نذكر ان ال brine coordinate هو
+
+311
+00:22:27,180 --> 00:22:30,720
+موضوع ال charge distribution هذا بشكل عام لو كان
+
+312
+00:22:30,720 --> 00:22:32,980
+عن ال lineage distribution او surface distribution
+
+313
+00:22:32,980 --> 00:22:37,780
+او volume distribution احنا قلنا هذه النقاط لازم
+
+314
+00:22:37,780 --> 00:22:42,010
+نحطها في عين الاعتبار انهأنا عشان أحسب ال
+
+315
+00:22:42,010 --> 00:22:45,850
+potential عند أي نقطة بحسبه مع reference وين ال
+
+316
+00:22:45,850 --> 00:22:49,790
+potential بساوة zero لو كان عند ال infinity هيكون
+
+317
+00:22:49,790 --> 00:22:52,730
+ال c بساوة zero لو كان ال reference مش عند ال
+
+318
+00:22:52,730 --> 00:22:56,950
+infinity هيكون له قيمة يعني قيمته zero بس مستخدمه
+
+319
+00:22:56,950 --> 00:23:00,330
+عشان نحسب ال c يعني بحسب ال v عند ال infinity
+
+320
+00:23:00,330 --> 00:23:03,230
+ومنها بقدر أجيب اللي هو ال constant of integration
+
+321
+00:23:03,230 --> 00:23:08,390
+لذن لو كان عند ال point is chosen عند ال reference
+
+322
+00:23:08,390 --> 00:23:12,340
+مش بضرورة تكون ال infinityبشكل عام يكون لدي
+
+323
+00:23:12,340 --> 00:23:16,320
+constant of integration هذا بحسبه طبعا من معرفتي
+
+324
+00:23:16,320 --> 00:23:19,140
+لل potential عن أي نقطة عن وين النقطة هي اللي انا
+
+325
+00:23:19,140 --> 00:23:21,100
+بقولها عندها ال reference اللي عندها ال potential
+
+326
+00:23:21,100 --> 00:23:26,260
+بسوا zero بشكل عام لي ايش بتساوي minus integral a
+
+327
+00:23:26,260 --> 00:23:28,040
+dot dl زائد c
+
+328
+00:23:33,600 --> 00:23:47,040
+بن بي مانوس بي ا بي ا بي ا بي ا بي اال example
+
+329
+00:23:47,040 --> 00:23:50,240
+عندي اخر حاجة احنا راكزناها في المحاضرة مثال
+
+330
+00:23:50,240 --> 00:23:54,520
+راكزوا معايا عندي two charges واحدة قمتها minus 4
+
+331
+00:23:54,520 --> 00:23:58,800
+micro column واحدة خمسة micro column واحدة قاعدة
+
+332
+00:23:58,800 --> 00:24:07,740
+انت x2 y ناقص واحد وz تلاتةوالتانية عند 0 ب X0 وY4
+
+333
+00:24:07,740 --> 00:24:11,280
+وZ-2 يعني هذه موقع ال charge الأولى وموقع ال
+
+334
+00:24:11,280 --> 00:24:15,960
+charge التانية وبدنا نوجد ال potential عند النقطة
+
+335
+00:24:15,960 --> 00:24:20,500
+101 إذا افترضنا ان ال potential 0 at infinity ال
+
+336
+00:24:20,500 --> 00:24:24,140
+reference تبعي ال infinity هتريحني ايش بيضل علي
+
+337
+00:24:24,140 --> 00:24:27,460
+أجيب عشان أجيب ال potential ال potential الناتج من
+
+338
+00:24:27,460 --> 00:24:29,360
+ال charge الأولى و ال potential الناتج من ال
+
+339
+00:24:29,360 --> 00:24:30,000
+charge التانية
+
+340
+00:24:38,110 --> 00:24:43,470
+ماله في الـ x,y,z، واضح يعني x,y,z الـ charge
+
+341
+00:24:43,470 --> 00:24:46,310
+الأولى وين located؟ جُحدة قيمتها ماينوس أربعة
+
+342
+00:24:46,310 --> 00:24:52,090
+ميكرو عن ميت عند x,2,y,1,6، لأ، فيعني خلّيني أقول
+
+343
+00:24:52,090 --> 00:24:55,570
+تقريبا، إذا أخدتنا هيكل هنا، هنبقى الـ charge
+
+344
+00:24:55,570 --> 00:24:59,370
+الأولى في واحد، اللي هي قيمتها ماينوس أربعة ميكرو،
+
+345
+00:24:59,370 --> 00:25:05,250
+والتانية، اللي هي خمسة ميكرو عند x بتساوي Zero
+
+346
+00:25:06,230 --> 00:25:11,270
+ياربع وزيد ناقص تلاني يعني somewhere هنا اي كيلو
+
+347
+00:25:11,270 --> 00:25:16,630
+تلاني اللي يعني Zero أربع ناقص تلاني هاي اللي ر
+
+348
+00:25:16,630 --> 00:25:24,970
+واحد فلنا نسميها و هاي ر تلاني او ر واحد ال prime
+
+349
+00:25:24,970 --> 00:25:27,450
+و ر تلاني ال prime اذا كنت تسميهم prime او can
+
+350
+00:25:27,450 --> 00:25:32,070
+اللي هي ال charges مش مشكلة بس لإني علمتهم ر واحد
+
+351
+00:25:32,070 --> 00:25:34,210
+و ر تلاني مفرقش انا عملت مرتين ال prime
+
+352
+00:25:39,340 --> 00:25:47,220
+بالنقطة X1 Y0 Z1 يعني في مكان ما هذه النقطة بتحسب
+
+353
+00:25:47,220 --> 00:25:54,240
+انها notation اذا
+
+354
+00:25:54,240 --> 00:26:01,240
+عندي انعافة R1 R1 ايش تمتها اتنين
+
+355
+00:26:01,240 --> 00:26:09,430
+ناقص واحد وتلاتةر2 هي قيمتها 0 4-2 وطبعا ر8 انا
+
+356
+00:26:09,430 --> 00:26:16,170
+عارفها هي 1 0 1 بدي ال potential عند هذه النقطة ال
+
+357
+00:26:16,170 --> 00:26:18,530
+potential عند هذه النقطة بيكون مجموع ال two
+
+358
+00:26:18,530 --> 00:26:21,210
+potentials اللي جاي من هنا و اللي جاي من هنا مجموع
+
+359
+00:26:21,210 --> 00:26:24,930
+2 اللي هيكون عشان اجيب ال potential اللي بتأثر
+
+360
+00:26:24,930 --> 00:26:27,010
+فيها اللي تشعرش على هذه النقطة ايش هيكون
+
+361
+00:26:37,520 --> 00:26:45,180
+R-R1 و ال potential اللي جاي من هاي T1 هيكون Q2
+
+362
+00:26:45,180 --> 00:26:52,420
+على 4Y إبسلنه يتزامر R-R2 و هاد احنا بنعرف نحسبها
+
+363
+00:26:52,420 --> 00:26:56,840
+لو بس عشان اتعلمنا الجسمة تربية لمربع طبعا بتجيب
+
+364
+00:26:56,840 --> 00:27:05,460
+الفرق بينها R-R1والفرق بتاعهم بدي أسعد أعمل ليه ال
+
+365
+00:27:05,460 --> 00:27:09,340
+magnetic بتاعهم الجزر التربيعي هاي الأولين هاي
+
+366
+00:27:09,340 --> 00:27:13,100
+الار وهاي الار واحد الفرق بينهم واحد ناقص مش واطين
+
+367
+00:27:13,100 --> 00:27:17,300
+ناقص واحد zero ناقص ناقص واحد واطين ال plus واحد
+
+368
+00:27:17,300 --> 00:27:22,100
+واحد منص ثلاثة في منص اتنين والجزر التربيعي المربع
+
+369
+00:27:22,100 --> 00:27:25,680
+الأول زي المربع التاني زي المربع التالت واحد زي
+
+370
+00:27:25,680 --> 00:27:31,790
+واحدهيكون جزر التربيع 6 المسافة تانية الار نقص
+
+371
+00:27:31,790 --> 00:27:32,510
+اربعة نقص اربعة نقص اربعة نقص اربعة نقص اربعة نقص
+
+372
+00:27:32,510 --> 00:27:37,430
+اربعة نقص اربعة نقص اربعة نقص اربعة نقص اربعة نقص
+
+373
+00:27:37,430 --> 00:27:39,750
+اربعة نقص اربعة نقص اربعة نقص اربعة نقص اربعة نقص
+
+374
+00:27:39,750 --> 00:27:42,010
+اربعة نقص اربعة نقص اربعة نقص اربعة نقص اربعة نقص
+
+375
+00:27:42,010 --> 00:27:43,390
+اربعة نقص اربعة نقص اربعة نقص اربعة نقص اربعة نقص
+
+376
+00:27:43,390 --> 00:27:45,670
+اربعة نقص اربعة نقص اربعة نقص اربعة نقص اربعة نقص
+
+377
+00:27:45,670 --> 00:27:50,190
+اربعة نقص اربعة نقص اربعة نقص اربعة
+
+378
+00:27:57,640 --> 00:28:00,680
+طبعا احنا دايما بنحط ال constant of integration ما
+
+379
+00:28:00,680 --> 00:28:04,440
+ننساهاش هو طبعا معطين ال hint انه عند ال infinity
+
+380
+00:28:04,440 --> 00:28:08,980
+بده يكون ال potential zero فإذا c not هتكون بتساوي
+
+381
+00:28:08,980 --> 00:28:09,300
+6
+
+382
+00:28:17,740 --> 00:28:20,880
+أذا ال potential هو مجموعة انتين بعوض عن قيم ال
+
+383
+00:28:20,880 --> 00:28:24,440
+charges و عن قيم المسافات و بحصل على ال potential
+
+384
+00:28:24,440 --> 00:28:29,920
+عند هذه النقطة و القائد التاني هنكون انه مثال تاني
+
+385
+00:28:29,920 --> 00:28:34,340
+على كيف تحسب ال potential عند أي نقطة في ال space
+
+386
+00:28:34,340 --> 00:28:38,700
+إذا كنت عندي charge, point of charge و line of
+
+387
+00:28:38,700 --> 00:28:43,350
+chargeأيش هو ال electric field؟ إنها تجميل ال line
+
+388
+00:28:43,350 --> 00:28:47,410
+distribution راجع كيف أنا أحسب ال potential من ال
+
+389
+00:28:47,410 --> 00:28:50,810
+line يعني اتطلعوا شويه على السريع على الكتاب و
+
+390
+00:28:50,810 --> 00:28:54,050
+شوفوا إيش إحنا المحاضرة القادمة المثال اللي بحلو
+
+391
+00:28:54,050 --> 00:28:57,330
+حاولوا يكون عندكم فكرة عنه عشان تستفيدوا منه أقصى
+
+392
+00:28:57,330 --> 00:29:00,850
+استفادة و نشوفكوا إن شاء الله اللقاء القادم على
+
+393
+00:29:00,850 --> 00:29:01,110
+الفيديو
+
diff --git a/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/xsHJkkk1-GI.srt b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/xsHJkkk1-GI.srt
new file mode 100644
index 0000000000000000000000000000000000000000..c5358732a6c2480624f4240886f752a547a02a45
--- /dev/null
+++ b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/xsHJkkk1-GI.srt
@@ -0,0 +1,2069 @@
+1
+00:00:20,940 --> 00:00:23,480
+بسم الله الرحمن الرحيم السلام عليكم و رحمة الله و 
+
+2
+00:00:23,480 --> 00:00:26,660
+بركاته إحنا اليوم إن شاء الله هنتبع موضوعنا اللي 
+
+3
+00:00:26,660 --> 00:00:30,680
+هو الـ potential electric potential أسوأ 
+
+4
+00:00:30,680 --> 00:00:34,080
+الـ absolute ولا الـ potential difference إحنا 
+
+5
+00:00:34,080 --> 00:00:36,980
+المحاضرة الماضية شوفنا كيف أن الـ potential مربوط 
+
+6
+00:00:36,980 --> 00:00:41,880
+بيه اللي هو الـ electric field شوفنا أن الـ
+
+7
+00:00:41,880 --> 00:00:45,100
+potential بين نقطتين A و B هو minus التكامل من A 
+
+8
+00:00:45,100 --> 00:00:46,760
+لـ B لـ E ضد DL
+
+9
+00:00:49,210 --> 00:00:51,730
+إذا كنا عارفين الـ electric field فقدر أحسب الـ
+
+10
+00:00:51,730 --> 00:00:55,490
+potential قولنا الـ absolute potential بيكون لو أنا 
+
+11
+00:00:55,490 --> 00:01:00,770
+أخدت مثلًا النقطة a عند الـ infinity هيكون عندها الـ
+
+12
+00:01:00,770 --> 00:01:03,230
+potential بيساوي zero فهيكون الـ potential عند
+
+13
+00:01:03,230 --> 00:01:07,850
+النقطة b بيساوي q على 4 by epsilon not في الـ Rb
+
+14
+00:01:07,850 --> 00:01:11,110
+فأنا 
+
+15
+00:01:11,110 --> 00:01:13,810
+لو أخدنا أن الـ R a مثلًا عند الـ infinity هذا قولنا 
+
+16
+00:01:13,810 --> 00:01:15,710
+بيسميه الـ absolute potential
+
+17
+00:01:17,930 --> 00:01:20,470
+كمان قولنا لو أن الـ charge مش عند الـ origin إحنا 
+
+18
+00:01:20,470 --> 00:01:24,170
+كنا عملنا هذا الحكي أن V بيساوي Q على 4 by Epsilon 
+
+19
+00:01:24,170 --> 00:01:28,030
+Note R لما الـ charge فرضاه عند الـ origin و لو الـ
+
+20
+00:01:28,030 --> 00:01:32,290
+charge مش عند الـ origin لو 
+
+21
+00:01:32,290 --> 00:01:34,850
+الـ charge مش عند الـ origin هيكون الـ potential إيش 
+
+22
+00:01:34,850 --> 00:01:38,590
+بيساوي Q على 4 by Epsilon Note الفرق ما بين R و R 
+
+23
+00:01:38,590 --> 00:01:42,290
+prime حيث R اللي هو الموقع اللي أنا بدأ أَقيس عنده
+
+24
+00:01:42,290 --> 00:01:47,770
+الـ potential و R prime اللي هو مكان الـ charge لو 
+
+25
+00:01:47,770 --> 00:01:51,130
+كان عندي أكثر من الـ charge نحسبه بالطريقة طبعًا على 
+
+26
+00:01:51,130 --> 00:01:54,070
+أساس أن إحنا فرضين أنه عند الـ infinity الـ
+
+27
+00:01:54,070 --> 00:01:57,850
+potential بيساوي zero لو كان عندي distribution 
+
+28
+00:01:57,850 --> 00:02:01,790
+charge distribution لو كانت line أو surface أو 
+
+29
+00:02:01,790 --> 00:02:06,020
+volume قولنا هيك نحسب الـ potential بشكل عام لو أنا 
+
+30
+00:02:06,020 --> 00:02:08,980
+ما قلتش عند الـ infinity هي الـ zero بشكل عام لو في
+
+31
+00:02:08,980 --> 00:02:12,860
+عندي أنا الـ reference point مش الـ infinity هيكون
+
+32
+00:02:12,860 --> 00:02:15,800
+الـ potential بشكل عام بيساوي q على four by y not r 
+
+33
+00:02:15,800 --> 00:02:19,340
+زائد c، c هِيحسبها من وين؟ من عند الـ reference 
+
+34
+00:02:19,340 --> 00:02:22,160
+point يعني وين أنا حددت للـ reference point اللي 
+
+35
+00:02:22,160 --> 00:02:25,820
+عند الـ potential؟ zero، بنحسب اللي هو قيمة c، لذا 
+
+36
+00:02:25,820 --> 00:02:29,660
+بشكل عام بيبقى minus integral a dot d l plus c
+
+37
+00:02:34,790 --> 00:02:39,770
+المثال اللي قدامنا كانت 
+
+38
+00:02:39,770 --> 00:02:43,250
+أن حسابات الـ potential عند الـ infinity بيساوي 
+
+39
+00:02:43,250 --> 00:02:46,550
+zero عند كنتوا charges كل واحدة عارفة الـ location 
+
+40
+00:02:46,550 --> 00:02:50,190
+تبعهم و مش عند الـ zero كل واحدة لها location محدد
+
+41
+00:02:50,190 --> 00:02:53,770
+R1 سمّيناها وR2 و عند النقطة البدائية عندها الـ
+
+42
+00:02:53,770 --> 00:02:54,770
+potential هي R
+
+43
+00:03:13,860 --> 00:03:17,660
+هذا ما حللناه المحاضرة الماضية
+
+44
+00:03:21,670 --> 00:03:25,470
+بدّينا عن مثال ثاني قولنا هنحله المحاضرة هاي
+
+45
+00:03:25,470 --> 00:03:28,690
+المثال اللي عندنا بيقول أن في عندي charge مقدارها 
+
+46
+00:03:28,690 --> 00:03:33,730
+خمسة nano column موجودة عند النقطة minus 3 4 0
+
+47
+00:03:33,730 --> 00:03:38,530
+وعندي كمان خط line of charge يعني عندي حاجتين 
+
+48
+00:03:38,530 --> 00:03:41,630
+point of charge و line of charge الـ point of
+
+49
+00:03:41,630 --> 00:03:45,790
+charge قاعدة في الـ space عند النقطة minus 3 4 0 و
+
+50
+00:03:45,790 --> 00:03:50,050
+الـ line of charge عند y 1 زي 1 يعني الـ x ماله 
+
+51
+00:03:50,050 --> 00:03:55,200
+موازية الـ xكاليز يونيفيرمت شارج مقدارها اتنين نانو 
+
+52
+00:03:55,200 --> 00:03:59,900
+كولوم بيرمتر يعني رؤال بتساوي اتنين كولوم نانو 
+
+53
+00:03:59,900 --> 00:04:04,200
+كولوم بيرمتر إيش طالب منهم؟ مناقشة إحنا قولنا أن
+
+54
+00:04:04,200 --> 00:04:07,200
+الـ reference اللي هو الـ voltage بتساوي زيرو عند الـ
+
+55
+00:04:07,200 --> 00:04:10,100
+origin يعني الـ reference بتاعته هلّأته وين؟ عند الـ
+
+56
+00:04:10,100 --> 00:04:15,240
+origin بده الـ voltage عند النقطة A اللي عند خمسة 
+
+57
+00:04:15,240 --> 00:04:20,160
+و زيرو واحد يعني المثال 
+
+58
+00:04:24,230 --> 00:04:33,430
+عند الـ charge 
+
+59
+00:04:33,430 --> 00:04:38,490
+اللي هي الخمسة nano عند minus تلاتة و أربعة و على الـ
+
+60
+00:04:38,490 --> 00:04:42,570
+X يعني في الـ X Y بلان الـ Z أقل منها Zero لذلك هذه 
+
+61
+00:04:42,570 --> 00:04:47,230
+الخمسة nano كلّه اللي عند ناقص تلاتة و أربعة و صفر في
+
+62
+00:04:47,230 --> 00:04:53,580
+الـ X Y بلان الـ line y واحد و z واحد يعني لو حطينا 
+
+63
+00:04:53,580 --> 00:04:57,360
+هنا واحد واحد هنا خط شماله هيكون قولنا و زي الـ X 
+
+64
+00:04:57,360 --> 00:05:06,100
+axis فالـ 
+
+65
+00:05:06,100 --> 00:05:10,860
+X Y plane لأن Z equal 0 هاي الـ charge الأولى ليه؟ 
+
+66
+00:05:10,860 --> 00:05:15,280
+خمسة نان كولوم و X ناقص ثلاثة و Y أربعة في الـ X Y 
+
+67
+00:05:15,280 --> 00:05:21,530
+هتكون قاعدة هنا في الـ X Y الـ line and واحد واحد
+
+68
+00:05:21,530 --> 00:05:27,790
+يعني معناه الموازي بالـ x-axis هذا 
+
+69
+00:05:27,790 --> 00:05:34,110
+الـ line of charge موازي بالـ x-axis الـ
+
+70
+00:05:34,110 --> 00:05:43,790
+charge density ρL تساوي اتنين نانو كولوم درهم 
+
+71
+00:05:43,790 --> 00:05:49,110
+قالنا المعلومة أن الـ reference point هنا بتساوي 0 
+
+72
+00:05:49,900 --> 00:05:54,660
+عند الـ origin، عند الـ 000 الـ reference point
+
+73
+00:05:54,660 --> 00:06:02,820
+و بدّه الـ potential عند X بتساوي 5Y0 و Z1 يعني وين
+
+74
+00:06:02,820 --> 00:06:07,620
+هتكون في الـ X دي plane هاي النقطة اللي بتوع عندها 
+
+75
+00:06:07,620 --> 00:06:13,960
+الـ potential اللي 
+
+76
+00:06:13,960 --> 00:06:16,880
+هي 501
+
+77
+00:06:21,420 --> 00:06:25,280
+أو بشكل عام إذا
+
+78
+00:06:25,280 --> 00:06:32,280
+أنا
+
+79
+00:06:32,280 --> 00:06:38,620
+أول حاجة بتحسبها اللي هي الأبعاد بتاعة الـ line و 
+
+80
+00:06:38,620 --> 00:06:43,780
+بتاعة الـ point عن نقطة اللي بتحسب عندها الـ
+
+81
+00:06:43,780 --> 00:06:44,240
+potential
+
+82
+00:06:49,720 --> 00:06:52,040
+طبعًا إحنا الـ potential عند أي نقطة في الـ space في
+
+83
+00:06:52,040 --> 00:06:54,340
+هذه الحالة مش عند النقطة اللي أنا بس بدّه احسب
+
+84
+00:06:54,340 --> 00:06:57,520
+عندها الـ potential عند أي نقطة هتكون مجموعة two
+
+85
+00:06:57,520 --> 00:07:00,360
+potentials الـ potential اللي جاي من الـ point at
+
+86
+00:07:00,360 --> 00:07:03,140
+charge زائد الـ potential اللي جاي من مين من line at
+
+87
+00:07:03,140 --> 00:07:05,680
+charge و إحنا عارفين نحسب كيف كل واحد على حدّه كيف
+
+88
+00:07:05,680 --> 00:07:08,220
+أحسب الـ potential اللي جاي من point at charge و
+
+89
+00:07:08,220 --> 00:07:10,840
+كيف أحسب potential اللي من الـ line
+
+90
+00:07:15,390 --> 00:07:18,090
+إحنا الـ point of charge قلنا دي Q إيش بيساوي minus
+
+91
+00:07:18,090 --> 00:07:21,670
+الـ integer لـ A dot DL هو minus الـ integer لـ Q four
+
+92
+00:07:21,670 --> 00:07:26,070
+by epsilon dot R تبعيّه R hat dot DR لـ R hat اللي هي 
+
+93
+00:07:26,070 --> 00:07:29,330
+إحنا اشتغلناها Q على four by epsilon dot R زائد C1
+
+94
+00:07:29,330 --> 00:07:33,830
+هسمّي C1 لأن هيطلع لنا C2 من line of charge هذا الـ
+
+95
+00:07:33,830 --> 00:07:36,750
+constant of integration قلنا اللي هو بنحسبه من الـ
+
+96
+00:07:36,750 --> 00:07:39,690
+reference point من ما عرفتي وين الـ reference يعني
+
+97
+00:07:39,690 --> 00:07:44,900
+وين الـ zero voltage ما قدر أحسب الـ constant هذا الـ
+
+98
+00:07:44,900 --> 00:07:47,960
+اللي هي الـ line charge هي نتيجة لإيده الـ dl اللي 
+
+99
+00:07:47,960 --> 00:07:54,500
+هي الـ charge density دي raw اللي هو الـ line على 
+
+100
+00:07:54,500 --> 00:07:57,160
+طول الـ line الـ dl هي اللي هي على طول الـ line دي
+
+101
+00:07:57,160 --> 00:08:01,040
+raw أو دي ال يعني لو بنسمّيها دي التغير على طول الـ
+
+102
+00:08:01,040 --> 00:08:07,300
+line على two by epsilon not raw هتكون 
+
+103
+00:08:07,300 --> 00:08:10,840
+raw L على two by epsilon not plus الـ raw زائد CT
+
+104
+00:08:18,520 --> 00:08:25,000
+هنا نحسب قيم R ربط طبعًا هذا الـ total voltage total 
+
+105
+00:08:25,000 --> 00:08:29,420
+electric voltage قول إن هو VQ زي VL هيكون Q على 
+
+106
+00:08:29,420 --> 00:08:33,740
+four by epsilon ر زي C واحد بالنسبة للـ electric
+
+107
+00:08:33,740 --> 00:08:40,510
+field إنها تجمع الـ line هيكون رو L minus رو L على
+
+108
+00:08:40,510 --> 00:08:44,130
+اتنين باي أبسل not blend الرو وعندنا الـ C الـ C ما 
+
+109
+00:08:44,130 --> 00:08:47,850
+هو عندي constant C واحد و constant C تنين مجموعهم
+
+110
+00:08:47,850 --> 00:08:51,750
+constant هسمّيه C اللي أنا هجيبه من وين من الـ
+
+111
+00:08:51,750 --> 00:08:52,070
+reference
+
+112
+00:08:59,980 --> 00:09:03,240
+إحنا بناخد المثال الأولاني لو طالب مني لو أنا عندي
+
+113
+00:09:03,240 --> 00:09:07,300
+الـ reference voltage عند الـ 0 و طالب عندي V عند 5
+
+114
+00:09:07,300 --> 00:09:13,960
+0 1 أول حاجة بدّي أجيب قيم Raw وقيم Min R Raw بشكل 
+
+115
+00:09:13,960 --> 00:09:18,600
+عام اللي هو أنا عندي هاي line of charge أي نقطة 
+
+116
+00:09:18,600 --> 00:09:26,200
+تبعد عنه عن xyz هتكون الـ absolute value لـ xyz-x11
+
+117
+00:09:26,200 --> 00:09:30,820
+لأنه عندي ثابت قيم الـ y و الـ z واحد واحد فأي نقطة
+
+118
+00:09:30,820 --> 00:09:34,480
+في الـ space xyz قيمة رؤش هتكون هي المسافة بين هي 
+
+119
+00:09:34,480 --> 00:09:42,920
+النقطة و الـ line xyz-x11 يكون x-x هو zero فهي y-1
+
+120
+00:09:42,920 --> 00:09:47,400
+كل تربيع زائد z-1 كل تربيع تحت الجذر هي قيمة raw
+
+121
+00:09:47,400 --> 00:09:51,180
+أنا
+
+122
+00:09:51,180 --> 00:09:56,280
+بتحسب raw اللي هي بُعد الـ origin عن الـ line و برضه 
+
+123
+00:09:56,280 --> 00:10:00,190
+raw بُعد النقطة اللي احسبها عن الـ line بعد الـ
+
+124
+00:10:00,190 --> 00:10:05,590
+origin عن الـ line هيكون 000-011 هتكون الجذر الثاني 
+
+125
+00:10:05,590 --> 00:10:10,090
+و النقطة اللي بتحسب عندها الـ potential اللي هي 501 
+
+126
+00:10:10,090 --> 00:10:13,310
+هتعطيني 1 إيش اللي بدّي أعمله بدّي أجيب الـ potential 
+
+127
+00:10:13,310 --> 00:10:16,530
+عند الـ origin بدّي أجيب الـ potential عند النقطة
+
+128
+00:10:16,530 --> 00:10:20,230
+اللي بدّي عندها الـ potential ليش أنا بدّي الـ
+
+129
+00:10:20,230 --> 00:10:23,290
+potential عند الـ origin لإنه يعطيني معلومة عنه إيه
+
+130
+00:10:23,290 --> 00:10:26,450
+الـ potential عند الـ origin إيش بيساوي 0 وهذا اللي 
+
+131
+00:10:26,450 --> 00:10:31,130
+هيساعدني أن أعرف قيمة الـ constant عشان هي أنا جبت الـ 
+
+132
+00:10:31,130 --> 00:10:34,410
+raw اللي هي بُعد الـ line عن الـ origin و مرة ثانية 
+
+133
+00:10:34,410 --> 00:10:38,750
+الـ raw اللي هي بُعد الـ line عن النقطة اللي بدّه يقيس 
+
+134
+00:10:38,750 --> 00:10:41,990
+عندها الـ potential نفس الشيء الـ raw node بُعد الـ
+
+135
+00:10:41,990 --> 00:10:44,990
+charge عن الـ origin و بُعد الـ charge عن النقطة اللي 
+
+136
+00:10:44,990 --> 00:10:49,010
+بدّه يجيب عندها الـ potential و بتحسب ببساطة قيمة
+
+137
+00:10:49,010 --> 00:10:51,550
+raw node و R node اللي هو زي ما قلنا بُعد الـ line 
+
+138
+00:10:51,550 --> 00:10:57,790
+عن الـ origin و الـ raw A و الـ R A فقعدت و أخذته الـ 
+
+139
+00:10:57,790 --> 00:11:00,050
+line of charge كيف نجيب الـ electric field اللي هو 
+
+140
+00:11:00,050 --> 00:11:05,770
+باستخدامك أو slope تأخذه اللي هو contour حوالينه 
+
+141
+00:11:05,770 --> 00:11:11,510
+تمام بس ما علينا أن نكمل و نحصل على الـ potential
+
+142
+00:11:14,750 --> 00:11:18,690
+عشان أجيب الـ constant أنا صرت عارفة بس بدّي أعوض
+
+143
+00:11:18,690 --> 00:11:24,270
+فيها القيم عن هذه المعادلة مرتين بدّي أعوض مرة لـ V
+
+144
+00:11:24,270 --> 00:11:27,750
+عند النقطة اللي بدّي أحسب عندها الـ potential و مرة
+
+145
+00:11:27,750 --> 00:11:30,990
+عند الـ origin الـ constant ماله بيظل constant بتفضل
+
+146
+00:11:30,990 --> 00:11:37,170
+نظر أنا حسبت الـ potential عند النقطة اللي 5 0 1 و 
+
+147
+00:11:37,170 --> 00:11:39,590
+لا حسبت الـ potential عند الـ origin الـ constant
+
+148
+00:11:39,590 --> 00:11:46,530
+constant فاللي هيتغير قيم الـ raw و الـ a raw L و Q 
+
+149
+00:11:46,530 --> 00:11:49,590
+17 و الـ two by epsilon node و هنا four by epsilon 
+
+150
+00:11:49,590 --> 00:11:53,090
+node كلّها أرقام إحنا عارفينها بعوّض مرة عن الـ raw 
+
+151
+00:11:53,090 --> 00:11:56,670
+node و R node و مرة ثانية بحسب الـ potential عند
+
+152
+00:11:56,670 --> 00:12:01,650
+النقطة اللي إمدّيتها يعني بحسب raw A و R A سمّيناها 
+
+153
+00:12:01,650 --> 00:12:05,910
+بتظل constant لأن هو مجرد constant رقم عشان أحسب
+
+154
+00:12:05,910 --> 00:12:12,180
+قيم الـ potential عند النقطة المطلوبة ماذا سأفعل؟ 
+
+155
+00:12:12,180 --> 00:12:17,300
+سأطرح الـ two potential من بعض V0 معنى ZE مين اللي
+
+156
+00:12:17,300 --> 00:12:20,000
+راح في هالحالة؟ الـ constant اللي لمش لازمنيه 
+
+157
+00:12:20,000 --> 00:12:24,540
+سأطرحهم من بعض و في عندي معلومة أن V0 ماله بيساوي
+
+158
+00:12:24,540 --> 00:12:28,800
+Zero فعوض عن V0 بيساوي Zero بحصل على قيمة الـ
+
+159
+00:12:28,800 --> 00:12:33,960
+potential in الـ A واضح الشيء اللي عملناه؟ إذا عندي
+
+160
+00:12:33,960 --> 00:12:36,600
+line of charge وعندي point of charge هاي الأسئلة 
+
+161
+00:12:36,600 --> 00:12:37,960
+اللي بتيجي في المتحنات المانعة 
+
+162
+00:12:41,300 --> 00:12:45,760
+عندي معلومة غير عن اللي إحنا شفناه في المثال
+
+163
+00:12:45,760 --> 00:12:48,500
+الماضي أنّه عند الـ infinity الـ potential بيساوي 0
+
+164
+00:12:48,500 --> 00:12:52,240
+هنا الـ reference point هي الـ origin عند الـ origin 
+
+165
+00:12:52,240 --> 00:12:55,980
+عندي الـ potential بيساوي 0 في أي نقطة في الـ space 
+
+166
+00:12:55,980 --> 00:12:58,400
+أن البوتنيشال بيساوي مجموعة، البوتنيشال اللي جاي من
+
+167
+00:12:58,400 --> 00:13:01,800
+الـ charge زي البوتنيشال اللي جاي من الـ line charge
+
+168
+00:13:02,580 --> 00:13:05,060
+قيم الـ potential جاية من الـ charge معروف اللي هو q
+
+169
+00:13:05,060 --> 00:13:09,000
+على 4pi epsilon node R زائد some constant واللي 
+
+170
+00:13:09,000 --> 00:13:11,100
+جاية من الـ electric field ده كامل الـ electric 
+
+171
+00:13:11,100 --> 00:13:14,560
+field في dot dl بالنسبة لـ line of charge و أنتو
+
+172
+00:13:14,560 --> 00:13:19,120
+جبتوها لـ infinite line من جا عصله صحيح؟ تذكروا
+
+173
+00:13:19,120 --> 00:13:22,140
+عند أي نقطة حوالين الـ line اللي بتساوي الـ clause
+
+174
+00:13:22,140 --> 00:13:25,820
+integral أي dot dl بتساوي q enclosed على epsilon
+
+175
+00:13:25,820 --> 00:13:32,260
+node من جا عصله بعد ما جبنا الـ potential عند الـ
+
+176
+00:13:
+
+201
+00:15:18,160 --> 00:15:23,280
+حياتنا بس بإشارة سالبة بما أن الـ Potential
+
+202
+00:15:23,280 --> 00:15:26,920
+difference بين أي نقطتين باص independent يعني لا 
+
+203
+00:15:26,920 --> 00:15:29,920
+يتمدد على الباص سيكون الـ Potential ما بين الـ PA
+
+204
+00:15:29,920 --> 00:15:33,980
+سالب الـ Potential بين A و B و هذا احنا بنعرفه حتى
+
+205
+00:15:33,980 --> 00:15:39,160
+الدائرة أحسب الفرق الجهد بين النقطتين أعكس القراءة
+
+206
+00:15:39,160 --> 00:15:43,160
+بتعطيني إشارة سالبة لكن إذا قملته بيبقى نفس الحاجة
+
+207
+00:15:43,160 --> 00:15:46,730
+نفس القيمة إذا معناه مجموعة دولة with two
+
+208
+00:15:46,730 --> 00:15:49,150
+potentials، يعني لو أنا أخذت close loop، إيش معناه
+
+209
+00:15:49,150 --> 00:15:51,810
+مجموعة with two potentials دولة؟ لو أنا بدأت من
+
+210
+00:15:51,810 --> 00:15:58,370
+نقطة A، لو أنا بدأت من نقطة A، وجئت عن نقطة A،
+
+211
+00:15:58,370 --> 00:16:01,470
+يعني بدأت من A لـ B، وبعدين من B لـ A، إيش هي 
+
+212
+00:16:01,470 --> 00:16:05,650
+مجموعة الـ potential؟ Zero، يعني واحد منهم قاعد 
+
+213
+00:16:05,650 --> 00:16:08,590
+سالب خمسة، الثاني موجب خمسة، إذا مجموع
+
+214
+00:16:08,590 --> 00:16:14,650
+ما هيصير؟ صفر إذا مجموع الـ potential VBA زائد VAB
+
+215
+00:16:14,650 --> 00:16:18,510
+هو Zero وهذا ماذا يساوي الـ potential؟ بيساوي الـ
+
+216
+00:16:18,510 --> 00:16:23,990
+Integral من B لـ A لـ E ضد DL زائد الـ Integral من A لـ B
+
+217
+00:16:23,990 --> 00:16:28,390
+E ضد DL هي مجموعة هذا الـ Integral بيساوي الـ
+
+218
+00:16:28,390 --> 00:16:36,170
+Integral من B لـ A E ضد DL وهذا التكامل من A لـ B E ضد 
+
+219
+00:16:36,170 --> 00:16:43,340
+DL مجموعهم هيكون من B لـ A closed path مسار مغلق
+
+220
+00:16:43,340 --> 00:16:46,920
+loop بروح من نفس النقطة و برجع لها هيكل مغلق 
+
+221
+00:16:46,920 --> 00:16:50,780
+integral لـ E ضد dl إذا الـ closed integral إيش
+
+222
+00:16:50,780 --> 00:16:54,100
+بيساوي؟ Zero احنا فعودنا إن هاي دائرة معناها
+
+223
+00:16:54,100 --> 00:16:59,060
+closed integral إذا الـ closed integral لـ E ضد dl
+
+224
+00:16:59,060 --> 00:17:02,940
+إيش بيساوي؟ Zero بس احنا أخذنا Stokes theorem
+
+225
+00:17:02,940 --> 00:17:06,140
+بتذكروا لما كنا بناخد الـ mathematics في أول
+
+226
+00:17:06,140 --> 00:17:09,080
+شابتر بينا Stokes theorem بس إيش بتقولي الـ closed 
+
+227
+00:17:09,080 --> 00:17:14,970
+integral؟ للـ line integral بيساوي الـ surface
+
+228
+00:17:14,970 --> 00:17:18,630
+integral لـ Curl الـ field كنا بناخدها بشكل عام، أي
+
+229
+00:17:18,630 --> 00:17:22,290
+field نسميه A، قول الـ line integral لـ A dot D ..
+
+230
+00:17:22,290 --> 00:17:25,790
+الـ closed line integral لـ A dot DL بيساوي الـ
+
+231
+00:17:25,790 --> 00:17:29,170
+surface integral لـ Curl الـ A dot DS، احنا هالأيه
+
+232
+00:17:29,170 --> 00:17:31,010
+تعرفين من الـ field اللي بنحكي عنه؟ بنحكي عن الـ
+
+233
+00:17:31,010 --> 00:17:34,970
+electric field، إذا الـ closed integral لـ E ضد DL
+
+234
+00:17:34,970 --> 00:17:40,650
+بيساوي الـ Curl E ضد DS هذا ما يعني بيساوي Zero إذا
+
+235
+00:17:40,650 --> 00:17:43,890
+هذا الـ Integral بيساوي Zero إذا ما أنا Curl E لأنه 
+
+236
+00:17:43,890 --> 00:17:47,010
+DS أنا باخد عينة يعرف أنه باخد عينة من الـ surface
+
+237
+00:17:47,010 --> 00:17:50,230
+من الـ Zero متأكدة أنها عينة عند الـ surface هذا
+
+238
+00:17:50,230 --> 00:17:54,570
+القدر وبقعد بدي DS اللي هي مثلاً DX DY DZ مش
+
+239
+00:17:54,570 --> 00:17:58,230
+محتاجة Zero مين اللي لازم يساوي Zero Curl الـ E
+
+240
+00:17:58,230 --> 00:18:01,710
+إذا Curl الـ E بيساوي Zero حيصيرنا قبل هيك
+
+241
+00:18:01,710 --> 00:18:05,210
+متذكرين إيش اللي معناه إنه أي Potential الـ Curl
+
+242
+00:18:05,210 --> 00:18:10,710
+تبعه بيساوي Zero ما هو الـ rotational بلفش صح
+
+243
+00:18:10,710 --> 00:18:14,610
+متذكرين؟ والـ electric field إنه من أمثلة الناس
+
+244
+00:18:14,610 --> 00:18:18,250
+اللي ما لها الـ rotational بتلفش ما لها لها Source
+
+245
+00:18:18,250 --> 00:18:22,690
+يا Sink يا إيش Emerge لكن بتلفش الـ electric field
+
+246
+00:18:23,740 --> 00:18:28,580
+طبعاً هذا Maxwell والـ equation المعادلة اللي احنا 
+
+247
+00:18:28,580 --> 00:18:33,140
+شفناها قبل هي Curl E بتساوي Zero هاي هي بتكون
+
+248
+00:18:33,140 --> 00:18:38,200
+معكم ثاني Maxwell
+
+249
+00:18:38,200 --> 00:18:41,560
+والـ equation لإن أخذت Divergence E بتساوي rho على
+
+250
+00:18:41,560 --> 00:18:47,520
+Epsilon not Maxwell والـ equation صحيح؟ وهاي ثاني
+
+251
+00:18:47,520 --> 00:18:47,920
+واحدة 
+
+252
+00:18:52,700 --> 00:18:56,860
+مش كمان احنا ممكن نوصل من تعريف الـ potential الـ
+
+253
+00:18:56,860 --> 00:18:59,740
+potential إن هو عبارة عن minus الـ Integral لـ E dot
+
+254
+00:18:59,740 --> 00:19:02,780
+DL أنا يعني حملت الـ minus لما عملت عشان آخذ الـ
+
+255
+00:19:02,780 --> 00:19:06,900
+close Integral بس يعني أنتم تأخذوه بالانتباه أنا 
+
+256
+00:19:06,900 --> 00:19:09,620
+كانت الفكرة إن أفرجيكم إن الـ Integral لـ E dot DL
+
+257
+00:19:09,620 --> 00:19:12,460
+زي الـ Integral لـ E dot DL بيعطيني الـ close loop
+
+258
+00:19:12,460 --> 00:19:15,100
+بس في minus برا و Zero مش فارقة يعني
+
+259
+00:19:26,670 --> 00:19:30,270
+dV بيكون dV بيكون minus E dot DL
+
+260
+00:19:33,200 --> 00:19:35,800
+طب هذا إيش معناه؟ هذا Dot Product بين Vector
+
+261
+00:19:35,800 --> 00:19:38,640
+Field و DL و DL ما احنا عارفينها مثلاً من الـ
+
+262
+00:19:38,640 --> 00:19:42,680
+Cartesian إيش اللي بيساوي DL؟ DX X hat, DY Y hat,
+
+263
+00:19:43,020 --> 00:19:47,880
+DZ Z hat و E هذا Field، Vector يعني عمّا دربه بـ EX
+
+264
+00:19:47,880 --> 00:19:52,620
+X hat زي EY Y hat زي EZ Z hat إذا Dot Product
+
+265
+00:19:52,620 --> 00:20:02,470
+مش هيحطني EX DX EY DY EZ DZ معين؟ طب كمان dV هي دي
+
+266
+00:20:02,470 --> 00:20:05,070
+ما قالها Total Differential و الـ Total 
+
+267
+00:20:05,070 --> 00:20:08,910
+Differential بتلاقي الـ Partial Differential اللي
+
+268
+00:20:08,910 --> 00:20:15,950
+هي dV by dx dx زائد dV by dy dy زائد dV by dz dz في
+
+269
+00:20:15,950 --> 00:20:19,570
+حد عنده مشكلة في هاي الـ Total Differential؟ لو أنا 
+
+270
+00:20:19,570 --> 00:20:23,030
+قرنت المعادلتين مع بعض إيش بلاحظ إنه EX إيش بتساوي
+
+271
+00:20:23,030 --> 00:20:29,970
+minus dV by dx EY إيش بتساوي minus dV by dy EZ إيش
+
+272
+00:20:29,970 --> 00:20:34,510
+بتساوي minus dV by dz لو طلعت على هذه المعادلة إيش
+
+273
+00:20:34,510 --> 00:20:37,290
+بتقول لي إن في عندي X component للـ electric field
+
+274
+00:20:37,290 --> 00:20:41,650
+بتساوي minus dV by dx وعندي Y component بتساوي
+
+275
+00:20:41,650 --> 00:20:46,070
+minus dV by dy و Z component بتساوي minus dV by dz
+
+276
+00:20:49,620 --> 00:20:58,680
+-dv by dx x hat -dv by dy y hat فـ dv
+
+277
+00:20:58,680 --> 00:21:03,840
+by dz زدها
+
+278
+00:21:03,840 --> 00:21:12,520
+قريبة تساوي -d by dx x hat -d by dy y hat -d by dz
+
+279
+00:21:13,170 --> 00:21:17,950
+زدها ما لها مؤثرة على مين على مين وهذه مين تعريفها
+
+280
+00:21:17,950 --> 00:21:20,810
+في الـ partition coordinate اللي هي الـ Del هتكون هذه
+
+281
+00:21:20,810 --> 00:21:28,810
+minus فبحث عن minus هنا هذا
+
+282
+00:21:28,810 --> 00:21:33,850
+بالتامة اللي هو الـ Del هتكون minus Del V منطقي إن 
+
+283
+00:21:33,850 --> 00:21:38,270
+تكون E بتساوي minus Del V ليش منطقي ليش E لازم
+
+284
+00:21:38,270 --> 00:21:43,430
+تكون minus gradient للـ Potential  لأن الـ شاردة اللي طلع لنا شيء 
+
+285
+00:21:43,430 --> 00:21:49,470
+متوقع مش شيء مش متوقع الـ potential بيساوي الـ 
+
+286
+00:21:49,470 --> 00:21:56,210
+Integral زائد حاجة ثانية مادام إن الـ potential هو 
+
+287
+00:21:56,210 --> 00:22:00,510
+الـ Integral ايه للـ DL هو احنا اشتقيناها من هنا صح
+
+288
+00:22:00,510 --> 00:22:05,630
+اشتقيناها من هنا وصلنا إنه ايه بيساوي ما نذكرت فيه 
+
+289
+00:22:05,630 --> 00:22:09,210
+شيء هاي المعادلة المنطقية من اللي اخذناها من
+
+290
+00:22:09,210 --> 00:22:14,780
+الشباتر قبل ما أنا أغيب عنكم أي معلومة أخذناها Curl
+
+291
+00:22:14,780 --> 00:22:22,200
+الـ Del إيش بيساوي أنا سميته عشان احنا قدرنا أخذناهم
+
+292
+00:22:22,200 --> 00:22:27,500
+إيش بيساوي Curl الـ Del إيش Curl الـ Del بيساوي Zero
+
+293
+00:22:27,500 --> 00:22:33,560
+Curl الـ Del بيساوي Zero الله عليكم طب مش خايفين احنا
+
+294
+00:22:33,560 --> 00:22:37,440
+قلنا Curl Del ما له قوى لسه في الـ Study الصحيحة إيش
+
+295
+00:22:37,440 --> 00:22:41,980
+بيساوي Curl Del ايه Zero إيش ما له الكثير الكثير الـ
+
+296
+00:22:41,980 --> 00:22:47,260
+Rotational كان الـ E بيساوي 0 وعناه إن E لازم يكون
+
+297
+00:22:47,260 --> 00:22:51,660
+Gradient لـ Scalar Potential لإن كان الـ Gradient لـ
+
+298
+00:22:51,660 --> 00:22:59,260
+Scalar Potential بيساوي 0، واضح؟ فهموني
+
+299
+00:22:59,260 --> 00:23:03,980
+هي كيف بتدرسوا، ما تطفوا ساكتين يعني، ما شعورين بقلب
+
+300
+00:23:03,980 --> 00:23:04,240
+يعني
+
+301
+00:23:13,890 --> 00:23:17,210
+هذا احنا حكيناه إن إذا أنا E بيساوي minus الـ
+
+302
+00:23:17,210 --> 00:23:20,950
+Gradient لـ Scalar Potential لإن صعب إن نفكر إن الـ
+
+303
+00:23:20,950 --> 00:23:25,290
+Gradient بيساوي Zero إذا معناه إن هذه الكلمة مرة
+
+304
+00:23:25,290 --> 00:23:28,230
+باكد لنا إن الـ electric field هو غير Rotational
+
+305
+00:23:28,230 --> 00:23:32,250
+بيساوي minus الـ Gradient لـ Potential طب احنا اول 
+
+306
+00:23:32,250 --> 00:23:34,370
+متذكرين ما بدنا بنحكي عن الـ Potential قلنا إن الـ
+
+307
+00:23:34,370 --> 00:23:37,650
+electric field هو دريجته من ثلاث جهات يا من
+
+308
+00:23:37,650 --> 00:23:42,380
+Coulomb's Law يا من Gauss's Law يا من الـ Potential يعني 
+
+309
+00:23:42,380 --> 00:23:45,120
+إذا كنت عارفة الـ Potential أنا فقدر أجيب الـ 
+
+310
+00:23:45,120 --> 00:23:46,800
+electric field لإني صرت عارفة ايه ايه ايه ايه ايه 
+
+311
+00:23:46,800 --> 00:23:48,560
+ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه
+
+312
+00:23:48,560 --> 00:23:48,760
+ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه
+
+313
+00:23:48,760 --> 00:23:49,040
+ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه
+
+314
+00:23:49,040 --> 00:23:52,000
+ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه
+
+315
+00:23:52,000 --> 00:24:01,140
+ايه ايه ايه ايه ايه ايه ايه
+
+316
+00:24:01,140 --> 00:24:05,400
+ايه
+
+317
+00:24:09,680 --> 00:24:13,120
+باي على اثنين أو زيرو هذا إيش نوع الـ coordinate؟ 
+
+318
+00:24:13,120 --> 00:24:21,500
+Spherical Coordinate عند θ و φ فعندي قيمة r و θ
+
+319
+00:24:21,500 --> 00:24:26,640
+و φ كمان بده إني بعد ما أجيب دي Calculate the
+
+320
+00:24:26,640 --> 00:24:30,200
+work done in moving a ten micro column which are
+
+321
+00:24:30,200 --> 00:24:35,280
+from النقطة a و نقطة b يعني أول حاجة بده دي طبعاً دي 
+
+322
+00:24:35,280 --> 00:24:38,020
+سمع في المهم إن أجيبها أقول إن أجيب E احنا لسه
+
+323
+00:24:38,020 --> 00:24:41,360
+طولنا E بقدر أجيبها مهم الـ potential يعني E بقدر
+
+324
+00:24:41,360 --> 00:24:45,100
+أقول إنّها minus Gradient V بجيب E و D ماهي إلا Epsilon
+
+325
+00:24:45,100 --> 00:24:50,780
+times E فـ Epsilon not times E بجيب D الجزء الثاني
+
+326
+00:24:50,780 --> 00:24:55,640
+بدو الـ Work اللي احتاجه عشان ينقل الـ Charge معينة
+
+327
+00:24:55,640 --> 00:24:59,260
+قيمتها عشرة micro column من نقطة في الـ space هذا
+
+328
+00:24:59,260 --> 00:25:00,680
+اللي هو فيه electric field
+
+329
+00:25:09,920 --> 00:25:15,020
+نبدأ بالجزء الأول يعني ايه قلنا دي بتساوي Epsilon
+
+330
+00:25:15,020 --> 00:25:20,140
+not E وانت هتجيب E يقول لنا minus Del الـ V بس هستخدم 
+
+331
+00:25:20,140 --> 00:25:24,400
+مين الـ Spherical Coordinate مش حاجة غصب عنها
+
+332
+00:25:24,400 --> 00:25:27,300
+أستخدم الـ Cartesian Coordinate أنا بتعود على D by
+
+333
+00:25:27,300 --> 00:25:30,520
+D X X hat زي D by D Y Y hat زي D by D Z Z hat
+
+334
+00:25:30,520 --> 00:25:34,800
+ما بتعرفش أحفظش تاني فبدأت أحول الـ V من sin θ أو cos
+
+335
+00:25:34,800 --> 00:25:38,560
+φ لـ X Y Z بتفرق بضيع وقت كثير في الامتحان الأسهل
+
+336
+00:25:38,560 --> 00:25:41,360
+أكون عارفة Del بي الـ Spherical Coordinate
+
+337
+00:25:43,930 --> 00:25:49,250
+مناسب بالـ V اللي هي مناسب مفتاح القوس D V by D R
+
+338
+00:25:49,250 --> 00:25:53,650
+R Hat زائد واحد على R D V by D Theta Theta Hat زائد
+
+339
+00:25:53,650 --> 00:25:58,370
+واحد على R Sine Theta D V by D Phi Phi Hat معايا 
+
+340
+00:25:58,370 --> 00:26:03,450
+دودة بالـ V بدي أفرض بالنسبة لـ R إيش هتعطيني minus
+
+341
+00:26:03,450 --> 00:26:09,120
+عشرين على R تكعيب Sine Theta Cosine Phi معايا طب
+
+342
+00:26:09,120 --> 00:26:13,320
+بالنسبة لـ θ في عندي 1 على R 10 على R تربيع و 1 على 
+
+343
+00:26:13,320 --> 00:26:17,340
+R تصير 10 على R تكعيب التفاضل بالنسبة لـ Sin Sin إيش
+
+344
+00:26:17,340 --> 00:26:22,840
+بتصير Cos في Cos فـ؟ 1 على R Sin θ يعني هتصير 10
+
+345
+00:26:22,840 --> 00:26:26,300
+على R تكعيب Sin θ بالنسبة لـ فيه Cos فـ إيش بتصير
+
+346
+00:26:26,300 --> 00:26:31,460
+minus Sin فـ؟ تمام، إذا هي عند الـ Electric Field،
+
+347
+00:26:31,460 --> 00:26:36,370
+ببساطة لإن أنا عارفة الـ Potential لهنا عرفت قيم 
+
+348
+00:26:36,370 --> 00:26:38,830
+الـ Charges و لا نوع من أنواع الـ Distribution
+
+349
+00:26:38,830 --> 00:26:42,810
+عشان أقول إني بدي أجيبه من Coulomb's ولا من Gauss's
+
+350
+00:26:42,810 --> 00:26:45,690
+هنا الحل الوحيد أو الطريقة الوحيدة إني أجيبه من
+
+351
+00:26:45,690 --> 00:26:48,410
+وين؟ من خلال الـ Potential لإنه ما أعطيني الـ Potential
+
+352
+00:26:48,410 --> 00:26:52,870
+طب بده يعني نقطة معينة أول حاجة بدي أجيبه الـ D الـ
+
+353
+00:26:52,870 --> 00:26:57,090
+D اللي بدي أقوله هي Epsilon not في E و أعوض على 
+
+354
+00:26:57,090 --> 00:27:02,090
+النقطة R 2 Theta باي على 2 و Phi بتساوي 0
+
+355
+00:27:04,860 --> 00:27:08,340
+بحصل على قيمة اللي هو D اللي هو طلبه في الجزء
+
+356
+00:27:08,340 --> 00:27:13,100
+الأولاني هل الطلب دو الـ Work؟ الجزء الثاني من 
+
+357
+00:27:13,100 --> 00:27:15,480
+السؤال بده الـ Work
+
+358
+00:27:19,790 --> 00:27:22,770
+عندي طريقتين إن أحسب الـ Work أول طريقة اللي 
+
+359
+00:27:22,770 --> 00:27:26,310
+تعلمناها قبل قليل هي minus q الـ Integral لـ E ضد DL
+
+360
+00:27:26,310 --> 00:27:30,490
+لمنها اشتقينا الـ Potential الـ Work هو minus q الـ
+
+361
+00:27:30,490 --> 00:27:34,030
+Integral لـ E ضد DL اللي قلنا ما له من وين جبناها
+
+362
+00:27:34,030 --> 00:27:37,490
+احنا من الـ Integral لـ F ضد DL minus الـ Integral لـ
+
+363
+00:27:37,490 --> 00:27:41,610
+F ضد DL minus
+
+364
+00:27:41,610 --> 00:27:45,970
+W على q بتساوي الـ Integral لـ E ضد DL طب أنا عندي من
+
+365
+00:27:45,970 --> 00:27:52,200
+وين بده ينقل من عندي خليني أرجع نشوف اللي عندها R 
+
+366
+00:27:52,200 --> 00:27:58,770
+ثلاثين R واحد ستة ثلاثين و طالع مائة و عشرين لنقطة 
+
+367
+00:27:58,770 --> 00:28:04,030
+ثانية في الـ Space اللي فيها R تغيرت من 1 لـ 4 و θ 
+
+368
+00:28:04,030 --> 00:28:08,210
+تغيرت يعني لو كنت أخذ الـ path أنا بدي عندي في ..
+
+369
+00:28:08,210 --> 00:28:13,670
+أكيد في عندي DR و في عندي تغير في θ Dθ و في عندي
+
+370
+00:28:13,670 --> 00:28:17,810
+path اللي في تغير في Dφ عندي الـ three paths احنا الـ 
+
+371
+00:28:17,810 --> 00:28:20,510
+paths في الـ Spherical Coordinate كنت مذاكرينهم لما
+
+372
+00:28:20,
+
+401
+00:30:41,410 --> 00:30:45,780
+ثلاثين ثلاثين ثلاثين عشان أنا المفروض الثلاثين
+
+402
+00:30:45,780 --> 00:30:49,260
+آخذها أنا هي اللي بحكي هي الـ theta عشان اللي
+
+403
+00:30:49,260 --> 00:30:54,080
+أظهرتها وهي اللي هتكون على الـ axis هذا أنا عشان
+
+404
+00:30:54,080 --> 00:31:01,080
+آخذ الصورة هي هذه هي ثلاثين درجة وهي النقطة A اللي
+
+405
+00:31:01,080 --> 00:31:08,520
+هي واحد ثلاثين درجة ومئة وعشرين درجة فعلاً
+
+406
+00:31:08,520 --> 00:31:11,840
+وعشرين يعني برضه كتيرة فعلاً يعني هتكون مئة وعشرين هي 
+
+407
+00:31:11,840 --> 00:31:16,760
+فعلاً كده من هنا يعني تخيلوها عند الـ 120 اه تتخيل ال
+
+408
+00:31:16,760 --> 00:31:20,400
+axis كلهم يعني لو هنُسقطناها ستسقطها بقى في الربع
+
+409
+00:31:20,400 --> 00:31:28,680
+120 درجة فلت انتقلنا قلنا لنخلي هد أربعة تروح من
+
+410
+00:31:28,680 --> 00:31:32,660
+واحد لأربعة ليه A prime A prime اللي هو أربعة
+
+411
+00:31:32,660 --> 00:31:40,350
+ثلاثين درجة ومئة وعشرين درجة بعدين هننزل بقى النقطة
+
+412
+00:31:40,350 --> 00:31:43,630
+اللي عندها setup تساوي 90 هذه عندنا  أقعد ضالة
+
+413
+00:31:43,630 --> 00:31:44,810
+تسابق تسابق تسابق تسابق تسابق تسابق تسابق تسابق
+
+414
+00:31:44,810 --> 00:31:47,950
+تسابق تسابق تسابق تسابق تسابق تسابق تسابق تسابق
+
+415
+00:31:47,950 --> 00:31:48,390
+تسابق تسابق تسابق تسابق تسابق تسابق تسابق تسابق
+
+416
+00:31:48,390 --> 00:31:48,410
+تسابق تسابق تسابق تسابق تسابق تسابق تسابق تسابق
+
+417
+00:31:48,410 --> 00:31:48,650
+تسابق تسابق تسابق تسابق تسابق تسابق تسابق تسابق
+
+418
+00:31:48,650 --> 00:31:49,730
+تسابق تسابق تسابق تسابق تسابق تسابق تسابق تسابق
+
+419
+00:31:49,730 --> 00:32:04,310
+تسابق تساب
+
+420
+00:32:04,850 --> 00:32:08,950
+هذه عندنا R أربعة ضلت ومين اللي اتغير عندي الـ ستة
+
+421
+00:32:08,950 --> 00:32:16,230
+صارت 90 درجة وضلت الـ alpha 120 درجة الـ alpha احنا بنحسبها
+
+422
+00:32:16,230 --> 00:32:25,270
+للـ X عندي لحد 120 درجة فهي 120 درجة إذا 
+
+423
+00:32:25,270 --> 00:32:29,690
+متقلنا من A prime لـ B prime آخر واحدة اللي بيبدو
+
+424
+00:32:29,690 --> 00:32:40,860
+أنه لحد الستين يعني نبدأ جهة على الـ Phi اللي
+
+425
+00:32:40,860 --> 00:32:48,460
+هي نقطة الأخيرة اللي عندها هيكون 94 درجة و 60 درجة
+
+426
+00:32:48,460 --> 00:32:53,600
+تمام؟ واضحة الصورة؟ هذا الـ basis اللي أنا هاخده 
+
+427
+00:32:53,600 --> 00:32:56,300
+ليش هاخد هيك الـ basis؟ لأن هذا الـ basis هيكون عند
+
+428
+00:32:56,300 --> 00:33:03,150
+الـ DL تغير من هنا لهنا هيكون بتساوي DR التغيير من
+
+429
+00:33:03,150 --> 00:33:08,110
+هنا إلى هنا ايش هيكون R Dθ وهنا ايش هيكون التغيير
+
+430
+00:33:08,110 --> 00:33:10,890
+R Sine Theta
+
+431
+00:33:16,210 --> 00:33:19,610
+واضحة النقطة هي؟ إذا بدل ما أنا أخدهم كلهم مرة
+
+432
+00:33:19,610 --> 00:33:23,570
+واحدة تغيرات بل أنا بأخذهم واحدة واحدة line line
+
+433
+00:33:23,570 --> 00:33:28,830
+وأنا عارفة إنه لأنه التكامل من a لـ b باصن
+
+434
+00:33:28,830 --> 00:33:31,450
+independent فأنا بقدر أقول من a لـ a prime من a 
+
+435
+00:33:31,450 --> 00:33:34,870
+prime لـ b prime و b prime لـ b اللي هي النقطة اللي
+
+436
+00:33:34,870 --> 00:33:39,150
+أنا بدي أحسب عندها الـ work نيجي مع بعض نحسب هذا
+
+437
+00:33:39,150 --> 00:33:39,610
+الحكيم
+
+438
+00:33:43,770 --> 00:33:48,310
+زي ما أنتم شايفين هبدأ من A اللي عندها R واحد ستة
+
+439
+00:33:48,310 --> 00:33:53,390
+ثلاثين ومئة وعشرين لـ A prime اللي اتغير فيها R
+
+440
+00:33:53,390 --> 00:33:57,610
+لأربعة ستة ضلت ثابتة و five ثابتة هيك أسهل التكامل
+
+441
+00:33:57,610 --> 00:34:01,270
+لما أسبب اثنين وأغير واحد أسهل من إن أخلي الـ ثلاث 
+
+442
+00:34:01,270 --> 00:34:05,610
+متغيرين ودي L ايش هتكون في هذه الحالة دي R R hat
+
+443
+00:34:06,630 --> 00:34:09,610
+لما أجي أغير من a prime لـ b prime أنا مين غيرتها
+
+444
+00:34:09,610 --> 00:34:13,610
+لقيته الـ theta خلتها بتروح من ثلاثين لـ تسعين R
+
+445
+00:34:13,610 --> 00:34:16,050
+ضلت ثابتة على أربعة و Phi ضلت ثابتة على مائة و
+
+446
+00:34:16,050 --> 00:34:21,950
+وعشرين قيمة الـ DL بتساوي R D theta ثتا hat آخر حاجة
+
+447
+00:34:21,950 --> 00:34:26,350
+اللي هي أخلي الـ R ثتا و Theta ثابتة وأغير الـ الفاعل 
+
+448
+00:34:26,350 --> 00:34:30,250
+من مائة وعشرين لستين هتكون DL بتساوي R sine theta
+
+449
+00:34:30,250 --> 00:34:35,330
+D Phi Phi hat إذا صار لي التكامل ما لو قسمته لـ 3 
+
+450
+00:34:35,330 --> 00:34:40,550
+integrals من a لـ a' زائد الـ integral من a' لـ b'
+
+451
+00:34:40,990 --> 00:34:45,710
+زائد الـ integral من b' لـ b، في أي حاجة مش واضحة
+
+452
+00:34:45,710 --> 00:34:52,050
+لحد هنا؟ مش واضح؟ إذا عندي (-w على cube)(-1 على
+
+453
+00:34:52,050 --> 00:34:55,510
+cube تكمل من a لـ a prime أو يعني الـ work من a لـ a 
+
+454
+00:34:55,510 --> 00:34:57,990
+prime زائد الـ work من a prime لـ b prime زائد الـ work
+
+455
+00:34:57,990 --> 00:35:00,830
+من b prime لـ b prime اللي هو عبارة عن الـ integrant
+
+456
+00:35:00,830 --> 00:35:03,250
+من a لـ a prime زائد الـ integrant من a prime لـ b
+
+457
+00:35:03,250 --> 00:35:05,510
+prime زائد الـ integrant من b prime لـ b prime إلى e
+
+458
+00:35:05,510 --> 00:35:11,390
+dot dl اي ما احنا حسبناها مع بعض نعرفها بنعوض في 
+
+459
+00:35:11,390 --> 00:35:15,330
+المعادلة ونعمل نتيجة إذا رجعنا لـ E بتعوض طبعًا لما
+
+460
+00:35:15,330 --> 00:35:20,170
+أسفت الـ D الـ theta والـ five بتعوض عنه مباشرة و
+
+461
+00:35:20,170 --> 00:35:22,750
+أخلي مين فقط اللي هو الـ R المتغير
+
+462
+00:35:30,100 --> 00:35:35,060
+أعود أنا وبحط قيام الـ theta والـ phi في قلب الـ
+
+463
+00:35:35,060 --> 00:35:39,300
+integrals كلهم فعند الـ integrant من R1 لـ R4 20 sin
+
+464
+00:35:39,300 --> 00:35:44,500
+theta cos phi R cubed DR theta 30 و phi 20 التكامل 
+
+465
+00:35:44,500 --> 00:35:50,010
+الثاني مين هيسبب الـ RI ستثبت على أربعة وفاي على
+
+466
+00:35:50,010 --> 00:35:53,890
+مائة وعشرين ومن يتغير هو الـ θيتا والإنتجر الأخير
+
+467
+00:35:53,890 --> 00:35:57,810
+فايل سيتغير من مائة وعشرين لستين وحسبته الـ R
+
+468
+00:35:57,810 --> 00:36:02,450
+والثيتا إذا عملنا هيك بنحصل على قيمة ماينسة W على Q
+
+469
+00:36:02,450 --> 00:36:07,490
+وبنحصل
+
+470
+00:36:07,490 --> 00:36:13,820
+على W بمجرد أن أعود عن EQ تمام هذه أول طريقة لكن هو
+
+471
+00:36:13,820 --> 00:36:19,320
+مش محدد عليّ طريقة إن كيف أستخدم وحسن اللي هو كل
+
+472
+00:36:19,320 --> 00:36:23,660
+طلبه في السؤال ستتذكروا الـ work done in moving
+
+473
+00:36:23,660 --> 00:36:31,680
+الهدف من الـ Integra
+
+474
+00:36:31,680 --> 00:36:36,420
+هدف من الـ Integra هدف من الـ Integra هدف من الـ
+
+475
+00:36:36,420 --> 00:36:42,080
+Integra هدف من الـ Integra هدف من الـ Integra هدف من
+
+476
+00:36:42,080 --> 00:36:44,250
+الـ Integra هدف من الـ Integra هدف من الـ Integra عارف
+
+477
+00:36:44,250 --> 00:36:46,350
+الـ potential بين النقطة التي هو لأنه عارف الـ
+
+478
+00:36:46,350 --> 00:36:49,230
+potential في أي نقطة في الـ space إذا عارف الـ
+
+479
+00:36:49,230 --> 00:36:51,390
+potential في أي نقطة في الـ space بقدر أجيبه في 
+
+480
+00:36:51,390 --> 00:36:58,490
+نقطة محددة والواقع عبارة عن ماله QVB-VA لأنه
+
+481
+00:36:58,490 --> 00:37:02,050
+عبارة عن minus Q الـ Integra من A لـ B E ضد DL اللي
+
+482
+00:37:02,050 --> 00:37:03,990
+هو عبارة عن QVAB
+
+483
+00:37:05,760 --> 00:37:09,160
+لأن ماينوس انتيجرال من A لـ B E ضد L هو الـ 
+
+484
+00:37:09,160 --> 00:37:14,040
+potential ما بين النقطة A و B يعني هيكون الـ Q VB-
+
+485
+00:37:14,040 --> 00:37:19,760
+VA قلنا دائمًا هذا ناقص هذا VAB هيبقى VB- VA
+
+486
+00:37:22,260 --> 00:37:27,120
+عند الـ potential بعود عن قيمة النقطة B وعن قيمة
+
+487
+00:37:27,120 --> 00:37:30,980
+النقطة A بُحصل على نفس الجواب طبعًا هاي الطريقة أسهل 
+
+488
+00:37:30,980 --> 00:37:35,060
+بكتير بالذات إنه أنا مواطئل الـ potential مش زي الـ 
+
+489
+00:37:35,060 --> 00:37:37,820
+electric field أنا حسبته ممكن أنا أخطر في حساب الـ 
+
+490
+00:37:37,820 --> 00:37:40,440
+electric field لكن مش متشرط عليّ أن أستخدم أي
+
+491
+00:37:40,440 --> 00:37:44,980
+طريقة بحسب الـ work من الـ potential مباشرة بحسبهاش
+
+492
+00:37:44,980 --> 00:37:47,780
+من الـ electric field وبالذات إن شفتوا طريقة الـ
+
+493
+00:37:47,780 --> 00:37:50,860
+electric field مالها طويلة شوية، بدي أقعد كامل 
+
+494
+00:37:50,860 --> 00:37:55,280
+على الـ three buses عشان أحصر على الـ work في عيسى
+
+495
+00:37:55,280 --> 00:37:59,860
+أفسار لحد هنا نيجي لحاجة اسمها الـ electric diaper
+
+496
+00:37:59,860 --> 00:38:03,600
+and flux lines ايش هو الـ electric diaper؟ الـ
+
+497
+00:38:03,600 --> 00:38:06,560
+diaper أكيد مرّت عليكم كلمة diaper الـ diaper يعني
+
+498
+00:38:06,560 --> 00:38:09,540
+لما يكون عندي two charges plus و minus فيبقى البعض
+
+499
+00:38:09,540 --> 00:38:13,420
+زي قطرة الميه، لما تكون تحت الـ electric field،
+
+500
+00:38:13,420 --> 00:38:19,620
+بتلاقوا هنا بيصير الشحنة موجة الدايبول يعني عندي
+
+501
+00:38:19,620 --> 00:38:24,720
+فيه two charges اللي هم opposite sign وما اللي هم
+
+502
+00:38:24,720 --> 00:38:29,200
+قرابين بكتير من بعض يعني المسافة بينهم صغيرة يعني
+
+503
+00:38:29,200 --> 00:38:32,280
+مرة اللي كتب دايبول هو عبارة عن two point charges
+
+504
+00:38:32,280 --> 00:38:36,520
+اللي هم opposite sign والمسافة بينهم صغيرة كتير
+
+505
+00:38:44,160 --> 00:38:46,700
+دعوني أريكم الصورة تاعتهم هاي الـ dipole هاي عندي
+
+506
+00:38:46,700 --> 00:38:51,700
+XYZ عندي two charges plus و minus الـ Q والمسافة 
+
+507
+00:38:51,700 --> 00:38:56,040
+بينهم D بتكون صغيرة كتير هذا الـ electric dipole
+
+508
+00:38:56,040 --> 00:38:59,460
+لو أنا بدي أحسب potential مثلًا للنقطة B الناتجة عن
+
+509
+00:38:59,460 --> 00:39:01,660
+الـ dipole يعني صار المفهوم إنها الـ dipole الـ
+
+510
+00:39:01,660 --> 00:39:04,900
+dipole two pointed charges المسافة بينهم صغيرة و
+
+511
+00:39:04,900 --> 00:39:07,520
+اللي هم opposite signs لو أنا بدي أحسب الـ
+
+512
+00:39:07,520 --> 00:39:11,840
+potential عن النقطة B هيكون
+
+513
+00:39:13,370 --> 00:39:17,430
+مجموع الـ potentials الناتجين من positive و
+
+514
+00:39:17,430 --> 00:39:21,290
+negative charge الـ potential ناتج من Q ايش هيساوي؟
+
+515
+00:39:21,290 --> 00:39:25,330
+Q على 4 by Y node في 1 على R1 وهذا هيكون minus Q
+
+516
+00:39:25,330 --> 00:39:31,710
+على 4 by Y node في 1 على R2 إذا الـ potential عند
+
+517
+00:39:31,710 --> 00:39:35,570
+النقطة B هيكون الـ potential ناتج من Q minus Q
+
+518
+00:39:39,220 --> 00:39:42,600
+بقى Q على 4 by epsilon node في 1 على R1 minus 1
+
+519
+00:39:42,600 --> 00:39:50,920
+على R2 لو أنا عملت توحيد مقامات هيكون عند Q على 4
+
+520
+00:39:50,920 --> 00:39:55,480
+by epsilon node R1 في R2 والـ boss بيصير R2 minus
+
+521
+00:39:55,480 --> 00:40:01,020
+R1 انت دورك اعرف ايش هي R2 minus R1 واعرف ايش هي
+
+522
+00:40:01,020 --> 00:40:08,500
+R1 وR2 ارجع للرسم عرفت إن أنا بدي الفرق بين R2 و R1
+
+523
+00:40:08,500 --> 00:40:12,400
+R2 هي المسافة بين minus Q ونقطة B اللي بتحسب عندها
+
+524
+00:40:12,400 --> 00:40:16,900
+الـ potential و R1 هي المسافة بين نقطة Q point of
+
+525
+00:40:16,900 --> 00:40:21,960
+charge Q plus Q ونقطة B لو أنا طلعت على الرسمة أنا
+
+526
+00:40:21,960 --> 00:40:25,380
+هلاحظ إن الفرق بينهم هو بالتمام هذه المسافة لو أنا 
+
+527
+00:40:25,380 --> 00:40:30,460
+أزلت عمود من plus Q على R2 هيكون الفرق بينهم هي
+
+528
+00:40:30,460 --> 00:40:37,280
+هذه المسافة لو أنا عرفت زاوية θ هي الزاوية المابين
+
+529
+00:40:37,280 --> 00:40:40,900
+الـ line اللي بوصل مابين الـ center تبع الـ dipole
+
+530
+00:40:40,900 --> 00:40:45,420
+هذه النقطة هي هنا الـ dipole المسافة بين الـ q و
+
+531
+00:40:45,420 --> 00:40:49,540
+minus q هي دي بس هذا الـ dipole بالذات أنا حاطه بحيث
+
+532
+00:40:49,540 --> 00:40:53,420
+الـ center تبعه جاية على الـ origin الـ center تبع الـ
+
+533
+00:40:53,420 --> 00:40:56,400
+dipole جاية على الـ origin قصدت لو أنا عرفتها إن هي
+
+534
+00:40:56,400 --> 00:41:03,170
+الزاوية المابين الخط الواصل ما بين الـ two charges و
+
+535
+00:41:03,170 --> 00:41:06,770
+الخط الواصل ما بين الـ origin تبع الـ dipole و
+
+536
+00:41:06,770 --> 00:41:09,410
+النقطة اللي بدأ يسعدها الـ potential هي theta، الـ 
+
+537
+00:41:09,410 --> 00:41:13,110
+theta مع التلاغر هي نفس الـ theta هي، صح؟ إذا هي
+
+538
+00:41:13,110 --> 00:41:18,530
+المسافة اللي بحسب بها عبارة عن مين D cos theta إذا
+
+539
+00:41:18,530 --> 00:41:22,830
+الفرق بين R2 و R1 بقدر أكتب بدلالة D اللي هي 
+
+540
+00:41:22,830 --> 00:41:25,450
+المسافة بين الـ two charges الـ positive والـ 
+
+541
+00:41:25,450 --> 00:41:29,250
+negative of الـ charges و θ اللي هي الزاوية اللي
+
+542
+00:41:29,250 --> 00:41:32,870
+ما بين الـ line اللي واصل بين الـ two charges و الـ
+
+543
+00:41:32,870 --> 00:41:36,090
+line اللي واصل ما بين الـ center تبع الـ dipole و
+
+544
+00:41:36,090 --> 00:41:39,170
+النقطة اللي بقيس عندها الـ potential إذا الـ
+
+545
+00:41:39,170 --> 00:41:42,750
+difference هو D cos θ الحاجة الثانية اللي أنا بدأت
+
+546
+00:41:42,750 --> 00:41:46,130
+أخذها بعلية بارعة إن لو أنا فرضت إن R1 و R2 أكبر
+
+547
+00:41:46,130 --> 00:41:53,460
+بكتير من المسافة D إذا تقريبًا بقدر أقول إن R1 في R2
+
+548
+00:41:53,460 --> 00:42:00,100
+هي R تربيع تقريبًا لأنه منهم المسافة الفرق اللي
+
+549
+00:42:00,100 --> 00:42:05,960
+بينهم أصغر كتير R2 مقاس R1 اللي هي D Cos θ وتقريبًا 
+
+550
+00:42:05,960 --> 00:42:13,270
+R2 و R1 هسويها بـ R تربيع إذا رجعت للرسم هذول كلهم
+
+551
+00:42:13,270 --> 00:42:18,750
+حيبينوا كإنهم متساويين في حالة الضرب R1 و R2 و R ..
+
+552
+00:42:18,750 --> 00:42:24,990
+و R فبقدر أقول أن R1 تقريبًا تساوي R2 تقريبًا تساوي R
+
+553
+00:42:24,990 --> 00:42:32,620
+فـ R1 في R2 هتكون R تربيع إذا الـ potential الناتج عن
+
+554
+00:42:32,620 --> 00:42:36,280
+الـ dipole هو 
+
+555
+00:42:36,280 --> 00:42:40,060
+Q على 4 by epsilon note بدل R تنين minus R واحد
+
+556
+00:42:40,060 --> 00:42:44,500
+عشان حطيت دي cos θ بدل R واحد في R تنين حطيت R
+
+557
+00:42:44,500 --> 00:42:49,640
+تربيع تمام؟ في أي سؤال لحد هنا؟
+
+558
+00:42:53,450 --> 00:42:59,990
+D cos θ هي
+
+559
+00:42:59,990 --> 00:43:08,110
+البروجيكشن تبع D في اتجاه D وهذا الاتجاه θ لأن دي
+
+560
+00:43:08,110 --> 00:43:12,150
+كوساين ثتا هأقول إن هذا الاتجاه مين هو R hat هو
+
+561
+00:43:12,150 --> 00:43:15,890
+البروجيكشن تبع D على اتجاه R hat
+
+562
+00:43:19,830 --> 00:43:24,370
+دي مالها اتجاهها اتجاه الـ z axis احنا ماخدينها دي
+
+563
+00:43:24,370 --> 00:43:29,250
+vector هي عبارة عن d z hat الـ projection تبعها في
+
+564
+00:43:29,250 --> 00:43:31,690
+الـ R hat هو عبارة عن d cos θ
+
+565
+00:43:35,570 --> 00:43:40,150
+وهأعمل رف كمان بي اللي هو الدايبول Q في D إذا بقدر
+
+566
+00:43:40,150 --> 00:43:44,890
+أعيد كتابة الـ potential تبعي اللي هو QD cos θ على
+
+567
+00:43:44,890 --> 00:43:48,710
+4 pi epsilon نوت R تربيع عشان كان QD قلنا منه هال
+
+568
+00:43:48,710 --> 00:43:53,610
+D cos θ بتعبر عن D dot D R hat و QD vector هأسميها
+
+569
+00:43:53,610 --> 00:43:58,770
+بي فهتصير بي بتساوي بي dot R hat على 4 pi epsilon
+
+570
+00:43:58,770 --> 00:44:02,530
+نوت R
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/xsHJkkk1-GI_postprocess.srt b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/xsHJkkk1-GI_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..24a381f0b599e325c97f55a774624fc65f7d1128
--- /dev/null
+++ b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/xsHJkkk1-GI_postprocess.srt
@@ -0,0 +1,2324 @@
+1
+00:00:20,940 --> 00:00:23,480
+بسم الله الرحمن الرحيم السلام عليكم و رحمة الله و
+
+2
+00:00:23,480 --> 00:00:26,660
+بركاته احنا اليوم ان شاء الله هنتبع موضوعنا اللي
+
+3
+00:00:26,660 --> 00:00:30,680
+هو ال potential potential electric potential اسوأ
+
+4
+00:00:30,680 --> 00:00:34,080
+ال absolute ولا ال potential difference احنا
+
+5
+00:00:34,080 --> 00:00:36,980
+المحاضرة الماضية شوفنا كيف ان ال potential مربوط
+
+6
+00:00:36,980 --> 00:00:41,880
+بيه اللي هو ال electric field شوفنا ان ال
+
+7
+00:00:41,880 --> 00:00:45,100
+potential بين نقطتين A و B هو minus التكامل من A
+
+8
+00:00:45,100 --> 00:00:46,760
+لB لE ضد DL
+
+9
+00:00:49,210 --> 00:00:51,730
+أذا كنا عارفين الـ electric field فقدر أحسب ال
+
+10
+00:00:51,730 --> 00:00:55,490
+potential قولنا ال absolute potential بيكون لو أنا
+
+11
+00:00:55,490 --> 00:01:00,770
+أخدت مثلا النقطة a عند ال infinity هيكون عندها ال
+
+12
+00:01:00,770 --> 00:01:03,230
+potential بيسوا zero فهيكون ال potential عند
+
+13
+00:01:03,230 --> 00:01:07,850
+النقطة b بيسوا q على 4 by epsilon not في ال Rb
+
+14
+00:01:07,850 --> 00:01:11,110
+فانا
+
+15
+00:01:11,110 --> 00:01:13,810
+لو أخدنا ان ال R a مثلا عند ال infinity هذا قولنا
+
+16
+00:01:13,810 --> 00:01:15,710
+بيسميه ال absolute potential
+
+17
+00:01:17,930 --> 00:01:20,470
+كمان قولنا لو ان ال charge مش عند ال origin احنا
+
+18
+00:01:20,470 --> 00:01:24,170
+كنا عملنا هذا الحكي ان V بيساوي Q على 4 by Epsilon
+
+19
+00:01:24,170 --> 00:01:28,030
+Note R لما ال charge فرضاه عند ال origin و لو ال
+
+20
+00:01:28,030 --> 00:01:32,290
+charge مش عند ال origin لو
+
+21
+00:01:32,290 --> 00:01:34,850
+ال charge مش عند ال origin هيكون ال potential ايش
+
+22
+00:01:34,850 --> 00:01:38,590
+بيساوي Q على 4 by Epsilon Note الفرق ما بين R و R
+
+23
+00:01:38,590 --> 00:01:42,290
+prime حيث R اللي هو الموقع اللي انا بدأ ادقيس عنده
+
+24
+00:01:42,290 --> 00:01:47,770
+ال potential و R prime اللي هو مكان ال chargeلو
+
+25
+00:01:47,770 --> 00:01:51,130
+كان عندى اكتر من ال charge نحسبه بالطريقة طبعا على
+
+26
+00:01:51,130 --> 00:01:54,070
+أساس ان احنا فرضين انه عند ال infinity ال
+
+27
+00:01:54,070 --> 00:01:57,850
+potential بساوة zero لو كان عندى distribution
+
+28
+00:01:57,850 --> 00:02:01,790
+charge distribution لو كانت line او surface او
+
+29
+00:02:01,790 --> 00:02:06,020
+volume قولنا هيك نحسب ال potentialبشكل عام لو أنا
+
+30
+00:02:06,020 --> 00:02:08,980
+ماقلتش عند ال infinity هي ال zero بشكل عام لو في
+
+31
+00:02:08,980 --> 00:02:12,860
+عندي انا ال reference point مش ال infinity هيكون
+
+32
+00:02:12,860 --> 00:02:15,800
+ال potential بشكل عام بيساوة q على four by y not r
+
+33
+00:02:15,800 --> 00:02:19,340
+زائد c، c هيبحسبها من وين؟ من عند ال reference
+
+34
+00:02:19,340 --> 00:02:22,160
+point يعني وين انا حددت لل reference point اللي
+
+35
+00:02:22,160 --> 00:02:25,820
+عند ال potential؟ zero، بنحسب اللي هو قيمة c، لذا
+
+36
+00:02:25,820 --> 00:02:29,660
+بشكل عام بيبسوة minus integral a dot d l plus c
+
+37
+00:02:34,790 --> 00:02:39,770
+المثال اللى قدامنا كانت
+
+38
+00:02:39,770 --> 00:02:43,250
+ان احسابات ال potential عند ال infinity بيسووا
+
+39
+00:02:43,250 --> 00:02:46,550
+zero عند كنتوا charges كل واحدة عارفة ال location
+
+40
+00:02:46,550 --> 00:02:50,190
+تبعهم و مش عند ال zero كل واحدة لها location محدد
+
+41
+00:02:50,190 --> 00:02:53,770
+R1 سمنها وR2 و عند النقطة البدئيسية عندها ال
+
+42
+00:02:53,770 --> 00:02:54,770
+potential هي R
+
+43
+00:03:13,860 --> 00:03:17,660
+هذا ما حللناه المحاضرة الماضية
+
+44
+00:03:21,670 --> 00:03:25,470
+بدّينا عن مثال تاني قولنا هنحله المحاضرة هاي
+
+45
+00:03:25,470 --> 00:03:28,690
+المثال اللي عندنا بيقول ان في عندي charge مقدارها
+
+46
+00:03:28,690 --> 00:03:33,730
+خمسة nano column موجودة عند النقطة minus 3 4 0
+
+47
+00:03:33,730 --> 00:03:38,530
+وعندي كمان خط line of charge يعني عندي حاجتين
+
+48
+00:03:38,530 --> 00:03:41,630
+point of charge و line of charge ال point of
+
+49
+00:03:41,630 --> 00:03:45,790
+charge قاعدة في ال space عند النقطة minus 3 4 0 و
+
+50
+00:03:45,790 --> 00:03:50,050
+ال line of charge عند y 1 زي 1 يعني ال x ماله
+
+51
+00:03:50,050 --> 00:03:55,200
+موازلة ال xكاليز يونيفيرمت شارج مقدارها اتنين نانو
+
+52
+00:03:55,200 --> 00:03:59,900
+كولوم بيرمتر يعني رؤال بتساوي اتنين كولوم نانو
+
+53
+00:03:59,900 --> 00:04:04,200
+كولوم بيرمتر ايش طالب منهم؟ مناقزة احنا قولنا ان
+
+54
+00:04:04,200 --> 00:04:07,200
+ال reference اللي هو ال voltage بتساوي زيرو عند ال
+
+55
+00:04:07,200 --> 00:04:10,100
+origin يعني ال reference بتاعته هلقته وين؟ عند ال
+
+56
+00:04:10,100 --> 00:04:15,240
+origin بده ال voltage عند النقطة A اللي عند خمسة
+
+57
+00:04:15,240 --> 00:04:20,160
+وزيرو واحد يعني المثال
+
+58
+00:04:24,230 --> 00:04:33,430
+عند الـ charge
+
+59
+00:04:33,430 --> 00:04:38,490
+اللي هي الخمسة nano عند minus تلاتة واربعة وعلى ال
+
+60
+00:04:38,490 --> 00:04:42,570
+X يعني في ال X Y بلان ال Z أقل منها Zero لذلك هذه
+
+61
+00:04:42,570 --> 00:04:47,230
+الخمسة nano كله اللي عند مائس تلاتة واربعة وزرع في
+
+62
+00:04:47,230 --> 00:04:53,580
+ال X Y بلانالـ line y واحد و z واحد يعني لو حطنا
+
+63
+00:04:53,580 --> 00:04:57,360
+هنا واحد واحد هنا خط شماله هيكون قولنا وزي ال X
+
+64
+00:04:57,360 --> 00:05:06,100
+axis فال
+
+65
+00:05:06,100 --> 00:05:10,860
+X Y plane لأن Z equal 0 هاي ال charge الأولى ليه؟
+
+66
+00:05:10,860 --> 00:05:15,280
+خمسة نان كلوم و X ناقص ثلاثة و Y أربعة في ال X Y
+
+67
+00:05:15,280 --> 00:05:21,530
+هتكون قاعدة هنا في ال X Yالـ line and واحد واحد
+
+68
+00:05:21,530 --> 00:05:27,790
+يعني معناه الموازي بالـ x-axis هذا
+
+69
+00:05:27,790 --> 00:05:34,110
+الـ line of charge موازي بالـ x-axis الـ
+
+70
+00:05:34,110 --> 00:05:43,790
+charge density ρL تساوي اتنين نانو كولوم درهم
+
+71
+00:05:43,790 --> 00:05:49,110
+قالنا المعلومة ان ال reference point هنا بتساوي 0
+
+72
+00:05:49,900 --> 00:05:54,660
+عند الـ origin، عند الـ 000 ال reference point
+
+73
+00:05:54,660 --> 00:06:02,820
+وبدو ال potential عند X بتساوي 5Y0 و Z1 يعني وين
+
+74
+00:06:02,820 --> 00:06:07,620
+هتكون في ال X دي plane هاي النقطة اللي بتوع عندها
+
+75
+00:06:07,620 --> 00:06:13,960
+ال potential اللي
+
+76
+00:06:13,960 --> 00:06:16,880
+هي 501
+
+77
+00:06:21,420 --> 00:06:25,280
+أو بشكل عام اذا
+
+78
+00:06:25,280 --> 00:06:32,280
+انا
+
+79
+00:06:32,280 --> 00:06:38,620
+اول حاجة بتحسبها اللي هي الأبعاد بتاعة ال line و
+
+80
+00:06:38,620 --> 00:06:43,780
+بتاعة ال point عن نقطة اللي بتحسب عندها ال
+
+81
+00:06:43,780 --> 00:06:44,240
+potential
+
+82
+00:06:49,720 --> 00:06:52,040
+طبعا احنا ال potential عند اي نقطة في ال space في
+
+83
+00:06:52,040 --> 00:06:54,340
+هذه الحالة مش عند النقطة اللى انا بس بده احسب
+
+84
+00:06:54,340 --> 00:06:57,520
+عندها ال potential عند اي نقطة هتكون مجموعة two
+
+85
+00:06:57,520 --> 00:07:00,360
+potentials ال potential اللى جاى من ال point at
+
+86
+00:07:00,360 --> 00:07:03,140
+charge زاد ال potential اللى جاى من مين من line at
+
+87
+00:07:03,140 --> 00:07:05,680
+charge و احنا عارفين نحسب كيف كل واحد على حدى كيف
+
+88
+00:07:05,680 --> 00:07:08,220
+احسب ال potential اللى جاى من point at charge و
+
+89
+00:07:08,220 --> 00:07:10,840
+كيف احسب potential اللى من ال line
+
+90
+00:07:15,390 --> 00:07:18,090
+أحنا ال point of charge قلنا دي Q إيش بيساوي minus
+
+91
+00:07:18,090 --> 00:07:21,670
+ال integer ل A dot DL هو minus ال integer ل Q four
+
+92
+00:07:21,670 --> 00:07:26,070
+by epsilon dot R تبعيه R hat dot DR لR hat اللي هي
+
+93
+00:07:26,070 --> 00:07:29,330
+احنا اشتغلناها Q على four by epsilon dot R زائد C1
+
+94
+00:07:29,330 --> 00:07:33,830
+هسمي C1 لإن هيطلع لنا C2 من line of charge هذا ال
+
+95
+00:07:33,830 --> 00:07:36,750
+constant of integration قلنا اللي هو بنحسبه من ال
+
+96
+00:07:36,750 --> 00:07:39,690
+reference point من ما عرفتي وين ال reference يعني
+
+97
+00:07:39,690 --> 00:07:44,900
+وين ال zero voltage ماقدر أحسب ال constant هذالأ
+
+98
+00:07:44,900 --> 00:07:47,960
+اللى هى ال line charge هى انتيجة لإيده ال dl اللى
+
+99
+00:07:47,960 --> 00:07:54,500
+هى ال charge density دى raw اللى هو ال line على
+
+100
+00:07:54,500 --> 00:07:57,160
+طول ال line ال dl هى اللى هى على طول ال line دى
+
+101
+00:07:57,160 --> 00:08:01,040
+raw او دي ال يعنى لو بنسميها دى التغير على طول ال
+
+102
+00:08:01,040 --> 00:08:07,300
+line على two by epsilon not raw هتكون
+
+103
+00:08:07,300 --> 00:08:10,840
+raw L على two by epsilon not plus ال raw زائد CT
+
+104
+00:08:18,520 --> 00:08:25,000
+هنا نحسب قيم R ربط طبعا هذا ال total voltage total
+
+105
+00:08:25,000 --> 00:08:29,420
+electric voltage قول إن هو VQ زي VL هيكون Q على
+
+106
+00:08:29,420 --> 00:08:33,740
+four by epsilon ر زي C واحد بالنسبة لل electric
+
+107
+00:08:33,740 --> 00:08:40,510
+field إنها تجمن ال lineهيكون رو L minus رو L على
+
+108
+00:08:40,510 --> 00:08:44,130
+اتنين باي أبسل not blend الرو وعندنا ال C ال C ما
+
+109
+00:08:44,130 --> 00:08:47,850
+هو عندى constant C واحد و constant C تنين مجموعهم
+
+110
+00:08:47,850 --> 00:08:51,750
+constant هسميه C اللي انا هجيبه من وين من ال
+
+111
+00:08:51,750 --> 00:08:52,070
+reference
+
+112
+00:08:59,980 --> 00:09:03,240
+أحنا بناخد المثال أولاني لو اطالب مني لو انا عندي
+
+113
+00:09:03,240 --> 00:09:07,300
+ال reference voltage عند ال 0 واطالب عندي V عند 5
+
+114
+00:09:07,300 --> 00:09:13,960
+0 1 أول حاجة بدي أجيب قيم Raw وقيم Min R Raw بشكل
+
+115
+00:09:13,960 --> 00:09:18,600
+عام اللي هو انا عندي هاي line of chargeأى نقطة
+
+116
+00:09:18,600 --> 00:09:26,200
+تبعد عنه عن xyz هتكون ال absolute value لxyz-x11
+
+117
+00:09:26,200 --> 00:09:30,820
+لأنه عندي ثابت قيم ال y و ال z واحد واحد فأى نقطة
+
+118
+00:09:30,820 --> 00:09:34,480
+فى ال space xyz قيمة رؤش هتكون هي المسافة بين هى
+
+119
+00:09:34,480 --> 00:09:42,920
+النقطة و ال line xyz-x11يكون x-x هو zero فهي y-1
+
+120
+00:09:42,920 --> 00:09:47,400
+كل تربية زائد z-1 كل تربية تحت الجزرة هي كيمة raw
+
+121
+00:09:47,400 --> 00:09:51,180
+انا
+
+122
+00:09:51,180 --> 00:09:56,280
+بتحسب raw اللي هي بُعد ال origin عن ال line و برضه
+
+123
+00:09:56,280 --> 00:10:00,190
+raw بُعد النقطة اللي احسبها عن ال lineبعد ال
+
+124
+00:10:00,190 --> 00:10:05,590
+origin عن ال line هيكون 000-011 هتكون الجزر التانى
+
+125
+00:10:05,590 --> 00:10:10,090
+والنقطة اللى بتحسب عندها ال potential اللى هي 501
+
+126
+00:10:10,090 --> 00:10:13,310
+هتعطينى 1 ايش اللى بدى اعمله بدي اجيب ال potential
+
+127
+00:10:13,310 --> 00:10:16,530
+عند ال origin بدي اجيب ال potential عند النقطة
+
+128
+00:10:16,530 --> 00:10:20,230
+اللى بدى عندها ال potential ليش انا بدي ال
+
+129
+00:10:20,230 --> 00:10:23,290
+potential عند ال origin لإنه يعطينى معلومة عنه ايه
+
+130
+00:10:23,290 --> 00:10:26,450
+ال potential عند ال origin ايش بساوت 0 وهذا اللى
+
+131
+00:10:26,450 --> 00:10:31,130
+هساعدني ان اعرف قيمة ال constantعشان هي انا جبت ال
+
+132
+00:10:31,130 --> 00:10:34,410
+raw اللي هي بعض ال line عن ال origin و مرة تانية
+
+133
+00:10:34,410 --> 00:10:38,750
+ال raw اللي هي بعض ال line عن النقطة اللي بده ايس
+
+134
+00:10:38,750 --> 00:10:41,990
+عندها ال potential نفس الشيء ال raw node بعض ال
+
+135
+00:10:41,990 --> 00:10:44,990
+charge عن ال origin و بعض ال charge عن النقطة اللي
+
+136
+00:10:44,990 --> 00:10:49,010
+بده اجيب عندها ال potential و بتنحسب ببساطة قيمة
+
+137
+00:10:49,010 --> 00:10:51,550
+raw node و R node اللي هو زي ما قلنا بعض ال line
+
+138
+00:10:51,550 --> 00:10:57,790
+عن ال origin و ال raw A و ال R Aفقعدت و أخدته ال
+
+139
+00:10:57,790 --> 00:11:00,050
+line of charge كيف نجيب ال electric field اللي هو
+
+140
+00:11:00,050 --> 00:11:05,770
+باستخدامك او slope تاخده اللي هو contour حولانه
+
+141
+00:11:05,770 --> 00:11:11,510
+تمام بس ما علينا ان نكمل و نحصل على ال potential
+
+142
+00:11:14,750 --> 00:11:18,690
+عشان اجيب ال constant انا صرت عارفة بس بدي اعوض
+
+143
+00:11:18,690 --> 00:11:24,270
+فيها القيم عن هذه المعادلة مرتين بدي اعوض مرة ل V
+
+144
+00:11:24,270 --> 00:11:27,750
+عند النقطة اللى بدي احسب عندها ال potential و مرة
+
+145
+00:11:27,750 --> 00:11:30,990
+عند ال origin ال constant ماله بيظل constant بتفضل
+
+146
+00:11:30,990 --> 00:11:37,170
+نظر انا حسبت ال potential عند النقطة اللى 5 0 1 و
+
+147
+00:11:37,170 --> 00:11:39,590
+لا حسبت ال potential عند ال origin ال constant
+
+148
+00:11:39,590 --> 00:11:46,530
+constantفاللي هيتغير قيم ال raw و ال a raw L و Q
+
+149
+00:11:46,530 --> 00:11:49,590
+17 و ال two by epsilon node و هنا four by epsilon
+
+150
+00:11:49,590 --> 00:11:53,090
+node كلها أرقام احنا عارفينها بعوض مرة عن ال raw
+
+151
+00:11:53,090 --> 00:11:56,670
+node و R node و مرة تانية بحسب ال potential عند
+
+152
+00:11:56,670 --> 00:12:01,650
+النقطة اللي امديها يعني بحسب raw A و R A سيملها
+
+153
+00:12:01,650 --> 00:12:05,910
+بتظلها constant لإن هو مجرد constant رقم عشان أحسب
+
+154
+00:12:05,910 --> 00:12:12,180
+قيم ال potential عند النقطة المطلوبةماذا سأفعل؟
+
+155
+00:12:12,180 --> 00:12:17,300
+سأطرح الـ two potential من بعض V0 معنى ZE مين اللي
+
+156
+00:12:17,300 --> 00:12:20,000
+راح في هالحالة؟ ال constant اللي لمش لازمنيه
+
+157
+00:12:20,000 --> 00:12:24,540
+سأطرحهم من بعض و في عندي معلومة ان V0 ماله بسوء
+
+158
+00:12:24,540 --> 00:12:28,800
+Zero فعامض عن V0 بسوء Zero بحصل على قيمة ال
+
+159
+00:12:28,800 --> 00:12:33,960
+potential in ال A واضح الشي اللي عملناه؟ اذا عندي
+
+160
+00:12:33,960 --> 00:12:36,600
+line of charge وعندي point of charge هاي الأسئلة
+
+161
+00:12:36,600 --> 00:12:37,960
+اللي بتيجي في المتحنات المانعة
+
+162
+00:12:41,300 --> 00:12:45,760
+عندي معلومة غير عن اللي احنا شوفناه في المثال
+
+163
+00:12:45,760 --> 00:12:48,500
+الماضي انه عند ال infinity ال potential بيساوي 0
+
+164
+00:12:48,500 --> 00:12:52,240
+هنا ال reference point هي ال origin عند ال origin
+
+165
+00:12:52,240 --> 00:12:55,980
+عندي ال potential بيساوي 0 في اي نقطة في ال space
+
+166
+00:12:55,980 --> 00:12:58,400
+ان البوتنشال بيساوي مجموعة، البوتنشال اللي جاي من
+
+167
+00:12:58,400 --> 00:13:01,800
+ال charge زي البوتنشال اللي جاي من ال line charge
+
+168
+00:13:02,580 --> 00:13:05,060
+قيم ال potential جاية من ال charge معروف اللي هو q
+
+169
+00:13:05,060 --> 00:13:09,000
+على 4pi epsilon node R زائد some constant واللي
+
+170
+00:13:09,000 --> 00:13:11,100
+جاية من ال electric field ده كامل ال electric
+
+171
+00:13:11,100 --> 00:13:14,560
+field في dot dl بالنسبة لل line of charge وانتوا
+
+172
+00:13:14,560 --> 00:13:19,120
+جبتوها لل infinite line من جا عصله صحيح؟ تذكروا
+
+173
+00:13:19,120 --> 00:13:22,140
+عند أي نقطة حوالين ال line اللي بتساوي ال clause
+
+174
+00:13:22,140 --> 00:13:25,820
+integral أي dot dl بتساوي q enclosed على epsilon
+
+175
+00:13:25,820 --> 00:13:32,260
+node من جا عصلهبعد ما جيبنا ال potential عند ال
+
+176
+00:13:32,260 --> 00:13:34,820
+origin و ال potential عند النقطة a اللي هي انا بده
+
+177
+00:13:34,820 --> 00:13:37,500
+احسب انها potential باترحب من بعض بخلص من ميم ال
+
+178
+00:13:37,500 --> 00:13:41,060
+constant بعوض على V0 بساوة Zero بحصل على ال
+
+179
+00:13:41,060 --> 00:13:46,060
+potential عند النقطة a هنحاول
+
+180
+00:13:46,060 --> 00:13:50,300
+نربط اللي اتعلمناه عن ال electric field و
+
+181
+00:13:50,300 --> 00:13:54,430
+Maxwell's equationأول حاجة احنا قلنا ان ال
+
+182
+00:13:54,430 --> 00:13:57,730
+potential مايلوه time independent بعتمدش لا 6 ولا
+
+183
+00:13:57,730 --> 00:14:00,950
+5 المثال اللي اذا ذكرته من الحلقة الماضية قلنا ال
+
+184
+00:14:00,950 --> 00:14:04,650
+potential هو عبارة عن بعض independent بعتمدش على
+
+185
+00:14:04,650 --> 00:14:10,870
+المسار اللي بده يتاخذه أسوأ أخد المسار A ل B أو
+
+186
+00:14:10,870 --> 00:14:15,010
+المسار A ل B من هالماتجهة انسوا التجاه السامي
+
+187
+00:14:15,010 --> 00:14:17,470
+فلنفل أحكي عن التجاه السامي إذا أنا أخدت المسار
+
+188
+00:14:17,470 --> 00:14:20,370
+تبع A ل B هيك أو أخدت
+
+189
+00:14:25,400 --> 00:14:31,620
+فأخد المصار هنا أو المصار هنا أو المصار هنا مش
+
+190
+00:14:31,620 --> 00:14:34,880
+هيفرق معاها طريق path independent مايكمدش ال
+
+191
+00:14:34,880 --> 00:14:38,940
+integral تبع ال path او ال integral من a ل b مش
+
+192
+00:14:38,940 --> 00:14:43,720
+فارق عندي هذا ال integral من أي اتجاه جاي رايحت و
+
+193
+00:14:43,720 --> 00:14:48,020
+بعدين هيك مش فارقة الجواب دائما ثابت عشان هيك
+
+194
+00:14:48,020 --> 00:14:51,640
+بنسميه path independent مايكمدش علاء المصار تبع ال
+
+195
+00:14:51,640 --> 00:14:56,820
+integrationلو أخدته كك كك روحت على بي بتفرقش معاها
+
+196
+00:14:56,820 --> 00:14:59,800
+بعف independent ال integration بتبقى بعف
+
+197
+00:14:59,800 --> 00:15:05,980
+independent معناه
+
+198
+00:15:05,980 --> 00:15:10,800
+لو أنا أخدت طرح ال integration من مقطع a ل b و ال
+
+199
+00:15:10,800 --> 00:15:13,340
+integration من b ل a مش هيكون الجواب معلوم بس
+
+200
+00:15:13,340 --> 00:15:18,160
+إشارة سالبة بينهم لأنه بعف independent عكسته
+
+201
+00:15:18,160 --> 00:15:23,280
+حياتينا بس إشارة سالبةبما أن الـ Potential
+
+202
+00:15:23,280 --> 00:15:26,920
+difference بين أي نقطتين باص independent يعني لا
+
+203
+00:15:26,920 --> 00:15:29,920
+يتمدش على الباص سيكون الـ Potential ما بين الـ PA
+
+204
+00:15:29,920 --> 00:15:33,980
+سالب الـ Potential بين A و B و هدا احنا بنعرفه حتى
+
+205
+00:15:33,980 --> 00:15:39,160
+الدائرة أحسب الفرق الجهد بين النقطتين أعكس القراءة
+
+206
+00:15:39,160 --> 00:15:43,160
+بتعطيني إشارة سالبة لكن اذا قمّله بيبقى نفس الحاجة
+
+207
+00:15:43,160 --> 00:15:46,730
+نفس القيمةاذا معناه مجموعة دولة with two
+
+208
+00:15:46,730 --> 00:15:49,150
+potentials، يعني لو أنا خدت close boss، إيش معناه
+
+209
+00:15:49,150 --> 00:15:51,810
+مجموعة with two potentials دولة؟ لو أنا بدأت من
+
+210
+00:15:51,810 --> 00:15:58,370
+نقطة A، لو أنا بدأت من نقطة A، و جاءت عن نقطة A،
+
+211
+00:15:58,370 --> 00:16:01,470
+يعني بدأت من A ل B، و بعدين من B ل A، إيش هي
+
+212
+00:16:01,470 --> 00:16:05,650
+مجموعة ال potential؟ Zero، يعني واحد منهم قاعد
+
+213
+00:16:05,650 --> 00:16:08,590
+سؤال تاني، واحد خمسة، التاني ماقص خمسة، إذا مجموعة
+
+214
+00:16:08,590 --> 00:16:14,650
+ما هيصير؟ سفرإذا مجموع ال potential VBA زائد VAB
+
+215
+00:16:14,650 --> 00:16:18,510
+هو Zero وهذا ماذا يساوي ال potential؟ بيساوي ال
+
+216
+00:16:18,510 --> 00:16:23,990
+Integral من B لA لE ضد DL زاد ال Integral من A لB
+
+217
+00:16:23,990 --> 00:16:28,390
+E ضد DL هي مجموعة هذا ال Integral بيساوي ال
+
+218
+00:16:28,390 --> 00:16:36,170
+Integral من B لA E ضد DL وهذا التكامل من A لB E ضد
+
+219
+00:16:36,170 --> 00:16:43,340
+DL مجموعهم هيكون من B لA closed pathسكّه closed
+
+220
+00:16:43,340 --> 00:16:46,920
+boss بروح من نفس النقطة و برجعلها هيكل closed
+
+221
+00:16:46,920 --> 00:16:50,780
+integral لإيده ال dl إذا ال closed integral إيش
+
+222
+00:16:50,780 --> 00:16:54,100
+بيساوي؟ zero إحنا فعودنا إن هاي دوارة معناها
+
+223
+00:16:54,100 --> 00:16:59,060
+closed integral إذا ال closed integral لإيده ال dl
+
+224
+00:16:59,060 --> 00:17:02,940
+إيش بيساوي؟ zero بس إحنا أخدنا stock theorem
+
+225
+00:17:02,940 --> 00:17:06,140
+بتذاكرينها لما كنا بناخد ال mathematics في أول
+
+226
+00:17:06,140 --> 00:17:09,080
+شباتر بينا stock theorem بس إيش بتقولي ال closed
+
+227
+00:17:09,080 --> 00:17:14,970
+integral؟للـ line integral بساوي ال surface
+
+228
+00:17:14,970 --> 00:17:18,630
+integral ل curl ال field كنا ناخدها بشكل عام، أي
+
+229
+00:17:18,630 --> 00:17:22,290
+field نسميه A، قول ال line integral ل A dot D ..
+
+230
+00:17:22,290 --> 00:17:25,790
+ال closed line integral ل A dot DL بساوي ال
+
+231
+00:17:25,790 --> 00:17:29,170
+surface integral ل curl ال A dot DS، احنا هالأيه
+
+232
+00:17:29,170 --> 00:17:31,010
+تعرفين من ال field اللي بنحكي عنه؟ بنحكي عن ال
+
+233
+00:17:31,010 --> 00:17:34,970
+electric field، اذا ال closed integral ل A dot DL
+
+234
+00:17:34,970 --> 00:17:40,650
+بساويالـ Curl E ضد DS هذا ما يعني بيساوي Zero إذا
+
+235
+00:17:40,650 --> 00:17:43,890
+هذا ال Integral بيساوي Zero إذا ما أنا Curl E لأنه
+
+236
+00:17:43,890 --> 00:17:47,010
+DS أنا باخد عمال يعرف أنه باخد عينة من ال surface
+
+237
+00:17:47,010 --> 00:17:50,230
+من ال Zero متأكدة أنها عينة عند ال surface هذا
+
+238
+00:17:50,230 --> 00:17:54,570
+القدر و بقعد بدي DS اللي هي مثلا DX DY DZمش
+
+239
+00:17:54,570 --> 00:17:58,230
+محتاجها zero مين اللي لازم يساوي zero كيرل ال E
+
+240
+00:17:58,230 --> 00:18:01,710
+إذا كيرل ال E بيساوي zero حيشوفناها قبل هيك
+
+241
+00:18:01,710 --> 00:18:05,210
+متذاكرين إيش اللي معناه إنه أي potential الكيرل
+
+242
+00:18:05,210 --> 00:18:10,710
+تبعه بيساوي zero مانه ال rotational بلفش صح
+
+243
+00:18:10,710 --> 00:18:14,610
+متذاكرين؟ وال electric field إنه من أمثلة الناس
+
+244
+00:18:14,610 --> 00:18:18,250
+اللي مالها ال rotational بتلفش مالها إلها source
+
+245
+00:18:18,250 --> 00:18:22,690
+يا sink يا إيش emerge لكن بتلفش ال electric field
+
+246
+00:18:23,740 --> 00:18:28,580
+طبعا هذا max وال equation المعادلة اللي احنا
+
+247
+00:18:28,580 --> 00:18:33,140
+شوفناها قبل هي curl E بتساوي zero هاي هي بتكون
+
+248
+00:18:33,140 --> 00:18:38,200
+معاكم تاني max
+
+249
+00:18:38,200 --> 00:18:41,560
+وال equation لان اخدت diverge E بتساوي rho على
+
+250
+00:18:41,560 --> 00:18:47,520
+epsilon first max وال equation صحيح؟ و هاي تاني
+
+251
+00:18:47,520 --> 00:18:47,920
+واحدة
+
+252
+00:18:52,700 --> 00:18:56,860
+مش كمان احنا ممكن نوصل من تعريف ال potential ال
+
+253
+00:18:56,860 --> 00:18:59,740
+potential ان هو عبارة عن minus ال integral ل E dot
+
+254
+00:18:59,740 --> 00:19:02,780
+DL انا يعني احملت ال minus لما اعملت عشان اخد ال
+
+255
+00:19:02,780 --> 00:19:06,900
+clause integral بس يعني انتوا تاخدوه بالانتباه انا
+
+256
+00:19:06,900 --> 00:19:09,620
+كانت الفكرة ان افرجيكوا ان ال integral ل E dot DL
+
+257
+00:19:09,620 --> 00:19:12,460
+زي ال integral ل E dot DL بيعطيني ال clause boss
+
+258
+00:19:12,460 --> 00:19:15,100
+بس في minus برا و zero مش فارقة يعني
+
+259
+00:19:26,670 --> 00:19:30,270
+DV بيكون DV بيكون minus E dot DL
+
+260
+00:19:33,200 --> 00:19:35,800
+طب هد إيش معناها؟ هد دُت ال product بين vector
+
+261
+00:19:35,800 --> 00:19:38,640
+field و DL و DL ماحنا عارفينها مثلا من ال
+
+262
+00:19:38,640 --> 00:19:42,680
+Cartesian إيش اللي بيساوي DL؟ DX X hat, DY Y hat,
+
+263
+00:19:43,020 --> 00:19:47,880
+DZ Z hat و E هد field، vector يعني عمّا دربته بEX
+
+264
+00:19:47,880 --> 00:19:52,620
+X hat زي EY Y hat زي EZ Z hat إذا دُت ال product
+
+265
+00:19:52,620 --> 00:20:02,470
+مش هيحطيني EX DX EY DY EZ DZ معين؟طب كمان dv هي دي
+
+266
+00:20:02,470 --> 00:20:05,070
+ما قالها total differential و ال total
+
+267
+00:20:05,070 --> 00:20:08,910
+differential بتلاقي ال partial differential اللي
+
+268
+00:20:08,910 --> 00:20:15,950
+هي dv by dx dx ذات dv by dy dy ذات dv by dz dz في
+
+269
+00:20:15,950 --> 00:20:19,570
+حد عنده مشكلة في هاي ال total differential؟لو أنا
+
+270
+00:20:19,570 --> 00:20:23,030
+قرنت المعادلتين مع بعض إيش بلاحظ إنه EX إيش بتساوي
+
+271
+00:20:23,030 --> 00:20:29,970
+minus dV by dx EY إيش بتساوي minus dV by dy EZ إيش
+
+272
+00:20:29,970 --> 00:20:34,510
+بتساوي minus dV by dz لو طلعت على هذه المعادلة إيش
+
+273
+00:20:34,510 --> 00:20:37,290
+بتقولّي إن في عندي X component لل electric field
+
+274
+00:20:37,290 --> 00:20:41,650
+بتساوي minus dV by dx وعندي Y component بتساوي
+
+275
+00:20:41,650 --> 00:20:46,070
+minus dV by dy و Z component بتساوي minus dV by dz
+
+276
+00:20:49,620 --> 00:20:58,680
+-dv by dx x hat-dv by dy y hat فdv
+
+277
+00:20:58,680 --> 00:21:03,840
+by dz زدها
+
+278
+00:21:03,840 --> 00:21:12,520
+قريبة ساوية-d by dx x hat-d by dy y hat-d by dz
+
+279
+00:21:13,170 --> 00:21:17,950
+زدها مالها مأثرة على مين على مين وهذه مين تعريفها
+
+280
+00:21:17,950 --> 00:21:20,810
+في ال partition coordinate اللي هي الدل هتكون هذه
+
+281
+00:21:20,810 --> 00:21:28,810
+minus فبحث عن minus هنا هذا
+
+282
+00:21:28,810 --> 00:21:33,850
+بالتامة اللي هو الدل هتكون minus del V منطقي ان
+
+283
+00:21:33,850 --> 00:21:38,270
+تكون E بتساول minus del V ليش منطقي ليش E لازم
+
+284
+00:21:38,270 --> 00:21:43,430
+تكون minus gradient لبطن شرالشهدة اللى طلع لنا اشي
+
+285
+00:21:43,430 --> 00:21:49,470
+متوقع مش اشي مش متوقع ال potential بساوة ال
+
+286
+00:21:49,470 --> 00:21:56,210
+integral زائد حاجة تانية مادام ان ال potential هو
+
+287
+00:21:56,210 --> 00:22:00,510
+ال integral ايه لل DL هو احنا اشتقناها من هنا صح
+
+288
+00:22:00,510 --> 00:22:05,630
+اشتقناها من هنا وصلنا انه ايه بساوة ما نذكرت فيه
+
+289
+00:22:05,630 --> 00:22:09,210
+اش هاي المعادلة المنطقية من اللى أخدناها من
+
+290
+00:22:09,210 --> 00:22:14,780
+الشباتر قبل ما انا اغيب عنكماي معلومة أخدناها كارل
+
+291
+00:22:14,780 --> 00:22:22,200
+الدل ايش بيساوي انا سميفه عشان احنا قدرنا اخدناهم
+
+292
+00:22:22,200 --> 00:22:27,500
+ايش بيساوي كارل الدل ايش كارل الدل بيساوي zero
+
+293
+00:22:27,500 --> 00:22:33,560
+كارل الدل بيساوي zero الله عليكم طب مش خايفين احنا
+
+294
+00:22:33,560 --> 00:22:37,440
+قلنا كارل دي ماله تقوى لسه في ال study السادقة ايش
+
+295
+00:22:37,440 --> 00:22:41,980
+بيساوي كارل دي ايه zero ايش ماله الكتير كتيرالـ
+
+296
+00:22:41,980 --> 00:22:47,260
+rotational كان الـ E بساوي 0 وعناه أن E لازم يكون
+
+297
+00:22:47,260 --> 00:22:51,660
+gradient ل scalar potential لأن كان ال gradient ل
+
+298
+00:22:51,660 --> 00:22:59,260
+scalar potential بساوي 0، واضح؟ فاهموني
+
+299
+00:22:59,260 --> 00:23:03,980
+هي كيف بتدرسوا، ماطفوا ساكتين يعني، ماشعورين بقلب
+
+300
+00:23:03,980 --> 00:23:04,240
+يعني
+
+301
+00:23:13,890 --> 00:23:17,210
+هذا احنا حكيناه ان اذا انا ايه بيساوى minus ال
+
+302
+00:23:17,210 --> 00:23:20,950
+grade لـ scalar potential لانه صعب ان نفكر ان ال
+
+303
+00:23:20,950 --> 00:23:25,290
+gradient بيساوي zero اذا معناه ان هذا كلمة مرة
+
+304
+00:23:25,290 --> 00:23:28,230
+باكد لنا ان ال electric field هو نقل روتيشنال
+
+305
+00:23:28,230 --> 00:23:32,250
+بيساوي minus ال gradient لpotential طب احنا اول
+
+306
+00:23:32,250 --> 00:23:34,370
+متذكرين ما بدنا بنحكي عن ال potential قلنا ان ال
+
+307
+00:23:34,370 --> 00:23:37,650
+electric field هو درجيبه من تلات جهات يا من
+
+308
+00:23:37,650 --> 00:23:42,380
+columns lawيا من gauss law يا من ال potential يعني
+
+309
+00:23:42,380 --> 00:23:45,120
+إذا كنت عارفة ال potential أنا فقدر أجيب ال
+
+310
+00:23:45,120 --> 00:23:46,800
+electric field لإنه صرت عارفة إيه إيه إيه إيه إيه
+
+311
+00:23:46,800 --> 00:23:48,560
+إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه
+
+312
+00:23:48,560 --> 00:23:48,760
+إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه
+
+313
+00:23:48,760 --> 00:23:49,040
+إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه
+
+314
+00:23:49,040 --> 00:23:52,000
+إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه
+
+315
+00:23:52,000 --> 00:24:01,140
+إيه إيه إيه إيه إيه إيه إيه
+
+316
+00:24:01,140 --> 00:24:05,400
+إي
+
+317
+00:24:09,680 --> 00:24:13,120
+باي على اتنين او زيرو هذا ايش نوع ال coordinate؟
+
+318
+00:24:13,120 --> 00:24:21,500
+spherical coordinate عند θ وفاي فعندى كيمة r وθ
+
+319
+00:24:21,500 --> 00:24:26,640
+وفاي كمان بده اني بعد ما اجيب دى calculate the
+
+320
+00:24:26,640 --> 00:24:30,200
+work done in moving a ten micro column which are
+
+321
+00:24:30,200 --> 00:24:35,280
+from النقطة a ونقطة b يعني اول حاجة بده دىطبعا دي
+
+322
+00:24:35,280 --> 00:24:38,020
+سمع في المهم ان اجيبها اقول ان اجيب E احنا لسه
+
+323
+00:24:38,020 --> 00:24:41,360
+طولنا E بقدر اجيبها مهم ال potential يعني E بقدر
+
+324
+00:24:41,360 --> 00:24:45,100
+اقول انها minus grade V بجيب E وD ماهي الا epsilon
+
+325
+00:24:45,100 --> 00:24:50,780
+times E فا epsilon not times E بجيب D الجزء التاني
+
+326
+00:24:50,780 --> 00:24:55,640
+بدو ال work اللي احتاجه عشان ينقل ال charge معينة
+
+327
+00:24:55,640 --> 00:24:59,260
+قيمتها عشرة micro column من نقطة في ال space هذا
+
+328
+00:24:59,260 --> 00:25:00,680
+اللي هو فيه electric field
+
+329
+00:25:09,920 --> 00:25:15,020
+نبدأ بالجزء الأول يعنيأيه قلنا دي بتساوي epsilon
+
+330
+00:25:15,020 --> 00:25:20,140
+node E وانت هجيب E يقولنا minus دل ال V بس هستخدم
+
+331
+00:25:20,140 --> 00:25:24,400
+مين ال spherical coordinate مش حاجة غصب عنها
+
+332
+00:25:24,400 --> 00:25:27,300
+أستخدم ال Cartesian coordinate أنا بتعود على D by
+
+333
+00:25:27,300 --> 00:25:30,520
+D X X hat زي D by D Y Y hat زي D by D Z Z hat
+
+334
+00:25:30,520 --> 00:25:34,800
+ماتبتش أحفظش تاني فبدأت أحول ال V من sin θ أو cos
+
+335
+00:25:34,800 --> 00:25:38,560
+φ ل X Y Z بتفرق بضيع وقت كتير في الامتحان الأسهل
+
+336
+00:25:38,560 --> 00:25:41,360
+أكون عارفة دل بي ال spherical coordinate
+
+337
+00:25:43,930 --> 00:25:49,250
+مناس بالم ال V اللي هي مناس مفتاح القوس D V by D R
+
+338
+00:25:49,250 --> 00:25:53,650
+R Hat زاد واحد على R D V by D Theta Theta Hat زاد
+
+339
+00:25:53,650 --> 00:25:58,370
+واحد على R Sine Theta D V by D Phi Phi Hat معايا
+
+340
+00:25:58,370 --> 00:26:03,450
+دعود بال V بدا فرض بالنسبة ل R إيش هتعطيني minus
+
+341
+00:26:03,450 --> 00:26:09,120
+عشرين على R cube Sine Theta Cosine Phi معاياطب
+
+342
+00:26:09,120 --> 00:26:13,320
+بالنسبة ل θ في عندي 1 على R 10 على R تربيه و 1 على
+
+343
+00:26:13,320 --> 00:26:17,340
+R تصير 10 على R cube التفاضى بالنسبة ل sin sin إيش
+
+344
+00:26:17,340 --> 00:26:22,840
+بتصير cos في cos ف؟ 1 على R sin θ يعني هتصير 10
+
+345
+00:26:22,840 --> 00:26:26,300
+على R cube sin θ بالنسبة ل فيه cos فإيش بتصير
+
+346
+00:26:26,300 --> 00:26:31,460
+minus sin ف؟ تمام، إذا هي عند ال electric field،
+
+347
+00:26:31,460 --> 00:26:36,370
+ببساطة لأن أنا عارفة ال potentialلأ هنا عرفت قيم
+
+348
+00:26:36,370 --> 00:26:38,830
+الـ charges و لا نوع من أنواع الـ distribution
+
+349
+00:26:38,830 --> 00:26:42,810
+عشان أقول أني بدي أجيبه من columns ولا من gauss
+
+350
+00:26:42,810 --> 00:26:45,690
+هنا الحل الوحيد أو الطريقة الوحيدة أني أجيبه من
+
+351
+00:26:45,690 --> 00:26:48,410
+وين من خلال ال potential لأنه ماعطيني ال potential
+
+352
+00:26:48,410 --> 00:26:52,870
+طب بده يعني نقطة معينة أول حاجة بدي أجيبه ال D ال
+
+353
+00:26:52,870 --> 00:26:57,090
+D اللي بدي أقوله هي epsilon not في E و أعوض على
+
+354
+00:26:57,090 --> 00:27:02,090
+النقطة R2 theta Pi على 2 و Phi بتساوي 0
+
+355
+00:27:04,860 --> 00:27:08,340
+بحصل على قيمة اللي هو دي اللي هو طلبها في الجزء
+
+356
+00:27:08,340 --> 00:27:13,100
+الأولاني هل الطلب دو ال work؟ الجزء التاني من
+
+357
+00:27:13,100 --> 00:27:15,480
+السؤال بده ال work
+
+358
+00:27:19,790 --> 00:27:22,770
+عندي طريقتين ان احسب ال work اول طريقة اللى
+
+359
+00:27:22,770 --> 00:27:26,310
+تعلمناها قبل قليل هي minus q ال integral ل E ضد DL
+
+360
+00:27:26,310 --> 00:27:30,490
+لمنها اشتقنا ال potential ال work هو minus q ال
+
+361
+00:27:30,490 --> 00:27:34,030
+integral ل E ضد DL اللى قولنا ماله من وين جيبناها
+
+362
+00:27:34,030 --> 00:27:37,490
+احنا من ال integral ل F ضد DL minus ال integral ل
+
+363
+00:27:37,490 --> 00:27:41,610
+F ضد DL minus
+
+364
+00:27:41,610 --> 00:27:45,970
+w على q بتسوي ال integral ل E ضد DL طب انا عندي من
+
+365
+00:27:45,970 --> 00:27:52,200
+وين بده ينقل من عندي خليني رجع نشوفاللي عندها R
+
+366
+00:27:52,200 --> 00:27:58,770
+تلاتين R واحد ستة تلاتين و طالع مائة و عشرينلنقطة
+
+367
+00:27:58,770 --> 00:28:04,030
+تانية في ال space اللى فيها R تغيرت من 1 ل 4 و θ
+
+368
+00:28:04,030 --> 00:28:08,210
+تغيرت يعني لو كنت اخد ال bus انا بدي عندى فى ..
+
+369
+00:28:08,210 --> 00:28:13,670
+اكيد فى عندى DR و فى عندى تغير فى θ Dθ و فى عندى
+
+370
+00:28:13,670 --> 00:28:17,810
+bus اللى فى تغير فى D5 عندى ال three buses احنا ال
+
+371
+00:28:17,810 --> 00:28:20,510
+buses في ال spherical coordinate كنت مذاكرينهم لما
+
+372
+00:28:20,510 --> 00:28:25,190
+R بتتغير ايش بيكون عندى على طول ال spherical DRلما
+
+373
+00:28:25,190 --> 00:28:29,030
+set تتغير ايش قلنا R دي ثتا لما five تتغير ايش
+
+374
+00:28:29,030 --> 00:28:34,670
+قلنا R sin theta دي five انا
+
+375
+00:28:34,670 --> 00:28:39,790
+تلت تغيرات طب احنا قولنا ان هذا ال work هتبع لما
+
+376
+00:28:39,790 --> 00:28:45,940
+اللغة تبندن لو انا بدي اخد التلت تغيراتأنا مش
+
+377
+00:28:45,940 --> 00:28:48,820
+قادرة كيف بدي أتخيلهم بدي أعمل التلات تغيرات مرة
+
+378
+00:28:48,820 --> 00:28:52,120
+واحدة بدي أغير ال R و أغير ال theta و أغير ال five
+
+379
+00:28:52,120 --> 00:28:56,360
+نفس الوقت و كامل اللي هي التلات انتجرالات كيف بدي
+
+380
+00:28:56,360 --> 00:29:00,080
+أغيرهم مرة واحدة فما أن هو boss independent إيش
+
+381
+00:29:00,080 --> 00:29:04,200
+هاخد boss صح شويه أطول بس هاخد boss اللي ما له
+
+382
+00:29:04,200 --> 00:29:08,040
+واحد واحد منهم بتغير يعني أول حاجة هنتقل من النقطة
+
+383
+00:29:08,040 --> 00:29:13,620
+A اللي عندها R واحد و theta تلاتين و مية وعشرين
+
+384
+00:29:17,700 --> 00:29:22,300
+وهي النقطة الأولى اللى هى A أقع النقطة A على مين؟
+
+385
+00:29:22,300 --> 00:29:31,340
+على 1 و 30 درجة و Phi إقدارها 120 درجة أول حاجة
+
+386
+00:29:31,340 --> 00:29:35,340
+هروح أخد ال Integra من هذه النقطة على طول لحد
+
+387
+00:29:35,340 --> 00:29:41,600
+ماوصل اللى هى A' اللى عندها اتغير R من 1 ل 4 و 30
+
+388
+00:29:41,600 --> 00:29:48,700
+درجة و 120 درجةبعدين هنتقل من النقطة A' لنقطة B'
+
+389
+00:29:49,020 --> 00:29:55,760
+اللي تغير فيها θ من 30 درجة ل 90 درجة أحنا قلنا
+
+390
+00:29:55,760 --> 00:30:01,260
+تبدأ من المفروض خطة هات من 0 ل 90، صح؟ بس هتهيأت،
+
+391
+00:30:01,260 --> 00:30:06,920
+بس هاي
+
+392
+00:30:06,920 --> 00:30:13,260
+النقطة اللي هي B' اللي عندها هيكون التغير 490
+
+393
+00:30:15,010 --> 00:30:21,710
+بس تسعين هي هتكون هيك هي هتكون هيك هي تلاتين
+
+394
+00:30:21,710 --> 00:30:31,850
+تلاتين تلاتين تلاتين تلاتين تلاتين تلاتين تلاتين
+
+395
+00:30:31,850 --> 00:30:38,430
+تلاتين تلاتين تلاتين تلاتين تلاتين
+
+396
+00:30:38,430 --> 00:30:39,690
+تلاتين تلاتين تلاتين تلاتين تلاتين تلاتين تلاتين
+
+397
+00:30:39,690 --> 00:30:40,230
+تلاتين تلاتين تلاتين تلاتين تلاتين تلاتين تلاتين
+
+398
+00:30:40,230 --> 00:30:40,290
+تلاتين تلاتين تلاتين تلاتين تلاتين تلاتين تلاتين
+
+399
+00:30:40,290 --> 00:30:40,310
+تلاتين تلاتين تلاتين تلاتين تلاتين تلاتين تلاتين
+
+400
+00:30:40,310 --> 00:30:41,410
+تلاتين تلاتين تلاتين تلاتين تلاتين تلاتين تلاتين
+
+401
+00:30:41,410 --> 00:30:45,780
+تلاتين تلاتين تلاتين تعشان انا المفروض التالتين
+
+402
+00:30:45,780 --> 00:30:49,260
+اخدها انا هى اللى بحكي هى ال theta عشان اللى
+
+403
+00:30:49,260 --> 00:30:54,080
+اظهرتها و هى اللى هتكون على ال axis هذا انا عشان
+
+404
+00:30:54,080 --> 00:31:01,080
+اخد الصورة هى هذه هي تلاتين درجة وهى النقطة A اللى
+
+405
+00:31:01,080 --> 00:31:08,520
+هى واحد تلاتين درجة ومية وعشرين درجة فعى مية
+
+406
+00:31:08,520 --> 00:31:11,840
+وعشرين يعني برضه كتره فعى يعني هتكون مية وعشرين هى
+
+407
+00:31:11,840 --> 00:31:16,760
+فعى كده من هنا يعني تخيلوهاعند ال 120 اه تتخيل ال
+
+408
+00:31:16,760 --> 00:31:20,400
+axis كلهم يعني لو هد أسقطناها ستسقطها بقى في الربع
+
+409
+00:31:20,400 --> 00:31:28,680
+120 درجة فلت انتقلنا قولنا لنخلي هد أربعة تروح من
+
+410
+00:31:28,680 --> 00:31:32,660
+واحد لأربعة ليه A prime A prime اللي هو اربعة
+
+411
+00:31:32,660 --> 00:31:40,350
+تلاتين درجة ومية وعشرين درجة بعدين هنزلبقى النقطة
+
+412
+00:31:40,350 --> 00:31:43,630
+اللى عندها setup تساوي 90 هذه عندنا اقعد ضالة
+
+413
+00:31:43,630 --> 00:31:44,810
+تسابق تسابق تسابق تسابق تسابق تسابق تسابق تسابق
+
+414
+00:31:44,810 --> 00:31:47,950
+تسابق تسابق تسابق تسابق تسابق تسابق تسابق تسابق
+
+415
+00:31:47,950 --> 00:31:48,390
+تسابق تسابق تسابق تسابق تسابق تسابق تسابق تسابق
+
+416
+00:31:48,390 --> 00:31:48,410
+تسابق تسابق تسابق تسابق تسابق تسابق تسابق تسابق
+
+417
+00:31:48,410 --> 00:31:48,650
+تسابق تسابق تسابق تسابق تسابق تسابق تسابق تسابق
+
+418
+00:31:48,650 --> 00:31:49,730
+تسابق تسابق تسابق تسابق تسابق تسابق تسابق تسابق
+
+419
+00:31:49,730 --> 00:32:04,310
+تسابق تساب
+
+420
+00:32:04,850 --> 00:32:08,950
+هذه عنا R أربعة ضلت و مين اللي اتغير عندى ال ستة
+
+421
+00:32:08,950 --> 00:32:16,230
+صارت 90 درجة وضلت الفا 120 درجة الفا احنا بنحسبها
+
+422
+00:32:16,230 --> 00:32:25,270
+لل X عندى لحد 120 درجة فهي 120 درجة اذا
+
+423
+00:32:25,270 --> 00:32:29,690
+متقلنا من A prime ل B prime اخر واحدة اللي بيبدو
+
+424
+00:32:29,690 --> 00:32:40,860
+انه لحد الستينيعني نبدأ جهة على الـ Phi اللي
+
+425
+00:32:40,860 --> 00:32:48,460
+هي نقطة الأخيرة اللي عندها هيكون 94 درجة و 60 درجة
+
+426
+00:32:48,460 --> 00:32:53,600
+تمام؟ واضحة الصورة؟ هذا ال basis اللي انا هاخده
+
+427
+00:32:53,600 --> 00:32:56,300
+ليش هاخد هيك ال basis؟ لإن هذا ال basis هيكون عند
+
+428
+00:32:56,300 --> 00:33:03,150
+ال DL تغير من هنا لهنا هيكون بتساوي DRالتغيير من
+
+429
+00:33:03,150 --> 00:33:08,110
+هنا إلى هنا ايش هيكون R Dθ وهنا ايش هيكون التغيير
+
+430
+00:33:08,110 --> 00:33:10,890
+R Sine Theta
+
+431
+00:33:16,210 --> 00:33:19,610
+واضحة النقطة هى؟ اذا بدل ما انا اخدهم كلهم مرة
+
+432
+00:33:19,610 --> 00:33:23,570
+واحدة تغيرات بل انا باخدهم واحدة واحدة line line
+
+433
+00:33:23,570 --> 00:33:28,830
+وانا عارفة انه لانه التكاوم من a لb باصن
+
+434
+00:33:28,830 --> 00:33:31,450
+independent فانا بقدر اقول من a ل a prime من a
+
+435
+00:33:31,450 --> 00:33:34,870
+prime ل b prime و b prime ل b اللى هى النقطة اللى
+
+436
+00:33:34,870 --> 00:33:39,150
+انا بدي احسب عندها ال work نيجي مع بعض نحسب هذا
+
+437
+00:33:39,150 --> 00:33:39,610
+الحكيم
+
+438
+00:33:43,770 --> 00:33:48,310
+زي ما انتوا شايفين هبدأ من A اللي عندها R واحد ستة
+
+439
+00:33:48,310 --> 00:33:53,390
+تلاتين ومية وعشرين ل A prime اللي اتغير فيها R
+
+440
+00:33:53,390 --> 00:33:57,610
+لاربع ستة ضلت سابتة و five سابتة هيك أسهل التكامل
+
+441
+00:33:57,610 --> 00:34:01,270
+لما أسبب اتنين و أغير واحد أسهل من ان اخل ال تلاتة
+
+442
+00:34:01,270 --> 00:34:05,610
+متغيرين و دي L إيش هتكون في هذه الحالة دي R R hat
+
+443
+00:34:06,630 --> 00:34:09,610
+لما اجى اتغير من a prime ل b prime انا مين غيرتها
+
+444
+00:34:09,610 --> 00:34:13,610
+لقيتها ال theta خلتها بتروح من تلاتين ل تسعين R
+
+445
+00:34:13,610 --> 00:34:16,050
+ضلت ثابتة على أربع و Phi ضلت ثابتة على مائة و
+
+446
+00:34:16,050 --> 00:34:21,950
+عشرين قيمة ال DL بتساوي R D theta ثتا hat اخر حاجة
+
+447
+00:34:21,950 --> 00:34:26,350
+اللي هي اخلي ال R ثتا و Theta ثابتة و اغير الفاعل
+
+448
+00:34:26,350 --> 00:34:30,250
+من مائة و عشرين لستين هتكون DL بتساوي R sine theta
+
+449
+00:34:30,250 --> 00:34:35,330
+D Phi Phi hatإذا صار لي التكامل ما لو قسمته ل 3
+
+450
+00:34:35,330 --> 00:34:40,550
+integrals من a ل a' زائد ال integral من a' ل b'
+
+451
+00:34:40,990 --> 00:34:45,710
+زائد ال integral من b' ل b، في أي حاجة مش واضحة
+
+452
+00:34:45,710 --> 00:34:52,050
+لحد هنا؟مش واضح؟ إذا عندي (-w على cube)(-1 على
+
+453
+00:34:52,050 --> 00:34:55,510
+cube تكمل من a ل a prime أو يعني ال work من a ل a
+
+454
+00:34:55,510 --> 00:34:57,990
+prime زاد ال work من a prime ل b prime زاد ال work
+
+455
+00:34:57,990 --> 00:35:00,830
+من b prime ل b prime اللي هو عبارة عن ال integrant
+
+456
+00:35:00,830 --> 00:35:03,250
+من a ل a prime زاد ال integrant من a prime ل b
+
+457
+00:35:03,250 --> 00:35:05,510
+prime زاد ال integrant من b prime ل b prime إلى e
+
+458
+00:35:05,510 --> 00:35:11,390
+dot dl اي ما احنا حسبناها مع بعض يعرفينهابنعوض في
+
+459
+00:35:11,390 --> 00:35:15,330
+المعادلة و أعمل نتيجة اذا رجعنا ل E بتعوض طبعا لما
+
+460
+00:35:15,330 --> 00:35:20,170
+أسفت ال D ال theta و ال five بتعوض عنه مباشرة و
+
+461
+00:35:20,170 --> 00:35:22,750
+أخل مين فقط اللي هو ال R المتغير
+
+462
+00:35:30,100 --> 00:35:35,060
+بعود انا و بحط قيام ال theta و ال phi في قلب ال
+
+463
+00:35:35,060 --> 00:35:39,300
+integrals كلهم فعند ال integrant من R1 ل R4 20 sin
+
+464
+00:35:39,300 --> 00:35:44,500
+theta cos phi R cubed DR theta 30 و phi 20 التكامل
+
+465
+00:35:44,500 --> 00:35:50,010
+التاني مين هيسبب ال RI ستثبت على أربعة وفاي على
+
+466
+00:35:50,010 --> 00:35:53,890
+مائة وعشرين ومن يتغير هو الـθيتا والإنتجر الأخير
+
+467
+00:35:53,890 --> 00:35:57,810
+فايل سيتغير من مائة وعشرين لستين وحسبته الـR
+
+468
+00:35:57,810 --> 00:36:02,450
+والثيتا إذا عملنا هك بنحصل على قيمة ماينسة W على Q
+
+469
+00:36:02,450 --> 00:36:07,490
+وبحصل
+
+470
+00:36:07,490 --> 00:36:13,820
+على W بمجرد أن أعود عن EQ تمام هذه أول طريقةلكن هو
+
+471
+00:36:13,820 --> 00:36:19,320
+مش محدد عليا طريقة إن كيف أستخدم وحسن اللي هو كل
+
+472
+00:36:19,320 --> 00:36:23,660
+طلبه في السؤال ستتذكرواالـ work done in moving
+
+473
+00:36:23,660 --> 00:36:31,680
+الهدف من الـ Integra
+
+474
+00:36:31,680 --> 00:36:36,420
+هدف من ال Integra هدف من ال Integra هدف من ال
+
+475
+00:36:36,420 --> 00:36:42,080
+Integra هدف من ال Integra هدف من ال Integra هدف من
+
+476
+00:36:42,080 --> 00:36:44,250
+ال Integra هدف من ال Integra هدف من ال Integraعارف
+
+477
+00:36:44,250 --> 00:36:46,350
+ال potential بين النقطة التي هو لأنه عارف ال
+
+478
+00:36:46,350 --> 00:36:49,230
+potential في أي نقطة في ال space إذا عارف ال
+
+479
+00:36:49,230 --> 00:36:51,390
+potential في أي نقطة في ال space بقدر أجيبه في
+
+480
+00:36:51,390 --> 00:36:58,490
+نقطة محددة و الواقع عبارة عن ماله QVB-VA لأنه
+
+481
+00:36:58,490 --> 00:37:02,050
+عبارة عن minus Q ال Integra من A لB E ضد DL اللي
+
+482
+00:37:02,050 --> 00:37:03,990
+هو عبارة عن QVAB
+
+483
+00:37:05,760 --> 00:37:09,160
+لأن ماينوس انتيجرال من A ل B E ضد L هو ال
+
+484
+00:37:09,160 --> 00:37:14,040
+potential ما بين النقطة A و B يعني هيكون ال Q VB-
+
+485
+00:37:14,040 --> 00:37:19,760
+VA قولنا دايما هذا ناقص هذا VAB هيبتسوق VB- VA
+
+486
+00:37:22,260 --> 00:37:27,120
+عند ال potential بعود عن قيمة النقطة B و عن قيمة
+
+487
+00:37:27,120 --> 00:37:30,980
+النقطة A بحصل على نفس الجواب طبعا هاي الطريقة أسهل
+
+488
+00:37:30,980 --> 00:37:35,060
+بكتير بالذات انه انا مواطئل ال potential مش زي ال
+
+489
+00:37:35,060 --> 00:37:37,820
+electric field انا حسبته ممكن انا اخطر في حساب ال
+
+490
+00:37:37,820 --> 00:37:40,440
+electric field لكن مش متشرط عليا ان استخدم اي
+
+491
+00:37:40,440 --> 00:37:44,980
+طريقة بحسب ال work من ال potential مباشرة بحسبهاش
+
+492
+00:37:44,980 --> 00:37:47,780
+من ال electric fieldو بالذات ان شفتوا طريقة ال
+
+493
+00:37:47,780 --> 00:37:50,860
+electric field مالها طويلة شوية، بدى أقعدة كامل
+
+494
+00:37:50,860 --> 00:37:55,280
+على ال three buses عشان أحصر على ال work في عيسى
+
+495
+00:37:55,280 --> 00:37:59,860
+افسار لحد هنا نيجي لحاجة اسمها ال electric diaper
+
+496
+00:37:59,860 --> 00:38:03,600
+and flux lines إيش هو ال electric diaper؟ ال
+
+497
+00:38:03,600 --> 00:38:06,560
+diaper أكيد مرعت عليكم كلمة diaper ال diaper يعني
+
+498
+00:38:06,560 --> 00:38:09,540
+لما يكون عندى two charges plus و minus فيبقى البعض
+
+499
+00:38:09,540 --> 00:38:13,420
+زي قطرة الميه، لما تكون تحت ال electric field،
+
+500
+00:38:13,420 --> 00:38:19,620
+بتلاقوا هنا بيصير الشحنة موجةالدايبول يعني عندى
+
+501
+00:38:19,620 --> 00:38:24,720
+فيه two charges اللى هم opposite sign وما اللى هم
+
+502
+00:38:24,720 --> 00:38:29,200
+قراه بكتير من بعض يعني المسافة بينهم صغيرة يعني
+
+503
+00:38:29,200 --> 00:38:32,280
+مرة اللى كتب دايبول هو عبارة عن two point charges
+
+504
+00:38:32,280 --> 00:38:36,520
+اللى هم opposite sign و المسافة بينهم صغيرة كتير
+
+505
+00:38:44,160 --> 00:38:46,700
+دعوني أريكم الصورة تاعتهم هاي الـ dipole هاي عندي
+
+506
+00:38:46,700 --> 00:38:51,700
+XYZ عندي two charges plus و minus ال Q والمسافة
+
+507
+00:38:51,700 --> 00:38:56,040
+بينهم D بتكون صغيرة كتير هذا الـ electric dipole
+
+508
+00:38:56,040 --> 00:38:59,460
+لو أنا بده أحسب potential مثلا للنقطة B الناتجة عن
+
+509
+00:38:59,460 --> 00:39:01,660
+ال dipole يعني صار المفهوم إنها ال dipole ال
+
+510
+00:39:01,660 --> 00:39:04,900
+dipole two pointed charges المسافة بينهم صغيرة و
+
+511
+00:39:04,900 --> 00:39:07,520
+اللي هم opposite signs لو أنا بده أحسب ال
+
+512
+00:39:07,520 --> 00:39:11,840
+potential عن النقطة B هيكون
+
+513
+00:39:13,370 --> 00:39:17,430
+مجموع ال potentials الناتجين من positive و
+
+514
+00:39:17,430 --> 00:39:21,290
+negative charge ال potential ناتج من Q ايش هيساوي؟
+
+515
+00:39:21,290 --> 00:39:25,330
+Q على 4 by Y node في 1 على R1 و هذا هيكون minus Q
+
+516
+00:39:25,330 --> 00:39:31,710
+على 4 by Y node في 1 على R2 اذا ال potential عند
+
+517
+00:39:31,710 --> 00:39:35,570
+النقطة B هيكون ال potential ناتج من Q minus Q
+
+518
+00:39:39,220 --> 00:39:42,600
+بقى Q على 4 by epsilon node في 1 على R1 minus 1
+
+519
+00:39:42,600 --> 00:39:50,920
+على R2 لو أنا عملت توحيد مقامات هيكون عند Q على 4
+
+520
+00:39:50,920 --> 00:39:55,480
+by epsilon node R1 في R2 و ال boss بيصير R2 minus
+
+521
+00:39:55,480 --> 00:40:01,020
+R1 انت دوري اعرف ايش هي R2 minus R1 و اعرف ايش هي
+
+522
+00:40:01,020 --> 00:40:08,500
+R1 و R2 ارجع للاسمقلت ان انا بدي الفرق بين R2 وR1
+
+523
+00:40:08,500 --> 00:40:12,400
+R2 هي المسافة بين minus Q ونقطة B اللى بتحسب عندها
+
+524
+00:40:12,400 --> 00:40:16,900
+ال potential وR1 هي المسافة بين نقطة Q point of
+
+525
+00:40:16,900 --> 00:40:21,960
+charge Q plus Q ونقطة B لو انا طلعت على الرسمة انا
+
+526
+00:40:21,960 --> 00:40:25,380
+هلاحظ ان الفرق بينهم هو بالتمام هذه المسافة لو انا
+
+527
+00:40:25,380 --> 00:40:30,460
+ازالت عمود من plus Q على R2 هيكون الفرق بينهم هي
+
+528
+00:40:30,460 --> 00:40:37,280
+هذه المسافة لو انا عرفت زوية θهي الزاوية المابين
+
+529
+00:40:37,280 --> 00:40:40,900
+ال line اللى بوصل مابين ال center تبع ال dipole
+
+530
+00:40:40,900 --> 00:40:45,420
+هذه النقطة هي هنا ال dipole المسافة بين ال q و
+
+531
+00:40:45,420 --> 00:40:49,540
+minus q هي دى بس هذا ال dipole بالذات انا حطه بحيث
+
+532
+00:40:49,540 --> 00:40:53,420
+ال center تبعه جاية على ال origin ال center تبع ال
+
+533
+00:40:53,420 --> 00:40:56,400
+dipole جاية على ال origin قصدت لو انا عرفتها ان هى
+
+534
+00:40:56,400 --> 00:41:03,170
+الزاوية المابينالخط الواصل ما بين ال two charges و
+
+535
+00:41:03,170 --> 00:41:06,770
+الخط الواصل ما بين ال origin تبع ال dipole و
+
+536
+00:41:06,770 --> 00:41:09,410
+النقطة اللى بدأ يسعدها ال potential هى theta، ال
+
+537
+00:41:09,410 --> 00:41:13,110
+theta مع التلاغر هى نفس ال theta هى، صح؟ اذا هى
+
+538
+00:41:13,110 --> 00:41:18,530
+المسافة اللى بحسب بها عبارة عن مين D cos thetaأذا
+
+539
+00:41:18,530 --> 00:41:22,830
+الفرق بين R2 وR1 بقدر أكتب بدلالة D اللي هي
+
+540
+00:41:22,830 --> 00:41:25,450
+المسافة بين ال two charges ال positive و ال
+
+541
+00:41:25,450 --> 00:41:29,250
+negative of ال charges و θة اللي هي الزاوية اللي
+
+542
+00:41:29,250 --> 00:41:32,870
+ما بين ال line اللي واصل بين ال two charges و ال
+
+543
+00:41:32,870 --> 00:41:36,090
+line اللي واصل ما بين ال center تبع ال dipole و
+
+544
+00:41:36,090 --> 00:41:39,170
+النقطة اللي بقيس عندها ال potential اذا ال
+
+545
+00:41:39,170 --> 00:41:42,750
+difference هو D cos θ الحاجة التانية اللي انا بدأ
+
+546
+00:41:42,750 --> 00:41:46,130
+اخدها بعلية بارعة ان لو انا فرضت ان R1 وR2 أكبر
+
+547
+00:41:46,130 --> 00:41:53,460
+بكتيرمن المسافة D اذا تقريبا بقدر اقول ان R1 في R2
+
+548
+00:41:53,460 --> 00:42:00,100
+هي R تربيان تقريبا لانه منهم المسافة الفرق اللي
+
+549
+00:42:00,100 --> 00:42:05,960
+بينهم اصغر كتير R2 مقاس R1 اللي هي D Cos θ وتقريبا
+
+550
+00:42:05,960 --> 00:42:13,270
+R2 وR1 هسويها بR تربيان اذا رجعت لرسمهاهدولة كلهم
+
+551
+00:42:13,270 --> 00:42:18,750
+حيبينوا كإن هم متساويين في حالة الضرب R1 وR2 وR ..
+
+552
+00:42:18,750 --> 00:42:24,990
+وR فبقدر أقول أن R1 تقريبا تسوى R2 تقريبا تسوى R
+
+553
+00:42:24,990 --> 00:42:32,620
+فR1 في R2 هتكون R تربيهأذا ال potential الناتج عن
+
+554
+00:42:32,620 --> 00:42:36,280
+ال dipole هو
+
+555
+00:42:36,280 --> 00:42:40,060
+Q على 4 by epsilon note بد ال R تنين minus R واحد
+
+556
+00:42:40,060 --> 00:42:44,500
+عشان حطيت دي cos θ بد ال R واحد في R تنين حطيت R
+
+557
+00:42:44,500 --> 00:42:49,640
+تربيه تمام؟ في أي سؤال لحد هنا؟
+
+558
+00:42:53,450 --> 00:42:59,990
+D cos θ هي
+
+559
+00:42:59,990 --> 00:43:08,110
+البروجيكشن تبع D في اتجاه D و هذا الاتجاه θ لأن دي
+
+560
+00:43:08,110 --> 00:43:12,150
+كوساين ثتا هقول ان هذا الاتجاه مين هو R hat هو
+
+561
+00:43:12,150 --> 00:43:15,890
+البروجيكشن تبع D على اتجاه R hat
+
+562
+00:43:19,830 --> 00:43:24,370
+دى مالها اتجاهها اتجاه ال z axis احنا ماخدينها دى
+
+563
+00:43:24,370 --> 00:43:29,250
+vector هي عبارة عن d z hat ال projection تبعها في
+
+564
+00:43:29,250 --> 00:43:31,690
+ال R hat هو عبارة عن d cos θ
+
+565
+00:43:35,570 --> 00:43:40,150
+و هعمل رف كمان بي اللي هو الدايبول Q في D إذا بقدر
+
+566
+00:43:40,150 --> 00:43:44,890
+أعيد كتابة ال potential تبعي اللي هو QD cos θ على
+
+567
+00:43:44,890 --> 00:43:48,710
+4 pi epsilon نوت R تربيه عشان كان QD قلنا منه هال
+
+568
+00:43:48,710 --> 00:43:53,610
+D cos θ بتعبر عن D dot D R hat و QD vector هسميها
+
+569
+00:43:53,610 --> 00:43:58,770
+بي فهتصير بي بتساوي بي dot R hat على 4 pi epsilon
+
+570
+00:43:58,770 --> 00:44:02,530
+نوت R تربيه هذه معادلات أنتوا لازم تكونوا حافظينها
+
+571
+00:44:03,500 --> 00:44:07,500
+الديابل انه بساوي بي اللي هو مي حسميه الديابل
+
+572
+00:44:07,500 --> 00:44:10,700
+moment اللي هو قيمة ال charge q في دي المسافة بين
+
+573
+00:44:10,700 --> 00:44:15,600
+ال two charges بي الديابل moment كمرة هو q في دي و
+
+574
+00:44:15,600 --> 00:44:18,240
+ال potential ناتج عن هذا الديابل هيكون قيمة
+
+575
+00:44:18,240 --> 00:44:22,900
+الديابل moment بي dot r hat اللي هو الاتجاهاللي
+
+576
+00:44:22,900 --> 00:44:27,240
+ناله موازي للحط الواصل بين ال center تبع ال dipole
+
+577
+00:44:27,240 --> 00:44:30,620
+للمقطة اللي بده احسب عندها ال potential على 4pi
+
+578
+00:44:30,620 --> 00:44:33,640
+epsilon not r تربية و r اللي هي المسافة بين ال
+
+579
+00:44:33,640 --> 00:44:36,500
+center تبع ال dipole للمقطة اللي بده احسب عندها ال
+
+580
+00:44:36,500 --> 00:44:39,300
+potential بيعطيكوا العافية الدقاء القادم ان شاء
+
+581
+00:44:39,300 --> 00:44:40,620
+الله نكمل
+
diff --git a/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/xsHJkkk1-GI_raw.srt b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/xsHJkkk1-GI_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..24a381f0b599e325c97f55a774624fc65f7d1128
--- /dev/null
+++ b/PL9fwy3NUQKwZmUETC1fUVV_edXSxxud2c/xsHJkkk1-GI_raw.srt
@@ -0,0 +1,2324 @@
+1
+00:00:20,940 --> 00:00:23,480
+بسم الله الرحمن الرحيم السلام عليكم و رحمة الله و
+
+2
+00:00:23,480 --> 00:00:26,660
+بركاته احنا اليوم ان شاء الله هنتبع موضوعنا اللي
+
+3
+00:00:26,660 --> 00:00:30,680
+هو ال potential potential electric potential اسوأ
+
+4
+00:00:30,680 --> 00:00:34,080
+ال absolute ولا ال potential difference احنا
+
+5
+00:00:34,080 --> 00:00:36,980
+المحاضرة الماضية شوفنا كيف ان ال potential مربوط
+
+6
+00:00:36,980 --> 00:00:41,880
+بيه اللي هو ال electric field شوفنا ان ال
+
+7
+00:00:41,880 --> 00:00:45,100
+potential بين نقطتين A و B هو minus التكامل من A
+
+8
+00:00:45,100 --> 00:00:46,760
+لB لE ضد DL
+
+9
+00:00:49,210 --> 00:00:51,730
+أذا كنا عارفين الـ electric field فقدر أحسب ال
+
+10
+00:00:51,730 --> 00:00:55,490
+potential قولنا ال absolute potential بيكون لو أنا
+
+11
+00:00:55,490 --> 00:01:00,770
+أخدت مثلا النقطة a عند ال infinity هيكون عندها ال
+
+12
+00:01:00,770 --> 00:01:03,230
+potential بيسوا zero فهيكون ال potential عند
+
+13
+00:01:03,230 --> 00:01:07,850
+النقطة b بيسوا q على 4 by epsilon not في ال Rb
+
+14
+00:01:07,850 --> 00:01:11,110
+فانا
+
+15
+00:01:11,110 --> 00:01:13,810
+لو أخدنا ان ال R a مثلا عند ال infinity هذا قولنا
+
+16
+00:01:13,810 --> 00:01:15,710
+بيسميه ال absolute potential
+
+17
+00:01:17,930 --> 00:01:20,470
+كمان قولنا لو ان ال charge مش عند ال origin احنا
+
+18
+00:01:20,470 --> 00:01:24,170
+كنا عملنا هذا الحكي ان V بيساوي Q على 4 by Epsilon
+
+19
+00:01:24,170 --> 00:01:28,030
+Note R لما ال charge فرضاه عند ال origin و لو ال
+
+20
+00:01:28,030 --> 00:01:32,290
+charge مش عند ال origin لو
+
+21
+00:01:32,290 --> 00:01:34,850
+ال charge مش عند ال origin هيكون ال potential ايش
+
+22
+00:01:34,850 --> 00:01:38,590
+بيساوي Q على 4 by Epsilon Note الفرق ما بين R و R
+
+23
+00:01:38,590 --> 00:01:42,290
+prime حيث R اللي هو الموقع اللي انا بدأ ادقيس عنده
+
+24
+00:01:42,290 --> 00:01:47,770
+ال potential و R prime اللي هو مكان ال chargeلو
+
+25
+00:01:47,770 --> 00:01:51,130
+كان عندى اكتر من ال charge نحسبه بالطريقة طبعا على
+
+26
+00:01:51,130 --> 00:01:54,070
+أساس ان احنا فرضين انه عند ال infinity ال
+
+27
+00:01:54,070 --> 00:01:57,850
+potential بساوة zero لو كان عندى distribution
+
+28
+00:01:57,850 --> 00:02:01,790
+charge distribution لو كانت line او surface او
+
+29
+00:02:01,790 --> 00:02:06,020
+volume قولنا هيك نحسب ال potentialبشكل عام لو أنا
+
+30
+00:02:06,020 --> 00:02:08,980
+ماقلتش عند ال infinity هي ال zero بشكل عام لو في
+
+31
+00:02:08,980 --> 00:02:12,860
+عندي انا ال reference point مش ال infinity هيكون
+
+32
+00:02:12,860 --> 00:02:15,800
+ال potential بشكل عام بيساوة q على four by y not r
+
+33
+00:02:15,800 --> 00:02:19,340
+زائد c، c هيبحسبها من وين؟ من عند ال reference
+
+34
+00:02:19,340 --> 00:02:22,160
+point يعني وين انا حددت لل reference point اللي
+
+35
+00:02:22,160 --> 00:02:25,820
+عند ال potential؟ zero، بنحسب اللي هو قيمة c، لذا
+
+36
+00:02:25,820 --> 00:02:29,660
+بشكل عام بيبسوة minus integral a dot d l plus c
+
+37
+00:02:34,790 --> 00:02:39,770
+المثال اللى قدامنا كانت
+
+38
+00:02:39,770 --> 00:02:43,250
+ان احسابات ال potential عند ال infinity بيسووا
+
+39
+00:02:43,250 --> 00:02:46,550
+zero عند كنتوا charges كل واحدة عارفة ال location
+
+40
+00:02:46,550 --> 00:02:50,190
+تبعهم و مش عند ال zero كل واحدة لها location محدد
+
+41
+00:02:50,190 --> 00:02:53,770
+R1 سمنها وR2 و عند النقطة البدئيسية عندها ال
+
+42
+00:02:53,770 --> 00:02:54,770
+potential هي R
+
+43
+00:03:13,860 --> 00:03:17,660
+هذا ما حللناه المحاضرة الماضية
+
+44
+00:03:21,670 --> 00:03:25,470
+بدّينا عن مثال تاني قولنا هنحله المحاضرة هاي
+
+45
+00:03:25,470 --> 00:03:28,690
+المثال اللي عندنا بيقول ان في عندي charge مقدارها
+
+46
+00:03:28,690 --> 00:03:33,730
+خمسة nano column موجودة عند النقطة minus 3 4 0
+
+47
+00:03:33,730 --> 00:03:38,530
+وعندي كمان خط line of charge يعني عندي حاجتين
+
+48
+00:03:38,530 --> 00:03:41,630
+point of charge و line of charge ال point of
+
+49
+00:03:41,630 --> 00:03:45,790
+charge قاعدة في ال space عند النقطة minus 3 4 0 و
+
+50
+00:03:45,790 --> 00:03:50,050
+ال line of charge عند y 1 زي 1 يعني ال x ماله
+
+51
+00:03:50,050 --> 00:03:55,200
+موازلة ال xكاليز يونيفيرمت شارج مقدارها اتنين نانو
+
+52
+00:03:55,200 --> 00:03:59,900
+كولوم بيرمتر يعني رؤال بتساوي اتنين كولوم نانو
+
+53
+00:03:59,900 --> 00:04:04,200
+كولوم بيرمتر ايش طالب منهم؟ مناقزة احنا قولنا ان
+
+54
+00:04:04,200 --> 00:04:07,200
+ال reference اللي هو ال voltage بتساوي زيرو عند ال
+
+55
+00:04:07,200 --> 00:04:10,100
+origin يعني ال reference بتاعته هلقته وين؟ عند ال
+
+56
+00:04:10,100 --> 00:04:15,240
+origin بده ال voltage عند النقطة A اللي عند خمسة
+
+57
+00:04:15,240 --> 00:04:20,160
+وزيرو واحد يعني المثال
+
+58
+00:04:24,230 --> 00:04:33,430
+عند الـ charge
+
+59
+00:04:33,430 --> 00:04:38,490
+اللي هي الخمسة nano عند minus تلاتة واربعة وعلى ال
+
+60
+00:04:38,490 --> 00:04:42,570
+X يعني في ال X Y بلان ال Z أقل منها Zero لذلك هذه
+
+61
+00:04:42,570 --> 00:04:47,230
+الخمسة nano كله اللي عند مائس تلاتة واربعة وزرع في
+
+62
+00:04:47,230 --> 00:04:53,580
+ال X Y بلانالـ line y واحد و z واحد يعني لو حطنا
+
+63
+00:04:53,580 --> 00:04:57,360
+هنا واحد واحد هنا خط شماله هيكون قولنا وزي ال X
+
+64
+00:04:57,360 --> 00:05:06,100
+axis فال
+
+65
+00:05:06,100 --> 00:05:10,860
+X Y plane لأن Z equal 0 هاي ال charge الأولى ليه؟
+
+66
+00:05:10,860 --> 00:05:15,280
+خمسة نان كلوم و X ناقص ثلاثة و Y أربعة في ال X Y
+
+67
+00:05:15,280 --> 00:05:21,530
+هتكون قاعدة هنا في ال X Yالـ line and واحد واحد
+
+68
+00:05:21,530 --> 00:05:27,790
+يعني معناه الموازي بالـ x-axis هذا
+
+69
+00:05:27,790 --> 00:05:34,110
+الـ line of charge موازي بالـ x-axis الـ
+
+70
+00:05:34,110 --> 00:05:43,790
+charge density ρL تساوي اتنين نانو كولوم درهم
+
+71
+00:05:43,790 --> 00:05:49,110
+قالنا المعلومة ان ال reference point هنا بتساوي 0
+
+72
+00:05:49,900 --> 00:05:54,660
+عند الـ origin، عند الـ 000 ال reference point
+
+73
+00:05:54,660 --> 00:06:02,820
+وبدو ال potential عند X بتساوي 5Y0 و Z1 يعني وين
+
+74
+00:06:02,820 --> 00:06:07,620
+هتكون في ال X دي plane هاي النقطة اللي بتوع عندها
+
+75
+00:06:07,620 --> 00:06:13,960
+ال potential اللي
+
+76
+00:06:13,960 --> 00:06:16,880
+هي 501
+
+77
+00:06:21,420 --> 00:06:25,280
+أو بشكل عام اذا
+
+78
+00:06:25,280 --> 00:06:32,280
+انا
+
+79
+00:06:32,280 --> 00:06:38,620
+اول حاجة بتحسبها اللي هي الأبعاد بتاعة ال line و
+
+80
+00:06:38,620 --> 00:06:43,780
+بتاعة ال point عن نقطة اللي بتحسب عندها ال
+
+81
+00:06:43,780 --> 00:06:44,240
+potential
+
+82
+00:06:49,720 --> 00:06:52,040
+طبعا احنا ال potential عند اي نقطة في ال space في
+
+83
+00:06:52,040 --> 00:06:54,340
+هذه الحالة مش عند النقطة اللى انا بس بده احسب
+
+84
+00:06:54,340 --> 00:06:57,520
+عندها ال potential عند اي نقطة هتكون مجموعة two
+
+85
+00:06:57,520 --> 00:07:00,360
+potentials ال potential اللى جاى من ال point at
+
+86
+00:07:00,360 --> 00:07:03,140
+charge زاد ال potential اللى جاى من مين من line at
+
+87
+00:07:03,140 --> 00:07:05,680
+charge و احنا عارفين نحسب كيف كل واحد على حدى كيف
+
+88
+00:07:05,680 --> 00:07:08,220
+احسب ال potential اللى جاى من point at charge و
+
+89
+00:07:08,220 --> 00:07:10,840
+كيف احسب potential اللى من ال line
+
+90
+00:07:15,390 --> 00:07:18,090
+أحنا ال point of charge قلنا دي Q إيش بيساوي minus
+
+91
+00:07:18,090 --> 00:07:21,670
+ال integer ل A dot DL هو minus ال integer ل Q four
+
+92
+00:07:21,670 --> 00:07:26,070
+by epsilon dot R تبعيه R hat dot DR لR hat اللي هي
+
+93
+00:07:26,070 --> 00:07:29,330
+احنا اشتغلناها Q على four by epsilon dot R زائد C1
+
+94
+00:07:29,330 --> 00:07:33,830
+هسمي C1 لإن هيطلع لنا C2 من line of charge هذا ال
+
+95
+00:07:33,830 --> 00:07:36,750
+constant of integration قلنا اللي هو بنحسبه من ال
+
+96
+00:07:36,750 --> 00:07:39,690
+reference point من ما عرفتي وين ال reference يعني
+
+97
+00:07:39,690 --> 00:07:44,900
+وين ال zero voltage ماقدر أحسب ال constant هذالأ
+
+98
+00:07:44,900 --> 00:07:47,960
+اللى هى ال line charge هى انتيجة لإيده ال dl اللى
+
+99
+00:07:47,960 --> 00:07:54,500
+هى ال charge density دى raw اللى هو ال line على
+
+100
+00:07:54,500 --> 00:07:57,160
+طول ال line ال dl هى اللى هى على طول ال line دى
+
+101
+00:07:57,160 --> 00:08:01,040
+raw او دي ال يعنى لو بنسميها دى التغير على طول ال
+
+102
+00:08:01,040 --> 00:08:07,300
+line على two by epsilon not raw هتكون
+
+103
+00:08:07,300 --> 00:08:10,840
+raw L على two by epsilon not plus ال raw زائد CT
+
+104
+00:08:18,520 --> 00:08:25,000
+هنا نحسب قيم R ربط طبعا هذا ال total voltage total
+
+105
+00:08:25,000 --> 00:08:29,420
+electric voltage قول إن هو VQ زي VL هيكون Q على
+
+106
+00:08:29,420 --> 00:08:33,740
+four by epsilon ر زي C واحد بالنسبة لل electric
+
+107
+00:08:33,740 --> 00:08:40,510
+field إنها تجمن ال lineهيكون رو L minus رو L على
+
+108
+00:08:40,510 --> 00:08:44,130
+اتنين باي أبسل not blend الرو وعندنا ال C ال C ما
+
+109
+00:08:44,130 --> 00:08:47,850
+هو عندى constant C واحد و constant C تنين مجموعهم
+
+110
+00:08:47,850 --> 00:08:51,750
+constant هسميه C اللي انا هجيبه من وين من ال
+
+111
+00:08:51,750 --> 00:08:52,070
+reference
+
+112
+00:08:59,980 --> 00:09:03,240
+أحنا بناخد المثال أولاني لو اطالب مني لو انا عندي
+
+113
+00:09:03,240 --> 00:09:07,300
+ال reference voltage عند ال 0 واطالب عندي V عند 5
+
+114
+00:09:07,300 --> 00:09:13,960
+0 1 أول حاجة بدي أجيب قيم Raw وقيم Min R Raw بشكل
+
+115
+00:09:13,960 --> 00:09:18,600
+عام اللي هو انا عندي هاي line of chargeأى نقطة
+
+116
+00:09:18,600 --> 00:09:26,200
+تبعد عنه عن xyz هتكون ال absolute value لxyz-x11
+
+117
+00:09:26,200 --> 00:09:30,820
+لأنه عندي ثابت قيم ال y و ال z واحد واحد فأى نقطة
+
+118
+00:09:30,820 --> 00:09:34,480
+فى ال space xyz قيمة رؤش هتكون هي المسافة بين هى
+
+119
+00:09:34,480 --> 00:09:42,920
+النقطة و ال line xyz-x11يكون x-x هو zero فهي y-1
+
+120
+00:09:42,920 --> 00:09:47,400
+كل تربية زائد z-1 كل تربية تحت الجزرة هي كيمة raw
+
+121
+00:09:47,400 --> 00:09:51,180
+انا
+
+122
+00:09:51,180 --> 00:09:56,280
+بتحسب raw اللي هي بُعد ال origin عن ال line و برضه
+
+123
+00:09:56,280 --> 00:10:00,190
+raw بُعد النقطة اللي احسبها عن ال lineبعد ال
+
+124
+00:10:00,190 --> 00:10:05,590
+origin عن ال line هيكون 000-011 هتكون الجزر التانى
+
+125
+00:10:05,590 --> 00:10:10,090
+والنقطة اللى بتحسب عندها ال potential اللى هي 501
+
+126
+00:10:10,090 --> 00:10:13,310
+هتعطينى 1 ايش اللى بدى اعمله بدي اجيب ال potential
+
+127
+00:10:13,310 --> 00:10:16,530
+عند ال origin بدي اجيب ال potential عند النقطة
+
+128
+00:10:16,530 --> 00:10:20,230
+اللى بدى عندها ال potential ليش انا بدي ال
+
+129
+00:10:20,230 --> 00:10:23,290
+potential عند ال origin لإنه يعطينى معلومة عنه ايه
+
+130
+00:10:23,290 --> 00:10:26,450
+ال potential عند ال origin ايش بساوت 0 وهذا اللى
+
+131
+00:10:26,450 --> 00:10:31,130
+هساعدني ان اعرف قيمة ال constantعشان هي انا جبت ال
+
+132
+00:10:31,130 --> 00:10:34,410
+raw اللي هي بعض ال line عن ال origin و مرة تانية
+
+133
+00:10:34,410 --> 00:10:38,750
+ال raw اللي هي بعض ال line عن النقطة اللي بده ايس
+
+134
+00:10:38,750 --> 00:10:41,990
+عندها ال potential نفس الشيء ال raw node بعض ال
+
+135
+00:10:41,990 --> 00:10:44,990
+charge عن ال origin و بعض ال charge عن النقطة اللي
+
+136
+00:10:44,990 --> 00:10:49,010
+بده اجيب عندها ال potential و بتنحسب ببساطة قيمة
+
+137
+00:10:49,010 --> 00:10:51,550
+raw node و R node اللي هو زي ما قلنا بعض ال line
+
+138
+00:10:51,550 --> 00:10:57,790
+عن ال origin و ال raw A و ال R Aفقعدت و أخدته ال
+
+139
+00:10:57,790 --> 00:11:00,050
+line of charge كيف نجيب ال electric field اللي هو
+
+140
+00:11:00,050 --> 00:11:05,770
+باستخدامك او slope تاخده اللي هو contour حولانه
+
+141
+00:11:05,770 --> 00:11:11,510
+تمام بس ما علينا ان نكمل و نحصل على ال potential
+
+142
+00:11:14,750 --> 00:11:18,690
+عشان اجيب ال constant انا صرت عارفة بس بدي اعوض
+
+143
+00:11:18,690 --> 00:11:24,270
+فيها القيم عن هذه المعادلة مرتين بدي اعوض مرة ل V
+
+144
+00:11:24,270 --> 00:11:27,750
+عند النقطة اللى بدي احسب عندها ال potential و مرة
+
+145
+00:11:27,750 --> 00:11:30,990
+عند ال origin ال constant ماله بيظل constant بتفضل
+
+146
+00:11:30,990 --> 00:11:37,170
+نظر انا حسبت ال potential عند النقطة اللى 5 0 1 و
+
+147
+00:11:37,170 --> 00:11:39,590
+لا حسبت ال potential عند ال origin ال constant
+
+148
+00:11:39,590 --> 00:11:46,530
+constantفاللي هيتغير قيم ال raw و ال a raw L و Q
+
+149
+00:11:46,530 --> 00:11:49,590
+17 و ال two by epsilon node و هنا four by epsilon
+
+150
+00:11:49,590 --> 00:11:53,090
+node كلها أرقام احنا عارفينها بعوض مرة عن ال raw
+
+151
+00:11:53,090 --> 00:11:56,670
+node و R node و مرة تانية بحسب ال potential عند
+
+152
+00:11:56,670 --> 00:12:01,650
+النقطة اللي امديها يعني بحسب raw A و R A سيملها
+
+153
+00:12:01,650 --> 00:12:05,910
+بتظلها constant لإن هو مجرد constant رقم عشان أحسب
+
+154
+00:12:05,910 --> 00:12:12,180
+قيم ال potential عند النقطة المطلوبةماذا سأفعل؟
+
+155
+00:12:12,180 --> 00:12:17,300
+سأطرح الـ two potential من بعض V0 معنى ZE مين اللي
+
+156
+00:12:17,300 --> 00:12:20,000
+راح في هالحالة؟ ال constant اللي لمش لازمنيه
+
+157
+00:12:20,000 --> 00:12:24,540
+سأطرحهم من بعض و في عندي معلومة ان V0 ماله بسوء
+
+158
+00:12:24,540 --> 00:12:28,800
+Zero فعامض عن V0 بسوء Zero بحصل على قيمة ال
+
+159
+00:12:28,800 --> 00:12:33,960
+potential in ال A واضح الشي اللي عملناه؟ اذا عندي
+
+160
+00:12:33,960 --> 00:12:36,600
+line of charge وعندي point of charge هاي الأسئلة
+
+161
+00:12:36,600 --> 00:12:37,960
+اللي بتيجي في المتحنات المانعة
+
+162
+00:12:41,300 --> 00:12:45,760
+عندي معلومة غير عن اللي احنا شوفناه في المثال
+
+163
+00:12:45,760 --> 00:12:48,500
+الماضي انه عند ال infinity ال potential بيساوي 0
+
+164
+00:12:48,500 --> 00:12:52,240
+هنا ال reference point هي ال origin عند ال origin
+
+165
+00:12:52,240 --> 00:12:55,980
+عندي ال potential بيساوي 0 في اي نقطة في ال space
+
+166
+00:12:55,980 --> 00:12:58,400
+ان البوتنشال بيساوي مجموعة، البوتنشال اللي جاي من
+
+167
+00:12:58,400 --> 00:13:01,800
+ال charge زي البوتنشال اللي جاي من ال line charge
+
+168
+00:13:02,580 --> 00:13:05,060
+قيم ال potential جاية من ال charge معروف اللي هو q
+
+169
+00:13:05,060 --> 00:13:09,000
+على 4pi epsilon node R زائد some constant واللي
+
+170
+00:13:09,000 --> 00:13:11,100
+جاية من ال electric field ده كامل ال electric
+
+171
+00:13:11,100 --> 00:13:14,560
+field في dot dl بالنسبة لل line of charge وانتوا
+
+172
+00:13:14,560 --> 00:13:19,120
+جبتوها لل infinite line من جا عصله صحيح؟ تذكروا
+
+173
+00:13:19,120 --> 00:13:22,140
+عند أي نقطة حوالين ال line اللي بتساوي ال clause
+
+174
+00:13:22,140 --> 00:13:25,820
+integral أي dot dl بتساوي q enclosed على epsilon
+
+175
+00:13:25,820 --> 00:13:32,260
+node من جا عصلهبعد ما جيبنا ال potential عند ال
+
+176
+00:13:32,260 --> 00:13:34,820
+origin و ال potential عند النقطة a اللي هي انا بده
+
+177
+00:13:34,820 --> 00:13:37,500
+احسب انها potential باترحب من بعض بخلص من ميم ال
+
+178
+00:13:37,500 --> 00:13:41,060
+constant بعوض على V0 بساوة Zero بحصل على ال
+
+179
+00:13:41,060 --> 00:13:46,060
+potential عند النقطة a هنحاول
+
+180
+00:13:46,060 --> 00:13:50,300
+نربط اللي اتعلمناه عن ال electric field و
+
+181
+00:13:50,300 --> 00:13:54,430
+Maxwell's equationأول حاجة احنا قلنا ان ال
+
+182
+00:13:54,430 --> 00:13:57,730
+potential مايلوه time independent بعتمدش لا 6 ولا
+
+183
+00:13:57,730 --> 00:14:00,950
+5 المثال اللي اذا ذكرته من الحلقة الماضية قلنا ال
+
+184
+00:14:00,950 --> 00:14:04,650
+potential هو عبارة عن بعض independent بعتمدش على
+
+185
+00:14:04,650 --> 00:14:10,870
+المسار اللي بده يتاخذه أسوأ أخد المسار A ل B أو
+
+186
+00:14:10,870 --> 00:14:15,010
+المسار A ل B من هالماتجهة انسوا التجاه السامي
+
+187
+00:14:15,010 --> 00:14:17,470
+فلنفل أحكي عن التجاه السامي إذا أنا أخدت المسار
+
+188
+00:14:17,470 --> 00:14:20,370
+تبع A ل B هيك أو أخدت
+
+189
+00:14:25,400 --> 00:14:31,620
+فأخد المصار هنا أو المصار هنا أو المصار هنا مش
+
+190
+00:14:31,620 --> 00:14:34,880
+هيفرق معاها طريق path independent مايكمدش ال
+
+191
+00:14:34,880 --> 00:14:38,940
+integral تبع ال path او ال integral من a ل b مش
+
+192
+00:14:38,940 --> 00:14:43,720
+فارق عندي هذا ال integral من أي اتجاه جاي رايحت و
+
+193
+00:14:43,720 --> 00:14:48,020
+بعدين هيك مش فارقة الجواب دائما ثابت عشان هيك
+
+194
+00:14:48,020 --> 00:14:51,640
+بنسميه path independent مايكمدش علاء المصار تبع ال
+
+195
+00:14:51,640 --> 00:14:56,820
+integrationلو أخدته كك كك روحت على بي بتفرقش معاها
+
+196
+00:14:56,820 --> 00:14:59,800
+بعف independent ال integration بتبقى بعف
+
+197
+00:14:59,800 --> 00:15:05,980
+independent معناه
+
+198
+00:15:05,980 --> 00:15:10,800
+لو أنا أخدت طرح ال integration من مقطع a ل b و ال
+
+199
+00:15:10,800 --> 00:15:13,340
+integration من b ل a مش هيكون الجواب معلوم بس
+
+200
+00:15:13,340 --> 00:15:18,160
+إشارة سالبة بينهم لأنه بعف independent عكسته
+
+201
+00:15:18,160 --> 00:15:23,280
+حياتينا بس إشارة سالبةبما أن الـ Potential
+
+202
+00:15:23,280 --> 00:15:26,920
+difference بين أي نقطتين باص independent يعني لا
+
+203
+00:15:26,920 --> 00:15:29,920
+يتمدش على الباص سيكون الـ Potential ما بين الـ PA
+
+204
+00:15:29,920 --> 00:15:33,980
+سالب الـ Potential بين A و B و هدا احنا بنعرفه حتى
+
+205
+00:15:33,980 --> 00:15:39,160
+الدائرة أحسب الفرق الجهد بين النقطتين أعكس القراءة
+
+206
+00:15:39,160 --> 00:15:43,160
+بتعطيني إشارة سالبة لكن اذا قمّله بيبقى نفس الحاجة
+
+207
+00:15:43,160 --> 00:15:46,730
+نفس القيمةاذا معناه مجموعة دولة with two
+
+208
+00:15:46,730 --> 00:15:49,150
+potentials، يعني لو أنا خدت close boss، إيش معناه
+
+209
+00:15:49,150 --> 00:15:51,810
+مجموعة with two potentials دولة؟ لو أنا بدأت من
+
+210
+00:15:51,810 --> 00:15:58,370
+نقطة A، لو أنا بدأت من نقطة A، و جاءت عن نقطة A،
+
+211
+00:15:58,370 --> 00:16:01,470
+يعني بدأت من A ل B، و بعدين من B ل A، إيش هي
+
+212
+00:16:01,470 --> 00:16:05,650
+مجموعة ال potential؟ Zero، يعني واحد منهم قاعد
+
+213
+00:16:05,650 --> 00:16:08,590
+سؤال تاني، واحد خمسة، التاني ماقص خمسة، إذا مجموعة
+
+214
+00:16:08,590 --> 00:16:14,650
+ما هيصير؟ سفرإذا مجموع ال potential VBA زائد VAB
+
+215
+00:16:14,650 --> 00:16:18,510
+هو Zero وهذا ماذا يساوي ال potential؟ بيساوي ال
+
+216
+00:16:18,510 --> 00:16:23,990
+Integral من B لA لE ضد DL زاد ال Integral من A لB
+
+217
+00:16:23,990 --> 00:16:28,390
+E ضد DL هي مجموعة هذا ال Integral بيساوي ال
+
+218
+00:16:28,390 --> 00:16:36,170
+Integral من B لA E ضد DL وهذا التكامل من A لB E ضد
+
+219
+00:16:36,170 --> 00:16:43,340
+DL مجموعهم هيكون من B لA closed pathسكّه closed
+
+220
+00:16:43,340 --> 00:16:46,920
+boss بروح من نفس النقطة و برجعلها هيكل closed
+
+221
+00:16:46,920 --> 00:16:50,780
+integral لإيده ال dl إذا ال closed integral إيش
+
+222
+00:16:50,780 --> 00:16:54,100
+بيساوي؟ zero إحنا فعودنا إن هاي دوارة معناها
+
+223
+00:16:54,100 --> 00:16:59,060
+closed integral إذا ال closed integral لإيده ال dl
+
+224
+00:16:59,060 --> 00:17:02,940
+إيش بيساوي؟ zero بس إحنا أخدنا stock theorem
+
+225
+00:17:02,940 --> 00:17:06,140
+بتذاكرينها لما كنا بناخد ال mathematics في أول
+
+226
+00:17:06,140 --> 00:17:09,080
+شباتر بينا stock theorem بس إيش بتقولي ال closed
+
+227
+00:17:09,080 --> 00:17:14,970
+integral؟للـ line integral بساوي ال surface
+
+228
+00:17:14,970 --> 00:17:18,630
+integral ل curl ال field كنا ناخدها بشكل عام، أي
+
+229
+00:17:18,630 --> 00:17:22,290
+field نسميه A، قول ال line integral ل A dot D ..
+
+230
+00:17:22,290 --> 00:17:25,790
+ال closed line integral ل A dot DL بساوي ال
+
+231
+00:17:25,790 --> 00:17:29,170
+surface integral ل curl ال A dot DS، احنا هالأيه
+
+232
+00:17:29,170 --> 00:17:31,010
+تعرفين من ال field اللي بنحكي عنه؟ بنحكي عن ال
+
+233
+00:17:31,010 --> 00:17:34,970
+electric field، اذا ال closed integral ل A dot DL
+
+234
+00:17:34,970 --> 00:17:40,650
+بساويالـ Curl E ضد DS هذا ما يعني بيساوي Zero إذا
+
+235
+00:17:40,650 --> 00:17:43,890
+هذا ال Integral بيساوي Zero إذا ما أنا Curl E لأنه
+
+236
+00:17:43,890 --> 00:17:47,010
+DS أنا باخد عمال يعرف أنه باخد عينة من ال surface
+
+237
+00:17:47,010 --> 00:17:50,230
+من ال Zero متأكدة أنها عينة عند ال surface هذا
+
+238
+00:17:50,230 --> 00:17:54,570
+القدر و بقعد بدي DS اللي هي مثلا DX DY DZمش
+
+239
+00:17:54,570 --> 00:17:58,230
+محتاجها zero مين اللي لازم يساوي zero كيرل ال E
+
+240
+00:17:58,230 --> 00:18:01,710
+إذا كيرل ال E بيساوي zero حيشوفناها قبل هيك
+
+241
+00:18:01,710 --> 00:18:05,210
+متذاكرين إيش اللي معناه إنه أي potential الكيرل
+
+242
+00:18:05,210 --> 00:18:10,710
+تبعه بيساوي zero مانه ال rotational بلفش صح
+
+243
+00:18:10,710 --> 00:18:14,610
+متذاكرين؟ وال electric field إنه من أمثلة الناس
+
+244
+00:18:14,610 --> 00:18:18,250
+اللي مالها ال rotational بتلفش مالها إلها source
+
+245
+00:18:18,250 --> 00:18:22,690
+يا sink يا إيش emerge لكن بتلفش ال electric field
+
+246
+00:18:23,740 --> 00:18:28,580
+طبعا هذا max وال equation المعادلة اللي احنا
+
+247
+00:18:28,580 --> 00:18:33,140
+شوفناها قبل هي curl E بتساوي zero هاي هي بتكون
+
+248
+00:18:33,140 --> 00:18:38,200
+معاكم تاني max
+
+249
+00:18:38,200 --> 00:18:41,560
+وال equation لان اخدت diverge E بتساوي rho على
+
+250
+00:18:41,560 --> 00:18:47,520
+epsilon first max وال equation صحيح؟ و هاي تاني
+
+251
+00:18:47,520 --> 00:18:47,920
+واحدة
+
+252
+00:18:52,700 --> 00:18:56,860
+مش كمان احنا ممكن نوصل من تعريف ال potential ال
+
+253
+00:18:56,860 --> 00:18:59,740
+potential ان هو عبارة عن minus ال integral ل E dot
+
+254
+00:18:59,740 --> 00:19:02,780
+DL انا يعني احملت ال minus لما اعملت عشان اخد ال
+
+255
+00:19:02,780 --> 00:19:06,900
+clause integral بس يعني انتوا تاخدوه بالانتباه انا
+
+256
+00:19:06,900 --> 00:19:09,620
+كانت الفكرة ان افرجيكوا ان ال integral ل E dot DL
+
+257
+00:19:09,620 --> 00:19:12,460
+زي ال integral ل E dot DL بيعطيني ال clause boss
+
+258
+00:19:12,460 --> 00:19:15,100
+بس في minus برا و zero مش فارقة يعني
+
+259
+00:19:26,670 --> 00:19:30,270
+DV بيكون DV بيكون minus E dot DL
+
+260
+00:19:33,200 --> 00:19:35,800
+طب هد إيش معناها؟ هد دُت ال product بين vector
+
+261
+00:19:35,800 --> 00:19:38,640
+field و DL و DL ماحنا عارفينها مثلا من ال
+
+262
+00:19:38,640 --> 00:19:42,680
+Cartesian إيش اللي بيساوي DL؟ DX X hat, DY Y hat,
+
+263
+00:19:43,020 --> 00:19:47,880
+DZ Z hat و E هد field، vector يعني عمّا دربته بEX
+
+264
+00:19:47,880 --> 00:19:52,620
+X hat زي EY Y hat زي EZ Z hat إذا دُت ال product
+
+265
+00:19:52,620 --> 00:20:02,470
+مش هيحطيني EX DX EY DY EZ DZ معين؟طب كمان dv هي دي
+
+266
+00:20:02,470 --> 00:20:05,070
+ما قالها total differential و ال total
+
+267
+00:20:05,070 --> 00:20:08,910
+differential بتلاقي ال partial differential اللي
+
+268
+00:20:08,910 --> 00:20:15,950
+هي dv by dx dx ذات dv by dy dy ذات dv by dz dz في
+
+269
+00:20:15,950 --> 00:20:19,570
+حد عنده مشكلة في هاي ال total differential؟لو أنا
+
+270
+00:20:19,570 --> 00:20:23,030
+قرنت المعادلتين مع بعض إيش بلاحظ إنه EX إيش بتساوي
+
+271
+00:20:23,030 --> 00:20:29,970
+minus dV by dx EY إيش بتساوي minus dV by dy EZ إيش
+
+272
+00:20:29,970 --> 00:20:34,510
+بتساوي minus dV by dz لو طلعت على هذه المعادلة إيش
+
+273
+00:20:34,510 --> 00:20:37,290
+بتقولّي إن في عندي X component لل electric field
+
+274
+00:20:37,290 --> 00:20:41,650
+بتساوي minus dV by dx وعندي Y component بتساوي
+
+275
+00:20:41,650 --> 00:20:46,070
+minus dV by dy و Z component بتساوي minus dV by dz
+
+276
+00:20:49,620 --> 00:20:58,680
+-dv by dx x hat-dv by dy y hat فdv
+
+277
+00:20:58,680 --> 00:21:03,840
+by dz زدها
+
+278
+00:21:03,840 --> 00:21:12,520
+قريبة ساوية-d by dx x hat-d by dy y hat-d by dz
+
+279
+00:21:13,170 --> 00:21:17,950
+زدها مالها مأثرة على مين على مين وهذه مين تعريفها
+
+280
+00:21:17,950 --> 00:21:20,810
+في ال partition coordinate اللي هي الدل هتكون هذه
+
+281
+00:21:20,810 --> 00:21:28,810
+minus فبحث عن minus هنا هذا
+
+282
+00:21:28,810 --> 00:21:33,850
+بالتامة اللي هو الدل هتكون minus del V منطقي ان
+
+283
+00:21:33,850 --> 00:21:38,270
+تكون E بتساول minus del V ليش منطقي ليش E لازم
+
+284
+00:21:38,270 --> 00:21:43,430
+تكون minus gradient لبطن شرالشهدة اللى طلع لنا اشي
+
+285
+00:21:43,430 --> 00:21:49,470
+متوقع مش اشي مش متوقع ال potential بساوة ال
+
+286
+00:21:49,470 --> 00:21:56,210
+integral زائد حاجة تانية مادام ان ال potential هو
+
+287
+00:21:56,210 --> 00:22:00,510
+ال integral ايه لل DL هو احنا اشتقناها من هنا صح
+
+288
+00:22:00,510 --> 00:22:05,630
+اشتقناها من هنا وصلنا انه ايه بساوة ما نذكرت فيه
+
+289
+00:22:05,630 --> 00:22:09,210
+اش هاي المعادلة المنطقية من اللى أخدناها من
+
+290
+00:22:09,210 --> 00:22:14,780
+الشباتر قبل ما انا اغيب عنكماي معلومة أخدناها كارل
+
+291
+00:22:14,780 --> 00:22:22,200
+الدل ايش بيساوي انا سميفه عشان احنا قدرنا اخدناهم
+
+292
+00:22:22,200 --> 00:22:27,500
+ايش بيساوي كارل الدل ايش كارل الدل بيساوي zero
+
+293
+00:22:27,500 --> 00:22:33,560
+كارل الدل بيساوي zero الله عليكم طب مش خايفين احنا
+
+294
+00:22:33,560 --> 00:22:37,440
+قلنا كارل دي ماله تقوى لسه في ال study السادقة ايش
+
+295
+00:22:37,440 --> 00:22:41,980
+بيساوي كارل دي ايه zero ايش ماله الكتير كتيرالـ
+
+296
+00:22:41,980 --> 00:22:47,260
+rotational كان الـ E بساوي 0 وعناه أن E لازم يكون
+
+297
+00:22:47,260 --> 00:22:51,660
+gradient ل scalar potential لأن كان ال gradient ل
+
+298
+00:22:51,660 --> 00:22:59,260
+scalar potential بساوي 0، واضح؟ فاهموني
+
+299
+00:22:59,260 --> 00:23:03,980
+هي كيف بتدرسوا، ماطفوا ساكتين يعني، ماشعورين بقلب
+
+300
+00:23:03,980 --> 00:23:04,240
+يعني
+
+301
+00:23:13,890 --> 00:23:17,210
+هذا احنا حكيناه ان اذا انا ايه بيساوى minus ال
+
+302
+00:23:17,210 --> 00:23:20,950
+grade لـ scalar potential لانه صعب ان نفكر ان ال
+
+303
+00:23:20,950 --> 00:23:25,290
+gradient بيساوي zero اذا معناه ان هذا كلمة مرة
+
+304
+00:23:25,290 --> 00:23:28,230
+باكد لنا ان ال electric field هو نقل روتيشنال
+
+305
+00:23:28,230 --> 00:23:32,250
+بيساوي minus ال gradient لpotential طب احنا اول
+
+306
+00:23:32,250 --> 00:23:34,370
+متذكرين ما بدنا بنحكي عن ال potential قلنا ان ال
+
+307
+00:23:34,370 --> 00:23:37,650
+electric field هو درجيبه من تلات جهات يا من
+
+308
+00:23:37,650 --> 00:23:42,380
+columns lawيا من gauss law يا من ال potential يعني
+
+309
+00:23:42,380 --> 00:23:45,120
+إذا كنت عارفة ال potential أنا فقدر أجيب ال
+
+310
+00:23:45,120 --> 00:23:46,800
+electric field لإنه صرت عارفة إيه إيه إيه إيه إيه
+
+311
+00:23:46,800 --> 00:23:48,560
+إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه
+
+312
+00:23:48,560 --> 00:23:48,760
+إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه
+
+313
+00:23:48,760 --> 00:23:49,040
+إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه
+
+314
+00:23:49,040 --> 00:23:52,000
+إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه إيه
+
+315
+00:23:52,000 --> 00:24:01,140
+إيه إيه إيه إيه إيه إيه إيه
+
+316
+00:24:01,140 --> 00:24:05,400
+إي
+
+317
+00:24:09,680 --> 00:24:13,120
+باي على اتنين او زيرو هذا ايش نوع ال coordinate؟
+
+318
+00:24:13,120 --> 00:24:21,500
+spherical coordinate عند θ وفاي فعندى كيمة r وθ
+
+319
+00:24:21,500 --> 00:24:26,640
+وفاي كمان بده اني بعد ما اجيب دى calculate the
+
+320
+00:24:26,640 --> 00:24:30,200
+work done in moving a ten micro column which are
+
+321
+00:24:30,200 --> 00:24:35,280
+from النقطة a ونقطة b يعني اول حاجة بده دىطبعا دي
+
+322
+00:24:35,280 --> 00:24:38,020
+سمع في المهم ان اجيبها اقول ان اجيب E احنا لسه
+
+323
+00:24:38,020 --> 00:24:41,360
+طولنا E بقدر اجيبها مهم ال potential يعني E بقدر
+
+324
+00:24:41,360 --> 00:24:45,100
+اقول انها minus grade V بجيب E وD ماهي الا epsilon
+
+325
+00:24:45,100 --> 00:24:50,780
+times E فا epsilon not times E بجيب D الجزء التاني
+
+326
+00:24:50,780 --> 00:24:55,640
+بدو ال work اللي احتاجه عشان ينقل ال charge معينة
+
+327
+00:24:55,640 --> 00:24:59,260
+قيمتها عشرة micro column من نقطة في ال space هذا
+
+328
+00:24:59,260 --> 00:25:00,680
+اللي هو فيه electric field
+
+329
+00:25:09,920 --> 00:25:15,020
+نبدأ بالجزء الأول يعنيأيه قلنا دي بتساوي epsilon
+
+330
+00:25:15,020 --> 00:25:20,140
+node E وانت هجيب E يقولنا minus دل ال V بس هستخدم
+
+331
+00:25:20,140 --> 00:25:24,400
+مين ال spherical coordinate مش حاجة غصب عنها
+
+332
+00:25:24,400 --> 00:25:27,300
+أستخدم ال Cartesian coordinate أنا بتعود على D by
+
+333
+00:25:27,300 --> 00:25:30,520
+D X X hat زي D by D Y Y hat زي D by D Z Z hat
+
+334
+00:25:30,520 --> 00:25:34,800
+ماتبتش أحفظش تاني فبدأت أحول ال V من sin θ أو cos
+
+335
+00:25:34,800 --> 00:25:38,560
+φ ل X Y Z بتفرق بضيع وقت كتير في الامتحان الأسهل
+
+336
+00:25:38,560 --> 00:25:41,360
+أكون عارفة دل بي ال spherical coordinate
+
+337
+00:25:43,930 --> 00:25:49,250
+مناس بالم ال V اللي هي مناس مفتاح القوس D V by D R
+
+338
+00:25:49,250 --> 00:25:53,650
+R Hat زاد واحد على R D V by D Theta Theta Hat زاد
+
+339
+00:25:53,650 --> 00:25:58,370
+واحد على R Sine Theta D V by D Phi Phi Hat معايا
+
+340
+00:25:58,370 --> 00:26:03,450
+دعود بال V بدا فرض بالنسبة ل R إيش هتعطيني minus
+
+341
+00:26:03,450 --> 00:26:09,120
+عشرين على R cube Sine Theta Cosine Phi معاياطب
+
+342
+00:26:09,120 --> 00:26:13,320
+بالنسبة ل θ في عندي 1 على R 10 على R تربيه و 1 على
+
+343
+00:26:13,320 --> 00:26:17,340
+R تصير 10 على R cube التفاضى بالنسبة ل sin sin إيش
+
+344
+00:26:17,340 --> 00:26:22,840
+بتصير cos في cos ف؟ 1 على R sin θ يعني هتصير 10
+
+345
+00:26:22,840 --> 00:26:26,300
+على R cube sin θ بالنسبة ل فيه cos فإيش بتصير
+
+346
+00:26:26,300 --> 00:26:31,460
+minus sin ف؟ تمام، إذا هي عند ال electric field،
+
+347
+00:26:31,460 --> 00:26:36,370
+ببساطة لأن أنا عارفة ال potentialلأ هنا عرفت قيم
+
+348
+00:26:36,370 --> 00:26:38,830
+الـ charges و لا نوع من أنواع الـ distribution
+
+349
+00:26:38,830 --> 00:26:42,810
+عشان أقول أني بدي أجيبه من columns ولا من gauss
+
+350
+00:26:42,810 --> 00:26:45,690
+هنا الحل الوحيد أو الطريقة الوحيدة أني أجيبه من
+
+351
+00:26:45,690 --> 00:26:48,410
+وين من خلال ال potential لأنه ماعطيني ال potential
+
+352
+00:26:48,410 --> 00:26:52,870
+طب بده يعني نقطة معينة أول حاجة بدي أجيبه ال D ال
+
+353
+00:26:52,870 --> 00:26:57,090
+D اللي بدي أقوله هي epsilon not في E و أعوض على
+
+354
+00:26:57,090 --> 00:27:02,090
+النقطة R2 theta Pi على 2 و Phi بتساوي 0
+
+355
+00:27:04,860 --> 00:27:08,340
+بحصل على قيمة اللي هو دي اللي هو طلبها في الجزء
+
+356
+00:27:08,340 --> 00:27:13,100
+الأولاني هل الطلب دو ال work؟ الجزء التاني من
+
+357
+00:27:13,100 --> 00:27:15,480
+السؤال بده ال work
+
+358
+00:27:19,790 --> 00:27:22,770
+عندي طريقتين ان احسب ال work اول طريقة اللى
+
+359
+00:27:22,770 --> 00:27:26,310
+تعلمناها قبل قليل هي minus q ال integral ل E ضد DL
+
+360
+00:27:26,310 --> 00:27:30,490
+لمنها اشتقنا ال potential ال work هو minus q ال
+
+361
+00:27:30,490 --> 00:27:34,030
+integral ل E ضد DL اللى قولنا ماله من وين جيبناها
+
+362
+00:27:34,030 --> 00:27:37,490
+احنا من ال integral ل F ضد DL minus ال integral ل
+
+363
+00:27:37,490 --> 00:27:41,610
+F ضد DL minus
+
+364
+00:27:41,610 --> 00:27:45,970
+w على q بتسوي ال integral ل E ضد DL طب انا عندي من
+
+365
+00:27:45,970 --> 00:27:52,200
+وين بده ينقل من عندي خليني رجع نشوفاللي عندها R
+
+366
+00:27:52,200 --> 00:27:58,770
+تلاتين R واحد ستة تلاتين و طالع مائة و عشرينلنقطة
+
+367
+00:27:58,770 --> 00:28:04,030
+تانية في ال space اللى فيها R تغيرت من 1 ل 4 و θ
+
+368
+00:28:04,030 --> 00:28:08,210
+تغيرت يعني لو كنت اخد ال bus انا بدي عندى فى ..
+
+369
+00:28:08,210 --> 00:28:13,670
+اكيد فى عندى DR و فى عندى تغير فى θ Dθ و فى عندى
+
+370
+00:28:13,670 --> 00:28:17,810
+bus اللى فى تغير فى D5 عندى ال three buses احنا ال
+
+371
+00:28:17,810 --> 00:28:20,510
+buses في ال spherical coordinate كنت مذاكرينهم لما
+
+372
+00:28:20,510 --> 00:28:25,190
+R بتتغير ايش بيكون عندى على طول ال spherical DRلما
+
+373
+00:28:25,190 --> 00:28:29,030
+set تتغير ايش قلنا R دي ثتا لما five تتغير ايش
+
+374
+00:28:29,030 --> 00:28:34,670
+قلنا R sin theta دي five انا
+
+375
+00:28:34,670 --> 00:28:39,790
+تلت تغيرات طب احنا قولنا ان هذا ال work هتبع لما
+
+376
+00:28:39,790 --> 00:28:45,940
+اللغة تبندن لو انا بدي اخد التلت تغيراتأنا مش
+
+377
+00:28:45,940 --> 00:28:48,820
+قادرة كيف بدي أتخيلهم بدي أعمل التلات تغيرات مرة
+
+378
+00:28:48,820 --> 00:28:52,120
+واحدة بدي أغير ال R و أغير ال theta و أغير ال five
+
+379
+00:28:52,120 --> 00:28:56,360
+نفس الوقت و كامل اللي هي التلات انتجرالات كيف بدي
+
+380
+00:28:56,360 --> 00:29:00,080
+أغيرهم مرة واحدة فما أن هو boss independent إيش
+
+381
+00:29:00,080 --> 00:29:04,200
+هاخد boss صح شويه أطول بس هاخد boss اللي ما له
+
+382
+00:29:04,200 --> 00:29:08,040
+واحد واحد منهم بتغير يعني أول حاجة هنتقل من النقطة
+
+383
+00:29:08,040 --> 00:29:13,620
+A اللي عندها R واحد و theta تلاتين و مية وعشرين
+
+384
+00:29:17,700 --> 00:29:22,300
+وهي النقطة الأولى اللى هى A أقع النقطة A على مين؟
+
+385
+00:29:22,300 --> 00:29:31,340
+على 1 و 30 درجة و Phi إقدارها 120 درجة أول حاجة
+
+386
+00:29:31,340 --> 00:29:35,340
+هروح أخد ال Integra من هذه النقطة على طول لحد
+
+387
+00:29:35,340 --> 00:29:41,600
+ماوصل اللى هى A' اللى عندها اتغير R من 1 ل 4 و 30
+
+388
+00:29:41,600 --> 00:29:48,700
+درجة و 120 درجةبعدين هنتقل من النقطة A' لنقطة B'
+
+389
+00:29:49,020 --> 00:29:55,760
+اللي تغير فيها θ من 30 درجة ل 90 درجة أحنا قلنا
+
+390
+00:29:55,760 --> 00:30:01,260
+تبدأ من المفروض خطة هات من 0 ل 90، صح؟ بس هتهيأت،
+
+391
+00:30:01,260 --> 00:30:06,920
+بس هاي
+
+392
+00:30:06,920 --> 00:30:13,260
+النقطة اللي هي B' اللي عندها هيكون التغير 490
+
+393
+00:30:15,010 --> 00:30:21,710
+بس تسعين هي هتكون هيك هي هتكون هيك هي تلاتين
+
+394
+00:30:21,710 --> 00:30:31,850
+تلاتين تلاتين تلاتين تلاتين تلاتين تلاتين تلاتين
+
+395
+00:30:31,850 --> 00:30:38,430
+تلاتين تلاتين تلاتين تلاتين تلاتين
+
+396
+00:30:38,430 --> 00:30:39,690
+تلاتين تلاتين تلاتين تلاتين تلاتين تلاتين تلاتين
+
+397
+00:30:39,690 --> 00:30:40,230
+تلاتين تلاتين تلاتين تلاتين تلاتين تلاتين تلاتين
+
+398
+00:30:40,230 --> 00:30:40,290
+تلاتين تلاتين تلاتين تلاتين تلاتين تلاتين تلاتين
+
+399
+00:30:40,290 --> 00:30:40,310
+تلاتين تلاتين تلاتين تلاتين تلاتين تلاتين تلاتين
+
+400
+00:30:40,310 --> 00:30:41,410
+تلاتين تلاتين تلاتين تلاتين تلاتين تلاتين تلاتين
+
+401
+00:30:41,410 --> 00:30:45,780
+تلاتين تلاتين تلاتين تعشان انا المفروض التالتين
+
+402
+00:30:45,780 --> 00:30:49,260
+اخدها انا هى اللى بحكي هى ال theta عشان اللى
+
+403
+00:30:49,260 --> 00:30:54,080
+اظهرتها و هى اللى هتكون على ال axis هذا انا عشان
+
+404
+00:30:54,080 --> 00:31:01,080
+اخد الصورة هى هذه هي تلاتين درجة وهى النقطة A اللى
+
+405
+00:31:01,080 --> 00:31:08,520
+هى واحد تلاتين درجة ومية وعشرين درجة فعى مية
+
+406
+00:31:08,520 --> 00:31:11,840
+وعشرين يعني برضه كتره فعى يعني هتكون مية وعشرين هى
+
+407
+00:31:11,840 --> 00:31:16,760
+فعى كده من هنا يعني تخيلوهاعند ال 120 اه تتخيل ال
+
+408
+00:31:16,760 --> 00:31:20,400
+axis كلهم يعني لو هد أسقطناها ستسقطها بقى في الربع
+
+409
+00:31:20,400 --> 00:31:28,680
+120 درجة فلت انتقلنا قولنا لنخلي هد أربعة تروح من
+
+410
+00:31:28,680 --> 00:31:32,660
+واحد لأربعة ليه A prime A prime اللي هو اربعة
+
+411
+00:31:32,660 --> 00:31:40,350
+تلاتين درجة ومية وعشرين درجة بعدين هنزلبقى النقطة
+
+412
+00:31:40,350 --> 00:31:43,630
+اللى عندها setup تساوي 90 هذه عندنا اقعد ضالة
+
+413
+00:31:43,630 --> 00:31:44,810
+تسابق تسابق تسابق تسابق تسابق تسابق تسابق تسابق
+
+414
+00:31:44,810 --> 00:31:47,950
+تسابق تسابق تسابق تسابق تسابق تسابق تسابق تسابق
+
+415
+00:31:47,950 --> 00:31:48,390
+تسابق تسابق تسابق تسابق تسابق تسابق تسابق تسابق
+
+416
+00:31:48,390 --> 00:31:48,410
+تسابق تسابق تسابق تسابق تسابق تسابق تسابق تسابق
+
+417
+00:31:48,410 --> 00:31:48,650
+تسابق تسابق تسابق تسابق تسابق تسابق تسابق تسابق
+
+418
+00:31:48,650 --> 00:31:49,730
+تسابق تسابق تسابق تسابق تسابق تسابق تسابق تسابق
+
+419
+00:31:49,730 --> 00:32:04,310
+تسابق تساب
+
+420
+00:32:04,850 --> 00:32:08,950
+هذه عنا R أربعة ضلت و مين اللي اتغير عندى ال ستة
+
+421
+00:32:08,950 --> 00:32:16,230
+صارت 90 درجة وضلت الفا 120 درجة الفا احنا بنحسبها
+
+422
+00:32:16,230 --> 00:32:25,270
+لل X عندى لحد 120 درجة فهي 120 درجة اذا
+
+423
+00:32:25,270 --> 00:32:29,690
+متقلنا من A prime ل B prime اخر واحدة اللي بيبدو
+
+424
+00:32:29,690 --> 00:32:40,860
+انه لحد الستينيعني نبدأ جهة على الـ Phi اللي
+
+425
+00:32:40,860 --> 00:32:48,460
+هي نقطة الأخيرة اللي عندها هيكون 94 درجة و 60 درجة
+
+426
+00:32:48,460 --> 00:32:53,600
+تمام؟ واضحة الصورة؟ هذا ال basis اللي انا هاخده
+
+427
+00:32:53,600 --> 00:32:56,300
+ليش هاخد هيك ال basis؟ لإن هذا ال basis هيكون عند
+
+428
+00:32:56,300 --> 00:33:03,150
+ال DL تغير من هنا لهنا هيكون بتساوي DRالتغيير من
+
+429
+00:33:03,150 --> 00:33:08,110
+هنا إلى هنا ايش هيكون R Dθ وهنا ايش هيكون التغيير
+
+430
+00:33:08,110 --> 00:33:10,890
+R Sine Theta
+
+431
+00:33:16,210 --> 00:33:19,610
+واضحة النقطة هى؟ اذا بدل ما انا اخدهم كلهم مرة
+
+432
+00:33:19,610 --> 00:33:23,570
+واحدة تغيرات بل انا باخدهم واحدة واحدة line line
+
+433
+00:33:23,570 --> 00:33:28,830
+وانا عارفة انه لانه التكاوم من a لb باصن
+
+434
+00:33:28,830 --> 00:33:31,450
+independent فانا بقدر اقول من a ل a prime من a
+
+435
+00:33:31,450 --> 00:33:34,870
+prime ل b prime و b prime ل b اللى هى النقطة اللى
+
+436
+00:33:34,870 --> 00:33:39,150
+انا بدي احسب عندها ال work نيجي مع بعض نحسب هذا
+
+437
+00:33:39,150 --> 00:33:39,610
+الحكيم
+
+438
+00:33:43,770 --> 00:33:48,310
+زي ما انتوا شايفين هبدأ من A اللي عندها R واحد ستة
+
+439
+00:33:48,310 --> 00:33:53,390
+تلاتين ومية وعشرين ل A prime اللي اتغير فيها R
+
+440
+00:33:53,390 --> 00:33:57,610
+لاربع ستة ضلت سابتة و five سابتة هيك أسهل التكامل
+
+441
+00:33:57,610 --> 00:34:01,270
+لما أسبب اتنين و أغير واحد أسهل من ان اخل ال تلاتة
+
+442
+00:34:01,270 --> 00:34:05,610
+متغيرين و دي L إيش هتكون في هذه الحالة دي R R hat
+
+443
+00:34:06,630 --> 00:34:09,610
+لما اجى اتغير من a prime ل b prime انا مين غيرتها
+
+444
+00:34:09,610 --> 00:34:13,610
+لقيتها ال theta خلتها بتروح من تلاتين ل تسعين R
+
+445
+00:34:13,610 --> 00:34:16,050
+ضلت ثابتة على أربع و Phi ضلت ثابتة على مائة و
+
+446
+00:34:16,050 --> 00:34:21,950
+عشرين قيمة ال DL بتساوي R D theta ثتا hat اخر حاجة
+
+447
+00:34:21,950 --> 00:34:26,350
+اللي هي اخلي ال R ثتا و Theta ثابتة و اغير الفاعل
+
+448
+00:34:26,350 --> 00:34:30,250
+من مائة و عشرين لستين هتكون DL بتساوي R sine theta
+
+449
+00:34:30,250 --> 00:34:35,330
+D Phi Phi hatإذا صار لي التكامل ما لو قسمته ل 3
+
+450
+00:34:35,330 --> 00:34:40,550
+integrals من a ل a' زائد ال integral من a' ل b'
+
+451
+00:34:40,990 --> 00:34:45,710
+زائد ال integral من b' ل b، في أي حاجة مش واضحة
+
+452
+00:34:45,710 --> 00:34:52,050
+لحد هنا؟مش واضح؟ إذا عندي (-w على cube)(-1 على
+
+453
+00:34:52,050 --> 00:34:55,510
+cube تكمل من a ل a prime أو يعني ال work من a ل a
+
+454
+00:34:55,510 --> 00:34:57,990
+prime زاد ال work من a prime ل b prime زاد ال work
+
+455
+00:34:57,990 --> 00:35:00,830
+من b prime ل b prime اللي هو عبارة عن ال integrant
+
+456
+00:35:00,830 --> 00:35:03,250
+من a ل a prime زاد ال integrant من a prime ل b
+
+457
+00:35:03,250 --> 00:35:05,510
+prime زاد ال integrant من b prime ل b prime إلى e
+
+458
+00:35:05,510 --> 00:35:11,390
+dot dl اي ما احنا حسبناها مع بعض يعرفينهابنعوض في
+
+459
+00:35:11,390 --> 00:35:15,330
+المعادلة و أعمل نتيجة اذا رجعنا ل E بتعوض طبعا لما
+
+460
+00:35:15,330 --> 00:35:20,170
+أسفت ال D ال theta و ال five بتعوض عنه مباشرة و
+
+461
+00:35:20,170 --> 00:35:22,750
+أخل مين فقط اللي هو ال R المتغير
+
+462
+00:35:30,100 --> 00:35:35,060
+بعود انا و بحط قيام ال theta و ال phi في قلب ال
+
+463
+00:35:35,060 --> 00:35:39,300
+integrals كلهم فعند ال integrant من R1 ل R4 20 sin
+
+464
+00:35:39,300 --> 00:35:44,500
+theta cos phi R cubed DR theta 30 و phi 20 التكامل
+
+465
+00:35:44,500 --> 00:35:50,010
+التاني مين هيسبب ال RI ستثبت على أربعة وفاي على
+
+466
+00:35:50,010 --> 00:35:53,890
+مائة وعشرين ومن يتغير هو الـθيتا والإنتجر الأخير
+
+467
+00:35:53,890 --> 00:35:57,810
+فايل سيتغير من مائة وعشرين لستين وحسبته الـR
+
+468
+00:35:57,810 --> 00:36:02,450
+والثيتا إذا عملنا هك بنحصل على قيمة ماينسة W على Q
+
+469
+00:36:02,450 --> 00:36:07,490
+وبحصل
+
+470
+00:36:07,490 --> 00:36:13,820
+على W بمجرد أن أعود عن EQ تمام هذه أول طريقةلكن هو
+
+471
+00:36:13,820 --> 00:36:19,320
+مش محدد عليا طريقة إن كيف أستخدم وحسن اللي هو كل
+
+472
+00:36:19,320 --> 00:36:23,660
+طلبه في السؤال ستتذكرواالـ work done in moving
+
+473
+00:36:23,660 --> 00:36:31,680
+الهدف من الـ Integra
+
+474
+00:36:31,680 --> 00:36:36,420
+هدف من ال Integra هدف من ال Integra هدف من ال
+
+475
+00:36:36,420 --> 00:36:42,080
+Integra هدف من ال Integra هدف من ال Integra هدف من
+
+476
+00:36:42,080 --> 00:36:44,250
+ال Integra هدف من ال Integra هدف من ال Integraعارف
+
+477
+00:36:44,250 --> 00:36:46,350
+ال potential بين النقطة التي هو لأنه عارف ال
+
+478
+00:36:46,350 --> 00:36:49,230
+potential في أي نقطة في ال space إذا عارف ال
+
+479
+00:36:49,230 --> 00:36:51,390
+potential في أي نقطة في ال space بقدر أجيبه في
+
+480
+00:36:51,390 --> 00:36:58,490
+نقطة محددة و الواقع عبارة عن ماله QVB-VA لأنه
+
+481
+00:36:58,490 --> 00:37:02,050
+عبارة عن minus Q ال Integra من A لB E ضد DL اللي
+
+482
+00:37:02,050 --> 00:37:03,990
+هو عبارة عن QVAB
+
+483
+00:37:05,760 --> 00:37:09,160
+لأن ماينوس انتيجرال من A ل B E ضد L هو ال
+
+484
+00:37:09,160 --> 00:37:14,040
+potential ما بين النقطة A و B يعني هيكون ال Q VB-
+
+485
+00:37:14,040 --> 00:37:19,760
+VA قولنا دايما هذا ناقص هذا VAB هيبتسوق VB- VA
+
+486
+00:37:22,260 --> 00:37:27,120
+عند ال potential بعود عن قيمة النقطة B و عن قيمة
+
+487
+00:37:27,120 --> 00:37:30,980
+النقطة A بحصل على نفس الجواب طبعا هاي الطريقة أسهل
+
+488
+00:37:30,980 --> 00:37:35,060
+بكتير بالذات انه انا مواطئل ال potential مش زي ال
+
+489
+00:37:35,060 --> 00:37:37,820
+electric field انا حسبته ممكن انا اخطر في حساب ال
+
+490
+00:37:37,820 --> 00:37:40,440
+electric field لكن مش متشرط عليا ان استخدم اي
+
+491
+00:37:40,440 --> 00:37:44,980
+طريقة بحسب ال work من ال potential مباشرة بحسبهاش
+
+492
+00:37:44,980 --> 00:37:47,780
+من ال electric fieldو بالذات ان شفتوا طريقة ال
+
+493
+00:37:47,780 --> 00:37:50,860
+electric field مالها طويلة شوية، بدى أقعدة كامل
+
+494
+00:37:50,860 --> 00:37:55,280
+على ال three buses عشان أحصر على ال work في عيسى
+
+495
+00:37:55,280 --> 00:37:59,860
+افسار لحد هنا نيجي لحاجة اسمها ال electric diaper
+
+496
+00:37:59,860 --> 00:38:03,600
+and flux lines إيش هو ال electric diaper؟ ال
+
+497
+00:38:03,600 --> 00:38:06,560
+diaper أكيد مرعت عليكم كلمة diaper ال diaper يعني
+
+498
+00:38:06,560 --> 00:38:09,540
+لما يكون عندى two charges plus و minus فيبقى البعض
+
+499
+00:38:09,540 --> 00:38:13,420
+زي قطرة الميه، لما تكون تحت ال electric field،
+
+500
+00:38:13,420 --> 00:38:19,620
+بتلاقوا هنا بيصير الشحنة موجةالدايبول يعني عندى
+
+501
+00:38:19,620 --> 00:38:24,720
+فيه two charges اللى هم opposite sign وما اللى هم
+
+502
+00:38:24,720 --> 00:38:29,200
+قراه بكتير من بعض يعني المسافة بينهم صغيرة يعني
+
+503
+00:38:29,200 --> 00:38:32,280
+مرة اللى كتب دايبول هو عبارة عن two point charges
+
+504
+00:38:32,280 --> 00:38:36,520
+اللى هم opposite sign و المسافة بينهم صغيرة كتير
+
+505
+00:38:44,160 --> 00:38:46,700
+دعوني أريكم الصورة تاعتهم هاي الـ dipole هاي عندي
+
+506
+00:38:46,700 --> 00:38:51,700
+XYZ عندي two charges plus و minus ال Q والمسافة
+
+507
+00:38:51,700 --> 00:38:56,040
+بينهم D بتكون صغيرة كتير هذا الـ electric dipole
+
+508
+00:38:56,040 --> 00:38:59,460
+لو أنا بده أحسب potential مثلا للنقطة B الناتجة عن
+
+509
+00:38:59,460 --> 00:39:01,660
+ال dipole يعني صار المفهوم إنها ال dipole ال
+
+510
+00:39:01,660 --> 00:39:04,900
+dipole two pointed charges المسافة بينهم صغيرة و
+
+511
+00:39:04,900 --> 00:39:07,520
+اللي هم opposite signs لو أنا بده أحسب ال
+
+512
+00:39:07,520 --> 00:39:11,840
+potential عن النقطة B هيكون
+
+513
+00:39:13,370 --> 00:39:17,430
+مجموع ال potentials الناتجين من positive و
+
+514
+00:39:17,430 --> 00:39:21,290
+negative charge ال potential ناتج من Q ايش هيساوي؟
+
+515
+00:39:21,290 --> 00:39:25,330
+Q على 4 by Y node في 1 على R1 و هذا هيكون minus Q
+
+516
+00:39:25,330 --> 00:39:31,710
+على 4 by Y node في 1 على R2 اذا ال potential عند
+
+517
+00:39:31,710 --> 00:39:35,570
+النقطة B هيكون ال potential ناتج من Q minus Q
+
+518
+00:39:39,220 --> 00:39:42,600
+بقى Q على 4 by epsilon node في 1 على R1 minus 1
+
+519
+00:39:42,600 --> 00:39:50,920
+على R2 لو أنا عملت توحيد مقامات هيكون عند Q على 4
+
+520
+00:39:50,920 --> 00:39:55,480
+by epsilon node R1 في R2 و ال boss بيصير R2 minus
+
+521
+00:39:55,480 --> 00:40:01,020
+R1 انت دوري اعرف ايش هي R2 minus R1 و اعرف ايش هي
+
+522
+00:40:01,020 --> 00:40:08,500
+R1 و R2 ارجع للاسمقلت ان انا بدي الفرق بين R2 وR1
+
+523
+00:40:08,500 --> 00:40:12,400
+R2 هي المسافة بين minus Q ونقطة B اللى بتحسب عندها
+
+524
+00:40:12,400 --> 00:40:16,900
+ال potential وR1 هي المسافة بين نقطة Q point of
+
+525
+00:40:16,900 --> 00:40:21,960
+charge Q plus Q ونقطة B لو انا طلعت على الرسمة انا
+
+526
+00:40:21,960 --> 00:40:25,380
+هلاحظ ان الفرق بينهم هو بالتمام هذه المسافة لو انا
+
+527
+00:40:25,380 --> 00:40:30,460
+ازالت عمود من plus Q على R2 هيكون الفرق بينهم هي
+
+528
+00:40:30,460 --> 00:40:37,280
+هذه المسافة لو انا عرفت زوية θهي الزاوية المابين
+
+529
+00:40:37,280 --> 00:40:40,900
+ال line اللى بوصل مابين ال center تبع ال dipole
+
+530
+00:40:40,900 --> 00:40:45,420
+هذه النقطة هي هنا ال dipole المسافة بين ال q و
+
+531
+00:40:45,420 --> 00:40:49,540
+minus q هي دى بس هذا ال dipole بالذات انا حطه بحيث
+
+532
+00:40:49,540 --> 00:40:53,420
+ال center تبعه جاية على ال origin ال center تبع ال
+
+533
+00:40:53,420 --> 00:40:56,400
+dipole جاية على ال origin قصدت لو انا عرفتها ان هى
+
+534
+00:40:56,400 --> 00:41:03,170
+الزاوية المابينالخط الواصل ما بين ال two charges و
+
+535
+00:41:03,170 --> 00:41:06,770
+الخط الواصل ما بين ال origin تبع ال dipole و
+
+536
+00:41:06,770 --> 00:41:09,410
+النقطة اللى بدأ يسعدها ال potential هى theta، ال
+
+537
+00:41:09,410 --> 00:41:13,110
+theta مع التلاغر هى نفس ال theta هى، صح؟ اذا هى
+
+538
+00:41:13,110 --> 00:41:18,530
+المسافة اللى بحسب بها عبارة عن مين D cos thetaأذا
+
+539
+00:41:18,530 --> 00:41:22,830
+الفرق بين R2 وR1 بقدر أكتب بدلالة D اللي هي
+
+540
+00:41:22,830 --> 00:41:25,450
+المسافة بين ال two charges ال positive و ال
+
+541
+00:41:25,450 --> 00:41:29,250
+negative of ال charges و θة اللي هي الزاوية اللي
+
+542
+00:41:29,250 --> 00:41:32,870
+ما بين ال line اللي واصل بين ال two charges و ال
+
+543
+00:41:32,870 --> 00:41:36,090
+line اللي واصل ما بين ال center تبع ال dipole و
+
+544
+00:41:36,090 --> 00:41:39,170
+النقطة اللي بقيس عندها ال potential اذا ال
+
+545
+00:41:39,170 --> 00:41:42,750
+difference هو D cos θ الحاجة التانية اللي انا بدأ
+
+546
+00:41:42,750 --> 00:41:46,130
+اخدها بعلية بارعة ان لو انا فرضت ان R1 وR2 أكبر
+
+547
+00:41:46,130 --> 00:41:53,460
+بكتيرمن المسافة D اذا تقريبا بقدر اقول ان R1 في R2
+
+548
+00:41:53,460 --> 00:42:00,100
+هي R تربيان تقريبا لانه منهم المسافة الفرق اللي
+
+549
+00:42:00,100 --> 00:42:05,960
+بينهم اصغر كتير R2 مقاس R1 اللي هي D Cos θ وتقريبا
+
+550
+00:42:05,960 --> 00:42:13,270
+R2 وR1 هسويها بR تربيان اذا رجعت لرسمهاهدولة كلهم
+
+551
+00:42:13,270 --> 00:42:18,750
+حيبينوا كإن هم متساويين في حالة الضرب R1 وR2 وR ..
+
+552
+00:42:18,750 --> 00:42:24,990
+وR فبقدر أقول أن R1 تقريبا تسوى R2 تقريبا تسوى R
+
+553
+00:42:24,990 --> 00:42:32,620
+فR1 في R2 هتكون R تربيهأذا ال potential الناتج عن
+
+554
+00:42:32,620 --> 00:42:36,280
+ال dipole هو
+
+555
+00:42:36,280 --> 00:42:40,060
+Q على 4 by epsilon note بد ال R تنين minus R واحد
+
+556
+00:42:40,060 --> 00:42:44,500
+عشان حطيت دي cos θ بد ال R واحد في R تنين حطيت R
+
+557
+00:42:44,500 --> 00:42:49,640
+تربيه تمام؟ في أي سؤال لحد هنا؟
+
+558
+00:42:53,450 --> 00:42:59,990
+D cos θ هي
+
+559
+00:42:59,990 --> 00:43:08,110
+البروجيكشن تبع D في اتجاه D و هذا الاتجاه θ لأن دي
+
+560
+00:43:08,110 --> 00:43:12,150
+كوساين ثتا هقول ان هذا الاتجاه مين هو R hat هو
+
+561
+00:43:12,150 --> 00:43:15,890
+البروجيكشن تبع D على اتجاه R hat
+
+562
+00:43:19,830 --> 00:43:24,370
+دى مالها اتجاهها اتجاه ال z axis احنا ماخدينها دى
+
+563
+00:43:24,370 --> 00:43:29,250
+vector هي عبارة عن d z hat ال projection تبعها في
+
+564
+00:43:29,250 --> 00:43:31,690
+ال R hat هو عبارة عن d cos θ
+
+565
+00:43:35,570 --> 00:43:40,150
+و هعمل رف كمان بي اللي هو الدايبول Q في D إذا بقدر
+
+566
+00:43:40,150 --> 00:43:44,890
+أعيد كتابة ال potential تبعي اللي هو QD cos θ على
+
+567
+00:43:44,890 --> 00:43:48,710
+4 pi epsilon نوت R تربيه عشان كان QD قلنا منه هال
+
+568
+00:43:48,710 --> 00:43:53,610
+D cos θ بتعبر عن D dot D R hat و QD vector هسميها
+
+569
+00:43:53,610 --> 00:43:58,770
+بي فهتصير بي بتساوي بي dot R hat على 4 pi epsilon
+
+570
+00:43:58,770 --> 00:44:02,530
+نوت R تربيه هذه معادلات أنتوا لازم تكونوا حافظينها
+
+571
+00:44:03,500 --> 00:44:07,500
+الديابل انه بساوي بي اللي هو مي حسميه الديابل
+
+572
+00:44:07,500 --> 00:44:10,700
+moment اللي هو قيمة ال charge q في دي المسافة بين
+
+573
+00:44:10,700 --> 00:44:15,600
+ال two charges بي الديابل moment كمرة هو q في دي و
+
+574
+00:44:15,600 --> 00:44:18,240
+ال potential ناتج عن هذا الديابل هيكون قيمة
+
+575
+00:44:18,240 --> 00:44:22,900
+الديابل moment بي dot r hat اللي هو الاتجاهاللي
+
+576
+00:44:22,900 --> 00:44:27,240
+ناله موازي للحط الواصل بين ال center تبع ال dipole
+
+577
+00:44:27,240 --> 00:44:30,620
+للمقطة اللي بده احسب عندها ال potential على 4pi
+
+578
+00:44:30,620 --> 00:44:33,640
+epsilon not r تربية و r اللي هي المسافة بين ال
+
+579
+00:44:33,640 --> 00:44:36,500
+center تبع ال dipole للمقطة اللي بده احسب عندها ال
+
+580
+00:44:36,500 --> 00:44:39,300
+potential بيعطيكوا العافية الدقاء القادم ان شاء
+
+581
+00:44:39,300 --> 00:44:40,620
+الله نكمل
+
diff --git a/PL9fwy3NUQKwa0nXiCdyQcTW4hWDLTGpDb/CZdXqTf4caw_raw.json b/PL9fwy3NUQKwa0nXiCdyQcTW4hWDLTGpDb/CZdXqTf4caw_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..ed5eaf4a719f8e3c9af62894d7496fdea879cc99
--- /dev/null
+++ b/PL9fwy3NUQKwa0nXiCdyQcTW4hWDLTGpDb/CZdXqTf4caw_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 3247, "start": 5.08, "end": 32.48, "text": "بسم الله الرحمن الرحيم السلام عليكم ورحمة الله وبركاته هنكمل في مادة نظرية الألات هنبدأ chapter جديد اللي هو ال gear trains اللي هي سلاسل المسننات طبعا ال gear trains ممكن أصنفها إلى أربع أنواع اللي هي symbol gear trains أو compound gear trains", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 21136, 37440, 25894, 24793, 4032, 2288, 35571, 3660, 21984, 4032, 26890, 4117, 9307, 3224, 8032, 1863, 24793, 1211, 8978, 3714, 18513, 3660, 8717, 19913, 2288, 10632, 16247, 1211, 9307, 8032, 1863, 44510, 10721, 7187, 10874, 16254, 3215, 13672, 1829, 31439, 2423, 7394, 16329, 13672, 1829, 39896, 8608, 15040, 3794, 1211, 9673, 3794, 1863, 1863, 9307, 23032, 3555, 3615, 995, 2423, 7394, 16329, 3714, 43020, 5551, 9381, 1863, 5172, 11296, 30731, 5551, 25513, 3615, 14739, 14407, 3615, 13672, 1829, 39896, 5986, 7394, 16329, 34051, 14154, 7394, 16329], "avg_logprob": -0.13216145259017745, 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"probability": 0.8684895833333334}, {"start": 10.82, "end": 11.5, "word": " نظرية", "probability": 0.95654296875}, {"start": 11.5, "end": 12.24, "word": " الألات", "probability": 0.7593587239583334}, {"start": 12.24, "end": 13.34, "word": " هنبدأ", "probability": 0.94482421875}, {"start": 13.34, "end": 13.72, "word": " chapter", "probability": 0.393310546875}, {"start": 13.72, "end": 14.18, "word": " جديد", "probability": 0.9806315104166666}, {"start": 14.18, "end": 14.32, "word": " اللي", "probability": 0.78515625}, {"start": 14.32, "end": 14.64, "word": " هو", "probability": 0.9755859375}, {"start": 14.64, "end": 14.92, "word": " ال", "probability": 0.6708984375}, {"start": 14.92, "end": 15.22, "word": " gear", "probability": 0.53515625}, {"start": 15.22, "end": 15.88, "word": " trains", "probability": 0.454345703125}, {"start": 15.88, "end": 16.38, "word": " اللي", "probability": 0.9541015625}, {"start": 16.38, "end": 16.7, "word": " هي", "probability": 0.908203125}, {"start": 16.7, 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ال gears ثابتة محور الأعمدة اللى راكب عليها ال gears ثابتة لكن فى النوع الرابع اللى بيساكلك جير ترين بيكون المحاور اللى راكب عليها ال gears تتحرك برضه بالنسبة لمحور ثابت يعنى أول تلاتة مش تركين فى أنه", "tokens": [6027, 10721, 25957, 41891, 13672, 7578, 12602, 995, 4117, 3555, 25894, 11296, 2423, 20915, 38637, 16758, 2655, 3660, 3714, 5016, 13063, 16247, 25957, 41891, 13672, 7578, 12602, 995, 4117, 3555, 25894, 11296, 2423, 20915, 38637, 16758, 2655, 3660, 44381, 6156, 7578, 28239, 45367, 34892, 16758, 3615, 13672, 7578, 4724, 1829, 3794, 995, 4117, 23275, 10874, 13546, 6055, 2288, 9957, 4724, 1829, 30544, 9673, 5016, 995, 13063, 13672, 7578, 12602, 995, 4117, 3555, 25894, 11296, 2423, 20915, 6055, 2655, 5016, 31747, 4724, 43042, 3224, 20666, 1863, 35457, 3660, 32767, 5016, 13063, 38637, 16758, 2655, 37495, 1863, 7578, 5551, 12610, 6055, 1211, 9307, 3660, 37893, 6055, 31747, 9957, 6156, 7578, 14739, 3224], "avg_logprob": -0.13626126421464457, "compression_ratio": 2.1777777777777776, 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232015, "start": 2299.67, "end": 2320.15, "text": "الان هذا اسمه reverted هانتقل حركة من هنا لهنا و من هنا لهنا وهذا و هذا اللي هم نفس المحور هذا reverted غيرة رانه هاي زي ما مبين عنده واحد هاي واحد", "tokens": [6027, 7649, 23758, 24525, 2304, 3224, 3698, 911, 292, 8032, 7649, 2655, 4587, 1211, 11331, 31747, 3660, 9154, 34105, 46740, 8315, 4032, 9154, 34105, 46740, 8315, 37037, 15730, 4032, 23758, 13672, 1829, 8032, 2304, 8717, 36178, 9673, 5016, 13063, 23758, 3698, 911, 292, 32771, 48923, 12602, 7649, 3224, 8032, 47302, 30767, 1829, 19446, 3714, 3555, 9957, 43242, 3224, 36764, 24401, 8032, 47302, 36764, 24401], "avg_logprob": -0.4012019230769231, "compression_ratio": 1.7394366197183098, "no_speech_prob": 0.0, "words": [{"start": 2299.67, "end": 2300.07, "word": "الان", "probability": 0.60205078125}, {"start": 2300.07, "end": 2300.45, "word": " هذا", "probability": 0.328857421875}, {"start": 2300.45, "end": 2301.25, "word": " اسمه", "probability": 0.91650390625}, {"start": 2301.25, 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هذا", "probability": 0.57470703125}, {"start": 2366.28, "end": 2366.76, "word": " shaft", "probability": 0.63916015625}, {"start": 2366.76, "end": 2367.24, "word": " وهذا", "probability": 0.770751953125}, {"start": 2367.24, "end": 2367.66, "word": " shaft", "probability": 0.697265625}, {"start": 2367.66, "end": 2368.2, "word": " بس", "probability": 0.82373046875}, {"start": 2368.2, "end": 2368.4, "word": " نفس", "probability": 0.97705078125}, {"start": 2368.4, "end": 2368.86, "word": " المحور", "probability": 0.9934895833333334}, {"start": 2368.86, "end": 2370.72, "word": " هذا", "probability": 0.76513671875}, {"start": 2370.72, "end": 2371.08, "word": " سمى", "probability": 0.5913899739583334}, {"start": 2371.08, "end": 2371.8, "word": " reverted", "probability": 0.53900146484375}, {"start": 2371.8, "end": 2373.16, "word": " جير", "probability": 0.49847412109375}, {"start": 2373.16, "end": 2374.04, "word": " التران", "probability": 0.77197265625}, {"start": 2374.04, "end": 2386.98, "word": " طبعا", "probability": 0.97216796875}, {"start": 2386.98, "end": 2387.84, "word": " مبين", "probability": 0.8194986979166666}, {"start": 2387.84, "end": 2387.98, "word": " ان", "probability": 0.75732421875}, {"start": 2387.98, "end": 2388.06, "word": " دي", "probability": 0.52801513671875}, {"start": 2388.06, "end": 2388.6, "word": " reverted", "probability": 0.6468505859375}, {"start": 2388.6, "end": 2389.22, "word": " جيرة", "probability": 0.917236328125}, {"start": 2389.22, "end": 2390.0, "word": " التران", "probability": 0.90185546875}], "temperature": 1.0}, {"id": 84, "seek": 242042, "start": 2394.32, "end": 2420.42, "text": "الـ T1 و T2 و T3 و T4 عدد الأسنان للتروس N1 و N2 و N3 و N4 الصراعات الصراعات الترس واحد صراعات الترس اتنين صراعات الترس تلاتة صراعات الترس أربعة و ال R1 ال R2 ال R3", "tokens": [6027, 39184, 314, 16, 4032, 314, 17, 4032, 314, 18, 4032, 314, 19, 6225, 3215, 3215, 16247, 3794, 1863, 7649, 24976, 2655, 32887, 3794, 426, 16, 4032, 426, 17, 4032, 426, 18, 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بيحطله", "probability": 0.748974609375}, {"start": 3416.14, "end": 3416.44, "word": " كصورة", "probability": 0.67047119140625}, {"start": 3416.44, "end": 3416.74, "word": " بيحطله", "probability": 0.83037109375}, {"start": 3416.74, "end": 3417.06, "word": " سفر", "probability": 0.8048502604166666}, {"start": 3417.06, "end": 3417.32, "word": " لو", "probability": 0.87158203125}, {"start": 3417.32, "end": 3417.56, "word": " حالة", "probability": 0.737060546875}, {"start": 3417.56, "end": 3417.98, "word": " الخمسية", "probability": 0.9234619140625}, {"start": 3417.98, "end": 3418.22, "word": " صح", "probability": 0.796630859375}, {"start": 3418.22, "end": 3420.98, "word": " نعم", "probability": 0.47894287109375}, {"start": 3420.98, "end": 3423.52, "word": " طيب", "probability": 0.9410807291666666}, {"start": 3423.52, "end": 3423.86, "word": " جرب", "probability": 0.971923828125}, {"start": 3423.86, "end": 3424.06, "word": " إيش", "probability": 0.7359212239583334}, {"start": 3424.06, 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwa0nXiCdyQcTW4hWDLTGpDb/CZdXqTf4caw_raw.srt b/PL9fwy3NUQKwa0nXiCdyQcTW4hWDLTGpDb/CZdXqTf4caw_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..87d4f9a8aedba38ff36d69ec0a60140c8c7c933e
--- /dev/null
+++ b/PL9fwy3NUQKwa0nXiCdyQcTW4hWDLTGpDb/CZdXqTf4caw_raw.srt
@@ -0,0 +1,2004 @@
+1
+00:00:05,080 --> 00:00:07,680
+بسم الله الرحمن الرحيم السلام عليكم ورحمة الله
+
+2
+00:00:07,680 --> 00:00:13,720
+وبركاته هنكمل في مادة نظرية الألات هنبدأ chapter
+
+3
+00:00:13,720 --> 00:00:19,280
+جديد اللي هو ال gear trains اللي هي سلاسل المسننات
+
+4
+00:00:19,280 --> 00:00:22,940
+طبعا
+
+5
+00:00:22,940 --> 00:00:28,800
+ال gear trains ممكن أصنفها إلى أربع أنواع اللي هي
+
+6
+00:00:28,800 --> 00:00:33,580
+symbol gear trains أو compound gear trainsأو
+
+7
+00:00:33,580 --> 00:00:41,940
+reverted gear trains أو apcyclic gear trains الأول
+
+8
+00:00:41,940 --> 00:00:46,020
+تلات أنواع اللي هي ال simple وال compound وال
+
+9
+00:00:46,020 --> 00:00:51,480
+reverted gear train المحاور
+
+10
+00:00:52,260 --> 00:00:56,040
+الأعمدة اللى راكب عليها ال gears ثابتة محور
+
+11
+00:00:56,040 --> 00:00:59,560
+الأعمدة اللى راكب عليها ال gears ثابتة لكن فى
+
+12
+00:00:59,560 --> 00:01:03,540
+النوع الرابع اللى بيساكلك جير ترين بيكون المحاور
+
+13
+00:01:03,540 --> 00:01:09,660
+اللى راكب عليها ال gears تتحرك برضه بالنسبة لمحور
+
+14
+00:01:09,660 --> 00:01:18,410
+ثابت يعنى أول تلاتة مش تركين فى أنهالـ gears ال
+
+15
+00:01:18,410 --> 00:01:22,070
+shafts in which gears are attached are fixed في
+
+16
+00:01:22,070 --> 00:01:27,010
+النوع الراجع ال shafts in which gears are mounted
+
+17
+00:01:27,010 --> 00:01:32,650
+بتحركوا بالنسبة ل fixed axis نبدأ
+
+18
+00:01:32,650 --> 00:01:39,770
+في الأول نوع ال simple gear train الان
+
+19
+00:01:39,770 --> 00:01:43,740
+كل gear بيكونعلى shaft يعني ال shaft الواحد اللي
+
+20
+00:01:43,740 --> 00:01:47,520
+عملي واحد عليه بيكون ترس واحد كل shaft عليه ترس
+
+21
+00:01:47,520 --> 00:01:50,980
+فقط عندي
+
+22
+00:01:50,980 --> 00:01:57,100
+مثلا عندي هين تلت تروس A وB وC هاي ال shaft shaft
+
+23
+00:01:57,100 --> 00:02:03,260
+shaft على كل shaft فيه عندي ترس واحد هين عندي أربع
+
+24
+00:02:03,260 --> 00:02:09,640
+تروس هاي one shaft اتنين تلت أربع كل ترس له الشافت
+
+25
+00:02:09,640 --> 00:02:11,180
+الخاص فيه
+
+26
+00:02:15,670 --> 00:02:24,250
+الان نفترض ان عندي .. عندي ترسين هاي ترس واحد و
+
+27
+00:02:24,250 --> 00:02:35,710
+ترس اتنين هذا واحد هذا اتنين عدد سنان الترس واحد T
+
+28
+00:02:35,710 --> 00:02:44,310
+واحد عدد سنان ترس اتنين T اتنين زي هذا بلفبعكس
+
+29
+00:02:44,310 --> 00:02:49,170
+عقارب الساعة بان واحد هذا هكون بلف باتجاه عقارب
+
+30
+00:02:49,170 --> 00:02:58,310
+الساعة بان اتنين ال speed ratio اللي هتكون سرعة ال
+
+31
+00:02:58,310 --> 00:03:05,570
+driver على سرعة ال driven فان دي ال train ratio
+
+32
+00:03:05,570 --> 00:03:09,150
+العكس
+
+33
+00:03:09,150 --> 00:03:19,900
+هي بالساويةن اتنين على ن واحد بيستوى T اتنين على T
+
+34
+00:03:19,900 --> 00:03:23,560
+واحد T
+
+35
+00:03:23,560 --> 00:03:27,680
+واحد على
+
+36
+00:03:27,680 --> 00:03:32,880
+T اتنين يعني ال train ratio هي عدد سنان الترس
+
+37
+00:03:32,880 --> 00:03:36,840
+الأول على عدد سنان الترس التاني ال speed ratio
+
+38
+00:03:36,840 --> 00:03:41,710
+سرعة الترس الأولعلى صورة الترس التانى اللى هى تمثل
+
+39
+00:03:41,710 --> 00:03:58,910
+T1 على T2 على T1 الآن
+
+40
+00:03:58,910 --> 00:04:04,150
+لما يكون عدد التروس الداخلية
+
+41
+00:04:06,850 --> 00:04:10,470
+ال driver driven بدور نفس الاتجاه يعني طلع الشكل
+
+42
+00:04:10,470 --> 00:04:17,350
+هذا هذا ال driver هذا ال driven وهذا اللي في النص
+
+43
+00:04:17,350 --> 00:04:21,710
+يسمى intermediate يعني الترس داخلي عند هاي ال
+
+44
+00:04:21,710 --> 00:04:25,710
+driver هاي ال driven هنا عندي هذا الدروس الداخلية
+
+45
+00:04:25,710 --> 00:04:30,250
+كام اتنين لما يكون هذا الدروس الداخلية مفرد واحد
+
+46
+00:04:30,250 --> 00:04:35,650
+او تلاتة او خمسة او سبعة بيكونالـ Drive و Drift
+
+47
+00:04:35,650 --> 00:04:39,490
+بدوروا نفس الاتجاه لأن هذا بدور .. هذا بدور إيش؟
+
+48
+00:04:39,490 --> 00:04:43,590
+مع عقار بالساعة واضح هذا بدور بعكس عقار بالساعة
+
+49
+00:04:43,590 --> 00:04:50,270
+هذا بدور .. هذا .. هذا بدور نفس الاتجاه إذا كان
+
+50
+00:04:50,270 --> 00:04:55,990
+عدد التروس الداخلية مزوج بدوروا عكس بعض هذا بدور
+
+51
+00:04:55,990 --> 00:05:05,310
+مع عقار بالساعة هذا عكس عقار بالساعةهذا مع عقار
+
+52
+00:05:05,310 --> 00:05:12,570
+بالسيعة، هذا عكس عقار بالسيعة واضح أن هذا بدور
+
+53
+00:05:12,570 --> 00:05:15,510
+باتجاه عقار بالسيعة، هذا عكس عقار بالسيعة المعنى
+
+54
+00:05:15,510 --> 00:05:20,330
+هو إذا كان عدد .. عدد لتروس الداخلية مفرد، بيكون
+
+55
+00:05:20,330 --> 00:05:23,530
+ال driver دارون بدوروا نفس الاتجاه إذا كان عدد
+
+56
+00:05:23,530 --> 00:05:29,650
+لتروس .. عدد لتروس الداخلية مزدوج، بيكون ال driver
+
+57
+00:05:29,650 --> 00:05:31,450
+دارون بدوروا عكس بعض
+
+58
+00:05:40,700 --> 00:05:48,220
+لو أخدت جير التران لو
+
+59
+00:05:48,220 --> 00:05:57,100
+أخدت جير التران وكامل
+
+60
+00:05:57,100 --> 00:05:58,100
+تلت روس
+
+61
+00:06:17,140 --> 00:06:24,060
+لو هذا بدور باتجاه عقارب الساعة هذا عكس عقارب
+
+62
+00:06:24,060 --> 00:06:29,740
+الساعة هذا باتجاه عقارب الساعة لو كان هذا ادس نانو
+
+63
+00:06:29,740 --> 00:06:43,700
+T1 هذا T2 هذا T3 هذا بدور بسرعة N1N اتنين و N
+
+64
+00:06:43,700 --> 00:06:50,420
+تلاتة ناقص
+
+65
+00:06:50,420 --> 00:07:00,100
+اللي في النص بالعكس صحيح
+
+66
+00:07:00,100 --> 00:07:03,640
+معناته
+
+67
+00:07:03,640 --> 00:07:07,160
+N
+
+68
+00:07:07,160 --> 00:07:08,720
+واحد على N اتنين مش الساوي
+
+69
+00:07:14,140 --> 00:07:33,520
+بساوي T2 على T1 صح و N2 على N3 بساوي T3 على T2 و
+
+70
+00:07:33,520 --> 00:07:39,180
+دلوقت المعادلة هتبقى المعادلة هتبقى N1 على N2 في
+
+71
+00:07:39,180 --> 00:07:53,430
+N2 على N3T2 على T1 في T3 على T2 هتروح هذه مع هذه
+
+72
+00:07:53,430 --> 00:08:10,350
+صح؟ معناته N1 على N3 بس T2 مع T2 هتساوي T3 معناته
+
+73
+00:08:10,350 --> 00:08:17,540
+ايش نستنتج؟ان في حالة simple جري تريان عارف؟
+
+74
+00:08:17,540 --> 00:08:22,280
+simple تيه يعني جري تريان؟ النسبة بين عدد الدروس
+
+75
+00:08:22,280 --> 00:08:28,980
+النسبة بين صرعة ال driver على driven بستو عدد
+
+76
+00:08:28,980 --> 00:08:35,240
+السنان ال driven driver يعني الدروس الداخلي اللي
+
+77
+00:08:35,240 --> 00:08:40,550
+مبينه في المعادلةمش ظاهرة مانتروس الداخل هي ال ..
+
+78
+00:08:40,550 --> 00:08:44,270
+ال .. ال .. الاشي الوحيد اللي بتسويه إذا كان مفرد
+
+79
+00:08:44,270 --> 00:08:47,110
+بتخلي ال driver و ال driverine يدوروا نفس الاتجاه
+
+80
+00:08:47,110 --> 00:08:53,490
+و إذا كان مزوج بيدوروا بعكس بعض زاد أنه أنا بتحكم
+
+81
+00:08:53,490 --> 00:08:57,290
+في ال center distance ببعد المسافة بتحكم في ال
+
+82
+00:08:57,290 --> 00:09:00,270
+center distance هاي ال .. الوظيفة بتاعة ال
+
+83
+00:09:00,270 --> 00:09:03,470
+intermediate gears في حالة ال simple gear trains
+
+84
+00:09:22,930 --> 00:09:28,110
+معناة ال speed ratio اللي هي ال speed ده driverع
+
+85
+00:09:28,110 --> 00:09:30,930
+ال speed of driven سواء number of teeth on driven
+
+86
+00:09:30,930 --> 00:09:34,290
+ع number of teeth on driver طبعا ال train value
+
+87
+00:09:34,290 --> 00:09:39,870
+عكسها هي ال speed of driven ع ال speed of driver
+
+88
+00:09:39,870 --> 00:09:42,390
+number of teeth of driver ع number of teeth of
+
+89
+00:09:42,390 --> 00:09:49,670
+driven زي
+
+90
+00:09:49,670 --> 00:09:53,210
+ما حكينا ال speed ratio و ال train value ما
+
+91
+00:09:53,210 --> 00:10:02,680
+بتعتمدشعلى ال size وعدد للتروس الداخلية للتروس
+
+92
+00:10:02,680 --> 00:10:05,040
+الداخلية عشانك بسموها ideal gears بسموها ideal
+
+93
+00:10:05,040 --> 00:10:12,520
+gears ال ideal gears تستخدم عشان اوصل connect
+
+94
+00:10:12,520 --> 00:10:16,000
+gears وبيدي center distance كبيرة فبحاط ال tours
+
+95
+00:10:16,000 --> 00:10:19,840
+في النص عشان ابعد للتروس ال driver undriven اخلي
+
+96
+00:10:19,840 --> 00:10:25,680
+منهم مسافةو الهدف التاني احصل على اتجاه الدوران
+
+97
+00:10:25,680 --> 00:10:28,800
+اللي بديها اذا بدي يكون اتجاه الدوران ال driver
+
+98
+00:10:28,800 --> 00:10:34,780
+driving نفس الاتجاه بخلي ال intermediate مفرد مفرد
+
+99
+00:10:34,780 --> 00:10:37,620
+اذا عكس الاتجاه بخلي ال intermediate عددهم يكون
+
+100
+00:10:37,620 --> 00:10:42,300
+زوجة هذا
+
+101
+00:10:42,300 --> 00:10:47,040
+النوع التاني من ال gears اللي هي ال compound gear
+
+102
+00:10:47,040 --> 00:10:53,080
+trends في ال compound gear trendsممكن يكون اكتر من
+
+103
+00:10:53,080 --> 00:10:55,980
+gear على الشافت الواحد على العمود الواحد بيكونوا
+
+104
+00:10:55,980 --> 00:10:59,580
+بيكون عنده اكتر من gear بدوروا مع بعض هذا بمعناته
+
+105
+00:10:59,580 --> 00:11:04,140
+compound ال simple gear ال simple gear train كل
+
+106
+00:11:04,140 --> 00:11:09,720
+شافت تحمل ترس واحد فقط لكن في ال compound year
+
+107
+00:11:09,720 --> 00:11:14,120
+trains الشافت الواحد ممكن يحمل اكتر من ترس طبعا ال
+
+108
+00:11:14,120 --> 00:11:15,800
+compound year trains تستخدم
+
+109
+00:11:19,200 --> 00:11:22,020
+لما بدي center distance صغيرة بستخدم compound gear
+
+110
+00:11:22,020 --> 00:11:24,740
+trains يعني انا محدود في المساحات في ال volume في
+
+111
+00:11:24,740 --> 00:11:31,820
+ال space بستخدم ال compound gear trains واذا
+
+112
+00:11:31,820 --> 00:11:35,400
+بدي speed ratio عالية بستخدم compound gear trains
+
+113
+00:11:35,400 --> 00:11:40,100
+طبعا
+
+114
+00:11:40,100 --> 00:11:44,840
+كل intermediate shaft كل shaft في المصل لان في
+
+115
+00:11:44,840 --> 00:11:49,820
+عنده input و في outputاي اش بينهم يعتبر اياش
+
+116
+00:11:49,820 --> 00:11:54,080
+intermediate كل intermediate shaft بيحمل two gears
+
+117
+00:11:54,080 --> 00:12:07,900
+كل intermediate shaft بيحمل two gears انا
+
+118
+00:12:07,900 --> 00:12:15,460
+عند هاي عند gear واحد اتنين تلاتة اربعة خمسة ستة
+
+119
+00:12:15,460 --> 00:12:30,260
+اللي هوهذه جير واحد جير
+
+120
+00:12:30,260 --> 00:12:37,140
+واحد محمول على shift a drive جير اتنين هذه واحد
+
+121
+00:12:37,140 --> 00:12:42,640
+drive جير اتنين هذه جير اتنين
+
+122
+00:12:48,420 --> 00:12:53,620
+هذا الشفت A الشفت B محمو عليه ترس اتنين و تلاتة
+
+123
+00:12:53,620 --> 00:12:57,840
+هاي تلاتة
+
+124
+00:12:57,840 --> 00:13:11,620
+معناه
+
+125
+00:13:11,620 --> 00:13:14,820
+اتنين و تلاتة بيدوروا في نفس السرعة اتنين و تلاتة
+
+126
+00:13:15,540 --> 00:13:20,260
+بدوروا بنفس السرعة تلاتة drive تلاتة هذا drive
+
+127
+00:13:20,260 --> 00:13:32,840
+اربع اربع
+
+128
+00:13:32,840 --> 00:13:33,960
+و خمسة على نفس ال shaft
+
+129
+00:13:47,800 --> 00:13:59,000
+خمسة drive ستة عند
+
+130
+00:13:59,000 --> 00:14:03,940
+ال ب is intermediate shaft و ال c intermediate
+
+131
+00:14:03,940 --> 00:14:07,580
+shaft لحظة كل intermediate shaft بيشيل اكم ترس
+
+132
+00:14:07,580 --> 00:14:12,240
+هيترس واحد اتنين اتنين و تلت على نفس الشافت و اربع
+
+133
+00:14:12,240 --> 00:14:19,590
+و خمسة على نفس الشافت لان لو نبدأنحكي سرعة واحد
+
+134
+00:14:19,590 --> 00:14:28,690
+drive اتنين N واحد N واحد على N اتنين بيساوي T
+
+135
+00:14:28,690 --> 00:14:40,730
+اتنين على T واحد و اتنين او نحكي تلاتة drive اربعة
+
+136
+00:14:40,730 --> 00:14:51,790
+T تلاتة ابنته N تلاتةعلى N أربعة سواء
+
+137
+00:14:51,790 --> 00:14:59,210
+T أربعة على T تلاتة وخمسة
+
+138
+00:14:59,210 --> 00:15:09,110
+drive ستة يعني N خمسة على N ستة سواء T ستة على T
+
+139
+00:15:09,110 --> 00:15:12,230
+خمسة نضرب تلاتة البعدة و تلاتة البعدة نحن نكون عند
+
+140
+00:15:12,230 --> 00:15:22,310
+N واحد على N اتنين في N تلاتةعلى N4 في N5 على N6
+
+141
+00:15:22,310 --> 00:15:42,590
+بالساوية T2 T4 T6 على T1 T3 T5 لاحظ T2 و T3 معناته
+
+142
+00:15:42,590 --> 00:15:45,090
+هادئ N2
+
+143
+00:15:46,520 --> 00:15:54,340
+بالساوية N ثلاثة و أربعة و خمسة نفس السرعة يعني N
+
+144
+00:15:54,340 --> 00:16:02,800
+أربعة بالساوية N خمسة معناته هذه هتروح مع هذه وهذه
+
+145
+00:16:02,800 --> 00:16:13,120
+مع هذه صح؟ معناته حصف N واحد على N ستة بالساوية T
+
+146
+00:16:13,120 --> 00:16:31,610
+اتنينT4 T6 على T1 T3 T5 هذا لـ Driver وهذا
+
+147
+00:16:31,610 --> 00:16:43,720
+لـ Driven معناه الصورة لـ Driver على الـ Drivenبس
+
+148
+00:16:43,720 --> 00:16:47,560
+لو حاصل ضرر بعدد أسنان ل driven إذا هنا عندي
+
+149
+00:16:47,560 --> 00:16:54,120
+driven، هنا driven هنا driver، هنا driver الآن كيف
+
+150
+00:16:54,120 --> 00:17:00,380
+نعملها؟ الآن بحكي أنا واحد drive اتنين، هاي واحد
+
+151
+00:17:00,380 --> 00:17:06,920
+drive اتنين تلاتة drive أربعة، هاي تلاتة drive
+
+152
+00:17:06,920 --> 00:17:12,960
+أربعةوخمسة drive ستة خمسة drive ستة معناته يعني
+
+153
+00:17:12,960 --> 00:17:36,960
+multiplication of teeth of drivers عادة
+
+154
+00:17:36,960 --> 00:17:42,770
+إذا كان ال speed reductionأكتر من سبعة بستخدمش
+
+155
+00:17:42,770 --> 00:17:47,970
+symbol جير ترين بستخدم compound جير ترين لإنه
+
+156
+00:17:47,970 --> 00:17:51,790
+بيصير عالي كتير إذا بدي reduction سبعة بدي مثلا ..
+
+157
+00:17:51,790 --> 00:17:55,990
+بدي يا إما ال truth يكبر كتير أو عدد ال
+
+158
+00:17:55,990 --> 00:17:59,830
+intermediate shaft يكتر فبصير مكلفة كتير في
+
+159
+00:17:59,830 --> 00:18:06,210
+الحالات بستخدم اللي هو ال compound جير ترينطبعا ال
+
+160
+00:18:06,210 --> 00:18:10,550
+gears which .. which mesh together must have the
+
+161
+00:18:10,550 --> 00:18:13,670
+same module او نفس ال circular pitch لأن gear مش
+
+162
+00:18:13,670 --> 00:18:17,390
+مع gear لازم يكون لهم نفس ال module او نفس ال
+
+163
+00:18:17,390 --> 00:18:23,150
+circular .. نفس ال circular pitch شوف
+
+164
+00:18:23,150 --> 00:18:23,610
+example
+
+165
+00:18:31,810 --> 00:18:34,870
+gearing of a machine tool is shown in some machine
+
+166
+00:18:34,870 --> 00:18:43,430
+فيها gearing a drive b و c drive d و e drive f
+
+167
+00:18:43,430 --> 00:18:50,530
+طبعا هذه compound جيرة هنا لأن ال shaft b بيشيل
+
+168
+00:18:50,530 --> 00:18:56,030
+ترسين ال shaft اللي هنا بيشيل ترسين c و b هذا
+
+169
+00:18:56,030 --> 00:18:59,250
+بيشيل a و d عشان هي compound جيرة
+
+170
+00:19:02,710 --> 00:19:08,510
+معطينا عدد سنان لكل جير اي عشرين بي خمسة و عشرين
+
+171
+00:19:08,510 --> 00:19:13,350
+سن سي خمسين دي خمسة و سبعين اي ستة و عشرين و اف
+
+172
+00:19:13,350 --> 00:19:26,730
+خمسة و ستين الان
+
+173
+00:19:26,730 --> 00:19:29,930
+الجير ايه بدور سرعة تسعة و خمسة و سبعين RPM
+
+174
+00:19:35,170 --> 00:19:45,090
+ستة و تسعة مية و خمسة و سبعين RPM بده
+
+175
+00:19:45,090 --> 00:19:53,510
+سرعة F حاجة يحكي NF على
+
+176
+00:19:53,510 --> 00:20:02,630
+NA F إيش معله Driven و
+
+177
+00:20:02,630 --> 00:20:08,730
+ADriver حيث هو .. الآن هنا عندي driver المقام اللي
+
+178
+00:20:08,730 --> 00:20:16,010
+هتكون حاصل ضرب ل drivers على driven الآن المقام
+
+179
+00:20:16,010 --> 00:20:18,930
+اللي هتقعد في ال bus هتكون drivers في المقام
+
+180
+00:20:18,930 --> 00:20:34,630
+driven الان A drive B يعني TA هي TA على TBو C D T
+
+181
+00:20:34,630 --> 00:20:38,130
+C T
+
+182
+00:20:38,130 --> 00:20:46,750
+D و E Drive F T E على
+
+183
+00:20:46,750 --> 00:20:54,310
+T F لأن عندي الإثنان إيه عندي عشرين في
+
+184
+00:20:54,310 --> 00:20:57,230
+خمسين
+
+185
+00:20:59,700 --> 00:21:15,620
+في A 26 على B 25 وD 75 وF
+
+186
+00:21:15,620 --> 00:21:22,840
+65 على ال 13 فيها اتنين مظبوط على ال 13 فيها عياش
+
+187
+00:21:22,840 --> 00:21:29,300
+خمسة على ال 25 واحد وعلى ال 25 عياش اتنين
+
+188
+00:21:30,970 --> 00:21:39,450
+وعلى الخمسة واحد على الخمسة فيها ايش اربعة يعني
+
+189
+00:21:39,450 --> 00:21:45,530
+ستاش على خمسة وسبعين هتساوي ستاش على
+
+190
+00:21:45,530 --> 00:21:52,930
+خمسة وسبعين معناته الان اف هتساوي الان اله تسعمية
+
+191
+00:21:52,930 --> 00:22:02,630
+وخمسة وسبعين في ستاش على خمسة وسبعينعالخمسة فيها
+
+192
+00:22:02,630 --> 00:22:14,530
+الواحد تسعة خمسة عالخمسة أكم فيها خمستاشر عالتلاتة
+
+193
+00:22:14,530 --> 00:22:21,550
+فيها خمسة خمسة تسعة اربتاشر عالتلاتة فيها أكم ستة
+
+194
+00:22:22,250 --> 00:22:26,330
+خمسة ستين على الخمسة فيها واحد على الخمسة فيها أيش
+
+195
+00:22:26,330 --> 00:22:31,910
+تلتاش يعني تلتاش في أربعة كام اتنين واربعين اربعة
+
+196
+00:22:31,910 --> 00:22:37,750
+تمانين مظبوط تلتاش
+
+197
+00:22:37,750 --> 00:22:44,470
+في الستاشة كام يعني تلتاش في أربعة اتنين واربعين
+
+198
+00:22:44,470 --> 00:22:49,030
+في اتنين اربعة تمانين في اتنين مية تمانى ستين
+
+199
+00:23:01,680 --> 00:23:09,140
+مظبوط؟ تلاتاش فاربه بقى كام؟ حاسو
+
+200
+00:23:09,140 --> 00:23:13,660
+الأرقام هدا هيك رقم هدا صح نعم
+
+201
+00:23:13,660 --> 00:23:17,620
+حاسو
+
+202
+00:23:17,620 --> 00:23:19,320
+الأرقام هذه هيك صح
+
+203
+00:23:23,590 --> 00:23:28,530
+احسبوها لحالكوا اذا صح اعتبروه صح اذا غلط صلحه
+
+204
+00:23:28,530 --> 00:23:37,530
+الغلط ماشي ماشي
+
+205
+00:23:37,530 --> 00:23:49,850
+ماشي ماتين و تمانية هاد ماتين و تمانية طيب
+
+206
+00:23:55,640 --> 00:23:58,860
+الان حساب ال center distance اذا عندي two gears
+
+207
+00:23:58,860 --> 00:24:06,900
+هذه
+
+208
+00:24:06,900 --> 00:24:18,740
+هي ال center distance هذا قطره five دي واحد و هذا
+
+209
+00:24:18,740 --> 00:24:26,230
+five دي اتنينالـ Center distance اللي هي C بيسميها
+
+210
+00:24:26,230 --> 00:24:35,910
+وهين X بيساوي D1 زي D2 على 2 وD1 إيش يساوي
+
+211
+00:24:35,910 --> 00:24:39,150
+الموديول
+
+212
+00:24:39,150 --> 00:24:42,290
+في
+
+213
+00:24:42,290 --> 00:24:49,970
+N1ودي اتنين بساوية ال module في N اتنين ال center
+
+214
+00:24:49,970 --> 00:25:02,050
+distance بالساوية ال module في N واحد زائد N اتنين
+
+215
+00:25:02,050 --> 00:25:07,850
+نشوف
+
+216
+00:25:07,850 --> 00:25:11,930
+example على ال center distance calculation
+
+217
+00:25:15,140 --> 00:25:20,580
+two parallel shafts about six hundred millimeters
+
+218
+00:25:20,580 --> 00:25:23,440
+apart are to be connected by spar gears يعني اندي
+
+219
+00:25:23,440 --> 00:25:32,240
+شافتين المسافة بينهم ستمية هحط عليهم ترسين يعني
+
+220
+00:25:32,240 --> 00:25:40,080
+هاي شافت و هاي شافت المسافة بينهم ستمية
+
+221
+00:25:40,080 --> 00:25:43,360
+مليمتر
+
+222
+00:25:45,790 --> 00:25:53,210
+one shaft is run at 360 rpm and the other at 120
+
+223
+00:25:53,210 --> 00:25:59,090
+rpm يعني عندي N واحدة N واحد فهذه N اتنين N واحد
+
+224
+00:25:59,090 --> 00:26:07,950
+بتساوي تلت مية وستين rpm و
+
+225
+00:26:07,950 --> 00:26:11,770
+N اتنين مية و عشرين
+
+226
+00:26:21,660 --> 00:26:26,920
+RPM Design the gears if the cycler pitch is to be
+
+227
+00:26:26,920 --> 00:26:32,720
+25mm عند ال PC بستوى
+
+228
+00:26:32,720 --> 00:26:35,920
+25 ملي متر
+
+229
+00:26:38,670 --> 00:26:42,430
+ال pc في الآخر انا بدأ اعمل design gears يعني ده
+
+230
+00:26:42,430 --> 00:26:47,410
+عرف عدد سنان الترس هذا و عدد سنان الترس هذا و عنده
+
+231
+00:26:47,410 --> 00:26:50,730
+معطيلة ال center distance 600 لأن هذه ال .. ال ..
+
+232
+00:26:50,730 --> 00:26:54,730
+ال sector picture شو تساوي الموديول في باي صح
+
+233
+00:26:54,730 --> 00:27:02,850
+معناته الموديول بقدر أحسبه هتكون
+
+234
+00:27:02,850 --> 00:27:10,670
+خمسة و عشرين على بايseven point nine six سبعة
+
+235
+00:27:10,670 --> 00:27:20,710
+point تسعة ستة تسعة ستة طيب
+
+236
+00:27:20,710 --> 00:27:27,870
+عنده معطيني ال speed ratio N واحد على N اتنين
+
+237
+00:27:27,870 --> 00:27:34,150
+بساوة تلتمية و ستين على مية و عشرين حساوة T اتنين
+
+238
+00:27:35,570 --> 00:27:42,950
+على T1 معناته T2 بيساوي
+
+239
+00:27:42,950 --> 00:27:49,030
+تلاتة T1 ومعطين
+
+240
+00:27:49,030 --> 00:27:58,670
+ال center distance بيساوي ستمية بيساوي
+
+241
+00:27:58,670 --> 00:28:10,280
+نص ال D1 زاد ال D2يعني انا هكون عندى الف و متين بس
+
+242
+00:28:10,280 --> 00:28:16,120
+هو دى واحد اللى هو عبارة عن ايش ال module في N
+
+243
+00:28:16,120 --> 00:28:22,880
+واحد زاد ال module في N اتنين معناه هكون عندى N
+
+244
+00:28:22,880 --> 00:28:28,460
+واحد زاد N اتنين بس هو الف و متين على M الف و متين
+
+245
+00:28:28,460 --> 00:28:34,240
+على 7.96 كم بيطلع 957
+
+246
+00:28:36,480 --> 00:28:42,460
+650 150 point
+
+247
+00:28:42,460 --> 00:28:47,860
+وعندي
+
+248
+00:28:47,860 --> 00:28:54,020
+معادلة تانية اللي هو تتنين بيسوا تلتة تواحد هنعوض
+
+249
+00:28:54,020 --> 00:28:55,100
+هنا انا بكتب هنا
+
+250
+00:29:09,750 --> 00:29:16,210
+تانية تانية تانية تانية تانية تانية تانية تانية
+
+251
+00:29:16,210 --> 00:29:31,630
+تانية تانية تانية تانية تانية تانية
+
+252
+00:29:31,630 --> 00:29:35,270
+تانية تانية تانية
+
+253
+00:29:38,510 --> 00:29:44,510
+بينفعش معناته هحكي النقطة تي واحد تمام
+
+254
+00:29:44,510 --> 00:29:52,210
+تلاتين السن تمام
+
+255
+00:29:52,210 --> 00:29:58,830
+تلاتين السن الان
+
+256
+00:29:58,830 --> 00:30:06,250
+معناته تي اتنين هتكون السوء اكم تمام تلاتين في
+
+257
+00:30:06,250 --> 00:30:07,890
+اتنين ستة و سبعين
+
+258
+00:30:11,170 --> 00:30:24,370
+صح ال 38 في 3 يعني 104 114 114
+
+259
+00:30:24,370 --> 00:30:36,630
+السن 114
+
+260
+00:30:36,630 --> 00:30:42,350
+السن خلينا نحصل ال center distance كمان مرةالان ال
+
+261
+00:30:42,350 --> 00:30:51,810
+center distance هتتغير هتكون تساوي M في T1 زائد T2
+
+262
+00:30:51,810 --> 00:30:59,830
+بس خلّيني انا اخد فكرة الأرقام D أكم هتساوي هتكون
+
+263
+00:30:59,830 --> 00:31:07,570
+38 في 7.6 أحصولي D1 اللي هي M في العدل السناني
+
+264
+00:31:13,350 --> 00:31:19,610
+تلاتمية و اتنين والتانية
+
+265
+00:31:19,610 --> 00:31:24,570
+تسعمية
+
+266
+00:31:24,570 --> 00:31:31,330
+اجمعهم
+
+267
+00:31:31,330 --> 00:31:32,130
+اقصهم على اتنين
+
+268
+00:31:42,050 --> 00:31:49,410
+ستمية واربعة وانتسعة ستة ستمية واربعة وانتسعة ستة
+
+269
+00:31:49,410 --> 00:31:53,670
+وانتسعة ستة معناته ال center distance الحقيقية
+
+270
+00:31:53,670 --> 00:31:58,210
+هتكون مش ستمية ستمية واربعة ستمية واربعة لأنه ليش
+
+271
+00:31:58,210 --> 00:32:06,270
+كاتبلك هنا about about يعني حوالي ستمية اذا بدك
+
+272
+00:32:06,270 --> 00:32:11,380
+مصر تخليها ستمية ممكن تخليها ستميةبس بت .. إيش
+
+273
+00:32:11,380 --> 00:32:16,540
+بتخلي؟ بتخلي عند السنان سبعة و تلاتين و بتبعد لما
+
+274
+00:32:16,540 --> 00:32:20,520
+تحكي سبعة و تلاتين أكم لو كان سبعة و تلاتين لو كان
+
+275
+00:32:20,520 --> 00:32:28,440
+عند السنان T1 سبعة و تلاتين هيكون T2 أكم مية و
+
+276
+00:32:28,440 --> 00:32:32,500
+أحداش مية
+
+277
+00:32:32,500 --> 00:32:34,760
+و أحداش، عنظموت؟ طيب
+
+278
+00:32:37,410 --> 00:32:43,010
+معناته ال دي واحد هتكون احسبوها والدي اتنين
+
+279
+00:32:43,010 --> 00:32:49,630
+احسبوها الموديول في حد اسناب سبعة و تسعة ستة كم؟
+
+280
+00:32:49,630 --> 00:32:56,830
+متين و أربع تسعين و التانية
+
+281
+00:32:56,830 --> 00:33:00,550
+تمنية تمنية تمنية و تمنية و تمنية و تمنية و تمنية
+
+282
+00:33:00,550 --> 00:33:04,870
+و تمنية و تمنية و تمنية و تمنية و تمنية و تمنية و
+
+283
+00:33:04,870 --> 00:33:05,150
+تمنية و تمنية و تمنية و تمنية و تمنية و تمنية و
+
+284
+00:33:05,150 --> 00:33:05,290
+تمنية و تمنية و تمنية و تمنية و تمنية و تمنية و
+
+285
+00:33:05,290 --> 00:33:05,290
+تمنية و تمنية و تمنية و تمنية و تمنية و تمنية و
+
+286
+00:33:05,290 --> 00:33:05,290
+تمنية و تمنية و تمنية و تمنية و تمنية و تمنية و
+
+287
+00:33:05,290 --> 00:33:07,550
+تمنية و تمنية و تمنية و تمارت سنتر دستانس اجمع دول
+
+288
+00:33:07,550 --> 00:33:11,770
+وعلى اتنين
+
+289
+00:33:11,770 --> 00:33:16,850
+خمسمية
+
+290
+00:33:16,850 --> 00:33:23,410
+و تسعة و احد مليون point in the up يعني
+
+291
+00:33:23,410 --> 00:33:27,190
+هنا في فرق احداشر مليون هنا في فرق حوالي خمسة
+
+292
+00:33:27,190 --> 00:33:32,710
+مليونمعناته هذا أقرب، معناته أنه أزود أخلي عدد
+
+293
+00:33:32,710 --> 00:33:36,810
+السنان التامن و التلاتيم تعطينا أقرب للست مية منها
+
+294
+00:33:36,810 --> 00:33:44,170
+لإن أنزل عدد السنان، فاضح؟ عدد
+
+295
+00:33:44,170 --> 00:33:50,190
+السنان، عدد السنان، اما جاوب مثلا point كذا، ولا
+
+296
+00:33:50,190 --> 00:33:55,610
+حسب الشغل أنت ماتحكيش والله هذا طريقة السؤال غلط
+
+297
+00:33:57,380 --> 00:34:00,600
+انت تحكي لما يطلع عندك كسر عدد السنان، هل أقلل،
+
+298
+00:34:00,600 --> 00:34:06,040
+أطلع ولا أنزل؟ من عارف، هو السؤال غلط، السؤال غلط
+
+299
+00:34:06,040 --> 00:34:09,200
+حسب هل عدد السنان اللي حسبته هو ال minimum number
+
+300
+00:34:09,200 --> 00:34:13,160
+of teeth to avoid interference مثلا؟ إذا .. إذا
+
+301
+00:34:13,160 --> 00:34:19,260
+هذا، بدك تزود، إذا .. إذا عدد السنان بيقل عن الـ
+
+302
+00:34:19,260 --> 00:34:23,680
+38 point 7، خلته 38 وبيعملش interference، بنفع
+
+303
+00:34:23,680 --> 00:34:27,780
+برضه يكون أقلانت بدك تفحص الموضوع ال interference
+
+304
+00:34:27,780 --> 00:34:31,300
+يعني إذا ما مش interference مسموح لك تروح تنزل أو
+
+305
+00:34:31,300 --> 00:34:37,260
+تطلع إذا في interference بدك تطلع دكتورة جيت على
+
+306
+00:34:37,260 --> 00:34:41,700
+الرسمة بنفع أن تكون الصغيرة سرعتها أكبر من
+
+307
+00:34:41,700 --> 00:34:44,280
+الكبيرة؟ بنفع يكون هذا ال driver، بدي أن أنزل
+
+308
+00:34:44,280 --> 00:34:47,820
+السرعة ال gearbox الهدف منها، يا بدي أرفع السرعة
+
+309
+00:34:47,820 --> 00:34:54,660
+أو أقل السرعة، مظبوط؟ مثلا في طيرات الهليكوبتر،
+
+310
+00:34:54,660 --> 00:35:01,910
+بدي أسرعهزبط؟ بدي سرع، معناته محتاج gearbox يسرع،
+
+311
+00:35:01,910 --> 00:35:10,350
+صح؟ اش
+
+312
+00:35:10,350 --> 00:35:16,930
+يعني بنفع .. اش يعني ع الرسم بنفع يبطئ؟
+
+313
+00:35:16,930 --> 00:35:22,800
+ما هو .. لما يكون الكبير أكبرالان ال ratio بين
+
+314
+00:35:22,800 --> 00:35:23,980
+اتقنق بين اتقنق بين اتقنق بين اتقنق بين اتقنق بين
+
+315
+00:35:23,980 --> 00:35:24,080
+اتقنق بين اتقنق بين اتقنق بين اتقنق بين اتقنق بين
+
+316
+00:35:24,080 --> 00:35:24,240
+اتقنق بين اتقنق بين اتقنق بين اتقنق بين اتقنق بين
+
+317
+00:35:24,240 --> 00:35:25,320
+اتقنق بين اتقنق بين اتقنق بين اتقنق بين اتقنق بين
+
+318
+00:35:25,320 --> 00:35:32,060
+اتقنق بين اتقنق بين اتقنق بين اتقنق
+
+319
+00:35:32,060 --> 00:35:38,220
+بين اتقنق بين اتقنق بين اتقنق بين اتقنق بين اتقنق
+
+320
+00:35:38,220 --> 00:35:45,140
+بين اتقنق بين اتقنق بين اتقنق بين اتقنق بين اتقنق
+
+321
+00:35:45,140 --> 00:35:48,880
+بين اتقنق بين اتقنق بين اتق
+
+322
+00:35:57,980 --> 00:36:11,440
+ممكن مباشر ممكن مباشر فهمت عليا؟ اه ممكن مباشر ايش
+
+323
+00:36:11,440 --> 00:36:17,280
+يعني intervener؟ هو ال gas turbine ايش هو في
+
+324
+00:36:17,280 --> 00:36:25,280
+الآخر؟ محرك كيف يعني خفض السرعة؟
+
+325
+00:36:26,190 --> 00:36:29,830
+عشان المرار نفسه .. الشرطة المركزية تقبع 15 ألف
+
+326
+00:36:29,830 --> 00:36:33,110
+نفر كل مرة فيه؟ لأ أنا بقصد فيه مش المرحلة الوية
+
+327
+00:36:33,110 --> 00:36:36,010
+بحكي المرحلة الطيارات العادية اللي هي ال
+
+328
+00:36:36,010 --> 00:36:40,670
+propulsion الدفع الدفع الأمامي المرحلة تكون سريعة
+
+329
+00:36:40,670 --> 00:36:46,530
+كتير الصغيرة مرحلة صغيرة طيب ال reverted gear
+
+330
+00:36:46,530 --> 00:36:46,910
+train
+
+331
+00:36:49,800 --> 00:36:52,200
+هذه النوع التالتة احنا حكينا عنها symbol جيري ترين
+
+332
+00:36:52,200 --> 00:36:56,300
+compound جيري ترين و reverted جيري ترين ال
+
+333
+00:36:56,300 --> 00:37:02,300
+reverted جيري ترين المحور الترس الأول او محور ل
+
+334
+00:37:02,300 --> 00:37:09,500
+driver و محور ل driven متطابقين يعني ال driver و
+
+335
+00:37:09,500 --> 00:37:12,080
+ال driven جاين على نفس المحور زي gearbox بتاع
+
+336
+00:37:12,080 --> 00:37:14,780
+السيارة بالظبط gearbox بتاع السيارة ايه اش?
+
+337
+00:37:15,420 --> 00:37:21,130
+reverted بيجي عندك من ال engine هي ال gearboxهي
+
+338
+00:37:21,130 --> 00:37:26,150
+بيجي عندك هجير هتجم
+
+339
+00:37:26,150 --> 00:37:34,770
+ال engine بعدين بيجي هنا دي هنا بنقل على عمود تاني
+
+340
+00:37:34,770 --> 00:37:45,970
+هناخد غير واحد مش ده يعني ناخد غير مثلا عندك
+
+341
+00:37:45,970 --> 00:37:52,640
+هنا الغيارات بتكون هنابعدين بيكون عندي مثلا هاي ال
+
+342
+00:37:52,640 --> 00:38:00,140
+output مش نفس ال shaft نفس المحور مش نفس ال shaft
+
+343
+00:38:00,140 --> 00:38:04,760
+يعني هاي المحور هاي التاني هاي عندي هاي الجيل هذا
+
+344
+00:38:04,760 --> 00:38:11,240
+يعني
+
+345
+00:38:11,240 --> 00:38:14,680
+هذا بدور هدور مش مابسكين مع بعض مابسكين مع بعض
+
+346
+00:38:14,680 --> 00:38:18,620
+هيتكسر مش هدور صح بالظبط
+
+347
+00:38:19,670 --> 00:38:25,670
+الان هذا اسمه reverted هانتقل حركة من هنا لهنا و
+
+348
+00:38:25,670 --> 00:38:29,110
+من هنا لهنا وهذا و هذا اللي هم نفس المحور هذا
+
+349
+00:38:29,110 --> 00:38:39,430
+reverted غيرة رانه هاي زي ما مبين عنده واحد
+
+350
+00:38:39,430 --> 00:38:40,150
+هاي واحد
+
+351
+00:38:51,990 --> 00:39:01,610
+drive اتنين هذا اتنين و
+
+352
+00:39:01,610 --> 00:39:15,870
+اتنين و تلاتة على نفس ال shaft و
+
+353
+00:39:15,870 --> 00:39:19,090
+تلاتة drive اربعة
+
+354
+00:39:25,760 --> 00:39:31,080
+طبعا هذا shaft وهذا shaft بس نفس المحور هذا سمى
+
+355
+00:39:31,080 --> 00:39:46,980
+reverted جير التران طبعا
+
+356
+00:39:46,980 --> 00:39:50,000
+مبين ان دي reverted جيرة التران
+
+357
+00:39:54,320 --> 00:40:01,240
+الـ T1 و T2 و T3 و T4 عدد الأسنان للتروس N1 و N2 و
+
+358
+00:40:01,240 --> 00:40:06,280
+N3 و N4 الصراعات الصراعات الترس واحد صراعات الترس
+
+359
+00:40:06,280 --> 00:40:13,460
+اتنين صراعات الترس تلاتة صراعات الترس أربعة و ال
+
+360
+00:40:13,460 --> 00:40:25,560
+R1 ال R2 ال R3و ال R أربعة هدول ال pitch رديعي لل
+
+361
+00:40:25,560 --> 00:40:31,720
+gears واحد اتنين و تلاتة و أربعة الان ال gear واحد
+
+362
+00:40:31,720 --> 00:40:34,780
+و ال gear اتنين لازم يكونوا نفس الموديول عشان
+
+363
+00:40:34,780 --> 00:40:39,580
+يشبكوا مع بعض صح او نفس ال circular pitch و ال
+
+364
+00:40:39,580 --> 00:40:44,880
+gear تلاتة و ال gear أربعة نفس الموديول مش بضروري
+
+365
+00:40:44,880 --> 00:40:49,820
+يكون الموديول لاتنين و تلاتة نفس الأشياءبس لازم
+
+366
+00:40:49,820 --> 00:40:52,800
+يكون بين اتنين واحد نفس ال module و بين تلاتة و
+
+367
+00:40:52,800 --> 00:40:56,940
+اربعة نفس ال module لان ال center distance بين
+
+368
+00:40:56,940 --> 00:41:02,140
+واحد و اتنين هي نفس ال center distance بين تلاتة و
+
+369
+00:41:02,140 --> 00:41:06,860
+اربعة اش
+
+370
+00:41:06,860 --> 00:41:09,540
+يعني بنزل ال gear
+
+371
+00:41:25,800 --> 00:41:36,300
+إيش هي؟ أحكي المشكلة عشان إذا عارف أجاوب أجاوب طيب
+
+372
+00:41:36,300 --> 00:41:39,340
+طيب
+
+373
+00:41:39,340 --> 00:41:50,270
+الآنحكي ان عندي T1 T2 T3 T4 R1 R2 R3 R4 وعندي N1
+
+374
+00:41:50,270 --> 00:41:55,470
+N2 N3 N4 وعندي ال center distance يعني هتكون عندي
+
+375
+00:41:55,470 --> 00:42:04,370
+R1 ال center distance بتستوى R1 زاد R2 بتستوى R3
+
+376
+00:42:04,370 --> 00:42:15,170
+زاد R4 هاي R1 R2هي R تلاتة و R أربعة يعني هاي
+
+377
+00:42:15,170 --> 00:42:24,730
+معادلة و بعد ده احكي الله N واحد N واحد على N
+
+378
+00:42:24,730 --> 00:42:30,650
+أربعة N واحد ايش هو ال
+
+379
+00:42:30,650 --> 00:42:34,490
+driver و
+
+380
+00:42:34,490 --> 00:42:38,930
+N أربعة هيكون
+
+381
+00:42:42,330 --> 00:42:53,010
+واحد drive اتنين يعني T واحد اتنين
+
+382
+00:42:53,010 --> 00:42:56,530
+و
+
+383
+00:42:56,530 --> 00:43:07,350
+تلاتة drive اربعة هذا
+
+384
+00:43:07,350 --> 00:43:10,370
+ال gear ratio او ال speed ratio
+
+385
+00:43:14,240 --> 00:43:17,100
+على فرض ان ال module للاربعة تروس نفس الشيء على
+
+386
+00:43:17,100 --> 00:43:22,540
+فرض ان ال module انه ال module لتروس واحد اتنين و
+
+387
+00:43:22,540 --> 00:43:27,400
+تلاتة اربعة نفس الشيء معناته هتكون عنده ال center
+
+388
+00:43:27,400 --> 00:43:31,380
+distance او لو ضربت يعني ال اتنين ال center
+
+389
+00:43:31,380 --> 00:43:37,180
+distance هتكون ساوى D واحد زائد D اتنين بالساوية D
+
+390
+00:43:37,180 --> 00:43:42,500
+تلاتة زائد D اربعة هتساوى
+
+391
+00:43:44,180 --> 00:43:51,280
+دى واحد هتكون ال module في ال T1 زاد ال module في
+
+392
+00:43:51,280 --> 00:44:00,620
+T2 ساوى ال module في T3 زاد ال module في T4 يعني
+
+393
+00:44:00,620 --> 00:44:08,700
+هتكون عنده T1 زاد T2 بساوية T3 زاد T4
+
+394
+00:44:18,620 --> 00:44:33,180
+هنشوف مثال زي
+
+395
+00:44:33,180 --> 00:44:37,900
+ما انتوا شايفين عندي
+
+396
+00:44:37,900 --> 00:44:46,440
+reversed gear train a drives b و c drives d و a و
+
+397
+00:44:46,440 --> 00:44:53,710
+d له نفس المحورنفس المحور هذا ايه ال driver و دي
+
+398
+00:44:53,710 --> 00:45:02,090
+ال driven و ال center distance ميتين speed
+
+399
+00:45:02,090 --> 00:45:05,050
+ratio of the reverted gear train is to be يعني
+
+400
+00:45:05,050 --> 00:45:11,190
+المعطين ال speed ratio هتكون اندي NA على
+
+401
+00:45:11,190 --> 00:45:14,990
+ND المعطينياها اتناش
+
+402
+00:45:20,180 --> 00:45:28,400
+module pitch of gears A and B يعني عند A و B لازم
+
+403
+00:45:28,400 --> 00:45:33,720
+يكون نفس الموديول و C و D نفس الموديول بس الموديول
+
+404
+00:45:33,720 --> 00:45:36,360
+بين C و D مش ضرور يكون نفس الموديول بين A و B بس
+
+405
+00:45:36,360 --> 00:45:39,160
+بين A و B لازم نفس الموديول و بين C و D نفس
+
+406
+00:45:39,160 --> 00:45:44,160
+الموديول خلنا نسمي ال
+
+407
+00:45:44,160 --> 00:45:46,700
+M بين A و B
+
+408
+00:45:49,850 --> 00:45:55,230
+تلاتة point واحد اتنين خمسة و ال module بين C و D
+
+409
+00:45:55,230 --> 00:46:04,390
+اتنين و نص Calculate
+
+410
+00:46:04,390 --> 00:46:08,330
+suitable numbers of teeth for the gears اعمل
+
+411
+00:46:08,330 --> 00:46:15,570
+design اختار عدد سنان لل gears A و B و C و Dمعطيني
+
+412
+00:46:15,570 --> 00:46:19,390
+معلومة no gear is to have less than twenty-four
+
+413
+00:46:19,390 --> 00:46:24,770
+teeth يعني أصغر ترس فيهم مش هيكون يعني لازم يكون
+
+414
+00:46:24,770 --> 00:46:29,310
+عندنا سنة أربع وعشرين او اكتر اربع وعشرين او اكتر
+
+415
+00:46:29,310 --> 00:46:33,330
+طيب
+
+416
+00:46:33,330 --> 00:46:38,510
+خلانا نعمل معادلات بتاعتنا عندي NA على ND بالساوية
+
+417
+00:46:38,510 --> 00:46:42,210
+اتناش في معلومة تانية
+
+418
+00:46:45,400 --> 00:46:53,060
+يعني انا عندي N A هذا هذا driver و
+
+419
+00:46:53,060 --> 00:47:02,400
+هذا ايش driven يعني انا هكون عندي اتناش بالساوية
+
+420
+00:47:02,400 --> 00:47:07,620
+A
+
+421
+00:47:07,620 --> 00:47:25,650
+drive B و Cdrive دي هذه معادلة بعدين
+
+422
+00:47:25,650 --> 00:47:30,630
+ال center distance عندي 200 بدأ أخد بين a و b أولا
+
+423
+00:47:30,630 --> 00:47:35,370
+200 في
+
+424
+00:47:35,370 --> 00:47:43,250
+2 اللي هي ال center distance بتساوي ال module a,b
+
+425
+00:47:45,190 --> 00:47:54,950
+فى TA زاد الموديول بين A وB فى TB يعني أربعمية
+
+426
+00:47:54,950 --> 00:48:00,210
+هتساوي تلاتة
+
+427
+00:48:00,210 --> 00:48:15,590
+واحد اتنين خمسة فى TA زاد TB معناته TA زاد TBهتكون
+
+428
+00:48:15,590 --> 00:48:19,870
+اربعمية على تلاتة point واحدة مية و تمانية و عشرين
+
+429
+00:48:19,870 --> 00:48:27,490
+هاي معادلة اتنين بعدين دي برضه ال center distance
+
+430
+00:48:27,490 --> 00:48:30,550
+جهة ال C و D هتكون متين في اتنين
+
+431
+00:48:36,030 --> 00:48:49,270
+هتكون MCD في TC زاد MCD في TD يعني أربعمية هتكون
+
+432
+00:48:49,270 --> 00:49:00,130
+اتنين و نص في TC TD معناته TC زاد TD
+
+433
+00:49:03,940 --> 00:49:11,280
+بالساوية مية و ستين الان انا عندي تلت معادلات و
+
+434
+00:49:11,280 --> 00:49:16,340
+اربع مجهيل معادل هم عطيل معلومة ان انا ممكن افرض
+
+435
+00:49:16,340 --> 00:49:23,980
+واحد منهم بس مش لازم يكون اصغر واحد نعم
+
+436
+00:49:23,980 --> 00:49:27,620
+افرض واحد منهم اربع عشرين
+
+437
+00:49:30,910 --> 00:49:35,470
+يعني واضح على الأغلب هيكون C أصغر ترس فيهم هعمل
+
+438
+00:49:35,470 --> 00:49:43,350
+جدول تحكي
+
+439
+00:49:43,350 --> 00:49:50,130
+TA
+
+440
+00:49:50,130 --> 00:49:53,870
+TB
+
+441
+00:49:53,870 --> 00:49:57,170
+TC
+
+442
+00:49:57,170 --> 00:50:00,290
+و TD
+
+443
+00:50:09,610 --> 00:50:16,650
+تاسي بتساوي اربع و عشرين تاسي
+
+444
+00:50:16,650 --> 00:50:23,350
+تاسي تاسي تاسي تاسي تاسي تاسي تاسي تاسي تاسي تاسي
+
+445
+00:50:23,350 --> 00:50:23,810
+تاسي تاسي تاسي تاسي تاسي تاسي تاسي تاسي تاسي تاسي
+
+446
+00:50:23,810 --> 00:50:23,810
+تاسي تاسي تاسي تاسي تاسي تاسي تاسي تاسي تاسي تاسي
+
+447
+00:50:23,810 --> 00:50:23,810
+تاسي تاسي تاسي تاسي تاسي تاسي تاسي تاسي تاسي تاسي
+
+448
+00:50:23,810 --> 00:50:23,810
+تاسي تاسي تاسي تاسي تاسي تاسي تاسي تاسي تاسي تاسي
+
+449
+00:50:23,810 --> 00:50:23,810
+تاسي تاسي تاسي تاسي تاسي تاسي تاسي تاسي تاسي تاسي
+
+450
+00:50:23,810 --> 00:50:23,890
+تاسي تاسي تاسي تاسي تاسي تاسي تاسي تاسي تاسي
+
+451
+00:50:35,560 --> 00:50:45,580
+هتكون تستوى مية و ستين minus TC يعني
+
+452
+00:50:45,580 --> 00:50:51,360
+اول شي ال algorithm بتاعتنا يعني TC بتسوى some
+
+453
+00:50:51,360 --> 00:51:02,500
+value بعدين TD بتسوى مية و ستين minus TC احنا
+
+454
+00:51:02,500 --> 00:51:04,020
+استخدمنا المعادلة هذه
+
+455
+00:51:06,810 --> 00:51:14,650
+الان اندي هين صارت تي سي و تي دي معروفة الان تي بي
+
+456
+00:51:14,650 --> 00:51:18,510
+تي بي
+
+457
+00:51:18,510 --> 00:51:29,170
+بالساوي اتناش تي سي الان
+
+458
+00:51:29,170 --> 00:51:34,530
+تي بي بيساوي اتناشر تي سي تي اي
+
+459
+00:51:37,050 --> 00:51:43,950
+على ت دي صح زيك؟ معناته
+
+460
+00:51:43,950 --> 00:51:54,670
+هنعود في المعادلة هذه الان TA زائد
+
+461
+00:51:54,670 --> 00:52:05,550
+اتناش TC TA على ت دي بالساوية
+
+462
+00:52:06,940 --> 00:52:15,240
+مية و تمانية و عشرين خد TA على المشترك بيصير
+
+463
+00:52:15,240 --> 00:52:26,480
+واحد زاد اتناش TC على TD ساوة مية و تمانية و عشرين
+
+464
+00:52:26,480 --> 00:52:35,800
+معناته هتكون عنده TA هتكون
+
+465
+00:52:35,800 --> 00:52:47,390
+تساويمية و تمانية و عشرين على واحد زاد اتماش تي سي
+
+466
+00:52:47,390 --> 00:52:55,350
+على تي دي بعدين تي بي بالساوي
+
+467
+00:52:57,120 --> 00:53:07,020
+12 T C T A على T D معناه ان هذه الخطوة رقم واحد
+
+468
+00:53:07,020 --> 00:53:18,160
+وهذا رقم اتنين وهذا رقم تلاتة وهذا رقم ايه؟ اربعة
+
+469
+00:53:18,160 --> 00:53:22,560
+مظهور؟ هنعملها ايه؟ اكسل شيت
+
+470
+00:53:31,590 --> 00:53:34,690
+بتدعوض بس في ديشة بتدعوض بسرعة انا ديتها على الشكل
+
+471
+00:53:34,690 --> 00:53:49,350
+انا عملتها على شكل المعادلات بالظبط
+
+472
+00:53:49,350 --> 00:53:49,830
+على TD
+
+473
+00:53:54,920 --> 00:53:58,300
+أيوة انا .. انا .. انا .. انا كيف؟ انا استخدمت هذه
+
+474
+00:53:58,300 --> 00:54:03,940
+حطيتها وين؟ حطيتها في المعادلة هذه عشان أحسب TA
+
+475
+00:54:03,940 --> 00:54:07,340
+يعني كل معادلة دي لها TA فانا حسبت TA في الأول
+
+476
+00:54:07,340 --> 00:54:22,380
+بعدين بيصير TA المعروف بيحسب إيش؟ ال TB يعني
+
+477
+00:54:22,380 --> 00:54:31,570
+أول خطوة احنا عندنا إيش؟تسي تسي
+
+478
+00:54:31,570 --> 00:54:36,790
+تسي
+
+479
+00:54:36,790 --> 00:54:37,150
+تسي تسي تسي تسي تسي تسي تسي تسي تسي تسي تسي تسي
+
+480
+00:54:37,150 --> 00:54:48,790
+تسي تسي تسي
+
+481
+00:54:58,300 --> 00:55:03,160
+وين ال home؟
+
+482
+00:55:03,160 --> 00:55:18,740
+ده وين بس طيب
+
+483
+00:55:18,740 --> 00:55:24,000
+حسبنا ال TA ال TA شو يساوي المعادلة هذه مية و
+
+484
+00:55:24,000 --> 00:55:34,270
+تمانية و عشرينعلى نفتح قوس واحد زائد اتناش في TC
+
+485
+00:55:34,270 --> 00:55:46,750
+على TD نسكر القوس TB ايش يستوي اتناش
+
+486
+00:55:48,400 --> 00:55:56,640
+في تسي تسي
+
+487
+00:55:56,640 --> 00:55:58,900
+تسي تسي تسي تسي تسي تسي تسي تسي تسي تسي تسي تسي
+
+488
+00:55:58,900 --> 00:55:58,920
+تسي تسي تسي تسي تسي تسي تسي تسي تسي تسي تسي تسي
+
+489
+00:55:58,920 --> 00:56:03,820
+تسي تسي تسي تسي تسي تسي تسي تسي تسي تسي تسي تسي
+
+490
+00:56:03,820 --> 00:56:03,820
+تسي تسي تسي تسي تسي تسي تسي تسي تسي تسي تسي تسي
+
+491
+00:56:03,820 --> 00:56:03,820
+تسي تسي تسي تسي تسي تسي تسي تسي تسي تسي تسي تسي
+
+492
+00:56:03,820 --> 00:56:09,800
+تسي تسي تسي تسي تسي تسي تسي تسي تسي تسي تسي تسي
+
+493
+00:56:09,800 --> 00:56:13,140
+ت
+
+494
+00:56:19,370 --> 00:56:26,890
+الاتحادات مش ظابط صح؟ بعدين ستة عشرين مش ظابط سبعة
+
+495
+00:56:26,890 --> 00:56:35,970
+عشرين تمانية عشرين تسعة عشرين خلصنا
+
+496
+00:56:35,970 --> 00:56:45,150
+اه فحكوا قندي عدد سنان C تسعة عشرين لو بدينا من A
+
+497
+00:56:45,150 --> 00:56:55,800
+خمسة و تلاتينبعدين B 93 C 29 و D 131 يعني حد اللي
+
+498
+00:56:55,800 --> 00:57:03,520
+بيحطله كصورة بيحطله سفر لو حالة الخمسية صح نعم طيب
+
+499
+00:57:03,520 --> 00:57:11,380
+جرب إيش المشكلة أنت هتعمل المعادلات بالشكل هذا ما
+
+500
+00:57:11,380 --> 00:57:17,580
+أنا عارف هاخد بقى جداطيب في أي سؤال؟ محاضرة جاي
+
+501
+00:57:17,580 --> 00:57:23,700
+بنكمل لل epicyclic gear التران، أعطيكوا العفو
+
diff --git a/PL9fwy3NUQKwa0nXiCdyQcTW4hWDLTGpDb/GIrNxOPiuT8_postprocess.srt b/PL9fwy3NUQKwa0nXiCdyQcTW4hWDLTGpDb/GIrNxOPiuT8_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..897b0d4fb97bf4fc038e045c1dfa3b226decf42b
--- /dev/null
+++ b/PL9fwy3NUQKwa0nXiCdyQcTW4hWDLTGpDb/GIrNxOPiuT8_postprocess.srt
@@ -0,0 +1,2064 @@
+1
+00:00:05,200 --> 00:00:07,980
+بسم الله الرحمن الرحيم السلام عليكم ورحمة الله
+
+2
+00:00:07,980 --> 00:00:12,520
+وبركاته اليوم هنكمل في مادة نظرية الألات المحاضرات
+
+3
+00:00:12,520 --> 00:00:17,420
+السابقة بدأنا نحكي عن ال gear trains نعمل مراجعة
+
+4
+00:00:17,420 --> 00:00:21,540
+للمحاضرة السابقة حكينا عن أنواع ال gear trains عند
+
+5
+00:00:21,540 --> 00:00:24,600
+ال simple gear train ال compound ال reverted و ال
+
+6
+00:00:24,600 --> 00:00:30,420
+epicycle train في حالة ال simple gear train كل شفت
+
+7
+00:00:30,420 --> 00:00:33,700
+بيكون عليه gearفي حالة ال compound gear train
+
+8
+00:00:33,700 --> 00:00:38,880
+بيكون كل ال .. يعني .. يعني ال intermediate shaft
+
+9
+00:00:38,880 --> 00:00:42,540
+بيكون عليها أكتر من gear, irreverted gear train,
+
+10
+00:00:42,660 --> 00:00:46,200
+ال input gear و ال output gear اللي هو نفس المحور,
+
+11
+00:00:47,080 --> 00:00:52,020
+ال epicyclic gear train في بعض ال .. ال gears او
+
+12
+00:00:52,020 --> 00:00:55,220
+الشافت اللي راكها ال gears بتكون متحركة بالاضافة
+
+13
+00:00:55,220 --> 00:01:00,890
+لل gearsعملنا .. خلينا نجمع الأمثلة على ال symbol
+
+14
+00:01:00,890 --> 00:01:08,250
+و ال compound و ال reverted a جيري train اليوم
+
+15
+00:01:08,250 --> 00:01:19,250
+ال a بيساكلك جيري train مبين عندي أنا هنا مبين
+
+16
+00:01:19,250 --> 00:01:33,900
+عندي جير a و فيه درعمحمول عليه جير B الان جير B مش
+
+17
+00:01:33,900 --> 00:01:39,800
+مع جير A لان الإدراع اللى هو من O واحدة واتنين
+
+18
+00:01:39,800 --> 00:01:45,700
+بدور و هو بدور برضه بيكوناش الترس .. الترس B بدور
+
+19
+00:01:45,700 --> 00:01:51,520
+هذا يسمى AB Cyclic Geary Train معناته ال axis بتاع
+
+20
+00:01:51,520 --> 00:01:55,620
+الجير B ما هو قومي ثابت بتغيرالمحور تلعب الجير B
+
+21
+00:01:55,620 --> 00:01:59,960
+متغير لأن
+
+22
+00:01:59,960 --> 00:02:03,880
+في طريقتين لل analysis في طريقة استخدام جداول
+
+23
+00:02:03,880 --> 00:02:07,260
+tabular method وفي طريقة استخدام معادلات تسمى
+
+24
+00:02:07,260 --> 00:02:14,560
+algebraic method عشان
+
+25
+00:02:14,560 --> 00:02:17,620
+نبدأ ال analysis لو حكينا عدد السنان على الجير A
+
+26
+00:02:17,620 --> 00:02:20,500
+TA عدد السنان على الجير B TB
+
+27
+00:02:22,720 --> 00:02:26,940
+و نعتبر اتجاه دوران الموجة اللى هو بعكس عقارب
+
+28
+00:02:26,940 --> 00:02:33,400
+الساعة و اتجاه دوران السالب باتجاه عقارب الساعة
+
+29
+00:02:33,400 --> 00:02:38,020
+الخطوة
+
+30
+00:02:38,020 --> 00:02:45,160
+ال tabular method ال
+
+31
+00:02:45,160 --> 00:02:49,140
+tabular method اول اشهر يسوي اشهر لان في عندي عندي
+
+32
+00:02:49,140 --> 00:02:49,760
+ال arm
+
+33
+00:02:56,170 --> 00:03:00,330
+عندي جير A و
+
+34
+00:03:00,330 --> 00:03:07,850
+جير B بعمل
+
+35
+00:03:07,850 --> 00:03:16,870
+fix لل arm أول خطوة fix ال
+
+36
+00:03:16,870 --> 00:03:23,610
+arm و
+
+37
+00:03:23,610 --> 00:03:23,930
+rotate
+
+38
+00:03:28,420 --> 00:03:37,680
+rotate a plus x rpm عكس القرص يعني انه هذا يصير
+
+39
+00:03:37,680 --> 00:03:44,200
+fixed بس هدا ترسين عاديات صح؟ اذا هدا ضار x كان
+
+40
+00:03:44,200 --> 00:03:49,780
+سرعته x سرعة x هتكون b سرعته ايش يساوي؟ اذا هدا
+
+41
+00:03:49,780 --> 00:03:55,200
+fixed بيبقى ناط سرعته ايش هتكون؟ zeroالـ A هيكون
+
+42
+00:03:55,200 --> 00:04:03,060
+plus X الـ B هيكون .. هيدور عكسه صح؟ هيكون minus X
+
+43
+00:04:03,060 --> 00:04:16,780
+في عدسنان A على عدسنان B بعدين add plus Y يعطيهم
+
+44
+00:04:16,780 --> 00:04:26,510
+إضافة plus Y to allهنا دي plus y هنا plus y هنا
+
+45
+00:04:26,510 --> 00:04:36,610
+plus y بعدين أجمع هيكون دي y x زائد y هنا y minus
+
+46
+00:04:36,610 --> 00:04:47,310
+x في TA على TB هدا هتكون ايش N ال arm هتكون مش
+
+47
+00:04:47,310 --> 00:05:00,110
+الساوية Yو N A سرعة الترس A هتكون X زي Y و N B
+
+48
+00:05:00,110 --> 00:05:03,270
+هتكون
+
+49
+00:05:03,270 --> 00:05:09,730
+Y minus X TA على
+
+50
+00:05:09,730 --> 00:05:14,170
+TB اللي
+
+51
+00:05:14,170 --> 00:05:14,810
+هو الجدول هذا
+
+52
+00:05:20,890 --> 00:05:28,450
+طريقة الجبرية هي relative speed NB NB
+
+53
+00:05:28,450 --> 00:05:40,430
+-NC NA-NC نشوف
+
+54
+00:05:40,430 --> 00:05:40,910
+مثال
+
+55
+00:05:56,210 --> 00:05:59,890
+in an epicyclic gear train, an arm carries two
+
+56
+00:05:59,890 --> 00:06:05,770
+gears, A and B, having thirty-six and forty-five
+
+57
+00:06:05,770 --> 00:06:15,670
+teeth عندي high gear high
+
+58
+00:06:15,670 --> 00:06:21,010
+gear و
+
+59
+00:06:21,010 --> 00:06:25,710
+high arm بينهم خلينا نسمي هذا A
+
+60
+00:06:28,800 --> 00:06:36,020
+B و ال arm C ان ال A بيسجي ترين and arm carries
+
+61
+00:06:36,020 --> 00:06:44,840
+two gears A and B يعطينا TA بالساوي
+
+62
+00:06:44,840 --> 00:06:56,020
+ست تلاتين و TB خمس و أربعين سنif the arm rotates
+
+63
+00:06:56,020 --> 00:07:05,980
+at 150 rpm counter clockwise about
+
+64
+00:07:05,980 --> 00:07:11,760
+center
+
+65
+00:07:11,760 --> 00:07:19,580
+of gear A which
+
+66
+00:07:19,580 --> 00:07:22,360
+is fixed
+
+67
+00:07:28,970 --> 00:07:33,230
+if the arm rotates at 150 rpm about center of gear
+
+68
+00:07:33,230 --> 00:07:37,830
+A which لا ال gear A is fixed determine speed of
+
+69
+00:07:37,830 --> 00:07:46,730
+gear B بده N يعني ن A بالساوية سفر ون C ون B
+
+70
+00:07:46,730 --> 00:07:50,910
+مطلوبة
+
+71
+00:07:50,910 --> 00:07:54,070
+هعمل جدول
+
+72
+00:08:04,750 --> 00:08:09,430
+هي a b
+
+73
+00:08:09,430 --> 00:08:12,690
+c
+
+74
+00:08:12,690 --> 00:08:27,590
+أولش هعمل fix fix ال R fix c rotate a at plus x
+
+75
+00:08:27,590 --> 00:08:31,130
+يعني
+
+76
+00:08:31,130 --> 00:08:37,930
+هدا هتكون plus xو C Fixed بيعني ايه صورته Zero
+
+77
+00:08:37,930 --> 00:08:49,370
+بيعني بيه هتكون minus X TA على TB Add
+
+78
+00:08:49,370 --> 00:08:56,470
+plus Y عندها
+
+79
+00:08:56,470 --> 00:08:58,970
+ال plus Y لا
+
+80
+00:09:04,500 --> 00:09:09,920
+لسه ماخلصتش انا لسه اصبر شويه بخلصه plus y plus y
+
+81
+00:09:09,920 --> 00:09:22,860
+اجمع هكوا اندي x plus y و y minus x ta على tb و y
+
+82
+00:09:22,860 --> 00:09:26,240
+هذه
+
+83
+00:09:26,240 --> 00:09:38,810
+المجموع بيمثل ايه؟سرعة A NA فكست صح؟ X زائد Y وهي
+
+84
+00:09:38,810 --> 00:09:43,230
+معادلة واحدة وهذه
+
+85
+00:09:43,230 --> 00:09:52,610
+NC اللي هي اكم؟ مية و خمسين ايش الساوية؟ Y معناته
+
+86
+00:09:52,610 --> 00:09:57,770
+عرفت ايش؟ Y معناته X ايش حتساوية؟
+
+87
+00:10:08,440 --> 00:10:22,020
+ن بي هتكون تساوي ال
+
+88
+00:10:22,020 --> 00:10:22,720
+Y عند 150
+
+89
+00:10:25,660 --> 00:10:37,080
+ناقص x بقى على الناقص 150 صح في TA 36
+
+90
+00:10:37,080 --> 00:10:40,560
+على
+
+91
+00:10:40,560 --> 00:10:48,780
+45 يعني على الخمستاش تلاتة على الخمستاش عشرة على
+
+92
+00:10:48,780 --> 00:10:52,880
+التلاتة واحد على التلاتة إيش اتناش 120 زاد 150
+
+93
+00:11:01,410 --> 00:11:07,850
+اربع يعني بيبقى
+
+94
+00:11:07,850 --> 00:11:11,610
+أي سؤال؟ شوف السؤال تاني
+
+95
+00:11:33,210 --> 00:11:37,930
+in a reverted apcyclic gear train هذا apcyclic و
+
+96
+00:11:37,930 --> 00:11:42,130
+reverted يعني ال axis بتاع ال input و ال output
+
+97
+00:11:42,130 --> 00:11:50,450
+نفس ال axis مش نفس ال shaft arm
+
+98
+00:11:50,450 --> 00:11:55,950
+a هذا ال arm a carries
+
+99
+00:11:55,950 --> 00:12:00,070
+two gears B
+
+100
+00:12:00,070 --> 00:12:02,610
+and C هذا حامل B and C
+
+101
+00:12:08,860 --> 00:12:16,620
+and a compound جير دي ايه دي و ايه compound معناته
+
+102
+00:12:16,620 --> 00:12:24,780
+اللي هو نفس السرعة يعني ن دي بيساوي ن ايه ن دي
+
+103
+00:12:24,780 --> 00:12:32,240
+بيساوي ن ايه the
+
+104
+00:12:32,240 --> 00:12:42,700
+number ofteeth on gears B,C and D are ماطينة T أكم
+
+105
+00:12:42,700 --> 00:12:58,340
+ماطينيها خمسة سبعين و T C تلاتين و T D تسعين find
+
+106
+00:12:58,340 --> 00:13:03,720
+the speed and direction of gear C بده N C
+
+107
+00:13:11,810 --> 00:13:19,750
+when gear b is fixed, b fixed يعني nb بالساوية
+
+108
+00:13:19,750 --> 00:13:28,270
+صفر and arm a makes one hundred rpm clockwise يعني
+
+109
+00:13:28,270 --> 00:13:36,130
+na بالساوية سالب اتفقنا
+
+110
+00:13:36,130 --> 00:13:42,080
+clockwise سالب counter clockwise موجةهعمل الجدول
+
+111
+00:13:42,080 --> 00:13:54,340
+هعندي
+
+112
+00:13:54,340 --> 00:14:02,600
+طبعا ال R و ال truth A B C D E هعندي هاي A
+
+113
+00:14:13,160 --> 00:14:24,260
+A B C
+
+114
+00:14:24,260 --> 00:14:28,880
+D
+
+115
+00:14:28,880 --> 00:14:30,600
+A
+
+116
+00:14:42,360 --> 00:14:47,460
+أول شي هعمل fix لل arm fix
+
+117
+00:14:47,460 --> 00:14:52,420
+arm
+
+118
+00:14:52,420 --> 00:15:01,680
+fix يعني هتكون السرعة ايه؟ zero خلينا
+
+119
+00:15:01,680 --> 00:15:07,120
+ادور ايه بي plus x rotate بي
+
+120
+00:15:15,350 --> 00:15:27,050
+at plus x B
+
+121
+00:15:27,050 --> 00:15:35,170
+drive A صح؟ B drive A معناه تسارة E مش هتكون ساوية
+
+122
+00:15:35,170 --> 00:15:42,030
+minus X TB على TA
+
+123
+00:15:45,120 --> 00:15:51,420
+و E نفس سرعة اذا D نفس سرعة اذا D نفس سرعة اذا D
+
+124
+00:15:51,420 --> 00:15:54,480
+نفس سرعة اذا D
+
+125
+00:15:54,480 --> 00:15:58,120
+نفس سرعة اذا D نفس سرعة اذا D نفس سرعة اذا D نفس
+
+126
+00:15:58,120 --> 00:16:02,660
+سرعة اذا D نفس سرعة اذا D نفس سرعة اذا D نفس سرعة
+
+127
+00:16:02,660 --> 00:16:02,700
+اذا D نفس سرعة اذا D نفس سرعة اذا D نفس سرعة اذا D
+
+128
+00:16:02,700 --> 00:16:02,760
+سرعة اذا D نفس سرعة اذا D نفس سرعة اذا D نفس سرعة
+
+129
+00:16:02,760 --> 00:16:02,820
+اذا D نفس سرعة اذا D نفس سرعة اذا D نفس سرعة اذا D
+
+130
+00:16:02,820 --> 00:16:09,000
+نفس سرعة اذا D نفس سرعة اذا D نفس سرعة اذا D نفس
+
+131
+00:16:09,000 --> 00:16:10,360
+سرعة ا
+
+132
+00:16:14,240 --> 00:16:41,000
+على TA هذا صورة D في TD على TC بعدين Add بعدين
+
+133
+00:16:41,000 --> 00:16:52,240
+أجمح هذا هتكون Yهنا X زائد Y هنا هتكون Y زائد XTB
+
+134
+00:16:52,240 --> 00:17:11,160
+على TE TD على TC Y minus XTB على TE ال Y minus XTB
+
+135
+00:17:12,430 --> 00:17:20,830
+على TA هو بيعطيني معلومات بيحكيلي
+
+136
+00:17:20,830 --> 00:17:28,870
+التالة NB بيستوى صفر NB بيستوى
+
+137
+00:17:28,870 --> 00:17:36,150
+صفر اللي هي هذه صح X زي Y هاي
+
+138
+00:17:36,150 --> 00:17:36,570
+واحد
+
+139
+00:17:40,250 --> 00:17:50,370
+و N A N A بالساوية سالب مية بالساوياش
+
+140
+00:17:50,370 --> 00:17:58,030
+Y معناته X بالساوياش
+
+141
+00:17:58,030 --> 00:18:06,430
+مية بدنا
+
+142
+00:18:06,430 --> 00:18:08,370
+N C N C مش الساوية
+
+143
+00:18:11,630 --> 00:18:17,450
+بتكون اللي هي بدنا ياها بالساوية Y زائد
+
+144
+00:18:17,450 --> 00:18:29,170
+X TB TD على TE في TC يعني هيكون الساوية ال Y عندى
+
+145
+00:18:29,170 --> 00:18:35,210
+سالب مية وال
+
+146
+00:18:35,210 --> 00:18:39,490
+X مية في
+
+147
+00:18:39,490 --> 00:18:54,520
+TB ايش بالساويةت بي خمسة سبعين في ت دي تسعين على ت
+
+148
+00:18:54,520 --> 00:19:07,260
+مش معروفة في تلتين يعني
+
+149
+00:19:07,260 --> 00:19:11,900
+هيصف عندي هنا ان سي بتساوي ناقص مية
+
+150
+00:19:16,340 --> 00:19:21,000
+زاد هاي التلاتة في خمس سبعين متين و خمس و عشرين
+
+151
+00:19:21,000 --> 00:19:32,740
+هتكون اتنين و عشرين ألف و خمسمية على TA مظبوط
+
+152
+00:19:32,740 --> 00:19:35,840
+هدى
+
+153
+00:19:35,840 --> 00:19:42,380
+أنسى مش هتفيدني ال ال ال ال und
+
+154
+00:19:46,140 --> 00:19:53,040
+بقى انا مش عارف ال N D مش عارف ال N D طيب الان
+
+155
+00:19:53,040 --> 00:19:59,000
+يعني بدي معادلات هنا اضافية كيف هساوي معادلة
+
+156
+00:19:59,000 --> 00:20:06,860
+اضافية N D بيساوي N A اتطلع على الشكل هذه
+
+157
+00:20:06,860 --> 00:20:16,600
+المسافة هذه المسافة بتساوي هذه زيدي هذه صحcenter
+
+158
+00:20:16,600 --> 00:20:26,620
+distance انك بي مع اي و دي مع سي صح ماانا بتحكول
+
+159
+00:20:26,620 --> 00:20:35,200
+ان دي ان بي زاد ان اي
+
+160
+00:20:35,200 --> 00:20:42,440
+زاد ان اي بالساوية ان دي زاد ان سي او ده مش ان هنا
+
+161
+00:20:42,440 --> 00:20:54,800
+تي بيB مع E صح تي بي زي تي إي بيساوي تي سي زي تي
+
+162
+00:20:54,800 --> 00:21:01,860
+دي تي بي اللي هي خمس و سبعين تي
+
+163
+00:21:01,860 --> 00:21:09,580
+إي مش عارفينها يعني
+
+164
+00:21:09,580 --> 00:21:14,160
+تي إي أكم تطلع خمس
+
+165
+00:21:14,160 --> 00:21:14,760
+و أربعين صح
+
+166
+00:21:20,730 --> 00:21:31,270
+معناه تحسين الان سي هتكون
+
+167
+00:21:31,270 --> 00:21:38,930
+سواء ناقص مية زي اتنين و عشرين الف و خمسمية على
+
+168
+00:21:38,930 --> 00:21:41,650
+خمسة و اربعين
+
+169
+00:21:50,300 --> 00:21:56,280
+RBM هو شده NC خلاص
+
+170
+00:21:56,280 --> 00:22:02,460
+بعدين تجيب سرعة ND ما هي هتكون التحصيل حاصل ND
+
+171
+00:22:02,460 --> 00:22:14,440
+بالساوي Y minus X TB على TA TE ال Y عندي اللي هي
+
+172
+00:22:14,440 --> 00:22:18,300
+سالب مية minus
+
+173
+00:22:26,430 --> 00:22:34,050
+x x مية في
+
+174
+00:22:34,050 --> 00:22:41,390
+أكم؟ في خمس و سبعين على
+
+175
+00:22:41,390 --> 00:22:48,290
+خمس و أربعين على الخمستاش على الخمستاش فيه تلاتة
+
+176
+00:22:49,790 --> 00:22:56,690
+الخمساش فياش خمسة يعني هتكون مية سالب
+
+177
+00:22:56,690 --> 00:23:04,410
+خمس مية ع تلاتة اكم مية و سبعة ستين point
+
+178
+00:23:04,410 --> 00:23:13,630
+ستة سبعة صح مية و ستة ستين point ستة سبعة سالب
+
+179
+00:23:13,630 --> 00:23:18,470
+طبعا يعني هتكون سالب ميتين و ستة ستين
+
+180
+00:23:22,480 --> 00:23:28,660
+يعني بالنظر clockwise في
+
+181
+00:23:28,660 --> 00:23:32,880
+اي سؤال طيب
+
+182
+00:23:32,880 --> 00:23:34,980
+نشوف example تالت
+
+183
+00:23:51,570 --> 00:23:55,810
+and a bicycle gear consist of three gears a,b and
+
+184
+00:23:55,810 --> 00:24:01,390
+c هي عندي a internal gear و b external و c
+
+185
+00:24:01,390 --> 00:24:14,130
+external و فيه الدراع هي حامل الجير b جير a has
+
+186
+00:24:14,130 --> 00:24:17,190
+seventy two internal teeth جير a سن داخلي
+
+187
+00:24:21,640 --> 00:24:26,940
+اتنين و سبعين جير
+
+188
+00:24:26,940 --> 00:24:33,240
+C اتنين
+
+189
+00:24:33,240 --> 00:24:44,240
+و تلاتين سن خارجي جير B مشes with A and C
+
+190
+00:24:48,260 --> 00:24:52,940
+طيب and is carried on arm EF which rotates about
+
+191
+00:24:52,940 --> 00:25:05,540
+the center of A at 18 rpm اللي هي N EF
+
+192
+00:25:05,540 --> 00:25:13,860
+أكم تساوي 18 اعتبرها موجة
+
+193
+00:25:17,130 --> 00:25:24,330
+if gear A is fixed معناته N A بالساعة سفر
+
+194
+00:25:24,330 --> 00:25:33,590
+determine the speed of gears B and C نفس
+
+195
+00:25:33,590 --> 00:25:34,510
+المنطق
+
+196
+00:25:53,160 --> 00:26:07,600
+أنا عندي واحد اتنين تلاتة أربعة ال
+
+197
+00:26:07,600 --> 00:26:30,000
+E F ال R عندي A B C و اشي fixed ال Rrotate C
+
+198
+00:26:30,000 --> 00:26:33,040
+rotate
+
+199
+00:26:33,040 --> 00:26:39,020
+C at plus
+
+200
+00:26:39,020 --> 00:26:50,520
+X يعني هذه الحاجة كون ال R مش سفر ال C plus X ال C
+
+201
+00:26:50,520 --> 00:26:58,990
+it drivesب هتكون minus minus
+
+202
+00:26:58,990 --> 00:27:07,110
+x في TC على TB وB
+
+203
+00:27:07,110 --> 00:27:12,150
+it drives A لكن انه external and internal هيدوره
+
+204
+00:27:12,150 --> 00:27:16,130
+نفس الاتجاه هتكون هادر برضه مش هيطير الاتجاه هتكون
+
+205
+00:27:16,130 --> 00:27:23,510
+minus x TC على TB في
+
+206
+00:27:38,870 --> 00:27:42,890
+طيب هدا واحد اتنين
+
+207
+00:27:57,950 --> 00:28:12,590
+هيكون Y Y minus X T C على T A هين Y minus X T C
+
+208
+00:28:12,590 --> 00:28:23,930
+على T B هين X زائد Y و بيعطيني معلومات NEF
+
+209
+00:28:27,210 --> 00:28:36,430
+بساوة طبنتاش اللي هي بساوة إيش؟ Y نعطينا A is
+
+210
+00:28:36,430 --> 00:28:49,750
+fixed NA بساوة سفر اللي هي عبارة عن Y minus X TC
+
+211
+00:28:49,750 --> 00:28:54,090
+على TA
+
+212
+00:28:56,730 --> 00:29:06,110
+ال Y يعني هكون عندى سفر سوى ال Y طمنتاش minus X TC
+
+213
+00:29:06,110 --> 00:29:19,210
+32 على 2 و 70 يعني ع ال 8 أربع ع ال 8 تسعة صح يعني
+
+214
+00:29:19,210 --> 00:29:29,750
+هتكون طمنتاشسفر بالساوية طمنتاش ناقص أربعة على
+
+215
+00:29:29,750 --> 00:29:37,590
+تسعة X يعني
+
+216
+00:29:37,590 --> 00:29:47,450
+X هتكون تساوية طمنتاش في تسعة على أربعة يعني تسعة
+
+217
+00:29:47,450 --> 00:29:49,690
+في تسعة واحد تمانين على اتنين اربعين ونص
+
+218
+00:29:55,400 --> 00:30:00,180
+هذه ال X الان
+
+219
+00:30:00,180 --> 00:30:12,620
+عندي NB NB
+
+220
+00:30:12,620 --> 00:30:17,020
+هتكون
+
+221
+00:30:17,020 --> 00:30:23,480
+تساوي Y minus X DC
+
+222
+00:30:28,470 --> 00:30:34,290
+على ال TV او
+
+223
+00:30:34,290 --> 00:30:41,990
+خلنا نقش .. نشوف أولا الاشي المعروف NC بيستوى
+
+224
+00:30:41,990 --> 00:30:52,490
+X زائد Y X عندي أكم؟ أربعين و نص زائد Y طمنتاش
+
+225
+00:30:52,490 --> 00:30:53,930
+يعني هتساوي
+
+226
+00:31:02,440 --> 00:31:06,760
+هذه N C N
+
+227
+00:31:06,760 --> 00:31:13,380
+B بتساوي
+
+228
+00:31:13,380 --> 00:31:29,400
+Y minus X في T C على T B يعني عند ال Y أكم 18
+
+229
+00:31:31,060 --> 00:31:39,920
+ناقص اربعين و نص ال TC في اتنين و تلاتين TB
+
+230
+00:31:39,920 --> 00:31:50,200
+مش عارفة صح على TB يعني
+
+231
+00:31:50,200 --> 00:31:55,200
+هيكون ساوى تمانتاش ناقص
+
+232
+00:31:55,200 --> 00:31:58,820
+على
+
+233
+00:31:58,820 --> 00:32:09,260
+TBالان بي طيب
+
+234
+00:32:09,260 --> 00:32:24,440
+في انا مجهول عدد سنة انت ع بي صح؟
+
+235
+00:32:24,440 --> 00:32:26,880
+نعم
+
+236
+00:32:29,280 --> 00:32:39,800
+أه دي بدك تروح اتنين يعني ألف ألف و متين طيب
+
+237
+00:32:39,800 --> 00:32:47,060
+اللي هى NB هيتعدي ال TB مش معروفة لكن ممكن أطلعها
+
+238
+00:32:47,060 --> 00:32:52,000
+ولا مش ممكن طلع
+
+239
+00:32:52,000 --> 00:32:55,920
+ال center distance مص قطر هذا RA اشو يستوي
+
+240
+00:32:58,780 --> 00:33:10,340
+مص قطر الترس A بيستوي RC زاد القطر هذا RC زاد
+
+241
+00:33:10,340 --> 00:33:17,680
+اتنين RB يعني
+
+242
+00:33:17,680 --> 00:33:21,360
+هيكون TA بيستوي TC
+
+243
+00:33:26,300 --> 00:33:36,720
+زائد اتنين TB TA
+
+244
+00:33:36,720 --> 00:33:40,400
+اكم عندي 72
+
+245
+00:33:40,400 --> 00:33:49,360
+و TC 32 زائد اتنين TB يعني TB اكم عشرين
+
+246
+00:33:55,190 --> 00:34:00,230
+يعني NB هتكون
+
+247
+00:34:00,230 --> 00:34:04,510
+تستاوي 18-1296
+
+248
+00:34:04,510 --> 00:34:10,330
+على 20 هتستاوي
+
+249
+00:34:10,330 --> 00:34:17,270
+تطلع بالسالب هذا سالب 46.80
+
+250
+00:34:24,670 --> 00:34:31,310
+revolution per minute في أي سؤال؟ طيب شوف السؤال
+
+251
+00:34:31,310 --> 00:34:35,150
+هذا how many revolutions does the arm to which
+
+252
+00:34:35,150 --> 00:34:42,920
+pinions B and C are attached make؟ عندي ال armهعمل
+
+253
+00:34:42,920 --> 00:34:49,340
+ال penion B و ال penion C و في ترس و نص A و في ترس
+
+254
+00:34:49,340 --> 00:35:00,140
+داخل .. سن داخل D فبده .. بده صرعة التروث الصغير B
+
+255
+00:35:00,140 --> 00:35:08,340
+و C يعني بده NB و
+
+256
+00:35:08,340 --> 00:35:09,000
+NC
+
+257
+00:35:12,510 --> 00:35:18,030
+when a makes one revolution clockwise a
+
+258
+00:35:18,030 --> 00:35:29,330
+and a minus واحد and
+
+259
+00:35:29,330 --> 00:35:35,850
+d هذا d makes half a revolution counter clockwise
+
+260
+00:35:35,850 --> 00:35:37,970
+and d
+
+261
+00:35:54,270 --> 00:36:05,050
+نص طيب انا
+
+262
+00:36:05,050 --> 00:36:12,750
+عند a a b c d 4 5 و ال R
+
+263
+00:36:27,990 --> 00:36:44,570
+الارم a b c d عامل fix للارم وليش ايه rotate
+
+264
+00:36:48,240 --> 00:36:54,000
+rotate a في الحلقة دي rotate a plus
+
+265
+00:36:54,000 --> 00:36:58,260
+x fix
+
+266
+00:36:58,260 --> 00:37:07,160
+ال arm zero plus x بيه
+
+267
+00:37:07,160 --> 00:37:09,320
+هتكون minus بيه و c نفس الاشي minus
+
+268
+00:37:15,770 --> 00:37:19,530
+هم عطينا number of teeth on gears A and D هم عطينا
+
+269
+00:37:19,530 --> 00:37:23,710
+TA أكم
+
+270
+00:37:23,710 --> 00:37:36,270
+أربعين و TD ساوي تسعين ال
+
+271
+00:37:36,270 --> 00:37:42,630
+B هيكون minus X
+
+272
+00:37:42,630 --> 00:37:52,290
+TAعلى ت بي هذا برضه نفس الشيء minus X TA على ت بي
+
+273
+00:37:52,290 --> 00:38:02,190
+نفس عدد سنة لأنهم نفس الموديول كلهم ال D مع
+
+274
+00:38:02,190 --> 00:38:07,710
+B أو C البداكية ال B هكون نفسه تجاههم هتكون minus
+
+275
+00:38:07,710 --> 00:38:11,090
+X TA
+
+276
+00:38:12,570 --> 00:38:30,530
+على ت بي في ت بي على ت دي plus
+
+277
+00:38:30,530 --> 00:38:37,590
+y y
+
+278
+00:38:37,590 --> 00:38:53,680
+x زائد yY minus X TA على TB Y minus X TA على TB Y
+
+279
+00:38:53,680 --> 00:38:58,680
+minus X TA على TD
+
+280
+00:39:18,170 --> 00:39:22,710
+الان صورة ال arm اللي هي بيستوى Y و Y مش عارفها
+
+281
+00:39:22,710 --> 00:39:33,150
+عندي هو بيحكيلي انه NA بيستوى سالب واحد بيستوى X
+
+282
+00:39:33,150 --> 00:39:42,830
+زائد Y هاي المعادلة ومعطيلي ND بيستوى
+
+283
+00:39:42,830 --> 00:39:43,250
+نص
+
+284
+00:39:47,190 --> 00:40:00,310
+اللي هي Y minus X TA على TD صح؟ يعني نص هتكون سوى
+
+285
+00:40:00,310 --> 00:40:10,810
+Y minus X TA أكمل عند إيه؟ أربعين على تسعين
+
+286
+00:40:16,030 --> 00:40:24,250
+يعني من واحد from one او ممكن ايش نسوي اجمع واحد
+
+287
+00:40:24,250 --> 00:40:38,850
+مع اتنين يعني واحد زائد اتنين ثانية
+
+288
+00:40:38,850 --> 00:40:44,110
+خليني اطرح واحد
+
+289
+00:40:46,760 --> 00:40:58,980
+نقص اتنين هزبط هزير عنده سالب واحد سالب نص سالب
+
+290
+00:40:58,980 --> 00:41:05,960
+واحد و نص بعدين عنده هتروح ال Y مع ال Y هزير plus
+
+291
+00:41:05,960 --> 00:41:15,640
+اتنين بالسواء X في واحد زاد اربع على تسعة صح؟
+
+292
+00:41:18,820 --> 00:41:26,820
+تلتاش على تسعة يعني X ستكون سالب واحد و نص في
+
+293
+00:41:26,820 --> 00:41:38,060
+تسعة و تلتاش مظبوط هذي X طيب
+
+294
+00:41:38,060 --> 00:41:47,120
+هذي X معناته ال Y ستكون سالب واحد سالب Xهتكون
+
+295
+00:41:47,120 --> 00:41:55,200
+تساوي سالب واحد زائد واحد
+
+296
+00:41:55,200 --> 00:42:00,180
+و نص في تسعة تلتاش
+
+297
+00:42:00,180 --> 00:42:04,260
+و نص ع
+
+298
+00:42:04,260 --> 00:42:12,560
+تلتاش صح؟ سالب زائد تلتاش و نص ع تلتاش يعني الواحد
+
+299
+00:42:12,560 --> 00:42:25,780
+هتكون تساوينص واحد ع ستة وعشر يعني صح طيب
+
+300
+00:42:25,780 --> 00:42:33,540
+حسبنا x و y هو ايش بده how man revolution does the
+
+301
+00:42:33,540 --> 00:42:40,500
+arm اللي هي ال .. ال arm اللي هي هتكون صرته اللي
+
+302
+00:42:40,500 --> 00:42:47,960
+هي أن .. أن ال armهتكون تساوي y لي واحد على ست
+
+303
+00:42:47,960 --> 00:42:51,920
+عشرين خربي
+
+304
+00:42:51,920 --> 00:43:03,320
+يا عم هذا
+
+305
+00:43:03,320 --> 00:43:08,680
+المطلوب المطلوب التاني يدخل صورة ال R وين A هذا
+
+306
+00:43:08,680 --> 00:43:10,240
+المطلوب الأول المطلوب التاني
+
+307
+00:43:13,910 --> 00:43:19,210
+when A makes one revolution clockwise يعني N A
+
+308
+00:43:19,210 --> 00:43:36,030
+سالب واحد RPM و D is stationary و N D ساو سفر N A
+
+309
+00:43:36,030 --> 00:43:43,440
+اللي هي هتكون سالب واحد ساو X زائد Yو أن دي
+
+310
+00:43:43,440 --> 00:43:53,720
+بالساوية صفر Y minus
+
+311
+00:43:53,720 --> 00:44:09,000
+X TA في أربع على تسعة طيب
+
+312
+00:44:09,000 --> 00:44:18,450
+هاي حسابين تلاتةو هذه أربعة نحن
+
+313
+00:44:18,450 --> 00:44:30,510
+بحكي تلاتة ناقص أربعة هيعطينا سالب واحد بالساوية
+
+314
+00:44:30,510 --> 00:44:36,210
+plus
+
+315
+00:44:36,210 --> 00:44:44,510
+تلاتاش على تسعة X يعني X ستكون ساوية سالب تسعةع
+
+316
+00:44:44,510 --> 00:44:48,470
+تلاتاش يعني
+
+317
+00:44:48,470 --> 00:44:55,630
+Y اللي هي N ال arm هتكون
+
+318
+00:44:55,630 --> 00:45:01,830
+تساوي minus
+
+319
+00:45:01,830 --> 00:45:12,070
+واحد زائد تسعة ع تلاتاش يعني هتكون minus
+
+320
+00:45:17,180 --> 00:45:26,780
+RBM شوف مثال فيه تفاصيل أكتر in an epicyclic gear
+
+321
+00:45:26,780 --> 00:45:30,180
+train the internal wheels A and B في عنده two
+
+322
+00:45:30,180 --> 00:45:37,920
+internal gears هذا ترس داخلي A و هذا ترس داخلي B
+
+323
+00:45:37,920 --> 00:45:43,160
+and compound wheels C and D يعني C and D مثبتين
+
+324
+00:45:43,160 --> 00:45:43,960
+مدوروا مع بعض
+
+325
+00:45:47,270 --> 00:45:53,690
+rotate independently about axis O يعني A و B بدور
+
+326
+00:45:53,690 --> 00:46:05,830
+حوالين O و C و D بدور حوالين O طيب
+
+327
+00:46:05,830 --> 00:46:19,140
+wheels E and F هاي E E مش مع C مع Aو F مش مع D و
+
+328
+00:46:19,140 --> 00:46:25,600
+مع B ماشي All
+
+329
+00:46:25,600 --> 00:46:28,160
+wheels have the same module and the number of
+
+330
+00:46:28,160 --> 00:46:38,180
+teeth are المعطين عدد الأسنان تاسي تاسي
+
+331
+00:46:38,180 --> 00:46:42,980
+تمانية
+
+332
+00:46:42,980 --> 00:46:53,370
+و عشرينت دي ستة و عشرين ت بساوة ت اف
+
+333
+00:46:53,370 --> 00:47:01,490
+بساوة تمانتاش find
+
+334
+00:47:01,490 --> 00:47:07,990
+number of teeth on a and b حسب العد السنان بتاع a
+
+335
+00:47:07,990 --> 00:47:08,470
+و b
+
+336
+00:47:16,040 --> 00:47:25,020
+انت تطلعه هذا نص القطر هذا نص القطر ايه عشان a نص
+
+337
+00:47:25,020 --> 00:47:31,360
+قطر a اللي هو ر a ايش يساوي؟
+
+338
+00:47:31,360 --> 00:47:42,060
+ر اي ر اي هذا IRC بالظبط RC
+
+339
+00:47:46,130 --> 00:47:53,490
+زاد اتنين RA طبعا
+
+340
+00:47:53,490 --> 00:47:56,110
+تقولوا لقب في المدينة و مانتوا هترجع للقب الأسنان
+
+341
+00:47:56,110 --> 00:48:00,710
+هيكون ال TA او
+
+342
+00:48:00,710 --> 00:48:05,430
+ال TC احنا
+
+343
+00:48:05,430 --> 00:48:13,350
+معطينا TC و TA يعني هيكون عندك TC أكم تمانية و
+
+344
+00:48:13,350 --> 00:48:13,750
+عشرين
+
+345
+00:48:17,370 --> 00:48:24,830
+زيادة اتنين في تمانتاش اربعة
+
+346
+00:48:24,830 --> 00:48:29,230
+ستين سنة
+
+347
+00:48:29,230 --> 00:48:36,650
+بالنسبالي بي هاي
+
+348
+00:48:36,650 --> 00:48:44,430
+بي هاي انا ر بي ر بي ايه مش ساوي
+
+349
+00:48:50,950 --> 00:49:04,090
+ر دي زي اتنين ر اف ر دي زي اتنين ر اف يعني هكون دي
+
+350
+00:49:04,090 --> 00:49:16,310
+ت بي ت دي زي اتنين ت اف ال ت دي تمانية ت دي ست و
+
+351
+00:49:16,310 --> 00:49:29,620
+عشرين زي اتنين في تمانتاش62 مظبوط خلصنا
+
+352
+00:49:29,620 --> 00:49:33,560
+من هذه if
+
+353
+00:49:33,560 --> 00:49:39,660
+arm g makes one hundred rpm clockwise يعني ماعطينا
+
+354
+00:49:39,660 --> 00:49:49,240
+هو أن g ماقص مائة و تمانين مائة rpm
+
+355
+00:49:52,590 --> 00:50:13,170
+and A is fixed و أن A سو Zero بده أن B أنا
+
+356
+00:50:13,170 --> 00:50:22,110
+عندي من A A B C D E F Gبدنا سبعة و بالنقطة بدنا
+
+357
+00:50:22,110 --> 00:50:29,290
+تمان عمدان أولش
+
+358
+00:50:29,290 --> 00:50:39,250
+عند ال arm هنحكي جي في الآخر هاي
+
+359
+00:50:39,250 --> 00:50:43,130
+جي، آخرش جي صح؟ جي
+
+360
+00:50:57,040 --> 00:51:04,760
+أحنا بدنا نحكي أنها سبعة يعني غير هذا .. يعني غير
+
+361
+00:51:04,760 --> 00:51:07,880
+هذا سبعة لأن هذا ستة
+
+362
+00:51:35,140 --> 00:51:49,380
+and a,b,c,d,e,f,g fix
+
+363
+00:51:49,380 --> 00:51:56,800
+ال arm g rotate لت واحد نعمل rotation
+
+364
+00:52:02,180 --> 00:52:09,080
+يا دي يا سي ما هو دي و سي مع بعض روتيت دي او سي
+
+365
+00:52:09,080 --> 00:52:23,280
+روتيت سي سي at plus X and fix G هد سفر سي دي plus
+
+366
+00:52:23,280 --> 00:52:27,980
+X plus X صح؟
+
+367
+00:52:30,340 --> 00:52:36,060
+الان C C
+
+368
+00:52:36,060 --> 00:52:50,880
+Drive E صح انا بتفتح تكون minus X T C على T E لسه
+
+369
+00:52:50,880 --> 00:52:54,780
+خنخلص الان E Drive A
+
+370
+00:52:59,210 --> 00:53:05,110
+هتكون انترال هتكون نفس الاتجاه هتكون اول واحدة ايه
+
+371
+00:53:05,110 --> 00:53:12,310
+اللي هي هصير minus هتكون هاده انا بحكي انا ايه مع
+
+372
+00:53:12,310 --> 00:53:18,070
+ايه؟ معناه تقريبا تي ايه هتروح هيكون minus x Tc تي
+
+373
+00:53:18,070 --> 00:53:27,030
+ايه في تي ايه على تي ايه هكون minus x Tc على تي
+
+374
+00:53:27,030 --> 00:53:27,330
+ايه
+
+375
+00:53:35,080 --> 00:53:53,560
+D Drive F يعني هتكون minus X T D على T F صح و F
+
+376
+00:53:53,560 --> 00:53:56,580
+Drive B هكون minus
+
+377
+00:53:59,710 --> 00:54:12,290
+X TD على TV صح لأن هذا هضربها في TF على TB هتروح
+
+378
+00:54:12,290 --> 00:54:12,510
+TF
+
+379
+00:54:28,920 --> 00:54:34,220
+نشبه Y-XTC
+
+380
+00:54:34,220 --> 00:54:53,420
+على TA Y-XTD على T ب X زائد Y X زائد Y Y-XTC على
+
+381
+00:54:53,420 --> 00:54:58,040
+TA Y-XTD
+
+382
+00:54:59,230 --> 00:55:08,530
+على TF و Y هو
+
+383
+00:55:08,530 --> 00:55:14,770
+معطيني NG NG ساوي
+
+384
+00:55:14,770 --> 00:55:19,810
+سالب مية بتساوي
+
+385
+00:55:19,810 --> 00:55:24,870
+Y يعني عرفنا Y معطيني NA
+
+386
+00:55:28,900 --> 00:55:34,020
+بتساوى سفر بتساوى
+
+387
+00:55:34,020 --> 00:55:44,860
+Y minus X TC على TA يعني هيكون ال Y اللي هو سالب
+
+388
+00:55:44,860 --> 00:55:55,560
+مية سالب X TC اللي هو تمانية و عشرين على
+
+389
+00:55:58,950 --> 00:56:05,750
+عشان حسبناها TA اللي هي اربع ستين يعني
+
+390
+00:56:05,750 --> 00:56:11,970
+على اربع سبعة على اربع ستاش احسبولي يعني هتكون
+
+391
+00:56:11,970 --> 00:56:24,930
+يعني منها بحسب X هتكون سالب سالب مية في
+
+392
+00:56:28,850 --> 00:56:43,650
+ستاش ع سبعة صح هاد
+
+393
+00:56:43,650 --> 00:56:52,790
+ال X هو بده NB ال NB هتساوي
+
+394
+00:56:52,790 --> 00:56:54,890
+Y
+
+395
+00:56:56,980 --> 00:57:05,080
+-x td على t بحيث
+
+396
+00:57:05,080 --> 00:57:12,580
+ساوي ال y سالب مية minus
+
+397
+00:57:12,580 --> 00:57:16,540
+x يصير minus minus plus صح؟
+
+398
+00:57:20,630 --> 00:57:32,690
+three plus مية في ستاش على سبعة في تي دي ستة و
+
+399
+00:57:32,690 --> 00:57:46,870
+عشرين على اتنين و ستين انا
+
+400
+00:57:46,870 --> 00:57:48,910
+بحسب ايش ال انبي
+
+401
+00:57:52,050 --> 00:57:59,690
+لأ هتكون ستاش أكمل
+
+402
+00:57:59,690 --> 00:58:08,710
+تطلع؟ سالب أربع هذا
+
+403
+00:58:08,710 --> 00:58:21,110
+مطلوب
+
+404
+00:58:21,110 --> 00:58:21,410
+إيه؟
+
+405
+00:58:27,630 --> 00:58:34,950
+التاني طلب التالت if arm g makes one hundred rpm
+
+406
+00:58:34,950 --> 00:58:40,970
+clockwise and g بالساوية
+
+407
+00:58:40,970 --> 00:58:49,470
+سالب مية بالساوية y and
+
+408
+00:58:49,470 --> 00:58:49,630
+a
+
+409
+00:58:57,170 --> 00:59:08,130
+بساوة عشرة اللي هي بساوة ايش Y minus X TC على TA
+
+410
+00:59:08,130 --> 00:59:11,590
+يعني
+
+411
+00:59:11,590 --> 00:59:23,830
+عشرة هتكون سالب مية سالب X في TC تمانية و عشرين
+
+412
+00:59:27,150 --> 00:59:37,330
+على اربع و ستين و منها بحسب ال X هتطلع
+
+413
+00:59:37,330 --> 00:59:43,270
+سالب تسعين
+
+414
+00:59:43,270 --> 00:59:53,110
+في اربع ستين على تمانية و عشرين كام؟
+
+415
+00:59:53,110 --> 00:59:59,700
+اه سالب لأ مية و عشرةفي اربع سنة ع تانية و عشرين
+
+416
+00:59:59,700 --> 01:00:14,420
+انا
+
+417
+01:00:14,420 --> 01:00:19,320
+بعدين بحسب NB بتساوي
+
+418
+01:00:19,320 --> 01:00:31,980
+Y minus X TD على TBهيكون الـ y عندي سالب مية ماينس
+
+419
+01:00:31,980 --> 01:00:38,980
+ماينس بصير زائد متين واحد وخمسين point أربعة اتنين
+
+420
+01:00:38,980 --> 01:00:43,460
+في ال TD ستة عشرين على اتنين وستين
+
+421
+01:00:59,240 --> 01:01:07,360
+فيها سؤال خنحل عشرة يعني
+
+422
+01:01:07,360 --> 01:01:21,940
+الأسئلة منوعة وفيها أفكار جديدة نعم لا
+
+423
+01:01:21,940 --> 01:01:28,910
+مش أسهل مجرب حل القوانينانت بتكون أسهل لو كان
+
+424
+01:01:28,910 --> 01:01:33,310
+ترسين و عدراع واحد بتكون أسهل .. اه لكن لما يكون
+
+425
+01:01:33,310 --> 01:01:39,230
+عندك .. عندك .. عندك يعني جيل train زي هذه في
+
+426
+01:01:39,230 --> 01:01:42,550
+طريقة الجدول أسهل بكتير و أسرع سريع جدا كما انت
+
+427
+01:01:42,550 --> 01:01:48,830
+شايف طيب
+
+428
+01:01:56,940 --> 01:02:02,260
+هنتطلع الشكل اول شي عندي انا عندي
+
+429
+01:02:02,260 --> 01:02:07,520
+هذا ال internal gear عندي gear c محمول على ال
+
+430
+01:02:07,520 --> 01:02:16,240
+shaft a gear c مش مع دي دي و ايه على نفس العمود دي
+
+431
+01:02:16,240 --> 01:02:25,970
+مع ايه ايه يعني c مش مع دي و ايه مش مع جيو في
+
+432
+01:02:25,970 --> 01:02:35,970
+إدراع هذا الإدراع ال arm شايل اللي هو D و E شايل D
+
+433
+01:02:35,970 --> 01:02:43,950
+و E نطلع من المنظر هنا أنا عندي هاي C في الإدراع
+
+434
+01:02:43,950 --> 01:02:55,170
+هذا شايل D و E الآن ال Cالـ C هيومش مع ال D هذا ال
+
+435
+01:02:55,170 --> 01:03:04,690
+D و E مش مع الترس الكبير ال G فهمته
+
+436
+01:03:04,690 --> 01:03:09,370
+جديد لان ال two shafts A و B are coaxial يعني اللي
+
+437
+01:03:09,370 --> 01:03:17,390
+هو نفس المحور بس هم ايش كل واحد بدور مستقل هاي
+
+438
+01:03:17,390 --> 01:03:22,240
+shaft A و Bاله نفس المحور بس هدا الشفت و هدا الشفت
+
+439
+01:03:22,240 --> 01:03:28,000
+بدوره مستقلين a
+
+440
+01:03:28,000 --> 01:03:34,020
+gear C عدسناه عند ال TC بساوة
+
+441
+01:03:34,020 --> 01:03:40,980
+خمسين سنه is rigidly mounted on shaft A a compound
+
+442
+01:03:40,980 --> 01:03:47,280
+gear DE gears with C and antenna gear Gطلعنا على
+
+443
+01:03:47,280 --> 01:03:54,920
+الشكل دي هات وانتي تيث تي دي بالساوية
+
+444
+01:03:54,920 --> 01:04:00,840
+عشرين سن and
+
+445
+01:04:00,840 --> 01:04:13,640
+gears with c ايه هات خمس تلاتين سن جيرجي
+
+446
+01:04:13,640 --> 01:04:15,120
+is fixed and
+
+447
+01:04:18,260 --> 01:04:22,580
+سوى صفر is
+
+448
+01:04:22,580 --> 01:04:27,040
+concentric with the shaft axis the compound gear
+
+449
+01:04:27,040 --> 01:04:30,340
+DE is mounted on a pin which projects from يعني هو
+
+450
+01:04:30,340 --> 01:04:36,380
+بتحكي أن ال DE محمول على الدراع find
+
+451
+01:04:36,380 --> 01:04:42,940
+the number of teeth on internal gear بده تي جي
+
+452
+01:04:47,810 --> 01:04:53,570
+assume that all gears have the same module بده
+
+453
+01:04:53,570 --> 01:04:56,530
+العدد السنان ع الجير جي بعدين if shaft A rotates
+
+454
+01:04:56,530 --> 01:05:01,370
+at 110 rpm
+
+455
+01:05:01,370 --> 01:05:06,770
+find the speed of shaft B هنشوف من الطول الأول أنه
+
+456
+01:05:06,770 --> 01:05:11,050
+وجد عدد سنان الجير جي
+
+457
+01:05:26,440 --> 01:05:31,860
+طلع اولش انا عندى
+
+458
+01:05:31,860 --> 01:05:35,020
+ال
+
+459
+01:05:35,020 --> 01:05:46,380
+R .. ال RG ال RG ايش بالساوية عندك النص القطر هذا
+
+460
+01:05:46,380 --> 01:05:51,620
+بالساوية
+
+461
+01:05:51,620 --> 01:06:04,410
+الطول هذازائد RA يعني RJ بدي
+
+462
+01:06:04,410 --> 01:06:12,350
+أسميه طول الدراع L L L زائد
+
+463
+01:06:12,350 --> 01:06:16,950
+RA أي واحد
+
+464
+01:06:21,640 --> 01:06:31,520
+اللي هو خاتة D مع C هيكون RC زي RD بيستوى L صح؟ RC
+
+465
+01:06:31,520 --> 01:06:46,480
+L زي RC زي RD صح؟ مظبوط؟ معناته كمان مرة هاي L
+
+466
+01:06:48,620 --> 01:06:59,800
+بساوة RC زاد RD وRG بساوة L زاد RA يعني انا حاسين
+
+467
+01:06:59,800 --> 01:07:04,360
+عند ال RG بساوة
+
+468
+01:07:04,360 --> 01:07:13,400
+.. هعوض عن L بساوة RC زاد RD يعني عند ال TG بساوة
+
+469
+01:07:13,400 --> 01:07:13,880
+TC
+
+470
+01:07:22,500 --> 01:07:32,640
+خمسين زاد عشرين زاد خمس وتلاتين هذا
+
+471
+01:07:32,640 --> 01:07:42,940
+تيجي المطلوب
+
+472
+01:07:42,940 --> 01:07:49,600
+التاني if shaft A rotates at one hundred rpm at
+
+473
+01:07:49,600 --> 01:07:59,030
+one hundred tenعند ال T N بسوة و مية و عشرة RPM
+
+474
+01:07:59,030 --> 01:08:05,010
+هعتبرها نموجة بده
+
+475
+01:08:05,010 --> 01:08:15,250
+N ب A طيب
+
+476
+01:08:23,710 --> 01:08:27,330
+أنا هسبت لدراع هسبت لدراع هدحط ال R من هنا الأخر
+
+477
+01:08:27,330 --> 01:08:31,190
+واحد هنا
+
+478
+01:08:31,190 --> 01:08:38,910
+عندنا A B C D لأ
+
+479
+01:08:38,910 --> 01:08:50,970
+في عند .. في عند .. عند .. عند C C و D و E و G
+
+480
+01:08:50,970 --> 01:09:05,260
+يعنيغير الإدراع C وD وE وG بس عشان نصلح هنا if
+
+481
+01:09:05,260 --> 01:09:09,900
+shaft A rotates at one hundred rpm shaft A حامل
+
+482
+01:09:09,900 --> 01:09:18,720
+النياترس shaft A حامل C صح؟ shaft A معناته هذي and
+
+483
+01:09:18,720 --> 01:09:19,020
+C
+
+484
+01:09:29,030 --> 01:09:40,370
+بدو سرعة ال shaft B ال shaft B ايش حامل؟ ال arm
+
+485
+01:09:40,370 --> 01:09:45,470
+بدو
+
+486
+01:09:45,470 --> 01:09:48,930
+N ال arm
+
+487
+01:10:02,550 --> 01:10:28,110
+اللي حكينا عنها غير ال R C D E G أربعة اوشي
+
+488
+01:10:28,110 --> 01:10:36,290
+فكسR rotate C
+
+489
+01:10:36,290 --> 01:10:48,630
+at plus X عملنا fix ها سفر plus X C مش معاش مع دي
+
+490
+01:10:48,630 --> 01:11:02,150
+minus X TC على TD وهذا minus X TC على TDو E مش مع
+
+491
+01:11:02,150 --> 01:11:14,970
+G هكون هو internal minus X T C على T D في T E في T
+
+492
+01:11:14,970 --> 01:11:18,550
+E minus
+
+493
+01:11:18,550 --> 01:11:27,450
+X T C على T D في T E على T G عشان مستيشي ترك
+
+494
+01:11:27,450 --> 01:11:34,210
+عدسنان D مش نفس عدسنان Eواضح؟ compound gear هنا
+
+495
+01:11:34,210 --> 01:11:38,430
+plus y
+
+496
+01:11:38,430 --> 01:11:41,530
+ع
+
+497
+01:11:41,530 --> 01:11:49,370
+نفس الشفت يعني انا هكون عندي x زائد y y minus x tc
+
+498
+01:11:49,370 --> 01:11:55,390
+على td y minus x tc على td
+
+499
+01:11:57,920 --> 01:12:08,540
+minus X TC TE على TD TG هو ماعطيني إياش هو Y
+
+500
+01:12:08,540 --> 01:12:18,960
+ماعطيني إياش ال NC NC ماعطيني إيها NC سوى مية و
+
+501
+01:12:18,960 --> 01:12:23,140
+عشرة بتسوى X زائد Y
+
+502
+01:12:30,290 --> 01:12:36,530
+ومعطين ال NG سوى
+
+503
+01:12:36,530 --> 01:12:50,570
+السفر Y minus X T C T E يعني
+
+504
+01:12:50,570 --> 01:12:58,430
+هكون عند ال Y أكم مش عارف مش معروفة minus X T C
+
+505
+01:12:58,430 --> 01:13:11,780
+خمسينفي خمسة و تلاتين على TD عشرين و
+
+506
+01:13:11,780 --> 01:13:26,400
+تي جي اللي هي كم مية و خمسة واحد تلاتة صح؟ هاي سفر
+
+507
+01:13:26,400 --> 01:13:37,990
+مع سفر يعني هتكون هتتساويY-5 ع 6 X
+
+508
+01:13:37,990 --> 01:13:48,510
+هاي واحد هاي اتنين هاي
+
+509
+01:13:48,510 --> 01:13:56,450
+واحد ناقص اتنين هتقوح ال Y مع ال Y
+
+510
+01:14:00,810 --> 01:14:07,930
+هذه سفر صح؟ يعني هكون مية و عشرة بتساوي و Y مع Y
+
+511
+01:14:07,930 --> 01:14:15,030
+هتكون .. يعني هتصير جامعة صح؟ يعني احداش على ستة X
+
+512
+01:14:15,030 --> 01:14:23,950
+معناته X هتكون تساوي ستين معناته
+
+513
+01:14:23,950 --> 01:14:28,330
+ال Y خمسين
+
+514
+01:14:31,000 --> 01:14:38,120
+معناته اللي هي هاجم السوء إيش ال N تاعة ال R ال N
+
+515
+01:14:38,120 --> 01:14:47,580
+تاعة ال R اللي بتطلع خمسين RPM في
+
+516
+01:14:47,580 --> 01:14:51,260
+أي سؤال؟ أعطيكم العفو
+
diff --git a/PL9fwy3NUQKwa0nXiCdyQcTW4hWDLTGpDb/NbPgLCNQjCg_postprocess.srt b/PL9fwy3NUQKwa0nXiCdyQcTW4hWDLTGpDb/NbPgLCNQjCg_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..88051bf32c39ac062e91088950a9c554c9701281
--- /dev/null
+++ b/PL9fwy3NUQKwa0nXiCdyQcTW4hWDLTGpDb/NbPgLCNQjCg_postprocess.srt
@@ -0,0 +1,1920 @@
+1
+00:00:05,280 --> 00:00:08,140
+بسم الله الرحمن الرحيم السلام عليكم و رحمة الله و
+
+2
+00:00:08,140 --> 00:00:11,720
+بركاته، اليوم هنكمل في مادة نظرية الألات،
+
+3
+00:00:11,720 --> 00:00:15,180
+المحاضرات السابقة حكينا عن ال cams و ال followers
+
+4
+00:00:15,180 --> 00:00:18,240
+عملنا
+
+5
+00:00:18,240 --> 00:00:22,620
+generate ال geometry ل ال cam ال profile من خلال
+
+6
+00:00:22,620 --> 00:00:27,890
+معرفتنا لحركة ال followerحالينا example حركة ال
+
+7
+00:00:27,890 --> 00:00:32,790
+follower كانت uniform velocity و example تاني كانت
+
+8
+00:00:32,790 --> 00:00:38,550
+simple harmonic motion في حالة sharp edge follower
+
+9
+00:00:38,550 --> 00:00:44,110
+هنكمل examples مرة باستخدام اللي هو roller
+
+10
+00:00:44,110 --> 00:00:49,030
+follower مرة flat faced follower هنحل example
+
+11
+00:00:49,030 --> 00:00:50,290
+عشرين تلاتة
+
+12
+00:00:53,240 --> 00:00:56,700
+عشرين تلاتة كلا كام with a minimum radius of
+
+13
+00:00:56,700 --> 00:01:00,980
+twenty five millimeter يعني هذا ال basic radius صح
+
+14
+00:01:00,980 --> 00:01:05,840
+ال
+
+15
+00:01:05,840 --> 00:01:10,460
+basic radius basic
+
+16
+00:01:10,460 --> 00:01:14,640
+circle radius
+
+17
+00:01:14,640 --> 00:01:17,880
+بالساوية
+
+18
+00:01:17,880 --> 00:01:21,600
+خمسة و عشرين millimeter
+
+19
+00:01:26,010 --> 00:01:28,810
+rotating clockwise at enforce speed is to be
+
+20
+00:01:28,810 --> 00:01:31,910
+designed to give a roller follower at the end of a
+
+21
+00:01:31,910 --> 00:01:34,450
+valve rod motion described بلو حتيها تحركة لل
+
+22
+00:01:34,450 --> 00:01:41,750
+follower طبقا للتالت أولش هو معطيني ال stroke
+
+23
+00:01:41,750 --> 00:01:47,490
+خمسين ملي متر ال stroke
+
+24
+00:01:47,490 --> 00:01:52,270
+بستوى خمسين ملي متر
+
+25
+00:01:58,750 --> 00:02:02,290
+في أول مئة و عشرين دوران للكام مئة و عشرين درجة
+
+26
+00:02:02,290 --> 00:02:07,610
+بيرتفع لخمسين ملي متر simple harmonic motion بعدين
+
+27
+00:02:07,610 --> 00:02:13,410
+تلاتين درجة التالية بيضلوا مكانه بعدين ستين درجة
+
+28
+00:02:13,410 --> 00:02:19,810
+التانية بنزل simple harmonic motion بعدين بيضلوا
+
+29
+00:02:19,810 --> 00:02:24,170
+مكانه مئة و خمسين درجة بعدين ال cycle بتتكرر
+
+30
+00:02:28,280 --> 00:02:36,680
+الان طبعا هكون دي المعطيل معلومات تانية ديامتر
+
+31
+00:02:36,680 --> 00:02:49,820
+ل رولر .. رولر ديامتر بتساوي
+
+32
+00:02:49,820 --> 00:02:53,260
+عشرين
+
+33
+00:02:53,260 --> 00:02:53,520
+ملي
+
+34
+00:03:02,250 --> 00:03:09,650
+and the diameter of the cam shaft اللي هو D للشافت
+
+35
+00:03:09,650 --> 00:03:12,930
+خمسة
+
+36
+00:03:12,930 --> 00:03:18,650
+عشرين مليمتر
+
+37
+00:03:18,650 --> 00:03:24,090
+draw
+
+38
+00:03:24,090 --> 00:03:28,530
+the profile of the camwhen the line of stroke of
+
+39
+00:03:28,530 --> 00:03:31,730
+the valve and rod passes through the axis of cam
+
+40
+00:03:31,730 --> 00:03:36,290
+لما يكون مركز محور حركة ال follower بيمور في مركز
+
+41
+00:03:36,290 --> 00:03:42,450
+دوران الكام هذه الحالة الأولى طبعا
+
+42
+00:03:42,450 --> 00:03:48,630
+الفكرة هتكون في الرسم هرسم
+
+43
+00:03:48,630 --> 00:03:49,530
+ال basic circle
+
+44
+00:03:53,460 --> 00:04:01,320
+ال basic circle اللي هي قطرها كم ال radius خمسين
+
+45
+00:04:01,320 --> 00:04:08,620
+القطر خمسين هيكون دائرة هذه مركز
+
+46
+00:04:08,620 --> 00:04:14,620
+رولر هيكون طب حارسهم هنا مركز رولر هيكون ع كم
+
+47
+00:04:14,620 --> 00:04:20,520
+عشرين يعني حارسهم دائرة كمان هعمل أفست لهذه
+
+48
+00:04:24,850 --> 00:04:30,850
+عشرة ملي صح يعني هذه المسافة عشرة ملي معناته هذا
+
+49
+00:04:30,850 --> 00:04:35,450
+اول location بعدين
+
+50
+00:04:35,450 --> 00:04:42,310
+عندي simple harmonic motion هذه
+
+51
+00:04:42,310 --> 00:04:49,390
+ال stroke ال
+
+52
+00:04:49,390 --> 00:04:50,290
+stroke خمسين
+
+53
+00:05:00,220 --> 00:05:12,660
+هجزق هذه مجزئها
+
+54
+00:05:12,660 --> 00:05:16,900
+ست أجزاء طبعا
+
+55
+00:05:16,900 --> 00:05:26,130
+هذا هتكون أول دائرة هذه التانية هذه التالتةهادي
+
+56
+00:05:26,130 --> 00:05:34,170
+ايش؟ الرابعة الخامسة السادسة
+
+57
+00:05:34,170 --> 00:05:44,030
+الان
+
+58
+00:05:44,030 --> 00:05:51,050
+ال .. مية و عشرين كام زوايا هذه؟ مية و عشرين درجة
+
+59
+00:05:51,050 --> 00:06:01,370
+هذه المية و عشرين120 لحد هنا صح؟ 120 120
+
+60
+00:06:01,370 --> 00:06:08,250
+فانا هجزي عندك واحد اتنين تلاتة اربعة خمسة ستة لأن
+
+61
+00:06:08,250 --> 00:06:13,730
+هو ماخد ال center هاي ال center الأولاني التاني
+
+62
+00:06:13,730 --> 00:06:18,730
+التالت الرابع خمس سادس
+
+63
+00:06:24,800 --> 00:06:39,200
+من كل مركز برسم رولر قطرها عشرين و
+
+64
+00:06:39,200 --> 00:06:44,780
+هكذا بعدين بعمل spline tangent لكل الدوار هدول
+
+65
+00:06:44,780 --> 00:06:48,320
+مابخدش
+
+66
+00:06:48,320 --> 00:06:55,720
+مركز رولر بعمل offset لأ بعمل tangentلكل الدوائر
+
+67
+00:06:55,720 --> 00:06:59,840
+هذه حصلنا
+
+68
+00:06:59,840 --> 00:07:05,440
+علي ايش على ال profile الأولاني بعدها دي راح تكمل
+
+69
+00:07:05,440 --> 00:07:09,800
+نفس الشي بنسوي الجهة في الغبوط خدنا نشوف كيف
+
+70
+00:07:09,800 --> 00:07:21,360
+هنسويها هيبدأ
+
+71
+00:07:21,360 --> 00:07:22,000
+new part
+
+72
+00:07:32,090 --> 00:07:37,750
+هناخد ال top view نعمل sketch عليه هبدأ أرسم إيهاش
+
+73
+00:07:37,750 --> 00:07:48,650
+ال basic circle اللي هي كترها خمسين
+
+74
+00:07:48,650 --> 00:07:55,290
+بعدين
+
+75
+00:07:55,290 --> 00:07:55,990
+هعمل لها offset
+
+76
+00:08:04,350 --> 00:08:13,310
+عشرة صح؟ اللي
+
+77
+00:08:13,310 --> 00:08:19,010
+هاد offset تتمثل على
+
+78
+00:08:19,010 --> 00:08:24,510
+فرضه بتحرك على دائرة واضح؟ لكن لو متحركش على دائرة
+
+79
+00:08:24,510 --> 00:08:29,560
+مش ضروري يكون نفس الشيءطيب هرسم أول الشخاق من هنا
+
+80
+00:08:29,560 --> 00:08:38,580
+طيب
+
+81
+00:08:38,580 --> 00:08:45,960
+اذا كان أول مائة و عشرين درجة هنقسمهم أنا عنده
+
+82
+00:08:45,960 --> 00:08:48,040
+هنعمل array
+
+83
+00:08:57,130 --> 00:09:02,630
+ماشي اتخيل مش حالك اش تتغير ال systematic لإن عندي
+
+84
+00:09:02,630 --> 00:09:10,910
+انا هاختار النقطة هذه مركز
+
+85
+00:09:10,910 --> 00:09:19,170
+الدائرة هذه ال parts اللي
+
+86
+00:09:19,170 --> 00:09:23,350
+هو الخط هذا العدد سبعة
+
+87
+00:09:29,720 --> 00:09:38,820
+سبعة والزاوية مائة و عشرين و نعكس الاتجاه فانا
+
+88
+00:09:38,820 --> 00:09:44,300
+بتدور clockwise هي مائة و عشرين ع ستة كم عشرين مش
+
+89
+00:09:44,300 --> 00:09:47,980
+تلاتين درجة حتى لو كان تلاتين يمشي ال systematic
+
+90
+00:09:47,980 --> 00:09:56,040
+أحسن طيب المرحلة
+
+91
+00:09:56,040 --> 00:10:04,880
+التانيةهعمل انا برضه secular pattern هاخد
+
+92
+00:10:04,880 --> 00:10:23,140
+الدائرة هذه هاخد
+
+93
+00:10:23,140 --> 00:10:37,080
+الخط هذا العدد اتنينوالزاوية تلاتين عكس اتجاه طيب
+
+94
+00:10:37,080 --> 00:10:50,500
+بعدين دي أكمل مية و خمسين صح نشوف
+
+95
+00:11:15,200 --> 00:11:23,120
+هذه ستين ستين طيب هنعمل
+
+96
+00:11:23,120 --> 00:11:35,880
+بره ست أقسام ستين هذه
+
+97
+00:11:35,880 --> 00:11:41,480
+ستين درجة وهنا ستة سبعة
+
+98
+00:11:45,880 --> 00:11:57,320
+الخط هذا معناه
+
+99
+00:11:57,320 --> 00:12:05,580
+اتعملنا تقسيمة تاعتنا لان اتعمل تقسيمة تاعت simple
+
+100
+00:12:05,580 --> 00:12:11,160
+harmonic motion ال stroke كم حكينا خمسين
+
+101
+00:12:11,160 --> 00:12:12,960
+معناه اتعمل
+
+102
+00:12:16,460 --> 00:12:30,160
+offset لدارها دي أكمل خمسين هذه خمسين مظبوط
+
+103
+00:12:30,160 --> 00:12:38,400
+خلنا
+
+104
+00:12:38,400 --> 00:12:39,800
+نتأكد من ال size بتاعها
+
+105
+00:12:43,930 --> 00:12:51,070
+مية و سبعين ماشي خليني
+
+106
+00:12:51,070 --> 00:12:58,290
+ارسم خط من هنا او خليني ارسم خط
+
+107
+00:12:58,290 --> 00:13:01,990
+بعدين ارسم دائرة
+
+108
+00:13:25,030 --> 00:13:30,550
+بعدين اعمله rotation
+
+109
+00:13:30,550 --> 00:13:40,650
+ع 180 درجة العدد
+
+110
+00:13:40,650 --> 00:13:40,970
+7
+
+111
+00:13:45,520 --> 00:13:58,840
+عدد سبعة و هاخد مركز دقرا هذا انا هاخد
+
+112
+00:13:58,840 --> 00:14:00,680
+ايش خط هذا
+
+113
+00:14:21,390 --> 00:14:29,570
+اه اللي هو الخط هذا بعدين المركز هذا اللي هو
+
+114
+00:14:29,570 --> 00:14:32,910
+الدائرة
+
+115
+00:14:32,910 --> 00:14:44,410
+هذه ليش بيجيلي هنا هو طيب
+
+116
+00:14:44,410 --> 00:14:46,190
+كمرة
+
+117
+00:14:49,600 --> 00:14:55,560
+ناخد المركز اللي هو هذه الدائرة طيب ناخدها بطريقة
+
+118
+00:14:55,560 --> 00:15:05,860
+تانية مازال مصر هاخد المركز هذا النقطة هذه واخد
+
+119
+00:15:05,860 --> 00:15:13,040
+الخط هذا هنحكي السبعة على مية و تمانين درجة صح؟
+
+120
+00:15:42,740 --> 00:15:50,880
+عندك circular اللي
+
+121
+00:15:50,880 --> 00:16:04,560
+هو هادا عندي السابعة عندي عشرين
+
+122
+00:16:04,560 --> 00:16:07,420
+نعم
+
+123
+00:16:15,160 --> 00:16:19,420
+الردر القطر هو عشرين مص قطر اكم يعني ايه عشرة انا
+
+124
+00:16:19,420 --> 00:16:27,580
+عملت اللي offset اكم عشرة صح بدك تتأكد يعني تخد
+
+125
+00:16:27,580 --> 00:16:31,740
+هذه ال dimension بتاعتها هتكون اخرد سبعين مظبوط
+
+126
+00:16:31,740 --> 00:16:42,570
+وهذه سبعين سبعين و ال stroke خمسينيعني هتكون ال ..
+
+127
+00:16:42,570 --> 00:16:49,890
+ال .. السبعين زاد مية الكتور هتكون مية و سبعين مية
+
+128
+00:16:49,890 --> 00:16:53,010
+و سبعين واضح طيب
+
+129
+00:17:11,260 --> 00:17:16,320
+الزاوية 180 والعدد
+
+130
+00:17:16,320 --> 00:17:23,180
+7 ماشي
+
+131
+00:17:23,180 --> 00:17:32,220
+ماشي
+
+132
+00:17:32,220 --> 00:17:37,260
+طيب كيف بدو مكانه المشكلة طيب الآن هرسم دوائر
+
+133
+00:17:37,260 --> 00:17:39,200
+circle
+
+134
+00:17:42,040 --> 00:17:51,800
+هذه الدائرة الأولى وهذه الدائرة التانية وهذه
+
+135
+00:17:51,800 --> 00:17:56,380
+الدائرة التالتة
+
+136
+00:17:56,380 --> 00:18:07,740
+والدائرة الرابعة
+
+137
+00:18:17,540 --> 00:18:25,220
+اه هى كان الشغل صح ولا غلط؟ لأ غلط هذا
+
+138
+00:18:25,220 --> 00:18:30,180
+غلط هيك المفروض احنا نعمل هيك اسقاط نرسم ده يعمل
+
+139
+00:18:30,180 --> 00:18:37,540
+اسقاط واضح؟ هيك غلط كان فانا انت حارس الخط من هنا
+
+140
+00:18:37,540 --> 00:18:45,840
+هي
+
+141
+00:18:45,840 --> 00:18:57,000
+هو الخطبعدين خط تاني بعدين
+
+142
+00:18:57,000 --> 00:19:07,520
+خط .. هذا خلصنا منه و
+
+143
+00:19:07,520 --> 00:19:08,320
+خط رابع
+
+144
+00:19:26,580 --> 00:19:32,140
+معدين دوائر يعني الدائرة اللي بتمر هنا كتر اكتر من
+
+145
+00:19:32,140 --> 00:19:37,920
+الدائرة هذه صح فبختلف الأشياء
+
+146
+00:19:37,920 --> 00:19:51,400
+بعدين كمان دائرة بعدين
+
+147
+00:19:51,400 --> 00:19:52,240
+كمان دائرة
+
+148
+00:19:59,560 --> 00:20:07,480
+بعدين كمان دائرة هيك
+
+149
+00:20:07,480 --> 00:20:14,160
+رسمنا الدوائر صح خلينا
+
+150
+00:20:14,160 --> 00:20:24,400
+نمد الآن extend يعني أول نقطة كانت
+
+151
+00:20:24,400 --> 00:20:30,940
+هنا صح تاني نقطة هو انها تكونيعني ده أول نقطة لل
+
+152
+00:20:30,940 --> 00:20:34,640
+center يعني
+
+153
+00:20:34,640 --> 00:20:37,360
+خليني عشان اوضح عشان انا مستيقظ خربشها هاي عندكوا
+
+154
+00:20:37,360 --> 00:20:52,500
+هنا هاي ال circle هاي مركزها نتأكد
+
+155
+00:20:52,500 --> 00:20:56,640
+أكم
+
+156
+00:20:56,640 --> 00:20:57,100
+كترها
+
+157
+00:21:01,250 --> 00:21:07,950
+عشر يعني، معناته صح، ماشي، معناته حلمت، بعدين
+
+158
+00:21:07,950 --> 00:21:11,590
+extend،
+
+159
+00:21:11,590 --> 00:21:17,250
+هذا أول واحد، هذا التاني،
+
+160
+00:21:17,250 --> 00:21:23,350
+بحكي على السينادر هي .. هذا
+
+161
+00:21:23,350 --> 00:21:24,570
+التالت مظلوط
+
+162
+00:21:34,070 --> 00:21:44,850
+هيك خلصنا ولا .. هذه هيك اه طيب هيك صح هذه .. هذه
+
+163
+00:21:44,850 --> 00:21:47,870
+الأولى صح هذه التانية هذه التالتة الرابعة حلمت
+
+164
+00:21:47,870 --> 00:21:53,150
+كمان صح هذه
+
+165
+00:21:53,150 --> 00:22:05,440
+صح هذه بتبقى صحهذه صح معناته اللي بعد ها
+
+166
+00:22:05,440 --> 00:22:11,340
+كمان
+
+167
+00:22:11,340 --> 00:22:11,860
+واحد
+
+168
+00:22:31,110 --> 00:22:37,350
+فيش غلط صح خمسانيس
+
+169
+00:22:37,350 --> 00:22:41,130
+الزاوية خلنا نتأكد smart dimension هذا الزاوية
+
+170
+00:22:41,130 --> 00:22:49,850
+وهذه عشرين طب هذه وهذه
+
+171
+00:22:49,850 --> 00:22:53,350
+هذه
+
+172
+00:22:53,350 --> 00:22:57,550
+عشرين
+
+173
+00:23:04,440 --> 00:23:12,280
+هذه عشرين يعني عندك مية و عشرين على ستة عشرين خلنا
+
+174
+00:23:12,280 --> 00:23:19,580
+نجيز في الزاوية هذه بين هذه و
+
+175
+00:23:19,580 --> 00:23:26,080
+هذه مية و عشرين معناته هذه أخر واحد معناته هدول مش
+
+176
+00:23:26,080 --> 00:23:33,140
+صح هدول كلهمنسينا التلاتين احنا صح؟ يعني نحكي
+
+177
+00:23:33,140 --> 00:23:47,680
+erase هنمسح هدول او هنمسح هذا اه
+
+178
+00:23:47,680 --> 00:23:52,480
+انا اللي بسير عشان ما بعرف AutoCAD بستخدم ال
+
+179
+00:23:52,480 --> 00:23:56,300
+command بتاعة ال .. بتاعة ال AutoCAD بعض الأحيان
+
+180
+00:23:56,300 --> 00:23:56,780
+بالغلط
+
+181
+00:24:05,120 --> 00:24:14,280
+هذا الخط هنعمله اكام؟ تلاتين اه
+
+182
+00:24:14,280 --> 00:24:23,180
+ماشي انا ماخدين الزاوية اللي هو انا
+
+183
+00:24:23,180 --> 00:24:34,140
+بده الخط هذا بعد المركز هيكون ايش دائرة هذه العدد
+
+184
+00:24:34,860 --> 00:24:44,700
+اتنين والزاوية تلاتين هعكسها
+
+185
+00:24:44,700 --> 00:24:57,460
+طيب okay طيب
+
+186
+00:24:57,460 --> 00:25:03,120
+كمان مرة هاي عند ال secular هذه النقطة
+
+187
+00:25:09,570 --> 00:25:23,770
+هذه تلاتين و العدد اتنين و نعكس الاتجاه و okay نعم
+
+188
+00:25:23,770 --> 00:25:30,930
+هاي هيك زبط طيب بعدين هكون عندي لستين درجة
+
+189
+00:25:42,310 --> 00:25:48,310
+ستين درجة سبعة هاي
+
+190
+00:25:48,310 --> 00:25:55,770
+ستين درجة okay
+
+191
+00:25:55,770 --> 00:26:02,890
+هيك مظبوط معناته
+
+192
+00:26:02,890 --> 00:26:03,550
+هانمد هذا
+
+193
+00:26:11,150 --> 00:26:22,450
+هذا اخر واحد صح؟ ماشي
+
+194
+00:26:22,450 --> 00:26:38,730
+و ال mid هذا بقى عنده ايش؟ هيدله مكانه طيب
+
+195
+00:26:40,610 --> 00:26:52,790
+بعدين هنمد هذا بعدين
+
+196
+00:26:52,790 --> 00:26:58,970
+هيك
+
+197
+00:26:58,970 --> 00:27:01,970
+صح بعدين هنمد هذا
+
+198
+00:27:15,170 --> 00:27:33,450
+أنا هذا مش شايف هو طيب
+
+199
+00:27:33,450 --> 00:27:40,610
+بنده
+
+200
+00:27:40,610 --> 00:27:45,560
+على الجهة التانية و ادهي بالك هو يا عزيزيطب يمكنك
+
+201
+00:27:45,560 --> 00:27:49,060
+..
+
+202
+00:27:49,060 --> 00:27:54,580
+يمكنك .. يمكنك .. يمكنك .. يمكنك .. يمكنك .. يمكنك
+
+203
+00:27:54,580 --> 00:27:59,160
+يمكنك .. يمكنك .. يمكنك .. يمكنك .. يمكنك
+
+204
+00:27:59,160 --> 00:28:03,420
+.. يمكنك .. يمكنك .. يمكنك .. يمكنك .. يمكنك ..
+
+205
+00:28:03,420 --> 00:28:03,480
+يمكنك .. يمكنك .. يمكنك .. يمكنك .. يمكنك .. يمكنك
+
+206
+00:28:03,480 --> 00:28:03,500
+يمكنك .. يمكنك .. يمكنك .. يمكنك .. يمكنك .. يمكنك
+
+207
+00:28:03,500 --> 00:28:12,580
+.. يمكنك .. يمكنك .. يمكنك .. يمكنك .. يمكنك
+
+208
+00:28:12,580 --> 00:28:13,680
+.. يمكن
+
+209
+00:28:15,670 --> 00:28:22,890
+الـ hide .. hide هنا
+
+210
+00:28:22,890 --> 00:28:37,650
+hide أيوة ماشي و بعدين هنعمل ال trim بلو هنشيل هذه
+
+211
+00:28:37,650 --> 00:28:44,570
+و هذه هيك مظبوط صح؟ مش مشكلة اللي ناشي يعني
+
+212
+00:28:53,170 --> 00:29:02,790
+extend لحد هنا صح؟ معناته كمان
+
+213
+00:29:02,790 --> 00:29:13,010
+واحد لأ لأ مظبوط زي هيك هيك مظبوط بعدين بس
+
+214
+00:29:15,570 --> 00:29:22,730
+مظبوط؟ الآن لسه مخلصناش هنرسم
+
+215
+00:29:22,730 --> 00:29:32,950
+دوائر هاي
+
+216
+00:29:32,950 --> 00:29:33,650
+دائرة هنا
+
+217
+00:30:36,160 --> 00:30:42,660
+طيب خلينا نحط عليهم .. خلنا نحط ال dimension على
+
+218
+00:30:42,660 --> 00:30:53,140
+هذهبنعرف هاي هذه عشرين fully defined طيب بعد ناخد
+
+219
+00:30:53,140 --> 00:30:53,560
+هذه
+
+220
+00:31:19,300 --> 00:31:27,860
+كلهم equal صح طيب
+
+221
+00:31:27,860 --> 00:31:33,360
+الآن
+
+222
+00:31:33,360 --> 00:31:38,320
+هرسم spline هي
+
+223
+00:31:38,320 --> 00:31:42,760
+spline يعني
+
+224
+00:31:42,760 --> 00:31:48,540
+لهذه و لهذه هذه التالتة صح
+
+225
+00:32:05,230 --> 00:32:11,950
+ماشي بس انتبه لشغل الآن الدوائر اذا عملت العلاقة
+
+226
+00:32:11,950 --> 00:32:19,570
+بينهم tangent هيحرك الدائرة بدك تعمل fix للدوائر
+
+227
+00:32:19,570 --> 00:32:21,570
+هدول عند هدول دوائر
+
+228
+00:32:38,570 --> 00:32:48,030
+fix هذا make fixed ماشي
+
+229
+00:32:48,030 --> 00:32:51,230
+خدنا
+
+230
+00:32:51,230 --> 00:32:56,870
+نعمل tangent اه
+
+231
+00:32:56,870 --> 00:33:00,150
+يعني
+
+232
+00:33:00,150 --> 00:33:03,010
+هناخد هذه خدنا نبدأ من هنا
+
+233
+00:33:07,310 --> 00:33:13,070
+عملت fixed للدائرة انا بدي احرك ال spline هاي
+
+234
+00:33:13,070 --> 00:33:16,610
+الفكرة هاي ال tangent شوفت شو حركته انا حركت ال
+
+235
+00:33:16,610 --> 00:33:19,810
+spline لكن لو ماعملتش زي هيك هيحرك الدائرة هيطلع
+
+236
+00:33:19,810 --> 00:33:26,150
+الرسم غلط بعدين
+
+237
+00:33:26,150 --> 00:33:30,490
+هاي
+
+238
+00:33:30,490 --> 00:33:35,050
+ال tangent بعدين
+
+239
+00:33:38,650 --> 00:33:43,750
+لسه ماخلصناش هاي
+
+240
+00:33:43,750 --> 00:33:49,250
+ال tangent كل ماله بنظبط اه لان فيه واضح انه هادى
+
+241
+00:33:49,250 --> 00:33:57,670
+مفروض جيبناله من تحت احنا طيب
+
+242
+00:33:57,670 --> 00:34:02,110
+اعمل
+
+243
+00:34:02,110 --> 00:34:06,530
+Ctrl Z هبدأ من الجهة التانية من هنا هبدأنا
+
+244
+00:34:09,920 --> 00:34:30,080
+حكيله هذه مع هذه هي tangent
+
+245
+00:34:30,080 --> 00:34:34,340
+بعدين
+
+246
+00:34:47,490 --> 00:34:59,650
+tangent بعدين هعمله ايه اش؟ tangent طيب
+
+247
+00:34:59,650 --> 00:35:06,110
+بعدين هذا بتعمله
+
+248
+00:35:06,110 --> 00:35:09,390
+اش
+
+249
+00:35:09,390 --> 00:35:09,790
+من 13
+
+250
+00:35:28,630 --> 00:35:34,610
+اللي أنا هعمل هذه مساحة relation هي
+
+251
+00:35:34,610 --> 00:35:45,350
+tangent طيب
+
+252
+00:35:45,350 --> 00:35:48,070
+هنا عندك relation
+
+253
+00:36:02,210 --> 00:36:03,510
+فيه مشكلة مش عارف
+
+254
+00:36:41,120 --> 00:36:43,780
+ماشي مسحت ال ratio هذه كانت من خربة ال linear اللي
+
+255
+00:36:43,780 --> 00:36:52,780
+هي بتاعت فمسحتها الآن هاخد هذه مع هذه وهي ايش
+
+256
+00:36:52,780 --> 00:36:59,960
+tangent بعدين
+
+257
+00:36:59,960 --> 00:37:07,360
+بدي امسح هذه عشان اعطيها حرية للحركة بدي احكيله
+
+258
+00:37:11,430 --> 00:37:27,990
+هذه مع هذه هي tangent بعدين
+
+259
+00:37:27,990 --> 00:37:37,750
+هذه مش هتظبط مع هذه هي tangent زي ما اتوقعت خليني
+
+260
+00:37:37,750 --> 00:37:39,130
+احركه حاول احركه
+
+261
+00:38:15,060 --> 00:38:16,460
+طيب
+
+262
+00:38:23,250 --> 00:38:30,090
+كمان مرة الان انا شيلت بشري relations هاي
+
+263
+00:38:30,090 --> 00:38:46,490
+ال tangent طب
+
+264
+00:38:46,490 --> 00:38:47,310
+في مشكلة عندنا
+
+265
+00:39:24,580 --> 00:39:28,260
+طيب على اي حال هذه مشكلة solid work خلاني اشوف ايش
+
+266
+00:39:28,260 --> 00:39:33,160
+المشكلة و بنعرفها المهم انا برسم الدوائر هذه برسم
+
+267
+00:39:33,160 --> 00:39:40,200
+الدوائر هذه بعمل tangency طبعا الدوائر بسبتها
+
+268
+00:39:40,200 --> 00:39:44,840
+بسبتها لان المواقع عليها تكون ثابتة اذا ما سبتتش
+
+269
+00:39:44,840 --> 00:39:48,540
+انا جربتها بارح اذا ما سبتتش يصير الدوائر تتحرك
+
+270
+00:39:48,540 --> 00:39:53,340
+تطيلك اشي تاني مختلففبتثبت الدواير وبعدين تعمل ال
+
+271
+00:39:53,340 --> 00:39:58,540
+spline spline تنجد لكل الدواير هذه وبعد نفس الشيء
+
+272
+00:39:58,540 --> 00:40:02,620
+نعمل spline لان تنجد لهذه الدواير وبعدين بيصير شغل
+
+273
+00:40:02,620 --> 00:40:08,160
+ال trim والتنظيفات بترسم إيهاش الكامة خلينا نشوف
+
+274
+00:40:08,160 --> 00:40:12,340
+الطريق الجزء التاني إنه لو كان offset إنه مش نفس
+
+275
+00:40:12,340 --> 00:40:14,740
+المحور خلنا نعملها save هذه ونشوف
+
+276
+00:40:25,340 --> 00:40:30,520
+أه لازم يطلع نفس الاشي say بقى مش الآن say بقى ده
+
+277
+00:40:30,520 --> 00:40:39,040
+خلنا نحفظها اللي هي example example عشرين تلاتة
+
+278
+00:40:39,040 --> 00:40:41,480
+ايه say
+
+279
+00:40:45,630 --> 00:40:53,150
+بخليك المرة الجاية تعملها اه طيب
+
+280
+00:40:53,150 --> 00:40:56,730
+الان هنرسم رسمة جديدة او خلينا نروح على ال .. على
+
+281
+00:40:56,730 --> 00:41:09,450
+ال .. على الحالة التانية انه هيكون انه
+
+282
+00:41:09,450 --> 00:41:15,660
+هيكونoffset يعني محور الفلور بمرش في محور الكم
+
+283
+00:41:15,660 --> 00:41:27,620
+اللي
+
+284
+00:41:27,620 --> 00:41:34,960
+هي الحالة هذه اللي هنسويه طبعا هذه ال base circle
+
+285
+00:41:34,960 --> 00:41:37,920
+هي هي هذه ال base circle
+
+286
+00:41:40,230 --> 00:41:44,590
+الان هنعمل offset circle نرسمه offset circle بعدين
+
+287
+00:41:44,590 --> 00:41:52,650
+بنعمل خط رأسي خط رأسي هذا بتمثل ال minimum point
+
+288
+00:41:52,650 --> 00:41:57,090
+ال minimum point لل follower معناته عرفة ال center
+
+289
+00:41:57,090 --> 00:42:02,230
+الأولاني لل roller هذا أول center باجي من مركز ال
+
+290
+00:42:02,230 --> 00:42:07,030
+base circle لمركز roller circle أول واحدة بعمل خط
+
+291
+00:42:08,180 --> 00:42:26,160
+بعمل خط هدا بعمل مائة و عشرين درجة هدا
+
+292
+00:42:26,160 --> 00:42:33,140
+ال base circle هاي مركزها هدا
+
+293
+00:42:33,140 --> 00:42:34,560
+ال offset line
+
+294
+00:42:39,940 --> 00:42:49,540
+هذه النقطة تمثل أول مركز من أول مركز برسم الخط هذا
+
+295
+00:42:49,540 --> 00:42:54,760
+بعدين
+
+296
+00:42:54,760 --> 00:42:59,760
+بجزقه ل مائة و عشرين درجة بجزقه ل مائة و عشرين
+
+297
+00:42:59,760 --> 00:43:06,480
+درجة ل أكم جزء ست أجزاء
+
+298
+00:43:10,680 --> 00:43:15,920
+أنا هاي من ال base circle ال base circle ال base
+
+299
+00:43:15,920 --> 00:43:25,840
+circle واحد
+
+300
+00:43:25,840 --> 00:43:35,100
+اتنين تلاتة أربعة خمسة ستة في تقسيم فيه أشي غلط اه
+
+301
+00:43:35,100 --> 00:43:37,100
+ماشي
+
+302
+00:43:41,920 --> 00:43:51,900
+أه خلاص ما غلط على أي حال طيب على أي حال الان هذه
+
+303
+00:43:51,900 --> 00:44:01,400
+أول طبعا هذه أول دائرة ال base circle هذه المفروض
+
+304
+00:44:01,400 --> 00:44:08,160
+هذا يطلع لحد ما يصل ل ال .. ل ال stroke الان من
+
+305
+00:44:08,160 --> 00:44:13,170
+هذهطب اللحظة الأول خط اشمله tangent لل offset
+
+306
+00:44:13,170 --> 00:44:20,790
+circle المعنى تحرصه من tangent هاي
+
+307
+00:44:20,790 --> 00:44:26,070
+أول tangent هاي
+
+308
+00:44:26,070 --> 00:44:36,950
+تاني هذا برضه tangent تاني tangent تالت
+
+309
+00:44:36,950 --> 00:44:37,430
+tangent
+
+310
+00:44:48,120 --> 00:44:56,640
+رابع tangent خامس
+
+311
+00:44:56,640 --> 00:45:05,360
+tangent بعدين
+
+312
+00:45:05,360 --> 00:45:09,080
+سادس tangent
+
+313
+00:45:19,400 --> 00:45:24,120
+الان المسافات .. المسافات بين الدوائر هذو ال
+
+314
+00:45:24,120 --> 00:45:31,860
+stroke خمسين ال stroke خمسين يعني هذه خمسين هذه نص
+
+315
+00:45:31,860 --> 00:45:45,400
+الدائرة هذا
+
+316
+00:45:45,400 --> 00:45:51,320
+يتمثل minimum value صح؟ هذا ال minimumvalue معناته
+
+317
+00:45:51,320 --> 00:45:56,460
+أول دائرة هذه اسميها
+
+318
+00:45:56,460 --> 00:46:05,180
+X واحد بعدين X
+
+319
+00:46:05,180 --> 00:46:14,720
+اتنين بعدين X تلاتة بعدين X تلاتة
+
+320
+00:46:17,320 --> 00:46:24,560
+بعدين اكس اتنين ماهي بتسويها اكس اتنين و بعدين اكس
+
+321
+00:46:24,560 --> 00:46:29,020
+واحد اكس واحد اكس اتنين اكس تلاتة اكس تلاتة اكس
+
+322
+00:46:29,020 --> 00:46:38,600
+اتنين اكس واحد معناته بعمل دوائر من هذه الدائرة ال
+
+323
+00:46:38,600 --> 00:46:44,040
+center line circle هذه
+
+324
+00:46:44,040 --> 00:46:44,700
+اول واحدة
+
+325
+00:46:47,290 --> 00:46:55,110
+التاني واحدة بعمل offset x1 هنا
+
+326
+00:46:55,110 --> 00:47:07,510
+أكبر شوية offset x1 التانية offset
+
+327
+00:47:07,510 --> 00:47:10,530
+x2
+
+328
+00:47:10,530 --> 00:47:14,730
+التالتة
+
+329
+00:47:19,500 --> 00:47:40,620
+offset X3 الرابع نفس الاشي X3 الخامسة X2 بعدين X1
+
+330
+00:47:40,620 --> 00:47:44,360
+أول
+
+331
+00:47:44,360 --> 00:47:49,300
+نقطة تقاطع الدائرة الأساسية هذا هو النقطةهذه
+
+332
+00:47:49,300 --> 00:47:55,800
+التانية اللى جاي بدي اكتب عشان اكون مع X واحد صح؟
+
+333
+00:47:55,800 --> 00:48:02,360
+وهذه متقاطعة مع دائرة X اتنين وهذه مع دائرة X
+
+334
+00:48:02,360 --> 00:48:13,360
+تلاتة وهذه مع دائرة X تلاتة هذه X اتنين وهذه مع X
+
+335
+00:48:13,360 --> 00:48:13,840
+واحد
+
+336
+00:48:18,470 --> 00:48:27,230
+حددت ال centers بعدين at each center برسم ال
+
+337
+00:48:27,230 --> 00:48:36,210
+code roller أكملناه عشرين برسم هاي roller الأولى
+
+338
+00:48:36,210 --> 00:48:42,550
+هاي roller التانية هاي
+
+339
+00:48:42,550 --> 00:48:43,470
+roller التالتة
+
+340
+00:48:47,730 --> 00:48:53,790
+hyroller الرابع hyroller
+
+341
+00:48:53,790 --> 00:49:03,870
+الخامسة hyroller السادسة وhyroller
+
+342
+00:49:03,870 --> 00:49:07,930
+السابع
+
+343
+00:49:07,930 --> 00:49:16,750
+ال spline هذا الحرص هو هذا ال spline tangent
+
+344
+00:49:18,150 --> 00:49:21,590
+يعني مارسمش spline في ال sonata و لا في ال offset
+
+345
+00:49:21,590 --> 00:49:30,010
+لأ بعمل spline tangent للدوارة دول spline tangent
+
+346
+00:49:30,010 --> 00:49:38,970
+للدوارة دول نفس الشيء على الجهة التانية واضح هذا
+
+347
+00:49:38,970 --> 00:49:46,570
+في حالة ال roller شوف حالة تانية ال flat .. flat
+
+348
+00:49:46,570 --> 00:49:54,180
+بدها شويةمش مفهوم يعني المسافة بين ال .. ال .. ال
+
+349
+00:49:54,180 --> 00:49:59,520
+.. التواءف هدول التروري و ال .. و ال .. و ال .. و
+
+350
+00:49:59,520 --> 00:50:03,860
+ال .. هذه الدائرة مش نفس الدائرة لأ مش .. مش نفسها
+
+351
+00:50:03,860 --> 00:50:06,840
+هتكون مش في الضروري تكون .. مش في الضروري تكون
+
+352
+00:50:06,840 --> 00:50:14,100
+نفسها مش ضروري يعني .. يعني إذا تعملت offsetتعيزك
+
+353
+00:50:14,100 --> 00:50:17,180
+لما تعمل لأن هذا ال tangent هذا هتكون عمودي هذه صح
+
+354
+00:50:17,180 --> 00:50:24,780
+عند ال tangent هذا و عند ال tangent هذا عمودي و
+
+355
+00:50:24,780 --> 00:50:29,820
+عند ال tangent هذا عمودي لأن ارسم لو انت رسمت
+
+356
+00:50:29,820 --> 00:50:36,980
+جربها انت ارسم spline في هدول و ارسم tangent و
+
+357
+00:50:36,980 --> 00:50:40,060
+بعدين اعملي هذا offset بس امشيلي في ال zoom عليها
+
+358
+00:50:41,300 --> 00:50:47,140
+امشي عليها شويه شويه شو بتطبق لوش ولا بتطبقوش لأن
+
+359
+00:50:47,140 --> 00:50:53,000
+ال spline طبعا في عشان في ال care fitting في care
+
+360
+00:50:53,000 --> 00:50:58,660
+fit و
+
+361
+00:50:58,660 --> 00:51:05,340
+في spline طبعا هحكي معلومات اللي أنا بعرفه متأكد
+
+362
+00:51:05,340 --> 00:51:12,430
+منه بعض أحيان في البريوك نستخدم مصطلحاتما تكونش
+
+363
+00:51:12,430 --> 00:51:16,850
+يعني نفس المتفق عليه رياضيا ال curve fit اذا عندي
+
+364
+00:51:16,850 --> 00:51:23,490
+مجموعة من النقاط و
+
+365
+00:51:23,490 --> 00:51:31,550
+حكيت اعملي curve fit فيهم بيعمل
+
+366
+00:51:31,550 --> 00:51:35,950
+smooth curve بس لازم يمر في كل النقاط لازم يمر في
+
+367
+00:51:35,950 --> 00:51:40,210
+كل النقاط ال curve ال spline
+
+368
+00:51:44,220 --> 00:51:48,600
+أقوله تفاصيل بس بدأ أذكر أهم تفاصيل تان لازم ال
+
+369
+00:51:48,600 --> 00:51:52,780
+curve ال spline يمر في النقطة الأولى و النقطة
+
+370
+00:51:52,780 --> 00:51:56,520
+الأخيرة بس
+
+371
+00:51:56,520 --> 00:51:59,200
+باطيله انه تولد انسى ايه اتحرك بينهم يعني اسمه
+
+372
+00:51:59,200 --> 00:52:06,080
+ممكن احكيه لازم
+
+373
+00:52:06,080 --> 00:52:08,260
+يمر في هذه و في هذه في تفاصيل تان طبعا هذا
+
+374
+00:52:08,260 --> 00:52:08,660
+basically
+
+375
+00:52:13,330 --> 00:52:24,230
+عشان هيك .. عشان هيك تعملش offset لأن هو هشوف يعني
+
+376
+00:52:24,230 --> 00:52:29,030
+أنعم curve ال curve fit مش دايما بيكون أنعم curve
+
+377
+00:52:29,030 --> 00:52:35,130
+ال spline بيكون أنعم منه يعني انا مجبراه و اتنقضت
+
+378
+00:52:35,130 --> 00:52:38,670
+بتحس انه في حدة في الانتقال و كنت بقوله لأ ينزلش
+
+379
+00:52:38,670 --> 00:52:43,460
+في عنهاأو يطلع هنا هذا ال spline ال spline يعني
+
+380
+00:52:43,460 --> 00:52:47,920
+انت بتحدد له how much يبدأ عشان هيك لما تعمل
+
+381
+00:52:47,920 --> 00:52:50,560
+spline شوف ممكن تلعب في ال slopes لإن تلعب في ال
+
+382
+00:52:50,560 --> 00:52:55,300
+slopes بتغير فهي
+
+383
+00:52:55,300 --> 00:53:04,180
+الفرق بين ال curve fit و ال spline روح
+
+384
+00:53:04,180 --> 00:53:06,920
+على ال net اكتب curve fit
+
+385
+00:53:13,890 --> 00:53:20,410
+versus spline مش
+
+386
+00:53:20,410 --> 00:53:25,210
+نفس الأشياء اختلفوا عن بعض وع
+
+387
+00:53:25,210 --> 00:53:28,850
+طول أريحلك بدون أن تدخل في text خش على images على
+
+388
+00:53:28,850 --> 00:53:32,170
+الصورة
+
+389
+00:53:32,170 --> 00:53:37,130
+طيب
+
+390
+00:53:37,130 --> 00:53:40,450
+خليني أعطي إيه تاني
+
+391
+00:54:01,130 --> 00:54:08,630
+flat-faced follower يعني نفس النظام عند كام
+
+392
+00:54:08,630 --> 00:54:12,330
+نعمل كام ال follower بتحرك في simple harmonic
+
+393
+00:54:12,330 --> 00:54:17,430
+motion ال base circle نص القطر تلعب على خمس و
+
+394
+00:54:17,430 --> 00:54:21,550
+عشرين أول
+
+395
+00:54:21,550 --> 00:54:26,810
+مائة و عشرين درجة أول مائة و عشرين درجة بتلعب في
+
+396
+00:54:26,810 --> 00:54:32,350
+simple harmonic motionبعدين التلاتين الدرجة
+
+397
+00:54:32,350 --> 00:54:38,230
+التانية بيضلوا مكانه بعدين ال مئو عشرين بعدهم بنزل
+
+398
+00:54:38,230 --> 00:54:47,770
+simple harmonic motion ال stroke عشرين
+
+399
+00:54:47,770 --> 00:54:53,990
+مليه يعني هيطلع
+
+400
+00:54:53,990 --> 00:55:01,010
+عشرين يعني لما يصل عند النقطة هذههيكون طالع عشرين
+
+401
+00:55:01,010 --> 00:55:08,770
+هنا عشرين بعدين هنا هيكون ع كام عند ال .. عند ال
+
+402
+00:55:08,770 --> 00:55:12,710
+zero يعني عند الدائرة خمسين و ال camp تقف
+
+403
+00:55:12,710 --> 00:55:18,230
+clockwise الحال
+
+404
+00:55:18,230 --> 00:55:22,370
+هو لو كان عندي ال axis of ال follower نفس المورف
+
+405
+00:55:22,370 --> 00:55:24,910
+ال axis بتاع ال camp
+
+406
+00:55:27,610 --> 00:55:32,230
+في كل أحوال ال face بتاع ال floor بيكون ايش
+
+407
+00:55:32,230 --> 00:55:36,630
+tangent لل camp profile tangent لل camp profile
+
+408
+00:55:36,630 --> 00:55:40,470
+فانا أول شي برسم ال base circle هاي رسم ال base
+
+409
+00:55:40,470 --> 00:55:53,510
+circle هاي
+
+410
+00:55:53,510 --> 00:55:58,720
+ال base circleو هاي ال start point هدى النقطة هدى
+
+411
+00:55:58,720 --> 00:56:09,480
+يبدأيش الصعود بيصعد بمية و عشرين درجة هدى
+
+412
+00:56:09,480 --> 00:56:16,960
+فترة الصعود هدى هيدله مكانه
+
+413
+00:56:16,960 --> 00:56:25,400
+بعدين مية و عشرين مية و عشرين متين و أربعينثلاثين
+
+414
+00:56:25,400 --> 00:56:27,340
+و اتنين سبعة درجات و تظل زي و تسعين درجة في الآخر
+
+415
+00:56:27,340 --> 00:56:32,560
+وهذا
+
+416
+00:56:32,560 --> 00:56:37,700
+فترة الهبوط الآن هو بيقسم الـ120 مثلا هو بيقسمها
+
+417
+00:56:37,700 --> 00:56:41,540
+ست أقسم واحد اتنين تلاتة اربعة خمسة ستة
+
+418
+00:57:03,580 --> 00:57:04,600
+نفسي مش في الهبوط
+
+419
+00:57:38,430 --> 00:57:44,090
+الأن simple harmonic motion معناته لو أنا روحت هنا
+
+420
+00:57:44,090 --> 00:57:48,630
+الدائرة
+
+421
+00:57:48,630 --> 00:57:49,670
+تاعت رسمتها
+
+422
+00:58:17,900 --> 00:58:36,280
+X1 X2 X3 X3 X2 X1 لاحظ
+
+423
+00:58:36,280 --> 00:58:42,770
+دايما ال center line عمودي على ال facecenter line
+
+424
+00:58:42,770 --> 00:58:47,390
+الفلور عمودي على ال face و ال face tangent لل
+
+425
+00:58:47,390 --> 00:58:53,090
+profile الان لو رسمنا الدار الأولى تبعد X واحد
+
+426
+00:58:53,090 --> 00:58:59,310
+مثلا هذه الدار الأولى هذه
+
+427
+00:58:59,310 --> 00:59:10,690
+المسافة X واحد والمسافة
+
+428
+00:59:10,690 --> 00:59:11,130
+التانية
+
+429
+00:59:16,250 --> 00:59:24,690
+X2 و X3 يعني هادي X واحد X2
+
+430
+00:59:24,690 --> 00:59:29,170
+و X3 عند كل واحدة عند كل واحدة برسم دوايا واحدة
+
+431
+00:59:29,170 --> 00:59:34,270
+تنتين .. واحدة تنتين تلاتة أربعة خمسة ستة السابعة
+
+432
+00:59:34,270 --> 00:59:39,230
+وان جاية عند البداية صح؟ لأن سفر واحد تنتين تلاتة
+
+433
+00:59:39,230 --> 00:59:39,990
+أربعة خمس ستة
+
+434
+00:59:45,240 --> 00:59:54,280
+عند كل واحدة بأرسم ايش tangent tangent
+
+435
+00:59:54,280 --> 00:59:57,940
+tangent
+
+436
+00:59:57,940 --> 01:00:01,380
+عمودي
+
+437
+01:00:01,380 --> 01:00:05,380
+على ال center line عمودي على ال center line مش
+
+438
+01:00:05,380 --> 01:00:09,620
+tangent هو عمودي على ال center line هذه زي وتسعين
+
+439
+01:00:09,620 --> 01:00:14,760
+هذه تسعين هذه تسعين هذه تسعين هذه تسعين وهكذا
+
+440
+01:00:20,750 --> 01:00:26,950
+طيب الآن ال
+
+441
+01:00:26,950 --> 01:00:35,170
+profile بتاع النقاط هذه اللي هو الخط المتقطع ال
+
+442
+01:00:35,170 --> 01:00:39,490
+cam profile بيكون tangent لل surface بتاعه في
+
+443
+01:00:39,490 --> 01:00:39,850
+الورق
+
+444
+01:00:46,230 --> 01:00:50,770
+الخط هذا والخط هذا والخط هذا والخط هذا والخط هذا
+
+445
+01:00:50,770 --> 01:00:52,010
+والخط هذا والخط هذا والخط هذا والخط هذا والخط هذا
+
+446
+01:00:52,010 --> 01:00:52,030
+والخط هذا والخط هذا والخط هذا والخط هذا والخط هذا
+
+447
+01:00:52,030 --> 01:00:52,110
+والخط هذا والخط هذا والخط هذا والخط هذا والخط هذا
+
+448
+01:00:52,110 --> 01:00:52,290
+والخط هذا والخط هذا والخط هذا والخط هذا والخط هذا
+
+449
+01:00:52,290 --> 01:00:53,370
+والخط هذا والخط هذا والخط هذا والخط هذا والخط هذا
+
+450
+01:00:53,370 --> 01:00:55,690
+والخط هذا
+
+451
+01:01:06,350 --> 01:01:11,370
+بكون tangent ل ال face of follower tangent ل ال
+
+452
+01:01:11,370 --> 01:01:16,690
+face of follower هذا
+
+453
+01:01:16,690 --> 01:01:22,130
+في حالة ال axis بمر في ال axis في حالة كان في
+
+454
+01:01:22,130 --> 01:01:33,350
+shift ال axis بمرش في ال axis بقى في shift مش
+
+455
+01:01:33,350 --> 01:01:48,990
+مبينهابس هتعملها انا هترسم
+
+456
+01:01:48,990 --> 01:01:52,510
+ال .. ال .. ال .. ال offset circle نفس الشيء ال
+
+457
+01:01:52,510 --> 01:01:57,990
+offset circle هترسمها هترسم
+
+458
+01:01:57,990 --> 01:02:03,870
+ايه اش تانية ال .. المفروض
+
+459
+01:02:09,640 --> 01:02:16,040
+هذه الفلور هذه
+
+460
+01:02:16,040 --> 01:02:24,220
+الفلور لأن
+
+461
+01:02:24,220 --> 01:02:29,880
+هذه النقطة المفروض ان ال base circle المفروض ان ال
+
+462
+01:02:29,880 --> 01:02:34,920
+base circle تمر هتكون
+
+463
+01:02:34,920 --> 01:02:44,320
+tangent هذه أول نقطةهدققاش أول نقطة يعني الفكرة
+
+464
+01:02:44,320 --> 01:02:52,960
+هتبدأ من هنا و
+
+465
+01:02:52,960 --> 01:02:59,660
+تجزئها لمية و عشرين تلاتين مية و عشرين مية
+
+466
+01:02:59,660 --> 01:03:09,190
+و عشرين تلاتين مية و عشرين لأن لاحظ من هنابيكون
+
+467
+01:03:09,190 --> 01:03:15,390
+ايش ال tangent لو أخدت التانية هتكون
+
+468
+01:03:15,390 --> 01:03:27,930
+tangent و هكذا جربوها في
+
+469
+01:03:27,930 --> 01:03:33,470
+اي سؤال فالمطلوب منك اللي هو ال sharp edge و
+
+470
+01:03:33,470 --> 01:03:37,390
+rollerو ال flat و برضه في example عشرين خمسة
+
+471
+01:03:37,390 --> 01:03:40,370
+مارجيكوا ال oscillating نفس الفكرة رسمها ال
+
+472
+01:03:40,370 --> 01:03:44,570
+oscillating هاي
+
+473
+01:03:44,570 --> 01:03:50,910
+عندي oscillating follower و
+
+474
+01:03:50,910 --> 01:03:57,730
+نوع ال end مش sharp edge ولا flat roller فى
+
+475
+01:03:57,730 --> 01:04:02,510
+البداية بيكون أفقه هو فهو
+
+476
+01:04:02,510 --> 01:04:07,700
+بيصيريطلع و ينزل بنيته هو بيطلع و ينزل إيش؟ زاوية
+
+477
+01:04:07,700 --> 01:04:13,820
+بس الزاوية إيش بيحولها؟ بيحولها لل sign هنا بحكي
+
+478
+01:04:13,820 --> 01:04:16,520
+اللي بيطلع في زاوية عشرين درجة و المسافة هذه
+
+479
+01:04:16,520 --> 01:04:26,400
+بيعطيني إياها مية و عشرين واضح؟
+
+480
+01:04:26,400 --> 01:04:28,640
+عشرة المحاضرة الجاية بنكمل
+
diff --git a/PL9fwy3NUQKwa0nXiCdyQcTW4hWDLTGpDb/PEpCpI0FwR0_postprocess.srt b/PL9fwy3NUQKwa0nXiCdyQcTW4hWDLTGpDb/PEpCpI0FwR0_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..4ac13603e40541edf915a9b737a1e00acc6792a8
--- /dev/null
+++ b/PL9fwy3NUQKwa0nXiCdyQcTW4hWDLTGpDb/PEpCpI0FwR0_postprocess.srt
@@ -0,0 +1,1308 @@
+1
+00:00:05,770 --> 00:00:08,410
+طبعا اليوم هندرس اللي هو ال inversion of
+
+2
+00:00:08,410 --> 00:00:13,730
+mechanisms ال inversion of mechanism اللي بيسوي
+
+3
+00:00:13,730 --> 00:00:21,070
+احنا ال mechanism يكون احد اللينكات ثابتة برخ ال
+
+4
+00:00:21,070 --> 00:00:26,830
+link ثابتة و بيثبت واحدة تانية بحص على mechanism
+
+5
+00:00:26,830 --> 00:00:32,530
+جديدة بحص على mechanismالحركة الموجودة بين ال
+
+6
+00:00:32,530 --> 00:00:38,210
+links تتغير بشكل كبير بالنسبة لـ Relative Motion
+
+7
+00:00:38,210 --> 00:00:42,130
+لـ Links Forming The Mechanism تتغير بشكل كبير
+
+8
+00:00:42,130 --> 00:00:47,210
+فاحنا انا هنبدأ في Slider Crank Mechanism اللي هي
+
+9
+00:00:47,210 --> 00:00:50,550
+أساسا عندك ال crank
+
+10
+00:00:59,250 --> 00:01:09,030
+عندنا هاي الأرض واحد اتنين تلاتة أربعة هاي A في
+
+11
+00:01:09,030 --> 00:01:15,090
+pair عند A في pair عند B و في pair عند C و في pair
+
+12
+00:01:15,090 --> 00:01:22,790
+ال D اللي جاي بين أربعة و واحد الآن التمثيل بتاعها
+
+13
+00:01:22,790 --> 00:01:23,350
+هيكون
+
+14
+00:01:35,660 --> 00:01:47,620
+هذه عندي A B C D ال link واحد جاية
+
+15
+00:01:47,620 --> 00:01:50,620
+بين A وB يعني في ال link واحد جاية عليها revolute
+
+16
+00:01:50,620 --> 00:01:58,660
+joint و الجاية عندهاش sliding joint هذي واحد ال
+
+17
+00:01:58,660 --> 00:01:59,400
+link اتنين
+
+18
+00:02:03,410 --> 00:02:07,610
+لسه ال link اتنين جاء بين a و b هى revolute و هى
+
+19
+00:02:07,610 --> 00:02:13,550
+revolute و ال link تلتة جاء بين b و c revolute و
+
+20
+00:02:13,550 --> 00:02:20,450
+revolute و ال link اربعة فيها revolute joint عند c
+
+21
+00:02:20,450 --> 00:02:26,330
+و فيها sliding joint عند واحد هذه ايه اش اربعة
+
+22
+00:02:31,650 --> 00:02:47,230
+حنبدأ في ال inversion رقم أربعة طبعا
+
+23
+00:02:47,230 --> 00:02:49,150
+ال inversions أرقامها
+
+24
+00:02:59,670 --> 00:03:19,350
+دكتور عن بى بتفضل دورة كاملة؟ طوالين بس عن
+
+25
+00:03:19,350 --> 00:03:25,450
+بى هو هسير تقريبا كاملة يعني هسير تاخد دورة كاملة
+
+26
+00:03:27,320 --> 00:03:34,000
+يعني خليني انا ممكن اعتبرها partial، ماشي لأ
+
+27
+00:03:34,000 --> 00:03:40,020
+لعندي هاي واحد، هاي اتنين، هاي تلاتة، هاي اربعة،
+
+28
+00:03:40,020 --> 00:03:43,740
+هاي عندى ال value ال joint عند a و a و b و c و عند
+
+29
+00:03:43,740 --> 00:03:47,800
+sliding joint بين اربعة و واحد عند نقطة D
+
+30
+00:03:53,230 --> 00:03:56,290
+اللي هنعمل ال fourth inversion fourth inversion
+
+31
+00:03:56,290 --> 00:03:59,050
+هذه ال first inversion ال first inversion يعني
+
+32
+00:03:59,050 --> 00:04:04,110
+واحد ثابت ال second inversion بتكون اتنين هي ثابت
+
+33
+00:04:04,110 --> 00:04:08,450
+ال third inversion التلاتة ثابت ال fourth
+
+34
+00:04:08,450 --> 00:04:13,390
+inversion اللي هي الأربعة ثابتة معناته في اربع
+
+35
+00:04:13,390 --> 00:04:16,570
+inversions من Slavic rank اللي يقولوا اللي احنا
+
+36
+00:04:16,570 --> 00:04:21,110
+عارفينه اللي هي هذه الرابعة هنثبت الرقم أربعة
+
+37
+00:04:22,690 --> 00:04:28,330
+وانحرك ايه اش واحد خلنا نبدأ من اول
+
+38
+00:04:28,330 --> 00:04:45,570
+خلنا
+
+39
+00:04:45,570 --> 00:05:00,080
+نثبت ممكن نضغط فيهعندي هاي ايه نفس الرصد دي بي سي
+
+40
+00:05:00,080 --> 00:05:16,160
+هذا video هاي اتنين هاي تلاتة هاي اربع وهاي
+
+41
+00:05:16,160 --> 00:05:16,660
+واحد
+
+42
+00:05:21,370 --> 00:05:30,210
+A B C D نفس اللي راسه و انا هنا واضح اللي هيسوي
+
+43
+00:05:30,210 --> 00:05:39,730
+ايه هنفك هذه و نثبت هذه الخطوة التالية هنفك واحد و
+
+44
+00:05:39,730 --> 00:05:42,110
+نثبت اربعه شوف ايش الميكانيزم اللي بيصير معنا
+
+45
+00:05:51,030 --> 00:05:55,830
+هو بيحكي حاليا إنه هيفك قاعدة و يثبت قاعدة الآن
+
+46
+00:05:55,830 --> 00:06:01,330
+خلّينا
+
+47
+00:06:01,330 --> 00:06:05,390
+نثبت ثبت
+
+48
+00:06:05,390 --> 00:06:12,490
+إيه؟ خلّيني
+
+49
+00:06:12,490 --> 00:06:19,690
+أعمل ميكانيزم هاي هاي A هاي
+
+50
+00:06:19,690 --> 00:06:32,520
+Bهي C هى D هى واحد هى اتنين هى تلاتة هى أربعة هذا
+
+51
+00:06:32,520 --> 00:06:39,460
+الوضع الأولاني الوضع التاني هثبت ايش اربعة هسيه
+
+52
+00:06:39,460 --> 00:06:43,160
+عندي هى
+
+53
+00:06:43,160 --> 00:06:58,650
+A B هى Cهي D هاي واحد هاي اتنين تلاتة اربعة احنا
+
+54
+00:06:58,650 --> 00:07:10,430
+هنثبت ايش اربعة link اربعة صارت ثابتة هي هنا عندنا
+
+55
+00:07:10,430 --> 00:07:30,660
+A B و Cوعندي ايش دي هاي واحد هاي اتنين تلاتة
+
+56
+00:07:30,660 --> 00:07:39,180
+اربع اربع صارت اشملها ثابتة
+
+57
+00:07:39,180 --> 00:07:42,320
+الان
+
+58
+00:07:42,320 --> 00:08:01,620
+في عندي نقطة C هي نقطة C نقطة Cأو اربع نحكي IIC بي
+
+59
+00:08:01,620 --> 00:08:07,500
+هاي
+
+60
+00:08:07,500 --> 00:08:07,760
+ايه
+
+61
+00:08:19,900 --> 00:08:26,480
+هذه أربعة أربعة صارت ثابتة صح؟ أربعة ثابتة وهذه
+
+62
+00:08:26,480 --> 00:08:35,920
+أربعة أربعة جاءة طرف من أطرافها revolute joint عند
+
+63
+00:08:35,920 --> 00:08:45,140
+C وفي عندها sliding joint عند D يعني هذه D هذه C C
+
+64
+00:08:45,140 --> 00:08:48,960
+و ال joint هذه ايش D
+
+65
+00:08:53,210 --> 00:09:01,630
+في عند ال link ال اقل
+
+66
+00:09:01,630 --> 00:09:09,810
+حكينا link four على طرف الأطراف في revolute وعلى
+
+67
+00:09:09,810 --> 00:09:14,730
+الطرف التاني فيه sliding معنى التثابت هذه اربعة
+
+68
+00:09:14,730 --> 00:09:18,170
+وهي نقطة C وهي نقطة D
+
+69
+00:09:20,990 --> 00:09:36,730
+C .. C .. C مع B هي معناته ايه ده هتكون؟ تلاتة و B
+
+70
+00:09:36,730 --> 00:09:46,370
+مع A اللي هي هذه ريوليوت معناته هذي هذي ايه؟ هذي
+
+71
+00:09:46,370 --> 00:09:47,130
+اتنين
+
+72
+00:09:50,200 --> 00:09:58,920
+وهذه ماذا ستكون؟ واحد لأن واحد هي واحد في طرف عنده
+
+73
+00:09:58,920 --> 00:10:04,620
+revolute هي نقطة a وفي طرف sliding بالنسبة لاربعة
+
+74
+00:10:04,620 --> 00:10:10,880
+واحد صار sliding بالنسبة لاربعة طبعا هو مادة هذه
+
+75
+00:10:10,880 --> 00:10:17,820
+اضافة هي ال link بالشكل الأساسي اللي هو هذا لكن
+
+76
+00:10:17,820 --> 00:10:28,400
+مادة لدراعوسمى هذه النقطة H يعني هذه صارت احنا
+
+77
+00:10:28,400 --> 00:10:34,080
+بنبدأ من ايه؟ من الثابتة الثابتة في عندي revolute
+
+78
+00:10:34,080 --> 00:10:39,620
+joint الاربع جاي بين revolute joint و sliding
+
+79
+00:10:39,620 --> 00:10:44,360
+joint فهذه ال sliding joint
+
+80
+00:10:44,360 --> 00:10:47,600
+معناته
+
+81
+00:10:47,600 --> 00:10:49,800
+هذه ايه؟ D
+
+82
+00:10:53,150 --> 00:11:03,150
+هذه معناته الثابت اربعة والثابت ايش اربعة واحد
+
+83
+00:11:03,150 --> 00:11:08,950
+انا ببدأها بطريقة بالعكس واحد sliding من ناس في
+
+84
+00:11:08,950 --> 00:11:18,590
+الأربعة صح؟ واحد هذه معناته هتكون واحد هذه واحد
+
+85
+00:11:18,590 --> 00:11:25,090
+sliding من ناس في الأربعةواحد طرف sliding وطرف فيه
+
+86
+00:11:25,090 --> 00:11:33,310
+revolute عند a هاي
+
+87
+00:11:33,310 --> 00:11:38,890
+ايش revolute عند a الآن
+
+88
+00:11:38,890 --> 00:11:40,730
+بعدين بتيجي B
+
+89
+00:11:52,120 --> 00:12:02,920
+هذا هتكون ايش اتنين و بي سا بي بي سي تلاتة
+
+90
+00:12:02,920 --> 00:12:12,980
+هو راح مد هذه و اسمها H طبعا
+
+91
+00:12:12,980 --> 00:12:20,810
+اذا بحرك الدراع هذا الأسفل و الأعلى هذا هتكونتطلع
+
+92
+00:12:20,810 --> 00:12:25,990
+و تنزل كأنها مكبس او نظام مضخات القديم اليدوية
+
+93
+00:12:25,990 --> 00:12:29,750
+بالظبط
+
+94
+00:12:29,750 --> 00:12:34,110
+بيكون فيه فتحات يعني ع جناب بنزل الحمام بعدين
+
+95
+00:12:34,110 --> 00:12:40,850
+بيضخوا الماء لأعلى فهذا زي نظام مضخة يدوية خد اه
+
+96
+00:12:42,080 --> 00:12:45,900
+السؤال يعني عملها على أرض واحدة، قبل ال inversion
+
+97
+00:12:45,900 --> 00:12:49,760
+و بعد ال inversion، كيف السبب؟ لأ، هد يعني هد
+
+98
+00:12:49,760 --> 00:12:52,200
+another mechanism، يعني هد هتطلع نتيجة ال
+
+99
+00:12:52,200 --> 00:12:55,080
+inversion، هد mechanism جديدة، يعني هد it is one
+
+100
+00:12:55,080 --> 00:12:59,540
+mechanism، هد عندك inversion رقم واحد، هد
+
+101
+00:12:59,540 --> 00:13:05,650
+inversion رقم four، هد يعني a new mechanismلأن ال
+
+102
+00:13:05,650 --> 00:13:09,690
+relative motion بين ال component بين ال 1 و 2 و 1
+
+103
+00:13:09,690 --> 00:13:13,830
+و 3 و 1 و 4 و 3 و 2 و 3 و 4 نفس ال relative motion
+
+104
+00:13:13,830 --> 00:13:18,530
+بس ايش اللي اتغير ال absolute motion اختلفت يعني
+
+105
+00:13:18,530 --> 00:13:24,150
+اللي اخدت في الأول يعني 1 في الحالة الأولى ما هي 4
+
+106
+00:13:24,150 --> 00:13:29,650
+تنزلت بالنسبة ل 1 نسبيا طب ما هي برضه 1 تنزلت
+
+107
+00:13:29,650 --> 00:13:37,790
+بالنسبة ل 4الحركة النسبية ما اختلفت انا
+
+108
+00:13:37,790 --> 00:13:41,610
+ماحكتش
+
+109
+00:13:41,610 --> 00:13:46,730
+تتحرك انا حكتلك واحد slide بالنسبة للاربعة واحد
+
+110
+00:13:46,730 --> 00:13:51,510
+slide بالنسبة للاربعة بحكي عن الحركة النسبية لكن
+
+111
+00:13:51,510 --> 00:13:55,250
+ال absolute motion بتاعة اربعة نتيجة ال inversion
+
+112
+00:13:55,250 --> 00:14:02,650
+اتغيرت صارت اربعة ثابتة واحد صارت ايهاشهي المتحركة
+
+113
+00:14:02,650 --> 00:14:09,690
+لكن من ناحية نسبية مايتغير الأشياء يعني still واحد
+
+114
+00:14:09,690 --> 00:14:12,830
+تتحرك من أسفل الأربع أو أربع تتحرك من أسفل الأواحد
+
+115
+00:14:12,830 --> 00:14:19,870
+هي هي أظهر يعني انت وانت ماشي في الشارع بالسيارة
+
+116
+00:14:19,870 --> 00:14:25,970
+اتطلع هتشوف الشارع بيمشي صح اطلع انزل على الشارع
+
+117
+00:14:25,970 --> 00:14:29,510
+هتشوف السيارة اللي بتمشي معناته
+
+118
+00:14:31,880 --> 00:14:38,520
+السيارة بالنسبة للشارع الثابت بتتحرك او لو كان
+
+119
+00:14:38,520 --> 00:14:41,560
+المرجع بتاعك السيارة انت كنت جوا السيارة الشارع
+
+120
+00:14:41,560 --> 00:14:46,080
+بيمشي بالنسبة للسيارة صح؟
+
+121
+00:14:46,080 --> 00:14:49,000
+لو كنت بسيارتين هاي سيارة و هاي سيارة ماشية بنفس
+
+122
+00:14:49,000 --> 00:14:52,420
+السرعة و انت كنت بالسيارة على الشمال و في عيونك
+
+123
+00:14:52,420 --> 00:14:56,180
+السيارة تركزت تنظر على السيارة اللي جانبك بتشوفها
+
+124
+00:14:56,180 --> 00:15:01,480
+تمشيشلكن اطلع انت و خلي واحد برا على الشارع هتشوف
+
+125
+00:15:01,480 --> 00:15:07,200
+تنتين ماشيين نفس السرعة لو كانت السيارة جانبك أسرع
+
+126
+00:15:07,200 --> 00:15:13,280
+هتتجوزك هتشوف بطيئة هتشوفه بطيئة انت بس هي أسرع
+
+127
+00:15:13,280 --> 00:15:19,700
+منك فعليا لو كانت معاكسة هتشوفها سريعة جدا فانا
+
+128
+00:15:19,700 --> 00:15:24,300
+اللي بدأ اصل انه الحركة النسبيةيعني محافظ عليها
+
+129
+00:15:24,300 --> 00:15:30,360
+لكن اختلفت الحركة المطلقة لكل link والدليل عندك
+
+130
+00:15:30,360 --> 00:15:35,120
+اربع صارت مطلقة تتحرك هذه ال fourth inversion
+
+131
+00:15:35,120 --> 00:15:49,860
+خلينا نشوف ال animation بتاعها هو
+
+132
+00:15:49,860 --> 00:15:50,800
+بس كبرها هنا
+
+133
+00:15:59,390 --> 00:16:05,090
+طيب عندك هاي واحد اتنين تلاتة اربعة فى revolute
+
+134
+00:16:05,090 --> 00:16:11,530
+عند a و b و c و اصلاح دي ان دي اربعة ثابتة واحد
+
+135
+00:16:11,530 --> 00:16:15,990
+اصلاح دي نصف الاربعة وفى عندك relative rotation
+
+136
+00:16:15,990 --> 00:16:17,570
+بين واحد و اتنين relative rotation بين اتنين و
+
+137
+00:16:17,570 --> 00:16:22,890
+تلاتة و relative rotation بين تلاتة و اربعة نشوف
+
+138
+00:16:22,890 --> 00:16:23,510
+ميكانزم
+
+139
+00:16:36,940 --> 00:16:46,760
+على اي حالة نزل على مودي الفيديوهات هذه
+
+140
+00:16:46,760 --> 00:16:55,920
+الميكانيزم بتاعتنا هي CBA هذي اربع اربع واحد اتنين
+
+141
+00:16:55,920 --> 00:16:59,740
+تلاتة
+
+142
+00:16:59,740 --> 00:17:05,560
+معناته
+
+143
+00:17:05,560 --> 00:17:05,960
+sliding
+
+144
+00:17:38,160 --> 00:17:50,600
+الان في two extreme positions لالميكانزم هذه لما
+
+145
+00:17:50,600 --> 00:17:55,560
+يصير BC عمودي على AH هذا أكتر بضاية ممكن تروح
+
+146
+00:17:55,560 --> 00:17:59,380
+لدراع على اليمين أو على الشمال يعني هذه لما تصير
+
+147
+00:17:59,380 --> 00:18:04,440
+91 درجة يعني هذا one extreme position وهذا one
+
+148
+00:18:04,440 --> 00:18:07,880
+extreme positionففي عندك two extreme positions لل
+
+149
+00:18:07,880 --> 00:18:16,840
+link اللي هي رقم تلاتة هاي واحد هاي اتنين و
+
+150
+00:18:16,840 --> 00:18:24,620
+اكبر مسافة لما تكون هذه التسعين طبعا
+
+151
+00:18:24,620 --> 00:18:29,820
+الان نفس الاشي يعني هاي عندك مكبس اللي هو ده عايش
+
+152
+00:18:29,820 --> 00:18:36,660
+تمثل واحد السليندر عايش تمثلأربعة، الإدراع هذا
+
+153
+00:18:36,660 --> 00:18:39,900
+تلاتة،
+
+154
+00:18:39,900 --> 00:18:52,400
+وهذا أيش؟ اتنين لأن هذا مضخة وأبعد
+
+155
+00:18:52,400 --> 00:18:55,800
+وضع ممكن تسألون اللي هي أيش؟ بالظبط
+
+156
+00:19:06,780 --> 00:19:14,260
+طيب هذه هي ال fourth inversion هنشوف ال third و ال
+
+157
+00:19:14,260 --> 00:19:29,800
+second انا عندي توضيح للمضخة هنا في ال slides سبعة
+
+158
+00:19:29,800 --> 00:19:30,320
+و خمسين
+
+159
+00:19:40,620 --> 00:19:52,380
+شايفين الصمام تحت هو نازل بيسكر الآن
+
+160
+00:19:52,380 --> 00:19:59,760
+ال slider اللي هو إيش رقم واحد ال cylinder أربعة
+
+161
+00:19:59,760 --> 00:20:04,160
+أربعة
+
+162
+00:20:04,160 --> 00:20:12,500
+و هذه إيش هذه البنيةتلاتة والدراع هذا اللي يصير
+
+163
+00:20:12,500 --> 00:20:18,320
+اتنين لان هذه المحور لان هذه القطع مع السيلندر
+
+164
+00:20:18,320 --> 00:20:23,760
+fixed هذه اربعة يعني اربعة وهذه الدراع هذا يعني
+
+165
+00:20:23,760 --> 00:20:31,100
+اننا حكينا هذه ايش هذه C وهذه B وهذه A و ال
+
+166
+00:20:31,100 --> 00:20:40,890
+sliding ايش D صح كمان مرة هذه C هذه Bهي a و ال
+
+167
+00:20:40,890 --> 00:20:47,530
+sliding دي ال slider اللي هو اربع السليندر ال
+
+168
+00:20:47,530 --> 00:20:52,630
+slider اللي هو واحد السليندر اربع لدراع البني
+
+169
+00:20:52,630 --> 00:20:59,030
+تلاتة لدراع الصغير الأخضر هذا اتنين
+
+170
+00:20:59,030 --> 00:21:02,930
+الان
+
+171
+00:21:02,930 --> 00:21:05,130
+في حيكون two extreme positions
+
+172
+00:21:07,990 --> 00:21:13,850
+two extreme positions يعني هتكون لما تكون الادراع
+
+173
+00:21:13,850 --> 00:21:18,730
+ده عمودي بيكون هو ال maximum position على الشمال
+
+174
+00:21:18,730 --> 00:21:21,130
+لو بيكون عمودي على الجهة التانية بيكون ال maximum
+
+175
+00:21:21,130 --> 00:21:27,650
+position على اليمين في زاوية تانية عندي زاوية
+
+176
+00:21:27,650 --> 00:21:35,210
+theta وزاوية beta الآن
+
+177
+00:21:35,210 --> 00:21:41,580
+من هذه لهذهمسافة لان ايش بدوران ده؟ حاجة يسموها ال
+
+178
+00:21:41,580 --> 00:21:44,860
+.. ال .. ال forward stroke الشوط الأمامي أو ال
+
+179
+00:21:44,860 --> 00:21:49,980
+cutting stroke وهذا شوط العودة شوط العودة حاجة
+
+180
+00:21:49,980 --> 00:21:54,960
+يسموها slotted liver quick cretein motion الآن ال
+
+181
+00:21:54,960 --> 00:22:02,560
+time ال .. ال .. ال quick cretein ratio بيساوي ال
+
+182
+00:22:02,560 --> 00:22:08,390
+time لل forward على ال time تارتينالـ time بتاع ال
+
+183
+00:22:08,390 --> 00:22:14,770
+forward بالساوية ال theta على السرعة الزاوية ال
+
+184
+00:22:14,770 --> 00:22:22,530
+theta على السرعة الزاوية omega هتكون ثابتة على ال
+
+185
+00:22:22,530 --> 00:22:28,750
+time بتاعها هتكون beta على omega فال
+
+186
+00:22:28,750 --> 00:22:34,190
+quicker التاني عشان هتكون theta على beta ال امين
+
+187
+00:22:34,190 --> 00:22:34,990
+أكبر عنده
+
+188
+00:22:38,320 --> 00:22:47,060
+فيتا صح؟ معناته في ال شواط و أنت رايح باخد وقت
+
+189
+00:22:47,060 --> 00:22:50,520
+أطول من الرجوع يعني برجع بسرعة عشان هي كما يسمونها
+
+190
+00:22:50,520 --> 00:22:55,520
+quick retain mechanism quick retain mechanism وين
+
+191
+00:22:55,520 --> 00:22:57,820
+موجود application ل quick retain mechanism تشوفوا
+
+192
+00:22:57,820 --> 00:23:06,070
+في مكان التصوير صحيحماكنتصفير بتعمل scan بدها وقت
+
+193
+00:23:06,070 --> 00:23:12,030
+بتكون بطيء بعدين بتكون بطيء بعدين ترجع بسرعة ف
+
+194
+00:23:12,030 --> 00:23:17,310
+quick retain ميكانيزم هذه ال quick retain ratio
+
+195
+00:23:17,310 --> 00:23:19,830
+يستوعب ثتا على بيتا طبعا ثتا و بيتا مجموعة تلات
+
+196
+00:23:19,830 --> 00:23:26,490
+مئو ستين درجة هيكون تلات مئو ستين ناقص بيتا على
+
+197
+00:23:26,490 --> 00:23:28,390
+بيتا
+
+198
+00:23:34,070 --> 00:23:38,410
+بنشوف مثال and
+
+199
+00:23:38,410 --> 00:23:53,050
+quick
+
+200
+00:23:53,050 --> 00:23:58,950
+return mechanism the
+
+201
+00:23:58,950 --> 00:24:03,390
+driving link اللي هي بي سي هاد الكرانك ال driving
+
+202
+00:24:06,860 --> 00:24:15,020
+بساوة تلاتين ملي ميتر بساوة
+
+203
+00:24:15,020 --> 00:24:16,260
+تلاتين ملي ميتر بساوة تلاتين ملي ميتر بساوة تلاتين
+
+204
+00:24:16,260 --> 00:24:22,060
+ملي ميتر بساوة تلاتين ملي ميتر بساوة
+
+205
+00:24:22,060 --> 00:24:23,520
+تلاتين ملي ميتر بساوة تلاتين ملي ميتر بساوة تلاتين
+
+206
+00:24:23,520 --> 00:24:24,060
+ملي ميتر بساوة تلاتين ملي ميتر بساوة تلاتين ملي
+
+207
+00:24:24,060 --> 00:24:24,300
+ميتر بساوة تلاتين ملي ميتر بساوة تلاتين ملي ميتر
+
+208
+00:24:24,300 --> 00:24:27,260
+بساوة تلاتين ملي ميتر بساوة تلاتين ملي ميتر بساوة
+
+209
+00:24:27,260 --> 00:24:33,380
+تلاتين ملي ميتر بساوة
+
+210
+00:24:33,380 --> 00:24:34,120
+تلاتين ملي ميتر
+
+211
+00:24:36,650 --> 00:24:42,330
+if the length of the working stroke لان هيكون فينا
+
+212
+00:24:42,330 --> 00:24:47,790
+في extreme position لما تكون BC عمودي على AB ع
+
+213
+00:24:47,790 --> 00:24:53,650
+الشمال و another position لما تكون AB جايهين و BC
+
+214
+00:24:53,650 --> 00:24:58,630
+عمودي عليه لان بين هذه و هذه بيصير اندي ال stroke
+
+215
+00:24:58,630 --> 00:25:02,250
+ال short ال stroke معطني
+
+216
+00:25:08,470 --> 00:25:15,150
+مئة و عشرين ملي دي
+
+217
+00:25:15,150 --> 00:25:18,650
+determine the dimensions of A,C and A,B بده يعني
+
+218
+00:25:18,650 --> 00:25:28,130
+المسافة بين A و C و طول الإدراح هذا طبعا انا هاخد
+
+219
+00:25:28,130 --> 00:25:33,130
+ال two extreme positions عند A
+
+220
+00:25:39,420 --> 00:25:47,440
+في عندي revolute joint وعند C في عندي revolute
+
+221
+00:25:47,440 --> 00:25:56,340
+joint هذا A هذا C بيكون
+
+222
+00:25:56,340 --> 00:26:03,460
+الادراع هذا بيصل ال maximum position لو تكون عندك
+
+223
+00:26:03,460 --> 00:26:06,820
+زاوية عمودية وع الجهة التانية
+
+224
+00:26:09,630 --> 00:26:17,770
+هذه تسعين معناته هذه الزاوية كلها بنسميها alpha كل
+
+225
+00:26:17,770 --> 00:26:28,010
+زاوية هذه لو خدت المثلث ايه طبعا
+
+226
+00:26:28,010 --> 00:26:36,210
+هذه تمثل ايه ال cutting او ال forward stroke وهذا
+
+227
+00:26:36,210 --> 00:26:45,740
+ايه العودة صح؟بنقطة ال quick retain ratio اللي
+
+228
+00:26:45,740 --> 00:26:49,480
+بيساوي واحد point سبعة بالساوية ال cutting اللي هو
+
+229
+00:26:49,480 --> 00:26:53,040
+الزاوية هذه اللي هي عبارة عن تلت مئو ستين نقص الف
+
+230
+00:26:53,040 --> 00:27:01,660
+صح تلت مئو ستين minus الف على الف يعني هكون تلت
+
+231
+00:27:01,660 --> 00:27:07,940
+مئو ستين minus الف بساوية واحد point سبعة الف يعني
+
+232
+00:27:07,940 --> 00:27:14,670
+هسينا عندي2.7 ألفة بس هو تلت مية و ستين معناته ألف
+
+233
+00:27:14,670 --> 00:27:20,650
+أكرا ما تستطلع ديجريز
+
+234
+00:27:20,650 --> 00:27:28,690
+عادياش الالفة اذا لو أخدت المثلث ABC
+
+235
+00:27:35,940 --> 00:27:38,520
+لأن ال short هيروح بين ال position هذا و ال
+
+236
+00:27:38,520 --> 00:27:41,640
+position هذا أكتر من ما أعطيه المسافة مائة و عشرين
+
+237
+00:27:41,640 --> 00:27:45,380
+صح؟
+
+238
+00:27:45,380 --> 00:27:59,160
+مائة و عشرين مصر و أكتر محيكون؟ ستين لأن
+
+239
+00:27:59,160 --> 00:28:04,680
+لما تاخد المثلث a b 2 c مثلا a مثلث
+
+240
+00:28:11,600 --> 00:28:17,960
+AB2C هذا قسم الزاوية والزاوية نص الزاوية أكتر تطلع
+
+241
+00:28:17,960 --> 00:28:27,940
+اللي ألف عتنين صح اللي 133 عتنين 66
+
+242
+00:28:27,940 --> 00:28:32,700
+point 6R
+
+243
+00:28:37,050 --> 00:28:43,790
+degrees ست أو سبعة طيب
+
+244
+00:28:43,790 --> 00:28:50,790
+المعروف
+
+245
+00:28:50,790 --> 00:28:54,510
+عند ال BC عند
+
+246
+00:28:54,510 --> 00:29:02,590
+BC معروف ال BC مجاور لل ألف ع اتنين صح؟ معناته AC
+
+247
+00:29:09,640 --> 00:29:16,620
+بالساوية بي سي على كساين اللي هو ستة و ستين point
+
+248
+00:29:16,620 --> 00:29:25,080
+ستة سبعة مستحيل
+
+249
+00:29:25,080 --> 00:29:29,840
+لأن بي سي اكمل تلاتين مليه هذا هتطلع اكتر من
+
+250
+00:29:29,840 --> 00:29:34,060
+تلاتين مليه والكساين
+
+251
+00:29:34,060 --> 00:29:34,840
+اقل من واحد
+
+252
+00:29:52,820 --> 00:29:57,820
+خمسة و سبعين؟
+
+253
+00:29:57,820 --> 00:30:02,380
+خمسة و سبعين درجة
+
+254
+00:30:08,050 --> 00:30:19,710
+الطول اللي هو ال AC مليمتر اللي
+
+255
+00:30:19,710 --> 00:30:24,790
+انا بيده الطول هذا الطول
+
+256
+00:30:24,790 --> 00:30:33,810
+هذا ان احنا بنعرف هذا الطول ستين ستين وهذه تسعين
+
+257
+00:30:33,810 --> 00:30:45,090
+وهذه كم هتكونالف ع اتنين صح؟ لأن هذه زاوية مشتركة
+
+258
+00:30:45,090 --> 00:30:49,210
+بين هذا المثلث الكبير والصغير هذا مشتركة و هذه
+
+259
+00:30:49,210 --> 00:30:56,030
+تسعين معناته هذه بتساوي هذه صح؟ يعني هذه هتكون
+
+260
+00:30:56,030 --> 00:31:02,830
+اللي هي ستة ستين point ستة سبعة انا
+
+261
+00:31:02,830 --> 00:31:10,370
+ماخد مثلث القائم الزاوية اه صحيح ماخد النصنفس
+
+262
+00:31:10,370 --> 00:31:21,810
+الاشياء هنا ال AV هيكون الساوي AV هيكون
+
+263
+00:31:21,810 --> 00:31:27,250
+الساوي ال stroke على اتنين على cosine ستة و ستين
+
+264
+00:31:27,250 --> 00:31:31,310
+point ستة سبعة ال stroke مية و عشرين على اتنين
+
+265
+00:31:31,310 --> 00:31:35,630
+ستين على cosine
+
+266
+00:31:41,380 --> 00:31:46,580
+151.5 151.5 151.5 151.5 151.5 151.5 151.5 151.5
+
+267
+00:31:46,580 --> 00:31:46,800
+151.5 151.5 151.5 151.5 151.5 151.5 151.5 151.5
+
+268
+00:31:46,800 --> 00:31:53,680
+151.5 151.5 151.5 151.5 151.5 151.5 151.5 151.5
+
+269
+00:31:53,680 --> 00:31:56,080
+151.5 151.5 151.5 151.5 151.5 151.5 151.5 151.5
+
+270
+00:31:56,080 --> 00:32:07,440
+151.5 151.5 151.5 151.5 151.5 151.5 151.5 151
+
+271
+00:32:07,440 --> 00:32:19,110
+.5لازم يكون اكبر من مية و اتنين و خمسين هو
+
+272
+00:32:19,110 --> 00:32:21,850
+نفس الشيء اللي بيحكيلك لسلادر الميكانيزم الأساسية
+
+273
+00:32:21,850 --> 00:32:31,170
+عندي
+
+274
+00:32:31,170 --> 00:32:37,670
+واحد ثابتة هاي واحد ثابتةهذا نقطة A في revolute
+
+275
+00:32:37,670 --> 00:32:42,890
+joint و B و بينهم link اتنين عندى نقطة C revolute
+
+276
+00:32:42,890 --> 00:32:48,190
+joint و بينهم link تلاتة هو عندى ال link اربعة
+
+277
+00:32:48,190 --> 00:32:52,450
+اللى هى ال slider جاى عليها revolute joint اللى هى
+
+278
+00:32:52,450 --> 00:32:56,550
+C و جاى sliding مع واحد يعني اربعة slide بالنسبالى
+
+279
+00:32:56,550 --> 00:33:02,770
+واحد اللى هسوي هو هيرخي واحد و يثبت تلاتة تشوفى
+
+280
+00:33:02,770 --> 00:33:03,290
+إيش اللي عايز يصير
+
+281
+00:33:22,990 --> 00:33:32,150
+لأنه هيثبت تلاتة اللي هي هذه ال link BC ويرخي ايش؟
+
+282
+00:33:32,150 --> 00:33:39,210
+واحد خليني اشوف ايش اللي صار عندنا هاي رخي واحد
+
+283
+00:33:39,210 --> 00:33:47,370
+وثبت BC لأن ال BC اعترفيها الجاي Revolute Joint
+
+284
+00:33:47,370 --> 00:33:52,170
+and B وRevolute Joint and C
+
+285
+00:33:55,220 --> 00:33:59,920
+هذه B وهذه
+
+286
+00:33:59,920 --> 00:34:07,540
+C وهذه Revolute وهذه
+
+287
+00:34:07,540 --> 00:34:15,120
+Revolute ما يعني تثبت هذه ايش هي؟ تلاتة
+
+288
+00:34:15,120 --> 00:34:19,540
+الان
+
+289
+00:34:19,540 --> 00:34:22,040
+B
+
+290
+00:34:25,790 --> 00:34:33,950
+لو طبعا ايه فى ايش عندى فى جاي مع واحد عند block
+
+291
+00:34:33,950 --> 00:34:40,010
+هى هذه
+
+292
+00:34:40,010 --> 00:34:43,970
+نقطة ايه هذه
+
+293
+00:34:43,970 --> 00:34:56,080
+link اتنين هتكون صح link اتنين link اتنينب جاي على
+
+294
+00:34:56,080 --> 00:35:11,460
+التلاتة fixed revolute هو a revolute joint الان
+
+295
+00:35:11,460 --> 00:35:18,540
+في عندي هنا هيكون sliding joint عند d sliding
+
+296
+00:35:18,540 --> 00:35:20,880
+joint كمان عند d
+
+297
+00:35:32,240 --> 00:35:39,860
+أربعة أربعة طرف فيه إيش؟ rotating يعني هذه هتكون
+
+298
+00:35:39,860 --> 00:35:50,000
+إيش؟ link أربعة و ال slider إيش؟ واحد ال slider
+
+299
+00:35:50,000 --> 00:35:54,120
+إيش؟ واحد واضحة؟ طيب
+
+300
+00:36:00,370 --> 00:36:02,830
+طبعا هذه الـ two extreme positions one extreme
+
+301
+00:36:02,830 --> 00:36:10,250
+position لما تكون لدراع هذا عمودة لدراع هذا هي one
+
+302
+00:36:10,250 --> 00:36:15,730
+position من الجهة الشمال و من الجهة اليمين برضه
+
+303
+00:36:15,730 --> 00:36:18,690
+يكون عمودة يعني في عندك two positions فعندك
+
+304
+00:36:18,690 --> 00:36:23,710
+position أقصى الشمال و position أقصى اليمين
+
+305
+00:36:37,430 --> 00:36:50,870
+يعني بيعيد نفس الكلام هو
+
+306
+00:36:50,870 --> 00:36:54,730
+بيورجينا ال two extreme positions ال a بيلف
+
+307
+00:36:54,730 --> 00:37:02,570
+فالدراع بيروح اصليت يمين اشمال معناه تحكيون عن دي
+
+308
+00:37:02,570 --> 00:37:16,910
+ايه؟الـ cutting angle هي هذه هو
+
+309
+00:37:16,910 --> 00:37:22,690
+اللي سوى راح ضاف link هنا بدي استفيد من الحركة ضاف
+
+310
+00:37:22,690 --> 00:37:29,150
+link و حط tool هنا حط tool ممكن ال tool هذا يكون
+
+311
+00:37:29,150 --> 00:37:32,930
+cutting tool زي في الشغل المجشطة مثلا فاندي هنا
+
+312
+00:37:32,930 --> 00:37:39,170
+cutting toolيعني هيروح هنا forward stroke و برجع
+
+313
+00:37:39,170 --> 00:37:42,670
+بسرعة return stroke فيله forward return forward
+
+314
+00:37:42,670 --> 00:37:49,910
+return ال
+
+315
+00:37:49,910 --> 00:37:51,030
+tool بتحرك أفقي
+
+316
+00:38:04,700 --> 00:38:19,260
+لاحظ برجع بسرعة الزاوية
+
+317
+00:38:19,260 --> 00:38:24,780
+الزاوية هذه زاوية
+
+318
+00:38:24,780 --> 00:38:30,650
+ال cutting أكبر و ال time بتاعة الزاوية هذهبساوية
+
+319
+00:38:30,650 --> 00:38:34,110
+الزاوية على نفسها لأن هذا مطور سيلف في نفس السرعة
+
+320
+00:38:34,110 --> 00:38:38,570
+سيكون الزاوية هذه على أمجا والزمن بتاعة هذه
+
+321
+00:38:38,570 --> 00:38:41,470
+الزاوية هذه على أمجا بتروح لأمجا اختصار فستير ال
+
+322
+00:38:41,470 --> 00:38:46,350
+ratio بين الزوايا فزاوية هذه أكبر وهذه أصغر
+
+323
+00:39:07,820 --> 00:39:12,100
+طبعا الأخضر هي ال fourth stroke والأحمر هي ال ..
+
+324
+00:39:12,100 --> 00:39:19,080
+ال .. ال retain stroke ال
+
+325
+00:39:19,080 --> 00:39:21,360
+ratio بين ال fourth stroke و ال .. و ال retain
+
+326
+00:39:21,360 --> 00:39:28,860
+stroke اللي هى يسموها ال quick retain ratio دي
+
+327
+00:39:28,860 --> 00:39:29,320
+كل عامة
+
diff --git a/PL9fwy3NUQKwa0nXiCdyQcTW4hWDLTGpDb/QApGXkq3K20_raw.json b/PL9fwy3NUQKwa0nXiCdyQcTW4hWDLTGpDb/QApGXkq3K20_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..6e9e4f6765e428eb3e018fbb93d5242b6426917f
--- /dev/null
+++ b/PL9fwy3NUQKwa0nXiCdyQcTW4hWDLTGpDb/QApGXkq3K20_raw.json
@@ -0,0 +1 @@
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crank تكون أفقية بتكون ال crank مع ال connecting rod على نفس الاستقامة collinear معناته ال piston بيصل له أقصى مدى عند P prime", "tokens": [6027, 7649, 8978, 732, 8084, 8432, 24976, 30002, 5296, 15042, 2423, 21263, 6055, 30544, 5551, 5172, 4587, 10632, 39894, 30544, 2423, 21263, 20449, 2423, 11015, 8685, 15844, 8717, 36178, 42963, 14851, 4587, 10943, 3660, 1263, 533, 289, 20449, 8315, 47395, 2423, 30002, 4724, 1829, 36520, 46740, 5551, 4587, 9381, 7578, 3714, 3215, 7578, 43242, 430, 5835], "avg_logprob": -0.2815241102586713, "compression_ratio": 1.4, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 110.07, "end": 111.19, "word": "الان", "probability": 0.88525390625}, {"start": 111.19, "end": 112.31, "word": " في", "probability": 0.62890625}, {"start": 112.31, "end": 112.61, "word": " two", "probability": 0.634765625}, {"start": 112.61, "end": 113.25, "word": " extreme", "probability": 0.88720703125}, {"start": 113.25, "end": 114.05, "word": " positions", "probability": 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minus cosine فيه لو خط R طلعتها على المشترك هتكون واحد ناقص cosine of theta زائد N", "tokens": [11622, 16373, 3215, 441, 8978, 36764, 24401, 3175, 23565, 8978, 3224, 45164, 16490, 9566, 497, 23032, 1211, 34268, 11296, 15844, 9673, 8592, 2655, 31747, 8032, 2655, 30544, 36764, 24401, 8717, 995, 4587, 9381, 23565, 295, 9725, 30767, 16373, 3215, 426], "avg_logprob": -0.2730564082541117, "compression_ratio": 1.2049180327868851, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 482.44, "end": 483.06, "word": "زائد", "probability": 0.69677734375}, {"start": 483.06, "end": 483.44, "word": " L", "probability": 0.80126953125}, {"start": 483.44, "end": 484.96, "word": " في", "probability": 0.429931640625}, {"start": 484.96, "end": 485.34, "word": " واحد", "probability": 0.7010498046875}, {"start": 485.34, "end": 485.76, "word": " minus", "probability": 0.68701171875}, {"start": 485.76, "end": 486.4, "word": " cosine", "probability": 0.794921875}, {"start": 486.4, "end": 488.9, "word": 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{"start": 624.32, "end": 624.68, "word": " لها", "probability": 0.58026123046875}, {"start": 624.68, "end": 625.22, "word": " بساوي", "probability": 0.865478515625}, {"start": 625.22, "end": 625.46, "word": " هاي", "probability": 0.759521484375}, {"start": 625.46, "end": 625.6, "word": " ال", "probability": 0.837890625}, {"start": 625.6, "end": 625.78, "word": " sine", "probability": 0.73095703125}, {"start": 625.78, "end": 626.26, "word": " ثتا", "probability": 0.6151529947916666}], "temperature": 1.0}, {"id": 24, "seek": 65484, "start": 629.3, "end": 654.84, "text": "مش هذا اللي نحكي المقابل وهذا الوطر على N معناته هذا هكون الجزر تربيه لياش N تربيه minus sin تربيه ثتا لحظه ال N دمينشن ليس فش الوحدة لأن هو اقارن ال ratio L على R معناته ال cosine فاي ال cosine فاي", "tokens": [2304, 8592, 23758, 13672, 1829, 8717, 5016, 4117, 1829, 9673, 4587, 16758, 1211, 37037, 15730, 2423, 2407, 9566, 2288, 15844, 426, 20449, 8315, 47395, 23758, 8032, 30544, 25724, 11622, 2288, 6055, 2288, 21292, 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{"id": 25, "seek": 68422, "start": 657.6, "end": 684.22, "text": "يعني بحكي سوى جزر التربية لواحد minus sign تربية فا او من هذه بحكي مجاور على وطر يعني لو استخدمت هذه او هذه بتطلع نفس الشيء هي هي هي هي الجزر التربية لواحد minus sign تربية", "tokens": [40228, 22653, 4724, 5016, 4117, 1829, 8608, 2407, 7578, 10874, 11622, 2288, 16712, 2288, 21292, 3660, 5296, 14407, 24401, 3175, 1465, 6055, 2288, 21292, 3660, 6156, 995, 1975, 2407, 9154, 29538, 4724, 5016, 4117, 1829, 3714, 7435, 995, 13063, 15844, 4032, 9566, 2288, 37495, 22653, 45164, 44713, 9778, 40448, 2655, 29538, 1975, 2407, 29538, 39894, 9566, 1211, 3615, 8717, 36178, 25124, 1829, 38207, 39896, 39896, 39896, 39896, 2423, 7435, 11622, 2288, 16712, 2288, 21292, 3660, 5296, 14407, 24401, 3175, 1465, 6055, 2288, 21292, 3660], "avg_logprob": -0.28639705601860493, "compression_ratio": 1.9019607843137254, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 657.6, "end": 657.86, "word": "يعني", "probability": 0.620849609375}, 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"end": 1000.31, "word": " sin", "probability": 0.53369140625}, {"start": 1000.31, "end": 1001.07, "word": " تربيه", "probability": 0.778564453125}, {"start": 1001.07, "end": 1002.35, "word": " ثتا", "probability": 0.6070963541666666}, {"start": 1002.35, "end": 1002.57, "word": " على", "probability": 0.5966796875}, {"start": 1002.57, "end": 1002.83, "word": " n", "probability": 0.306396484375}, {"start": 1002.83, "end": 1003.59, "word": " تربيه", "probability": 0.949462890625}, {"start": 1003.59, "end": 1004.05, "word": " أص", "probability": 0.5919189453125}, {"start": 1004.05, "end": 1004.45, "word": " نص", "probability": 0.912109375}, {"start": 1004.45, "end": 1006.57, "word": " يعني", "probability": 0.527099609375}, {"start": 1006.57, "end": 1008.23, "word": " دي", "probability": 0.69287109375}, {"start": 1008.23, "end": 1008.37, "word": " وي", "probability": 0.34228515625}, {"start": 1008.37, "end": 1008.63, "word": " بدي", "probability": 0.78955078125}, {"start": 1008.63, "end": 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على N تربيع اقصد ما اقصد نص في مشتقة اللي جوا هتكون سالب اتنين sin theta cosine theta على N تربيع", "tokens": [41185, 36764, 24401, 3175, 3343, 6055, 2288, 21292, 3615, 38637, 2655, 995, 15844, 426, 6055, 2288, 21292, 3615, 1975, 4587, 9381, 3215, 19446, 1975, 4587, 9381, 3215, 8717, 9381, 8978, 37893, 2655, 28671, 13672, 1829, 10874, 14407, 8032, 2655, 30544, 8608, 6027, 3555, 1975, 2655, 1863, 9957, 3343, 9725, 23565, 9725, 15844, 426, 6055, 2288, 21292, 3615], "avg_logprob": -0.3160021505479155, "compression_ratio": 1.4338235294117647, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 1021.74, "end": 1023.02, "word": "في", "probability": 0.339599609375}, {"start": 1023.02, "end": 1024.3, "word": " واحد", "probability": 0.616943359375}, {"start": 1024.3, "end": 1024.82, "word": " minus", "probability": 0.59765625}, {"start": 1024.82, "end": 1025.16, "word": " sin", "probability": 0.47607421875}, {"start": 1025.16, "end": 1025.78, "word": " تربيع", "probability": 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بيستوي minus omega square sin theta minus omega square sin theta على n طبعا هو انت الكتاب بالصح يا ميلا اذا هي هيك او هيك هذه تقريبا", "tokens": [3555, 2655, 30544, 2423, 10943, 7435, 995, 4724, 14851, 45865, 1975, 2304, 7435, 995, 9122, 41779, 995, 9957, 38637, 2655, 995, 15844, 297, 16070, 10721, 46538, 4724, 1829, 14851, 45865, 3175, 10498, 3732, 3343, 9725, 3175, 10498, 3732, 3343, 9725, 15844, 297, 23032, 3555, 3615, 995, 31439, 16472, 2655, 2423, 4117, 2655, 16758, 20666, 9381, 5016, 35186, 3714, 1829, 15040, 1975, 15730, 39896, 39896, 4117, 1975, 2407, 39896, 4117, 29538, 6055, 4587, 16572, 3555, 995], "avg_logprob": -0.5053454127750898, "compression_ratio": 1.6272189349112427, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 2190.19, "end": 2190.79, "word": "بتكون", "probability": 0.4919230143229167}, {"start": 2190.79, "end": 2191.33, "word": " الامجا", "probability": 0.48101806640625}, {"start": 2191.33, "end": 2191.83, "word": " بستوي", "probability": 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differentiation اذا عملت approximation نتيجة mathematical expression ناتج عن expansion بصير تعمل differentiation لكن اذا عملت", "tokens": [7649, 2655, 3555, 3224, 14407, 9673, 2407, 11242, 45367, 1975, 8315, 4724, 5016, 4117, 1829, 2423, 28023, 23758, 13672, 1829, 5296, 15042, 6055, 25957, 43761, 23758, 37893, 8978, 9673, 3215, 7578, 8978, 1975, 1829, 3714, 3215, 7578, 6055, 7649, 10632, 5296, 15042, 6055, 25957, 1211, 28023, 47525, 4117, 6055, 25957, 1211, 38902, 1975, 15730, 6225, 42213, 2655, 28023, 8717, 31371, 7435, 3660, 18894, 6114, 8717, 9307, 7435, 18871, 11260, 4724, 9381, 13546, 6055, 25957, 1211, 38902, 44381, 1975, 15730, 6225, 42213, 2655], "avg_logprob": -0.17996988454497004, "compression_ratio": 1.9567567567567568, "no_speech_prob": 1.4901161193847656e-06, "words": [{"start": 2220.7799999999997, "end": 2221.66, "word": "انتبهوا", "probability": 0.84150390625}, {"start": 2221.66, "end": 2221.92, "word": " الموضوع", "probability": 0.8026123046875}, {"start": 2221.92, 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جاي زي هيك التاني جاي زي هيك التاني جاي زي هيك بيعطيني بيجيبلي اللي هو ال signal اللي بديها بالظبط", "tokens": [3555, 2655, 3615, 9566, 9957, 1829, 25124, 28820, 13672, 1829, 4724, 16254, 11296, 5296, 15042, 5551, 7435, 2304, 3615, 3714, 7435, 2304, 45367, 3660, 9154, 2423, 3792, 4032, 3343, 9122, 2655, 13546, 20449, 45030, 11242, 13412, 31845, 9122, 3215, 3224, 31439, 294, 5574, 50113, 15040, 5551, 12610, 3792, 10874, 47302, 30767, 1829, 39896, 4117, 16712, 7649, 1829, 10874, 47302, 30767, 1829, 39896, 4117, 16712, 7649, 1829, 10874, 47302, 30767, 1829, 39896, 4117, 4724, 1829, 3615, 9566, 9957, 1829, 4724, 1829, 7435, 1829, 3555, 20292, 13672, 1829, 31439, 2423, 6358, 13672, 1829, 4724, 16254, 11296, 20666, 19913, 3555, 9566], "avg_logprob": -0.22269570044796877, "compression_ratio": 1.8770949720670391, "no_speech_prob": 2.384185791015625e-07, "words": [{"start": 2415.69, "end": 2416.41, "word": "بتعطيني", "probability": 0.68212890625}, {"start": 2416.41, "end": 2416.85, "word": " 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"مثلا في الماتماتيكا في عندهم .. عندهم function اسمه unsolve اذا حد نزله في الماتماتيكا بتحكي unsolve يعني في solve و في unsolve ال unsolve يعني numerical solution solve بلاطين exact solution", "tokens": [2304, 12984, 15040, 8978, 9673, 9307, 2304, 9307, 1829, 4117, 995, 8978, 43242, 16095, 4386, 43242, 16095, 2445, 24525, 2304, 3224, 2693, 37361, 1975, 15730, 11331, 3215, 8717, 11622, 43761, 8978, 9673, 9307, 2304, 9307, 1829, 4117, 995, 39894, 5016, 4117, 1829, 2693, 37361, 37495, 22653, 8978, 5039, 4032, 8978, 2693, 37361, 2423, 2693, 37361, 37495, 22653, 29054, 3827, 5039, 4724, 1211, 41193, 9957, 1900, 3827], "avg_logprob": -0.31599814856230324, "compression_ratio": 1.7371794871794872, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2778.16, "end": 2778.68, "word": "مثلا", "probability": 0.89404296875}, {"start": 2778.68, "end": 2778.86, "word": " في", "probability": 0.9345703125}, {"start": 2778.86, "end": 2779.4, "word": " الماتماتيكا", "probability": 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خلصتم الحاضرة", "tokens": [2655, 995, 28820, 14407, 18863, 31845, 10632, 7251, 20498, 16490, 1211, 9381, 39237, 21542, 46958, 25720], "avg_logprob": -0.375, "compression_ratio": 0.967741935483871, "no_speech_prob": 0.0, "words": [{"start": 2918.5699999999997, "end": 2919.33, "word": "تاكلوا", "probability": 0.68682861328125}, {"start": 2919.33, "end": 2919.75, "word": " العافية", "probability": 0.8767903645833334}, {"start": 2919.75, "end": 2920.01, "word": " يوم", "probability": 0.6402587890625}, {"start": 2920.01, "end": 2920.39, "word": " خلصتم", "probability": 0.7283935546875}, {"start": 2920.39, "end": 2920.73, "word": " الحاضرة", "probability": 0.6695963541666666}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2921.1631875, "duration_after_vad": 2702.52999999999}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwa0nXiCdyQcTW4hWDLTGpDb/WyayN6Eorf0_postprocess.srt b/PL9fwy3NUQKwa0nXiCdyQcTW4hWDLTGpDb/WyayN6Eorf0_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..d7c059c751421b8785bdcb97ef610d9cfb303b3a
--- /dev/null
+++ b/PL9fwy3NUQKwa0nXiCdyQcTW4hWDLTGpDb/WyayN6Eorf0_postprocess.srt
@@ -0,0 +1,1972 @@
+1
+00:00:05,090 --> 00:00:07,470
+بسم الله الرحمن الرحيم السلام عليكم ورحمة الله
+
+2
+00:00:07,470 --> 00:00:12,190
+وبركاته و اليوم هنكمل في مادة نظرية الألات هنكمل
+
+3
+00:00:12,190 --> 00:00:14,830
+في موضوع بده اسمه ال engine analysis ال chapter
+
+4
+00:00:14,830 --> 00:00:18,670
+خمساش غطين ال inertia forces حسبنا ال piston
+
+5
+00:00:18,670 --> 00:00:23,370
+effort عملنا equivalent two mass system لل
+
+6
+00:00:23,370 --> 00:00:28,830
+connecting rod و حسبنا ال torque على البصل ال
+
+7
+00:00:28,830 --> 00:00:32,960
+crankاليوم هنكمل في ال engine analysis موضوع ال
+
+8
+00:00:32,960 --> 00:00:39,360
+chapter هو tearing moment diagrams and flywheel من
+
+9
+00:00:39,360 --> 00:00:42,760
+اسم ال chapter tearing moment يعني مقصود ال moment
+
+10
+00:00:42,760 --> 00:00:46,160
+او العزم عند الكرانك انا في الحالة باهمن الشافت
+
+11
+00:00:46,160 --> 00:00:49,860
+اللي هيضور اللي هو عند الكرانك ال tearing moment
+
+12
+00:00:49,860 --> 00:00:54,080
+diagram هو عبارة عن تمثيل graphical representation
+
+13
+00:00:54,940 --> 00:01:00,100
+للـ torque عند الكرانك لأوضوع مختلف يعني as a
+
+14
+00:01:00,100 --> 00:01:08,220
+function of θ تمثيل بياني للعزم عند الكرانك as a
+
+15
+00:01:08,220 --> 00:01:14,540
+function of θ اللي هي θ زوية الكرانك طبعا الـ θ
+
+16
+00:01:14,540 --> 00:01:18,320
+الكرانك تتغير من صفر لتلتمية وستين
+
+17
+00:01:21,760 --> 00:01:24,460
+انبين عندى ال turning moment diagram for a single
+
+18
+00:01:24,460 --> 00:01:29,180
+cylinder double acting steam engineل .. يعني هذا
+
+19
+00:01:29,180 --> 00:01:34,960
+ال diagram لمحرك بخاري double acting يعني في ال ..
+
+20
+00:01:34,960 --> 00:01:40,340
+هو طالع بيكون فيه ضغط البخار و هو راجع برضه في شوط
+
+21
+00:01:40,340 --> 00:01:43,480
+power يعني ال power في الشوطين في الشوط اللي طالع
+
+22
+00:01:43,480 --> 00:01:48,200
+و الشوط اللي رايح إذا حابب الأول نتفرج على
+
+23
+00:01:48,200 --> 00:01:52,080
+فيديوهات نتعرف على ال .. ال two stroke engines و
+
+24
+00:01:52,080 --> 00:01:53,440
+ال four stroke engines
+
+25
+00:02:09,850 --> 00:02:12,830
+design is a piston that acts like a piston
+
+26
+00:02:46,650 --> 00:02:52,610
+يعني في عندنا piston و في عندناintake valve و
+
+27
+00:02:52,610 --> 00:02:58,790
+outtake يعني الدخول و الخروج go through its two
+
+28
+00:02:58,790 --> 00:03:05,170
+strokes you can see exactly what's happening let's
+
+29
+00:03:05,170 --> 00:03:08,130
+start with the spark plug firing at this point the
+
+30
+00:03:08,130 --> 00:03:11,530
+piston is at the top of its stroke the cylinder is
+
+31
+00:03:11,530 --> 00:03:13,810
+full of air and gasoline that has been compressed
+
+32
+00:03:13,810 --> 00:03:19,550
+لحظوا عندكم هذا بتكون عندى ال crankو ال connecting
+
+33
+00:03:19,550 --> 00:03:26,210
+rod على استقام واحدة لان هيعطي الشرارة فطبعا هذا
+
+34
+00:03:26,210 --> 00:03:34,270
+.. هذا يعني fuel هذا مش .. مش بخار هتس ترقب
+
+35
+00:03:34,270 --> 00:03:40,190
+بتاعة
+
+36
+00:03:40,190 --> 00:03:43,690
+الشرارة بيصير عند الاشتعال بيصير انفجار فهيرجع
+
+37
+00:03:43,690 --> 00:03:50,390
+لورا ال pistonأسحب الحرارة بطاقة كبيرة، تشاهد هذه
+
+38
+00:03:50,390 --> 00:03:54,070
+المنطقة خلف الحرارة؟ إنها مليئة بالهواء ومعالجة من
+
+39
+00:03:54,070 --> 00:03:58,010
+غلطان ومشروع كما يتحرك الحرارة إلى هذه المنطقة،
+
+40
+00:03:58,010 --> 00:04:04,030
+فتسحب المعالجة كما يتحرك الحرارة إلى أسفل أسطولها،
+
+41
+00:04:04,030 --> 00:04:08,510
+فتجهز مصدر مصدر مصدر مصدر مصدر مصدر مصدر مصدر مصدر
+
+42
+00:04:08,510 --> 00:04:09,890
+مصدر مصدر مصدر مصدر مصدر مصدر مصدر مصدر مصدر مصدر
+
+43
+00:04:09,890 --> 00:04:15,810
+مصدر مصدر مصدر مصدر مصدر مصدر مصدر مصدر مصدر ميعني
+
+44
+00:04:15,810 --> 00:04:20,030
+هو طالب مجرد مفتح ببدأش الدخل هتطلع من هنا وبعد
+
+45
+00:04:20,030 --> 00:04:31,950
+وشوية بفتح الظلب عشان يدخل وقود وهواء جديد هيتغط
+
+46
+00:04:36,840 --> 00:04:42,100
+هيدغط طبعا هو ضاغط بترد بقايا الدخانة لحد ما يوصل
+
+47
+00:04:42,100 --> 00:04:44,800
+هنا بيصير يدغط اكتر لحد ما يصير على استقام واحد
+
+48
+00:04:44,800 --> 00:04:48,100
+لسه فيه زاوية تنتبهوا ان في هنا زاوية
+
+49
+00:04:51,380 --> 00:05:05,820
+بعت شرارة و بتتكرر كمان مرة يعني
+
+50
+00:05:05,820 --> 00:05:12,300
+اللي عند ال piston مش piston و بس هو يستخدم لفتح و
+
+51
+00:05:12,300 --> 00:05:15,120
+غلق اللي هو الفتحات هذه صمم بشتغل
+
+52
+00:05:36,400 --> 00:05:41,940
+لحظة كل تلك بيستين دراية بيعطينا إيه؟ شرارة برجع
+
+53
+00:05:41,940 --> 00:05:48,810
+بعدين بضغطهي اول شهر مائة و تمانين كمان مائة و
+
+54
+00:05:48,810 --> 00:05:54,850
+تمانين بيعطي شرارة بندفع في الخلف بنرجعتها مضغط هي
+
+55
+00:05:54,850 --> 00:05:57,770
+كمان تلات مائة و ستين يعني كل تلات مائة و ستين
+
+56
+00:05:57,770 --> 00:06:03,970
+درجة بيعطيني شرارة في ال four stroke engine بيعطي
+
+57
+00:06:03,970 --> 00:06:07,970
+في ال .. في ال سبعة مائة و عشرين في دورتين بيعطيني
+
+58
+00:06:07,970 --> 00:06:12,530
+شرارة واحدة كل stroke مائة و اتوانين درجة هنشوف
+
+59
+00:06:12,530 --> 00:06:12,890
+الآن
+
+60
+00:06:34,620 --> 00:06:39,820
+انشوف ال four stroke صحيح
+
+61
+00:07:02,340 --> 00:07:06,100
+هذا الـ six cylinder V يعني تلاتة .. تلاتة هنا و
+
+62
+00:07:06,100 --> 00:07:23,880
+تلاتة هنا جايستة سيلندر اول
+
+63
+00:07:23,880 --> 00:07:30,160
+stroke intake يعني بيفتح الصنام هذا بدخل وقود مع
+
+64
+00:07:30,160 --> 00:07:35,480
+هوا هذا intake شفط بنزل لتحت مية و تمانين درجة
+
+65
+00:07:54,520 --> 00:08:05,040
+انتقل سحب هوا مع بقود بعد انتقال ايش بيجيه بدغط
+
+66
+00:08:07,920 --> 00:08:11,700
+لأن عشان يضغط لازم الصمامين هذي يكونوا مساكرين
+
+67
+00:08:11,700 --> 00:08:16,080
+مانفعش يكونوا فاتحين اذا فاتحين مش هيضغط both
+
+68
+00:08:16,080 --> 00:08:18,940
+valves are now closed and the pistons on its way
+
+69
+00:08:18,940 --> 00:08:23,100
+up pistons on its way up it's compressing the air
+
+70
+00:08:23,100 --> 00:08:25,080
+compressing the air raising the temperature
+
+71
+00:08:25,080 --> 00:08:28,300
+raising the energy potential of the air in the
+
+72
+00:08:28,300 --> 00:08:31,700
+chamber for the next stroke so at the top of this
+
+73
+00:08:31,700 --> 00:08:34,040
+stroke where the pistons all the way up you're now
+
+74
+00:08:34,040 --> 00:08:39,400
+ready for the next phaseالان خلص compression الغاز
+
+75
+00:08:39,400 --> 00:08:46,100
+و الوقود سخنوا مع الضغط اشعطينه شرارة يعني
+
+76
+00:08:46,100 --> 00:08:49,840
+compression stroke 180 درجة لان بيصير عندي
+
+77
+00:08:49,840 --> 00:08:54,180
+expansion بيصير احتراط فبندفع ال piston لتحت
+
+78
+00:08:56,860 --> 00:09:01,480
+هذه الاشة ال expansion أو ال power stroke هذه
+
+79
+00:09:01,480 --> 00:09:18,080
+الاشة
+
+80
+00:09:18,080 --> 00:09:21,280
+ال expansion
+
+81
+00:09:21,280 --> 00:09:22,820
+أو ال power stroke
+
+82
+00:09:27,030 --> 00:09:31,150
+الان خلصت العملية بدون ترد الدخنة معناته هيفتح
+
+83
+00:09:31,150 --> 00:09:41,550
+الصمام ال exhaust و يضغط تاني نرجع
+
+84
+00:09:41,550 --> 00:09:48,530
+لل slide معناته اذا بتلاحظوا في حالة ال four
+
+85
+00:09:48,530 --> 00:09:53,890
+stroke engine ال power كانت في one stroke ع كام
+
+86
+00:09:53,890 --> 00:09:57,900
+stroke هو؟أربعة كل stroke مية و تمانين درجة أربعة
+
+87
+00:09:57,900 --> 00:10:02,680
+و تمانين سبعة مية و عشرين معناته أنا الفترة اللي
+
+88
+00:10:02,680 --> 00:10:06,260
+باخد فيها power اللي هي في stroke واحدة من الأربعة
+
+89
+00:10:06,260 --> 00:10:10,380
+معناته ال power في الأربعة strokes لازم تكون كافية
+
+90
+00:10:10,380 --> 00:10:15,260
+للأربعة strokes لإن ال other three strokes مافي
+
+91
+00:10:15,260 --> 00:10:18,060
+عندي power كيف هكمل ال engine فمعناته لازم انا
+
+92
+00:10:18,060 --> 00:10:23,130
+اولدenough power فى ال power stroke او ال
+
+93
+00:10:23,130 --> 00:10:27,310
+expansion stroke و اخزنها فى ايش هخزنها فى ال
+
+94
+00:10:27,310 --> 00:10:32,450
+flywheel ال flywheel بخزن بخزنها ع شكل طاقة حركة
+
+95
+00:10:32,450 --> 00:10:37,050
+يعنى لما يكون عندى ال power سرعتها بتزيد لما بدي
+
+96
+00:10:37,050 --> 00:10:41,570
+استخلق منها هاخد من ال flywheel سرعتها ايش تنزل
+
+97
+00:10:41,570 --> 00:10:45,390
+شوف ال flywheel حتى في الجبل الجديد لان هنشوف شوف
+
+98
+00:10:45,390 --> 00:10:45,750
+ال flywheel
+
+99
+00:10:49,520 --> 00:10:52,740
+طيب معناته ال turning moment diagram هو عبارة عن
+
+100
+00:10:52,740 --> 00:10:57,200
+تمثيل بياني للعزم عند الكرانك as a function of
+
+101
+00:10:57,200 --> 00:11:02,540
+angle of rotation للكرانك التي هي θتا هعندي two
+
+102
+00:11:02,540 --> 00:11:07,200
+stroke engine او double acting steam engine احنا
+
+103
+00:11:07,200 --> 00:11:09,980
+حكينا كل مية و اتوين درجة في ال two stroke بيكون
+
+104
+00:11:09,980 --> 00:11:15,260
+عندى power مظلوط هعندي مية و اتوين درجة بيكون عندى
+
+105
+00:11:15,260 --> 00:11:23,120
+powerفي ال 120 درجة التانية عندي power الان انا
+
+106
+00:11:23,120 --> 00:11:32,060
+بولد power ليش بولد power عشان .. عشان استخدمها في
+
+107
+00:11:32,060 --> 00:11:35,640
+الآخر انا بقاوم اشي في عندي resisting torque اللي
+
+108
+00:11:35,640 --> 00:11:38,280
+هو ال main torque في عندي ال .. الان طبعا ال
+
+109
+00:11:38,280 --> 00:11:42,820
+torque ال torque متغير مع ال angle of rotation
+
+110
+00:11:42,820 --> 00:11:48,210
+بتاعةلكرانك مش ثابت لكن ال resisting torque في
+
+111
+00:11:48,210 --> 00:11:50,890
+حالة ال engine is constant ال resisting torque انا
+
+112
+00:11:50,890 --> 00:11:54,730
+بدي اسرع السيارة مثلا بدي اتغلب الاحتكاك في القطع
+
+113
+00:11:54,730 --> 00:11:58,210
+اللي بتدور القطع الميكانيكية بدي احرك ال masses
+
+114
+00:11:58,210 --> 00:12:02,770
+اللي هو ال gears و ال differential بدي اقوم الوزن
+
+115
+00:12:02,770 --> 00:12:07,230
+السيارة اذا طالع طلع بدي اقوم الريح ففي شيء كلها
+
+116
+00:12:07,230 --> 00:12:14,120
+انا بدي اغطيها تستنفذ جزء من طاقتىعشان يكون عنده
+
+117
+00:12:14,120 --> 00:12:18,460
+mean resisting torque اللي هو بيقاوم بيقاوم ال
+
+118
+00:12:18,460 --> 00:12:23,220
+power اللي جاية من ال engine اللي مصدرها عند ال
+
+119
+00:12:23,220 --> 00:12:29,080
+piston مصدرها عند ال piston في
+
+120
+00:12:29,080 --> 00:12:33,200
+شبط رحل خمستاش احنا طلعنا معادل لده turning moment
+
+121
+00:12:33,200 --> 00:12:37,940
+torque بالساوية ال piston effort في R في sin θ زي
+
+122
+00:12:37,940 --> 00:12:40,500
+sin 2θ على اتنين جزء تربيع ل N تربيع minus sin
+
+123
+00:12:40,500 --> 00:12:45,160
+تربيع θال FB هي ال piston effort ال R اللي هو ال
+
+124
+00:12:45,160 --> 00:12:51,000
+crank ال radius اللي على ال crank طبعا عندي ال out
+
+125
+00:12:51,000 --> 00:12:57,940
+stroke اللي هي اللي هو هذه ال stroke A B A B C هذه
+
+126
+00:12:57,940 --> 00:13:06,980
+ال out stroke ال N stroke الراجع اللي هي C D E
+
+127
+00:13:06,980 --> 00:13:11,560
+فعندي out stroke وعندي N stroke
+
+128
+00:13:16,730 --> 00:13:22,870
+الـ work done الشغل المبدول عبارة عن moment
+
+129
+00:13:22,870 --> 00:13:28,110
+لو أنا جسم بتحرك و بتحت أثير قوة أفقية تحرك أفقية
+
+130
+00:13:28,110 --> 00:13:34,710
+تحت أثير قوة الشغل إيش يستوي force في مسافة force
+
+131
+00:13:34,710 --> 00:13:38,950
+في مسافة ال distance في ال rotation إيش يقابلها
+
+132
+00:13:38,950 --> 00:13:42,490
+theta
+
+133
+00:13:42,490 --> 00:13:47,310
+و ال force في ال rotation إيش يقابلهاmoment عزم
+
+134
+00:13:47,310 --> 00:13:52,770
+معناته ال work done هو العزم في الزاوية العزم في
+
+135
+00:13:52,770 --> 00:13:55,850
+الزاوية تق ال work done turning moment في ال angle
+
+136
+00:13:55,850 --> 00:13:59,230
+طبعا
+
+137
+00:13:59,230 --> 00:14:02,010
+ال work done هو ال area لل turning moment diagram
+
+138
+00:14:02,010 --> 00:14:06,670
+اللي انا عندي عندي هذه ال torque as a function of
+
+139
+00:14:06,670 --> 00:14:11,940
+theta معناته المساحة تحت هذه الملحنةبتمثل الشغل
+
+140
+00:14:11,940 --> 00:14:16,180
+المبذول في دورة واحدة .. الشغل المبذول في دورة
+
+141
+00:14:16,180 --> 00:14:22,040
+واحدة لما بحكي انا عن شغل بحكي عن energy لإن في
+
+142
+00:14:22,040 --> 00:14:24,400
+energy و في power إيش الفرق من ال energy و ال
+
+143
+00:14:24,400 --> 00:14:30,440
+power بالظبط
+
+144
+00:14:30,440 --> 00:14:34,940
+ال power هي معدل استهلاكي للطاقة في وحدة الزمن
+
+145
+00:14:34,940 --> 00:14:40,310
+يعني انا ممكن استهلك ال meat جول في ثانيةمعناته
+
+146
+00:14:40,310 --> 00:14:47,170
+عندى ال power مت وات وكن استهلكهم بطيء استهلكهم
+
+147
+00:14:47,170 --> 00:14:49,810
+مثلا في عشر ثوان يعني معناته ال power بتكون في
+
+148
+00:14:49,810 --> 00:14:57,190
+الحالة هذه عشرة وات ف ال power اللى هو معدل
+
+149
+00:14:57,190 --> 00:15:01,290
+استهلاكي للطاقة إذا كان معدل استهلاكي سريع معناته
+
+150
+00:15:01,290 --> 00:15:05,130
+I need more power بدي أستهلك الطاقة بشكل سريع إذا
+
+151
+00:15:05,130 --> 00:15:09,740
+كان معدل استهلاكي بطيء معناتهال power هتكون اقل
+
+152
+00:15:09,740 --> 00:15:14,640
+عشان ذلك اذا بدي عزم كبير بروح بيحطه gearbox بيبطق
+
+153
+00:15:14,640 --> 00:15:19,720
+فبصير معدل استهلاك على output اقل فبستاخدك انا انا
+
+154
+00:15:19,720 --> 00:15:22,440
+بدي في الأخر عزم بستهلك طاقة ب .. ب .. ب .. ببطء
+
+155
+00:15:22,440 --> 00:15:30,800
+وبتالي بدي power اقل في
+
+156
+00:15:30,800 --> 00:15:39,120
+الممارسة العملية ال engine بيمارس او بيشتغلضد ال
+
+157
+00:15:39,120 --> 00:15:41,920
+mean resisting torque انا عندي mean resisting
+
+158
+00:15:41,920 --> 00:15:47,500
+torque المطلوب من ال engine انه يقاوم هذا او يتغلب
+
+159
+00:15:47,500 --> 00:15:51,540
+عليه و احنا حكينا ال resisting torque جاي من
+
+160
+00:15:51,540 --> 00:15:54,060
+الأحمال على السيارة الأحمال على السيارة ايش؟
+
+161
+00:15:54,060 --> 00:15:59,060
+الأحمال على السيارة الوزن .. وزنها ووزن اللي فيها
+
+162
+00:15:59,060 --> 00:16:03,500
+ايش كمان أحمال؟ الهواء الاحتكاك
+
+163
+00:16:07,590 --> 00:16:10,490
+اذى طالع اللى حكينا الوزن اللى انا فى عندى
+
+164
+00:16:10,490 --> 00:16:14,230
+rotating masses جوا انا بكون عندك ال .. ال crank
+
+165
+00:16:14,230 --> 00:16:16,990
+نفسها بتدور بعدين ال crank بتسلم ال clutch ال
+
+166
+00:16:16,990 --> 00:16:19,530
+clutch بيسلم gearbox ال gearbox بيسلم هو
+
+167
+00:16:19,530 --> 00:16:22,810
+differential فهيش شغلات بتدور عشان ادورها محتاج
+
+168
+00:16:22,810 --> 00:16:27,990
+لياش ل power او ل energy وفى شغلاء برضه الاحتكاك
+
+169
+00:16:27,990 --> 00:16:31,670
+بيكون العملية مش انه يعني مافيش احتكاك فى احتكاك
+
+170
+00:16:31,670 --> 00:16:36,810
+بيدا قام الاحتكاك فكل هذه أحمال يجب على المحرك انه
+
+171
+00:16:37,770 --> 00:16:42,890
+يقومها او يشيلها فال total resisting torque ناتج
+
+172
+00:16:42,890 --> 00:16:46,190
+عن هذه الأحمال وزي السيارة اذا انا طالع اطلع من
+
+173
+00:16:46,190 --> 00:16:50,270
+مقاومة الريح اللي هو ال energy to rotate masses و
+
+174
+00:16:50,270 --> 00:16:56,450
+ال friction المساحة
+
+175
+00:16:56,450 --> 00:17:02,430
+اللي هي هذه a small a capital F capital a اللي هي
+
+176
+00:17:02,430 --> 00:17:08,560
+اقل عن ال T meanتيمين في إياش في الزاوية اللي هو
+
+177
+00:17:08,560 --> 00:17:12,380
+ال torque في الزاوية بيعطينا إياش شغل هذا يمثل
+
+178
+00:17:12,380 --> 00:17:17,720
+الشغل المفذول against ال load against ال resisting
+
+179
+00:17:17,720 --> 00:17:21,300
+torque معناته ال load جاي من ال resisting torque
+
+180
+00:17:21,300 --> 00:17:27,220
+طبعا
+
+181
+00:17:27,220 --> 00:17:30,560
+هذا اللي جاي هذا ال resisting torque هذا ال
+
+182
+00:17:30,560 --> 00:17:32,360
+resisting torque
+
+183
+00:17:34,110 --> 00:17:41,170
+و هذا اللي جاي من عندى ال piston ل ال crank هذا ال
+
+184
+00:17:41,170 --> 00:17:46,090
+torque as a function of theta معناته لاحظوا فى بعض
+
+185
+00:17:46,090 --> 00:17:52,310
+الأحيان بيكون ال torque احنا حاكينا بيكون اعلى من
+
+186
+00:17:52,310 --> 00:17:57,890
+ال mean resisting اذا اعلى معناته انا ال engine او
+
+187
+00:17:57,890 --> 00:18:01,110
+ال crank موصلة ب flywheel ال engine موصلة ب
+
+188
+00:18:01,110 --> 00:18:01,570
+flywheel
+
+189
+00:18:13,400 --> 00:18:23,020
+عند هذه ال piston في
+
+190
+00:18:23,020 --> 00:18:26,460
+الآخر عند ال power جاية من عند ال piston هتتحول ل
+
+191
+00:18:26,460 --> 00:18:38,420
+torque على ال crank فيه انا بحط flywheel flywheel
+
+192
+00:18:38,420 --> 00:18:45,800
+flywheel عبارة عن جسم كتره كبير كترهكبير ال energy
+
+193
+00:18:45,800 --> 00:18:52,420
+بشكل عام بيستوى نص عند صورة معينة نص I Omega
+
+194
+00:18:52,420 --> 00:18:56,240
+تربيه صح معناته
+
+195
+00:18:56,240 --> 00:18:59,720
+انا بتحكم في كمية ال energy اللي بخزنها في ال
+
+196
+00:18:59,720 --> 00:19:07,640
+flywheel من خلال ال I ال I بتعتمد is a function of
+
+197
+00:19:07,640 --> 00:19:15,600
+mass و نص في القطر صحمعناته عشان ارفع قدرة ال
+
+198
+00:19:15,600 --> 00:19:19,980
+flywheel على التخزين يعني يا بزود طبعا تتناسب مع
+
+199
+00:19:19,980 --> 00:19:26,840
+ال mass و ال R تربية طبعا يا بزود ال mass او بزود
+
+200
+00:19:26,840 --> 00:19:33,580
+ال R او بزود التنين طبعا ال effect بتاعة تكبير نصف
+
+201
+00:19:33,580 --> 00:19:42,370
+القطر اعلى من ال massيعني لو كان ال radius عندي
+
+202
+00:19:42,370 --> 00:19:49,070
+خيار يعني ال radius بيكون عندى مثلا اتنين انش و
+
+203
+00:19:49,070 --> 00:19:55,050
+radius تاني اربعة انش مقدار هذه راح تكون اربعة على
+
+204
+00:19:55,050 --> 00:20:07,120
+اتنين تربيع اربعة يعني مجرد ان ضعفة ال radiusصارت
+
+205
+00:20:07,120 --> 00:20:10,240
+ال moment of inertia أربعة ضعف مجرد أن ضعف ال
+
+206
+00:20:10,240 --> 00:20:15,220
+radius صارت ال moment of inertia أربعة ضعف لكن لو
+
+207
+00:20:15,220 --> 00:20:20,300
+ضعفت ال mass بيصير انا ضعفت ال .. ال .. ال .. ال
+
+208
+00:20:20,300 --> 00:20:25,940
+energy بتاعة ال .. ال flywheel اضعف فانت تأثير نص
+
+209
+00:20:25,940 --> 00:20:34,940
+القطر ضعف تأثير او .. او ضعف تأثير ال .. بنفعش
+
+210
+00:20:34,940 --> 00:20:42,370
+احكي ضعفيعني ال I تتناسب
+
+211
+00:20:42,370 --> 00:20:52,930
+ترضي مع ال mass وال I تتناسب ترضي مع ال R² لأن
+
+212
+00:20:52,930 --> 00:21:01,530
+لو خلّيت نصف القطر تلت أضعاف تسعة الكتلة تلت أضعاف
+
+213
+00:21:01,530 --> 00:21:07,430
+تلتة تسعة تلتةفبنفعش احكي الضعيف انت اخدته حالة
+
+214
+00:21:07,430 --> 00:21:11,430
+خاصة فالصح انه بحكي ان ال R تتنسو تتنسو ترضي مع ال
+
+215
+00:21:11,430 --> 00:21:18,210
+M تتنسو تتنسو ترضي مع ال R ترضي يعني لما تكون ال
+
+216
+00:21:18,210 --> 00:21:22,410
+turning moment عندي is
+
+217
+00:21:22,410 --> 00:21:26,350
+positive يعني
+
+218
+00:21:26,350 --> 00:21:29,630
+عندي ال turning moment اللي جاء من ال engine هذي
+
+219
+00:21:29,630 --> 00:21:35,630
+أعلى من ال resisting torqueزي ما هو بين B وC بيكون
+
+220
+00:21:35,630 --> 00:21:41,050
+في عندي طاقة زيادة الطاقة الزيادة هتاخدها ال
+
+221
+00:21:41,050 --> 00:21:46,230
+flywheel معناته سرعتها هتزيد صح؟ سرعة ال flywheel
+
+222
+00:21:46,230 --> 00:21:50,930
+هتزيد في الحالة هذه ال crank shaft اكسلريات
+
+223
+00:21:50,930 --> 00:21:56,070
+هيتسارع و ال work is done by the steam or by the
+
+224
+00:21:56,070 --> 00:22:00,910
+fuel انا في شغل موضول من الوقود او من ال steam
+
+225
+00:22:05,430 --> 00:22:12,310
+لما في منطقة زي بين C و D الشغل او ال torque اللي
+
+226
+00:22:12,310 --> 00:22:18,250
+جاي من ال engine اقل من ال resisting طب
+
+227
+00:22:18,250 --> 00:22:24,430
+انا كيف هعوضه؟ من ون هاخده؟ من المخزن عندى في ال
+
+228
+00:22:24,430 --> 00:22:26,710
+flywheel معناه اتصارات ال flywheel لما اخد منها
+
+229
+00:22:26,710 --> 00:22:31,190
+هتقل فبصير retardation او بصير deceleration لل
+
+230
+00:22:31,190 --> 00:22:35,390
+crank shaftو ال work is done on the steam يعني ال
+
+231
+00:22:35,390 --> 00:22:39,590
+steam في الأول كان في ال .. بين B و C بيعمل شغل
+
+232
+00:22:39,590 --> 00:22:43,790
+بيعمل شغل بين C و D احنا بيعمل شغل على ال steam
+
+233
+00:22:43,790 --> 00:22:48,550
+طيب
+
+234
+00:22:48,550 --> 00:22:53,530
+خلنا
+
+235
+00:22:53,530 --> 00:23:00,680
+نعرف نعمل .. نعرف نبدأ نعمل شوية معدلاتT هو torque
+
+236
+00:23:00,680 --> 00:23:05,600
+on the crankshaft at any instant اللي جاي من إيش؟
+
+237
+00:23:05,600 --> 00:23:10,800
+من ال engine جاي من عندي ال piston هذا ال T ال T
+
+238
+00:23:10,800 --> 00:23:12,820
+يعني ال main resisting torque هذا ال main
+
+239
+00:23:12,820 --> 00:23:16,480
+resisting torque اللي هو اللي جاي عن الأحمال اللي
+
+240
+00:23:16,480 --> 00:23:21,100
+على ال engine أو على السيارة يعني نفترض اندي هذا
+
+241
+00:23:21,100 --> 00:23:24,560
+بيشغل سيارة ممكن يكون شغل إشي تاني صح؟بس على فرض
+
+242
+00:23:24,560 --> 00:23:28,980
+انه بيشغل سيارة بتكون ال teaming جاي من الأحمال
+
+243
+00:23:28,980 --> 00:23:33,060
+على السيارة اللي هي اللي هي جاي من مقامة الهواء من
+
+244
+00:23:33,060 --> 00:23:43,520
+الوزن من تحريك الكتل الدوارة من الاحتكاك نعم طبعا
+
+245
+00:23:43,520 --> 00:23:48,040
+في اللي هو ال axel الملحقات بتاعة السيارة الإضاءة
+
+246
+00:23:48,040 --> 00:23:52,520
+برضه تمثل ايش أحمال التبريد والتكييف يمثل برضه
+
+247
+00:23:52,520 --> 00:23:56,080
+أحمالفكل هذه كلها إيش؟ أحمال، يعني لما أنا أشغل
+
+248
+00:23:56,080 --> 00:24:00,360
+السيارة على التكييفيستي تسحب بنزين أكتر لأن الحمل
+
+249
+00:24:00,360 --> 00:24:03,980
+زاد، إذا أنا أشغال في الليل في إضاءة بقى، بكون
+
+250
+00:24:03,980 --> 00:24:07,780
+أشحن، بكون أسحب energy من البطارية، و البطارية إيش
+
+251
+00:24:07,780 --> 00:24:15,160
+بتكون؟ تشحن، مظبوط؟ طبعا، وزن، مع أن وزن السيارة،
+
+252
+00:24:15,160 --> 00:24:20,740
+وزن السيارة كلها بالحمل الحملاءإذا كان الفرق بين
+
+253
+00:24:20,740 --> 00:24:27,620
+ال T و ال T main positive فال flywheel تتسارع إذا
+
+254
+00:24:27,620 --> 00:24:31,380
+كانت T ناقص ال T main negative يعني ال torque اللي
+
+255
+00:24:31,380 --> 00:24:34,940
+جام ال engine أقل من الأحمال بيكون أن دي أنا بصير
+
+256
+00:24:34,940 --> 00:24:38,400
+أسحب من ال flywheel فال flywheel تتراجع بيصير ت
+
+257
+00:24:38,400 --> 00:24:44,980
+decelerate هذا ال turning moment diagram ل four
+
+258
+00:24:44,980 --> 00:24:49,540
+stroke internal combustion engineinternal
+
+259
+00:24:49,540 --> 00:24:54,300
+combustion engine
+
+260
+00:24:54,300 --> 00:24:57,120
+احنا حكينا في ال four stroke engine فيه أربع
+
+261
+00:24:57,120 --> 00:25:03,530
+strokes في السحبcompression بعدين هين بيصير ايش
+
+262
+00:25:03,530 --> 00:25:08,290
+اللي اللي هو ال working او ال ال ال power stroke
+
+263
+00:25:08,290 --> 00:25:12,890
+او ال expansion stroke كذا اسم ال power stroke او
+
+264
+00:25:12,890 --> 00:25:16,070
+ال working stroke او ال expansion stroke بعدين هين
+
+265
+00:25:16,070 --> 00:25:20,170
+بطرد الغازات المحترقة يعني اولش بسحب وقود و غاز
+
+266
+00:25:20,170 --> 00:25:25,950
+بعدين compression بعدين expansion بصير احتراق
+
+267
+00:25:25,950 --> 00:25:31,730
+بعدين بطرد الغازات لحظة ال power وين جايةفي ال
+
+268
+00:25:31,730 --> 00:25:34,250
+working هذه ال power المناطق ال power هذه لازم
+
+269
+00:25:34,250 --> 00:25:38,370
+تكون كافية عشان تغطي احتياجات ال other strokes
+
+270
+00:25:38,370 --> 00:25:45,250
+لازم تكون .. اه تفضل فليه كافي ال power يعني؟ اه
+
+271
+00:25:45,250 --> 00:25:51,650
+طبعا لازم تكون كافية تغطي كل الأربع strokes عشانك
+
+272
+00:25:51,650 --> 00:25:56,830
+انا بحط flywheel عشان اخزن واستفيد منها بقياش ايوة
+
+273
+00:25:56,830 --> 00:25:59,010
+انت اول ما تشغل السيارة ايش بتسويه؟
+
+274
+00:26:01,680 --> 00:26:04,520
+أول الشخصية اللى بتستعمل ال switch ال switch إيش
+
+275
+00:26:04,520 --> 00:26:11,520
+بيسوي؟ كيف بيحركها في الأول؟ في ال starter في مطور
+
+276
+00:26:11,520 --> 00:26:14,260
+على الكهربا بيلفها في الأول عشان يبدأ العملية
+
+277
+00:26:14,260 --> 00:26:18,660
+فبيسموها إيش starting up مستحيل تبدأ بدون ال
+
+278
+00:26:18,660 --> 00:26:22,760
+starter لأنه بدك في الأول تتحركها فانت اللى بتهدي
+
+279
+00:26:22,760 --> 00:26:28,600
+لثوانى بتشغل ال engine باستخدام مطور كهربا DC
+
+280
+00:26:28,600 --> 00:26:29,100
+motor
+
+281
+00:26:36,790 --> 00:26:42,290
+طيب لأن في حالة ال
+
+282
+00:26:42,290 --> 00:26:48,710
+suction stroke انا بكون أسحب شفط معناته هصير
+
+283
+00:26:48,710 --> 00:26:52,650
+negative pressure و الدليل انه بندفع الوقود و
+
+284
+00:26:52,650 --> 00:26:54,150
+الهواء لو مافيش negative pressure انا مابدخلش
+
+285
+00:26:54,150 --> 00:26:58,570
+الوقود و الهواء صح فبنزل تحت ال zero فبصير عندى
+
+286
+00:26:58,570 --> 00:26:59,130
+vacuum
+
+287
+00:27:01,690 --> 00:27:06,090
+في ال compression stroke انا بعمل شغل على مين؟
+
+288
+00:27:06,090 --> 00:27:13,670
+بعمل شغل على الوقود و الهواء، معناته انا بستنفذ من
+
+289
+00:27:13,670 --> 00:27:17,790
+الشغل، مظبوط؟ معناته بخش في ال negative برضه، في
+
+290
+00:27:17,790 --> 00:27:24,790
+ال power stroke الوقود هو بشتعل و بيعمللي اش،
+
+291
+00:27:24,790 --> 00:27:28,590
+بيعمللي شغل، بيعمل شغل على ال piston عشانك بيصير
+
+292
+00:27:28,590 --> 00:27:33,590
+في اش positive loop، بيصير في الموجةفي حالة ال
+
+293
+00:27:33,590 --> 00:27:38,690
+exhaust اللي هو طرد الغازات انا بعمل شغل على
+
+294
+00:27:38,690 --> 00:27:47,210
+الغازات فبقى طردها فبتكون دي negative loop نرجع
+
+295
+00:27:47,210 --> 00:27:49,970
+لل turning moment diagram بتاع اللي هو turning
+
+296
+00:27:49,970 --> 00:27:56,330
+moment diagram for two stroke engine اللي هو
+
+297
+00:27:56,330 --> 00:28:00,770
+double acting steam engine double acting steam
+
+298
+00:28:00,770 --> 00:28:01,110
+engine
+
+299
+00:28:07,780 --> 00:28:13,680
+طبعا في حالة ال steam engine عندى two strokes يعني
+
+300
+00:28:13,680 --> 00:28:18,940
+الدورة كاملة تلاتمية و ستين درجة في حالة ال four
+
+301
+00:28:18,940 --> 00:28:23,160
+stroke engine الدورة كاملة سبعمية و عشرين دورتين
+
+302
+00:28:23,160 --> 00:28:28,500
+كاملات تلاتمية و ستين درجة مقسمين لاربع كل واحدة
+
+303
+00:28:28,500 --> 00:28:34,960
+مية و تمانية درجةintake compression expansion
+
+304
+00:28:34,960 --> 00:28:41,240
+exhaust في حالة ال steam engine يكون عندى الدورة
+
+305
+00:28:41,240 --> 00:28:46,640
+360 درجة طيب
+
+306
+00:28:46,640 --> 00:28:56,000
+نتبع double acting steam engine نتبع بين نقطة a a
+
+307
+00:28:56,000 --> 00:28:56,440
+small
+
+308
+00:28:59,170 --> 00:29:06,370
+و P A و P من هنا لهنا لاحظوا
+
+309
+00:29:06,370 --> 00:29:11,870
+من A ل P ال
+
+310
+00:29:11,870 --> 00:29:16,750
+torque اللي جاي من ال engine أقل من ال torque
+
+311
+00:29:16,750 --> 00:29:21,910
+المطلوبأقل من ال torque المطلوب الشغل ال energy
+
+312
+00:29:21,910 --> 00:29:27,750
+المطلوب عشان اغطي ال T mean هتكون مساحة المستطيل A
+
+313
+00:29:27,750 --> 00:29:33,970
+small A capital B capital P small لكن الطاقة اللي
+
+314
+00:29:33,970 --> 00:29:40,230
+جاء من ال engine هي مساحة اللي هي بين A,B,P اللي
+
+315
+00:29:40,230 --> 00:29:45,610
+هو هذه المساحةبالظبط العجز عندي ايش المساحة هادئ
+
+316
+00:29:45,610 --> 00:29:52,170
+اللي هي a small a capital B هذا العجز لأن العجز
+
+317
+00:29:52,170 --> 00:29:59,070
+هاتبون هحصله ال engine شغال حاليا يعني تخطر موضوع
+
+318
+00:29:59,070 --> 00:30:03,110
+ال starting من ال flywheel معناته في المرحلة هادئ
+
+319
+00:30:03,110 --> 00:30:06,230
+اذا هاخد ال flywheel معناته سرعة ال flywheel هتمزل
+
+320
+00:30:06,230 --> 00:30:08,210
+طيب
+
+321
+00:30:09,990 --> 00:30:20,610
+في الفترة من P ل Q الطاقة المطلوبة اللي هي الطاقة
+
+322
+00:30:20,610 --> 00:30:28,090
+المطلوبة هي مساحة المستطيل P,B,C,Q هذا المطلوب انا
+
+323
+00:30:28,090 --> 00:30:32,430
+اكم باعطيه ال engine باعطيه المساحة هذه في زيادة
+
+324
+00:30:32,430 --> 00:30:39,940
+اللي هي المساحة P,B,C هذا زيادةبتخز ال flywheel
+
+325
+00:30:39,940 --> 00:30:44,640
+بتتصارع ال flywheel من
+
+326
+00:30:44,640 --> 00:30:50,760
+Q ل R الطاقة
+
+327
+00:30:50,760 --> 00:30:55,120
+المطلوبة عشان اغطي ال load مساحة المساطيل Q,C,D,R
+
+328
+00:30:55,120 --> 00:30:59,120
+اللي جامع ال engine المتاح عندي اللي هو المساحة
+
+329
+00:30:59,120 --> 00:31:04,740
+هذه والمساحة هذه العجز اللي هي المساحة اللي هي C,C
+
+330
+00:31:04,740 --> 00:31:11,030
+,Dباخد من flywheel ال flywheel هتت بطأ سرعتها من R
+
+331
+00:31:11,030 --> 00:31:19,470
+ل S الطاقة المطلوبة مساحة موسطيل D E S R المتاح من
+
+332
+00:31:19,470 --> 00:31:25,750
+ال engine اللي هو جاية R D D E S مع ان انا فيه
+
+333
+00:31:25,750 --> 00:31:32,910
+زيادة عن دي ايش D D Eبتخزين الفلاويل تتسارع كمان
+
+334
+00:31:32,910 --> 00:31:39,790
+مرة بعدين بين ال S و ال E بيكون الطاقة المطلوبة
+
+335
+00:31:39,790 --> 00:31:46,410
+اللي هي مساحة مستوطين S E F E الشغل المتاح من ال
+
+336
+00:31:46,410 --> 00:31:50,390
+engine اللي هو المساحة S E E اللي هي هذه العجز
+
+337
+00:31:50,390 --> 00:31:56,490
+اللي هو E F E فباخد الفلاويل ترجع تتباطئ الفلاويل
+
+338
+00:32:03,130 --> 00:32:07,490
+الان في واضح في تذبذب في الطاقة في fluctuation of
+
+339
+00:32:07,490 --> 00:32:12,590
+energy حوالين ال mean resisting torque طبعا في
+
+340
+00:32:12,590 --> 00:32:15,390
+fluctuation up and down يعني ال energy اللي جاي ال
+
+341
+00:32:15,390 --> 00:32:19,830
+energy بتكون بعض احيان تحت تحتالـ torque اللي جاي
+
+342
+00:32:19,830 --> 00:32:22,170
+من ال engine تحت ال resisting و بعض احيان بيكون
+
+343
+00:32:22,170 --> 00:32:27,630
+اعلى هنا اقل هنا اعلى هنا اقل ففي عندي fluctuation
+
+344
+00:32:27,630 --> 00:32:32,090
+او تذبذب لل torque اللي جاي من ال engine حوالين ال
+
+345
+00:32:32,090 --> 00:32:36,050
+main resisting torque او ال torque اللي جاي من ال
+
+346
+00:32:36,050 --> 00:32:41,250
+load فالمساحات
+
+347
+00:32:41,250 --> 00:32:48,950
+المساحات ناخد المساحة ديAAB عبارة عن energy
+
+348
+00:32:48,950 --> 00:32:57,830
+fluctuation of energy below المساحة BBC above CCD
+
+349
+00:32:57,830 --> 00:33:07,870
+below DDE above EEF below طبعا
+
+350
+00:33:07,870 --> 00:33:15,600
+متوقع متوقع احنا حكينا في المنطقة ها بين B و Cال
+
+351
+00:33:15,600 --> 00:33:18,580
+energy اللي جاية من ال engine في عندي زيادة في
+
+352
+00:33:18,580 --> 00:33:22,280
+الطاقة متوقع ان يكون ال engine أسرع سرعة يكون أكبر
+
+353
+00:33:22,280 --> 00:33:28,400
+سرعة عند Q عند Q متوقع لأن انا بضيف يعدي فهي تسارع
+
+354
+00:33:28,400 --> 00:33:32,720
+ال engine متوقع تكون السرعة أعلي عشان عند Q او عند
+
+355
+00:33:32,720 --> 00:33:39,620
+S برضه هين بضيف يا عند Q او عند S الآن
+
+356
+00:33:43,730 --> 00:33:50,950
+طبعا واضح بين P و Q انا بخزن بضيف لل energy ل ال
+
+357
+00:33:50,950 --> 00:33:55,070
+fly whale و بين R و S برضه انا بضيف energy لل fly
+
+358
+00:33:55,070 --> 00:34:01,210
+whale عند
+
+359
+00:34:01,210 --> 00:34:11,070
+P او R P ناخد R R واضح عندى لحظة من C ل Dعند هذا
+
+360
+00:34:11,070 --> 00:34:15,410
+فيه عجزة من اين هسحبه ال flywheel متوقع معناته
+
+361
+00:34:15,410 --> 00:34:18,610
+السرعة ان ال flywheel تكون minimum عند R تكون
+
+362
+00:34:18,610 --> 00:34:23,410
+minimum عند R او عند P P لانه جاية ادربالكوا هذا
+
+363
+00:34:23,410 --> 00:34:27,210
+دورة كاملة يعني هي تكمل يعني هذا C مع A بتكمل يعني
+
+364
+00:34:27,210 --> 00:34:31,690
+كأنا جاية من هنا C وA فهتكون minimum عند P او عند
+
+365
+00:34:31,690 --> 00:34:34,730
+R اللي هي ال flywheel speed
+
+366
+00:34:40,770 --> 00:34:43,090
+طبعا فى عندى ال maximum fluctuation of energy هو
+
+367
+00:34:43,090 --> 00:34:45,430
+difference between maximum and minimum energies ال
+
+368
+00:34:45,430 --> 00:34:47,590
+maximum fluctuation of energy هو الفرق بين ال
+
+369
+00:34:47,590 --> 00:34:53,310
+maximum و ال minimum انا
+
+370
+00:34:53,310 --> 00:34:57,350
+عندهين turning moment diagram ل some engine هدى
+
+371
+00:34:57,350 --> 00:35:02,230
+طبعا turning moment افترضية هذا هو الخط يمثل ال
+
+372
+00:35:02,230 --> 00:35:07,350
+main resisting torque وهذا يمثل ال fluctuation of
+
+373
+00:35:07,350 --> 00:35:10,050
+torque اللى جاى من ال engine
+
+374
+00:35:13,690 --> 00:35:22,410
+فالان المساحات اللي هي A1 وA2 وA3 وA4 وA5 تتمثل
+
+375
+00:35:22,410 --> 00:35:26,110
+تذبذب للطاقة above and below ال mean resisting
+
+376
+00:35:26,110 --> 00:35:33,250
+torque اللي هي A1 وA2 وA3 وA4 وA5 وA6 تتمثل تذبذب
+
+377
+00:35:33,250 --> 00:35:38,470
+للطاقة حوالين ال mean torque line
+
+378
+00:35:45,390 --> 00:35:53,690
+طبعا ال areas a1 و a3 و a5 تمثل تذبذب أعلى ال mean
+
+379
+00:35:53,690 --> 00:36:02,710
+resisting و ال a2 و ال a4 و ال a6 below خليني
+
+380
+00:36:02,710 --> 00:36:05,850
+افترض ان ال energy اللي في ال flywheel لما كان عند
+
+381
+00:36:05,850 --> 00:36:09,590
+نقطة a كانت تساوي E capital ال energy اللي كانت
+
+382
+00:36:09,590 --> 00:36:14,530
+الطاقة المخزنة في flywheelلما كنا عند A كانت
+
+383
+00:36:14,530 --> 00:36:20,770
+قيمتها E طيب عند B إيش هكون ساوى طاقتك؟ هتزود
+
+384
+00:36:20,770 --> 00:36:30,200
+عليها A واحدعند C هتطرح منها A2 عند D A3 عند E
+
+385
+00:36:30,200 --> 00:36:36,260
+هتطرح منها A4 عند F هتطرح منها A5 عند G هتطرح منها
+
+386
+00:36:36,260 --> 00:36:41,420
+A6 المعناته ال energy at B هي E زاد A1 عند C E زاد
+
+387
+00:36:41,420 --> 00:36:47,740
+A1 ناقص A2 عند D E زاد A1 معناه A2 زاد A3 و هكذا
+
+388
+00:36:47,740 --> 00:36:51,220
+طبعا ال cycle تتكرر بعد ذلك
+
+389
+00:36:54,250 --> 00:37:00,530
+لأ خد عمل فرضية أن ال energy عند B كانت maximum ال
+
+390
+00:37:00,530 --> 00:37:04,710
+maximum energy كانت عند B و ال minimum energy كانت
+
+391
+00:37:04,710 --> 00:37:12,850
+عند E يعني ال E max هي عند B و ال E minimum كانت
+
+392
+00:37:12,850 --> 00:37:16,790
+عند E هي ال energy عند B اللي هي ال maximum و ال
+
+393
+00:37:16,790 --> 00:37:23,030
+energy عند E هي ال minimumبعد ذاته انا فى عندى
+
+394
+00:37:23,030 --> 00:37:25,290
+maximum value و فى minimum value المعنى هو ال
+
+395
+00:37:25,290 --> 00:37:28,590
+maximum fluctuation هيكون ال maximum minus ال
+
+396
+00:37:28,590 --> 00:37:32,090
+minimum هتكون ال maximum fluctuation of energy E
+
+397
+00:37:32,090 --> 00:37:34,530
+بيستوى ال maximum energy minus ال minimum energy
+
+398
+00:37:34,530 --> 00:37:38,390
+اللى هى ال maximum اللى هى E زيادة A1 minus E
+
+399
+00:37:38,390 --> 00:37:42,610
+زيادة A1 minus A2 زيادة A3 minus A4 بتطلع A2 minus
+
+400
+00:37:42,610 --> 00:37:45,150
+A3 زيادة A4 طبعا هذا ايش افتراض لحتى اللحظة
+
+401
+00:37:48,720 --> 00:37:52,200
+هنعرف ما هو coefficient of fluctuation of energy
+
+402
+00:37:52,200 --> 00:37:57,020
+معامل التذبذب في الطاقة معامل التذبذب في الطاقة
+
+403
+00:37:57,020 --> 00:38:02,700
+بيساوي ال maximum fluctuation of energy على ال
+
+404
+00:38:02,700 --> 00:38:09,300
+work done per cycle ال work done per cycle بيمثل
+
+405
+00:38:09,300 --> 00:38:12,620
+مساحة المستطيل اللي تحت ال mean resisting curve
+
+406
+00:38:12,620 --> 00:38:23,030
+اللي هي T mean في ال thetaهذا هو المساحة هذه بتمثل
+
+407
+00:38:23,030 --> 00:38:28,310
+ال work done during the cycle المعامل التذبذب في
+
+408
+00:38:28,310 --> 00:38:31,450
+الطاقة بالساوية ال maximum fluctuation of energy
+
+409
+00:38:31,450 --> 00:38:33,690
+على ال work done per cycle ال work done per cycle
+
+410
+00:38:33,690 --> 00:38:38,990
+هو T mean في theta ال theta ال angle turned in one
+
+411
+00:38:38,990 --> 00:38:42,740
+revolutionطبعا ال theta بتكون سوى اتنين باى يعني
+
+412
+00:38:42,740 --> 00:38:46,440
+تلت مية و ستين درجة في حالة two stroke engine او
+
+413
+00:38:46,440 --> 00:38:49,760
+steam engine ال theta بتكون سوى اربع باى سبع مية و
+
+414
+00:38:49,760 --> 00:38:53,900
+عشرين درجة في حالة four stroke engine اربع stroke
+
+415
+00:38:53,900 --> 00:38:56,920
+و واحدة مية و تمانية مية و تمانية و اربعة سبع مية
+
+416
+00:38:56,920 --> 00:39:03,560
+و عشرين في النهاية ال power ايش بتساوي torque فى
+
+417
+00:39:03,560 --> 00:39:08,570
+omega ال power بتساوي torqueفى omega يعني ال
+
+418
+00:39:08,570 --> 00:39:15,810
+torque ايش يساوي power على omega ال T mean بيساوي
+
+419
+00:39:15,810 --> 00:39:21,830
+ال power بتاعة ال engine ال
+
+420
+00:39:21,830 --> 00:39:28,390
+T mean بيساوي ال power لل engine على omega بيساوي
+
+421
+00:39:28,390 --> 00:39:36,040
+ال power لل engine ال omega عبارة عن اتنين باىفي
+
+422
+00:39:36,040 --> 00:39:41,720
+عدد دورات اللي هي على ستين يعني
+
+423
+00:39:41,720 --> 00:39:47,080
+سيكون يساوي ستين سيصبح في ال bus ستين ال power على
+
+424
+00:39:47,080 --> 00:39:56,500
+اتنين باى فعلا اللي هي المعادلة دي هو
+
+425
+00:39:56,500 --> 00:40:01,380
+حاطط general equation ال work done per cycle بسواة
+
+426
+00:40:01,380 --> 00:40:08,010
+P في ستين على N smallان small بيستوى ال number of
+
+427
+00:40:08,010 --> 00:40:14,490
+working strokes per minute الان بيستوى ان capital
+
+428
+00:40:14,490 --> 00:40:21,830
+في حالة steam engine او two stroke engine الان
+
+429
+00:40:21,830 --> 00:40:24,930
+small بيستوى ان على اتنين in case of four stroke
+
+430
+00:40:24,930 --> 00:40:31,890
+engine لان في حالة ال two stroke engine بيصير عندي
+
+431
+00:40:31,890 --> 00:40:40,010
+power ضعفال four stroke صح؟ في حالة ال ال ال ال ال
+
+432
+00:40:40,010 --> 00:40:40,430
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+433
+00:40:40,430 --> 00:40:41,010
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+434
+00:40:41,010 --> 00:40:41,850
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+435
+00:40:41,850 --> 00:40:42,330
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+436
+00:40:42,330 --> 00:40:44,670
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+437
+00:40:44,670 --> 00:40:47,170
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+438
+00:40:47,170 --> 00:40:47,510
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+439
+00:40:47,510 --> 00:40:52,790
+ال ال ال ال
+
+440
+00:40:56,850 --> 00:41:00,370
+في حالة two stroke internal combustion engine او
+
+441
+00:41:00,370 --> 00:41:04,010
+في حالة steam engine بستوي N capital اللي هي ال
+
+442
+00:41:04,010 --> 00:41:07,830
+RPM على اتنين في حالة four stroke internal
+
+443
+00:41:07,830 --> 00:41:13,650
+combustion engine طبعا
+
+444
+00:41:13,650 --> 00:41:18,510
+متوقع كل ما زود ال number of cylinders التذبذب
+
+445
+00:41:18,510 --> 00:41:20,510
+حوالين ال main line يقل ولا يزيد
+
+446
+00:41:26,530 --> 00:41:31,210
+كل مزود قعدة ال cylinders تذبذب
+
+447
+00:41:31,210 --> 00:41:35,690
+و حتزيد ولا هتقل يعني
+
+448
+00:41:35,690 --> 00:41:38,090
+انا ممكن اعتبر اجابتكوا صحيح انا ممكن اعتبرها خطأ
+
+449
+00:41:38,090 --> 00:41:41,110
+حسب انتوا ما اعتبروها صحيح علي اسم اللي حكيته انه
+
+450
+00:41:41,110 --> 00:41:49,490
+حتزيد اذا
+
+451
+00:41:49,490 --> 00:41:55,790
+والله انا حكيت انه بدي اشغل الاربع cylindersو
+
+452
+00:41:55,790 --> 00:41:59,490
+ترتيب ال strokes نفسهم في الأربعة يعني يعني ال
+
+453
+00:41:59,490 --> 00:42:02,490
+power stroke هي نفسها نفس بيصير عند نفس اللحظة ال
+
+454
+00:42:02,490 --> 00:42:05,210
+power stroke في الأربعة معناته بيكون ال variation
+
+455
+00:42:05,210 --> 00:42:09,610
+تذبد في ال energy عالي جدا و هذا سيء جدا صح؟ لكن
+
+456
+00:42:09,610 --> 00:42:13,330
+لو خلت زاوية مش كلهم بيصير ال power stroke مع بعض
+
+457
+00:42:13,330 --> 00:42:18,410
+يعني بخلي زاوية بينهم معناته انا بوزع ال power و
+
+458
+00:42:18,410 --> 00:42:21,530
+بالتالي بقلل ايش ال fluctuation او تذبده
+
+459
+00:42:25,410 --> 00:42:28,850
+على أرض الواقع أنا بخليه زاوية، بخليهش كل .. يعني
+
+460
+00:42:28,850 --> 00:42:32,230
+عندي .. عندي مثلا أربعة سيلندر، بخليهش ال power
+
+461
+00:42:32,230 --> 00:42:35,850
+stroke لسيلندر أول والتان والتاتر و الرابع مع بعض
+
+462
+00:42:36,760 --> 00:42:40,780
+بخلي واحدة .. واحدة مثلا يعني هي stroke، التانية
+
+463
+00:42:40,780 --> 00:42:44,140
+stroke، التانية stroke، فانا بوزع .. بفرد ال power
+
+464
+00:42:44,140 --> 00:42:47,680
+على الأربع cycles عشان كل ما بزيد ال number of
+
+465
+00:42:47,680 --> 00:42:51,180
+cylinders كل ما ال coefficient of fluctuation of
+
+466
+00:42:51,180 --> 00:42:54,860
+energy بقل، انا بهمن يكون ال coefficient of
+
+467
+00:42:54,860 --> 00:43:00,880
+fluctuation of energy as minimum as I canفي حال
+
+468
+00:43:00,880 --> 00:43:03,780
+single cylinder double acting steam engine ال CE
+
+469
+00:43:03,780 --> 00:43:09,720
+بيساوي 0.21 طبعا هذه الارقام typical ال cross
+
+470
+00:43:09,720 --> 00:43:14,000
+compound steam engine 0.096 single cylinder single
+
+471
+00:43:14,000 --> 00:43:19,520
+acting four stroke gas engine 1.93 هذا سلندر واحدة
+
+472
+00:43:19,520 --> 00:43:26,980
+four stroke single acting 0.066 six cylinder يعني
+
+473
+00:43:26,980 --> 00:43:29,260
+صار من six cylinder single acting four stroke
+
+474
+00:43:29,260 --> 00:43:32,600
+لاحظوا أيشpoint O تلاتة واحد يعني كان عندي هين
+
+475
+00:43:32,600 --> 00:43:37,160
+cylinder واحدة كان ال coefficient of fluctuation
+
+476
+00:43:37,160 --> 00:43:40,500
+energy واحد point ستة تلاتة هين اربع cylinder
+
+477
+00:43:40,500 --> 00:43:43,580
+point O ستة ستة ستة ستة cylinder point O تلاتة
+
+478
+00:43:43,580 --> 00:43:48,560
+واحد لو عملت تمانى cylinder بيختلف بنزل اكتر برضه
+
+479
+00:43:48,560 --> 00:43:52,040
+لو عملت اتناشه انك السيارات مثلا كدلك السيارات ال
+
+480
+00:43:52,040 --> 00:44:00,040
+Toyota و Toyota ZX بتسمعش صوتهالأن بيكون عادة ال
+
+481
+00:44:00,040 --> 00:44:06,680
+cylinders كبير فيها، مافيش فيها fluctuation double
+
+482
+00:44:06,680 --> 00:44:12,020
+acting steam
+
+483
+00:44:12,020 --> 00:44:18,620
+engine في أنواع تانية، ماحكيتك هي single cylinder،
+
+484
+00:44:18,620 --> 00:44:22,210
+single acting، four strokeيعني بيصير الضغط في
+
+485
+00:44:22,210 --> 00:44:25,270
+اتجاه واحد double acting في اتجاه هنا فهمت على اي
+
+486
+00:44:25,270 --> 00:44:27,630
+كده يعني بيعمل power يعني بيزيد ال power في الحالة
+
+487
+00:44:27,630 --> 00:44:32,170
+هذه ال air compression engine معظمها بيكون single
+
+488
+00:44:32,170 --> 00:44:36,410
+acting خش على اليوتيوب هتشوف animations شوف single
+
+489
+00:44:36,410 --> 00:44:41,030
+cylinder single acting وشوف single cylinder double
+
+490
+00:44:41,030 --> 00:44:46,750
+acting for stroke هتشوف فيديوهات عليها compound خش
+
+491
+00:44:46,750 --> 00:44:49,690
+برضه على اليوتيوب شوف هتشوف فيديوهات كتير عن ال
+
+492
+00:44:49,690 --> 00:44:59,840
+compoundcross compound steam engine في
+
+493
+00:44:59,840 --> 00:45:02,720
+اي سؤال؟ اعطيكوا العافية
+
diff --git a/PL9fwy3NUQKwa0nXiCdyQcTW4hWDLTGpDb/WyayN6Eorf0_raw.srt b/PL9fwy3NUQKwa0nXiCdyQcTW4hWDLTGpDb/WyayN6Eorf0_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..f716c71eb7bd3c788c627e8d5b5c2ad3848a54f2
--- /dev/null
+++ b/PL9fwy3NUQKwa0nXiCdyQcTW4hWDLTGpDb/WyayN6Eorf0_raw.srt
@@ -0,0 +1,1996 @@
+1
+00:00:05,090 --> 00:00:07,470
+بسم الله الرحمن الرحيم السلام عليكم ورحمة الله
+
+2
+00:00:07,470 --> 00:00:12,190
+وبركاته و اليوم هنكمل في مادة نظرية الألات هنكمل
+
+3
+00:00:12,190 --> 00:00:14,830
+في موضوع بده اسمه ال engine analysis ال chapter
+
+4
+00:00:14,830 --> 00:00:18,670
+خمساش غطين ال inertia forces حسبنا ال piston
+
+5
+00:00:18,670 --> 00:00:23,370
+effort عملنا equivalent two mass system لل
+
+6
+00:00:23,370 --> 00:00:28,830
+connecting rod و حسبنا ال torque على البصل ال
+
+7
+00:00:28,830 --> 00:00:32,960
+crankاليوم هنكمل في ال engine analysis موضوع ال
+
+8
+00:00:32,960 --> 00:00:39,360
+chapter هو tearing moment diagrams and flywheel من
+
+9
+00:00:39,360 --> 00:00:42,760
+اسم ال chapter tearing moment يعني مقصود ال moment
+
+10
+00:00:42,760 --> 00:00:46,160
+او العزم عند الكرانك انا في الحالة باهمن الشافت
+
+11
+00:00:46,160 --> 00:00:49,860
+اللي هيضور اللي هو عند الكرانك ال tearing moment
+
+12
+00:00:49,860 --> 00:00:54,080
+diagram هو عبارة عن تمثيل graphical representation
+
+13
+00:00:54,940 --> 00:01:00,100
+للـ torque عند الكرانك لأوضوع مختلف يعني as a
+
+14
+00:01:00,100 --> 00:01:08,220
+function of θ تمثيل بياني للعزم عند الكرانك as a
+
+15
+00:01:08,220 --> 00:01:14,540
+function of θ اللي هي θ زوية الكرانك طبعا الـ θ
+
+16
+00:01:14,540 --> 00:01:18,320
+الكرانك تتغير من صفر لتلتمية وستين
+
+17
+00:01:21,760 --> 00:01:24,460
+انبين عندى ال turning moment diagram for a single
+
+18
+00:01:24,460 --> 00:01:29,180
+cylinder double acting steam engineل .. يعني هذا
+
+19
+00:01:29,180 --> 00:01:34,960
+ال diagram لمحرك بخاري double acting يعني في ال ..
+
+20
+00:01:34,960 --> 00:01:40,340
+هو طالع بيكون فيه ضغط البخار و هو راجع برضه في شوط
+
+21
+00:01:40,340 --> 00:01:43,480
+power يعني ال power في الشوطين في الشوط اللي طالع
+
+22
+00:01:43,480 --> 00:01:48,200
+و الشوط اللي رايح إذا حابب الأول نتفرج على
+
+23
+00:01:48,200 --> 00:01:52,080
+فيديوهات نتعرف على ال .. ال two stroke engines و
+
+24
+00:01:52,080 --> 00:01:53,440
+ال four stroke engines
+
+25
+00:02:09,850 --> 00:02:12,830
+design is a piston that acts like a piston
+
+26
+00:02:46,650 --> 00:02:52,610
+يعني في عندنا piston و في عندناintake valve و
+
+27
+00:02:52,610 --> 00:02:58,790
+outtake يعني الدخول و الخروج go through its two
+
+28
+00:02:58,790 --> 00:03:05,170
+strokes you can see exactly what's happening let's
+
+29
+00:03:05,170 --> 00:03:08,130
+start with the spark plug firing at this point the
+
+30
+00:03:08,130 --> 00:03:11,530
+piston is at the top of its stroke the cylinder is
+
+31
+00:03:11,530 --> 00:03:13,810
+full of air and gasoline that has been compressed
+
+32
+00:03:13,810 --> 00:03:19,550
+لحظوا عندكم هذا بتكون عندى ال crankو ال connecting
+
+33
+00:03:19,550 --> 00:03:26,210
+rod على استقام واحدة لان هيعطي الشرارة فطبعا هذا
+
+34
+00:03:26,210 --> 00:03:34,270
+.. هذا يعني fuel هذا مش .. مش بخار هتس ترقب
+
+35
+00:03:34,270 --> 00:03:40,190
+بتاعة
+
+36
+00:03:40,190 --> 00:03:43,690
+الشرارة بيصير عند الاشتعال بيصير انفجار فهيرجع
+
+37
+00:03:43,690 --> 00:03:50,390
+لورا ال pistonأسحب الحرارة بطاقة كبيرة، تشاهد هذه
+
+38
+00:03:50,390 --> 00:03:54,070
+المنطقة خلف الحرارة؟ إنها مليئة بالهواء ومعالجة من
+
+39
+00:03:54,070 --> 00:03:58,010
+غلطان ومشروع كما يتحرك الحرارة إلى هذه المنطقة،
+
+40
+00:03:58,010 --> 00:04:04,030
+فتسحب المعالجة كما يتحرك الحرارة إلى أسفل أسطولها،
+
+41
+00:04:04,030 --> 00:04:08,510
+فتجهز مصدر مصدر مصدر مصدر مصدر مصدر مصدر مصدر مصدر
+
+42
+00:04:08,510 --> 00:04:09,890
+مصدر مصدر مصدر مصدر مصدر مصدر مصدر مصدر مصدر مصدر
+
+43
+00:04:09,890 --> 00:04:15,810
+مصدر مصدر مصدر مصدر مصدر مصدر مصدر مصدر مصدر ميعني
+
+44
+00:04:15,810 --> 00:04:20,030
+هو طالب مجرد مفتح ببدأش الدخل هتطلع من هنا وبعد
+
+45
+00:04:20,030 --> 00:04:31,950
+وشوية بفتح الظلب عشان يدخل وقود وهواء جديد هيتغط
+
+46
+00:04:36,840 --> 00:04:42,100
+هيدغط طبعا هو ضاغط بترد بقايا الدخانة لحد ما يوصل
+
+47
+00:04:42,100 --> 00:04:44,800
+هنا بيصير يدغط اكتر لحد ما يصير على استقام واحد
+
+48
+00:04:44,800 --> 00:04:48,100
+لسه فيه زاوية تنتبهوا ان في هنا زاوية
+
+49
+00:04:51,380 --> 00:05:05,820
+بعت شرارة و بتتكرر كمان مرة يعني
+
+50
+00:05:05,820 --> 00:05:12,300
+اللي عند ال piston مش piston و بس هو يستخدم لفتح و
+
+51
+00:05:12,300 --> 00:05:15,120
+غلق اللي هو الفتحات هذه صمم بشتغل
+
+52
+00:05:36,400 --> 00:05:41,940
+لحظة كل تلك بيستين دراية بيعطينا إيه؟ شرارة برجع
+
+53
+00:05:41,940 --> 00:05:48,810
+بعدين بضغطهي اول شهر مائة و تمانين كمان مائة و
+
+54
+00:05:48,810 --> 00:05:54,850
+تمانين بيعطي شرارة بندفع في الخلف بنرجعتها مضغط هي
+
+55
+00:05:54,850 --> 00:05:57,770
+كمان تلات مائة و ستين يعني كل تلات مائة و ستين
+
+56
+00:05:57,770 --> 00:06:03,970
+درجة بيعطيني شرارة في ال four stroke engine بيعطي
+
+57
+00:06:03,970 --> 00:06:07,970
+في ال .. في ال سبعة مائة و عشرين في دورتين بيعطيني
+
+58
+00:06:07,970 --> 00:06:12,530
+شرارة واحدة كل stroke مائة و اتوانين درجة هنشوف
+
+59
+00:06:12,530 --> 00:06:12,890
+الآن
+
+60
+00:06:34,620 --> 00:06:39,820
+انشوف ال four stroke صحيح
+
+61
+00:07:02,340 --> 00:07:06,100
+هذا الـ six cylinder V يعني تلاتة .. تلاتة هنا و
+
+62
+00:07:06,100 --> 00:07:23,880
+تلاتة هنا جايستة سيلندر اول
+
+63
+00:07:23,880 --> 00:07:30,160
+stroke intake يعني بيفتح الصنام هذا بدخل وقود مع
+
+64
+00:07:30,160 --> 00:07:35,480
+هوا هذا intake شفط بنزل لتحت مية و تمانين درجة
+
+65
+00:07:54,520 --> 00:08:05,040
+انتقل سحب هوا مع بقود بعد انتقال ايش بيجيه بدغط
+
+66
+00:08:07,920 --> 00:08:11,700
+لأن عشان يضغط لازم الصمامين هذي يكونوا مساكرين
+
+67
+00:08:11,700 --> 00:08:16,080
+مانفعش يكونوا فاتحين اذا فاتحين مش هيضغط both
+
+68
+00:08:16,080 --> 00:08:18,940
+valves are now closed and the pistons on its way
+
+69
+00:08:18,940 --> 00:08:23,100
+up pistons on its way up it's compressing the air
+
+70
+00:08:23,100 --> 00:08:25,080
+compressing the air raising the temperature
+
+71
+00:08:25,080 --> 00:08:28,300
+raising the energy potential of the air in the
+
+72
+00:08:28,300 --> 00:08:31,700
+chamber for the next stroke so at the top of this
+
+73
+00:08:31,700 --> 00:08:34,040
+stroke where the pistons all the way up you're now
+
+74
+00:08:34,040 --> 00:08:39,400
+ready for the next phaseالان خلص compression الغاز
+
+75
+00:08:39,400 --> 00:08:46,100
+و الوقود سخنوا مع الضغط اشعطينه شرارة يعني
+
+76
+00:08:46,100 --> 00:08:49,840
+compression stroke 180 درجة لان بيصير عندي
+
+77
+00:08:49,840 --> 00:08:54,180
+expansion بيصير احتراط فبندفع ال piston لتحت
+
+78
+00:08:56,860 --> 00:09:01,480
+هذه الاشة ال expansion أو ال power stroke هذه
+
+79
+00:09:01,480 --> 00:09:18,080
+الاشة
+
+80
+00:09:18,080 --> 00:09:21,280
+ال expansion
+
+81
+00:09:21,280 --> 00:09:22,820
+أو ال power stroke
+
+82
+00:09:27,030 --> 00:09:31,150
+الان خلصت العملية بدون ترد الدخنة معناته هيفتح
+
+83
+00:09:31,150 --> 00:09:41,550
+الصمام ال exhaust و يضغط تاني نرجع
+
+84
+00:09:41,550 --> 00:09:48,530
+لل slide معناته اذا بتلاحظوا في حالة ال four
+
+85
+00:09:48,530 --> 00:09:53,890
+stroke engine ال power كانت في one stroke ع كام
+
+86
+00:09:53,890 --> 00:09:57,900
+stroke هو؟أربعة كل stroke مية و تمانين درجة أربعة
+
+87
+00:09:57,900 --> 00:10:02,680
+و تمانين سبعة مية و عشرين معناته أنا الفترة اللي
+
+88
+00:10:02,680 --> 00:10:06,260
+باخد فيها power اللي هي في stroke واحدة من الأربعة
+
+89
+00:10:06,260 --> 00:10:10,380
+معناته ال power في الأربعة strokes لازم تكون كافية
+
+90
+00:10:10,380 --> 00:10:15,260
+للأربعة strokes لإن ال other three strokes مافي
+
+91
+00:10:15,260 --> 00:10:18,060
+عندي power كيف هكمل ال engine فمعناته لازم انا
+
+92
+00:10:18,060 --> 00:10:23,130
+اولدenough power فى ال power stroke او ال
+
+93
+00:10:23,130 --> 00:10:27,310
+expansion stroke و اخزنها فى ايش هخزنها فى ال
+
+94
+00:10:27,310 --> 00:10:32,450
+flywheel ال flywheel بخزن بخزنها ع شكل طاقة حركة
+
+95
+00:10:32,450 --> 00:10:37,050
+يعنى لما يكون عندى ال power سرعتها بتزيد لما بدي
+
+96
+00:10:37,050 --> 00:10:41,570
+استخلق منها هاخد من ال flywheel سرعتها ايش تنزل
+
+97
+00:10:41,570 --> 00:10:45,390
+شوف ال flywheel حتى في الجبل الجديد لان هنشوف شوف
+
+98
+00:10:45,390 --> 00:10:45,750
+ال flywheel
+
+99
+00:10:49,520 --> 00:10:52,740
+طيب معناته ال turning moment diagram هو عبارة عن
+
+100
+00:10:52,740 --> 00:10:57,200
+تمثيل بياني للعزم عند الكرانك as a function of
+
+101
+00:10:57,200 --> 00:11:02,540
+angle of rotation للكرانك التي هي θتا هعندي two
+
+102
+00:11:02,540 --> 00:11:07,200
+stroke engine او double acting steam engine احنا
+
+103
+00:11:07,200 --> 00:11:09,980
+حكينا كل مية و اتوين درجة في ال two stroke بيكون
+
+104
+00:11:09,980 --> 00:11:15,260
+عندى power مظلوط هعندي مية و اتوين درجة بيكون عندى
+
+105
+00:11:15,260 --> 00:11:23,120
+powerفي ال 120 درجة التانية عندي power الان انا
+
+106
+00:11:23,120 --> 00:11:32,060
+بولد power ليش بولد power عشان .. عشان استخدمها في
+
+107
+00:11:32,060 --> 00:11:35,640
+الآخر انا بقاوم اشي في عندي resisting torque اللي
+
+108
+00:11:35,640 --> 00:11:38,280
+هو ال main torque في عندي ال .. الان طبعا ال
+
+109
+00:11:38,280 --> 00:11:42,820
+torque ال torque متغير مع ال angle of rotation
+
+110
+00:11:42,820 --> 00:11:48,210
+بتاعةلكرانك مش ثابت لكن ال resisting torque في
+
+111
+00:11:48,210 --> 00:11:50,890
+حالة ال engine is constant ال resisting torque انا
+
+112
+00:11:50,890 --> 00:11:54,730
+بدي اسرع السيارة مثلا بدي اتغلب الاحتكاك في القطع
+
+113
+00:11:54,730 --> 00:11:58,210
+اللي بتدور القطع الميكانيكية بدي احرك ال masses
+
+114
+00:11:58,210 --> 00:12:02,770
+اللي هو ال gears و ال differential بدي اقوم الوزن
+
+115
+00:12:02,770 --> 00:12:07,230
+السيارة اذا طالع طلع بدي اقوم الريح ففي شيء كلها
+
+116
+00:12:07,230 --> 00:12:14,120
+انا بدي اغطيها تستنفذ جزء من طاقتىعشان يكون عنده
+
+117
+00:12:14,120 --> 00:12:18,460
+mean resisting torque اللي هو بيقاوم بيقاوم ال
+
+118
+00:12:18,460 --> 00:12:23,220
+power اللي جاية من ال engine اللي مصدرها عند ال
+
+119
+00:12:23,220 --> 00:12:29,080
+piston مصدرها عند ال piston في
+
+120
+00:12:29,080 --> 00:12:33,200
+شبط رحل خمستاش احنا طلعنا معادل لده turning moment
+
+121
+00:12:33,200 --> 00:12:37,940
+torque بالساوية ال piston effort في R في sin θ زي
+
+122
+00:12:37,940 --> 00:12:40,500
+sin 2θ على اتنين جزء تربيع ل N تربيع minus sin
+
+123
+00:12:40,500 --> 00:12:45,160
+تربيع θال FB هي ال piston effort ال R اللي هو ال
+
+124
+00:12:45,160 --> 00:12:51,000
+crank ال radius اللي على ال crank طبعا عندي ال out
+
+125
+00:12:51,000 --> 00:12:57,940
+stroke اللي هي اللي هو هذه ال stroke A B A B C هذه
+
+126
+00:12:57,940 --> 00:13:06,980
+ال out stroke ال N stroke الراجع اللي هي C D E
+
+127
+00:13:06,980 --> 00:13:11,560
+فعندي out stroke وعندي N stroke
+
+128
+00:13:16,730 --> 00:13:22,870
+الـ work done الشغل المبدول عبارة عن moment
+
+129
+00:13:22,870 --> 00:13:28,110
+لو أنا جسم بتحرك و بتحت أثير قوة أفقية تحرك أفقية
+
+130
+00:13:28,110 --> 00:13:34,710
+تحت أثير قوة الشغل إيش يستوي force في مسافة force
+
+131
+00:13:34,710 --> 00:13:38,950
+في مسافة ال distance في ال rotation إيش يقابلها
+
+132
+00:13:38,950 --> 00:13:42,490
+theta
+
+133
+00:13:42,490 --> 00:13:47,310
+و ال force في ال rotation إيش يقابلهاmoment عزم
+
+134
+00:13:47,310 --> 00:13:52,770
+معناته ال work done هو العزم في الزاوية العزم في
+
+135
+00:13:52,770 --> 00:13:55,850
+الزاوية تق ال work done turning moment في ال angle
+
+136
+00:13:55,850 --> 00:13:59,230
+طبعا
+
+137
+00:13:59,230 --> 00:14:02,010
+ال work done هو ال area لل turning moment diagram
+
+138
+00:14:02,010 --> 00:14:06,670
+اللي انا عندي عندي هذه ال torque as a function of
+
+139
+00:14:06,670 --> 00:14:11,940
+theta معناته المساحة تحت هذه الملحنةبتمثل الشغل
+
+140
+00:14:11,940 --> 00:14:16,180
+المبذول في دورة واحدة .. الشغل المبذول في دورة
+
+141
+00:14:16,180 --> 00:14:22,040
+واحدة لما بحكي انا عن شغل بحكي عن energy لإن في
+
+142
+00:14:22,040 --> 00:14:24,400
+energy و في power إيش الفرق من ال energy و ال
+
+143
+00:14:24,400 --> 00:14:30,440
+power بالظبط
+
+144
+00:14:30,440 --> 00:14:34,940
+ال power هي معدل استهلاكي للطاقة في وحدة الزمن
+
+145
+00:14:34,940 --> 00:14:40,310
+يعني انا ممكن استهلك ال meat جول في ثانيةمعناته
+
+146
+00:14:40,310 --> 00:14:47,170
+عندى ال power مت وات وكن استهلكهم بطيء استهلكهم
+
+147
+00:14:47,170 --> 00:14:49,810
+مثلا في عشر ثوان يعني معناته ال power بتكون في
+
+148
+00:14:49,810 --> 00:14:57,190
+الحالة هذه عشرة وات ف ال power اللى هو معدل
+
+149
+00:14:57,190 --> 00:15:01,290
+استهلاكي للطاقة إذا كان معدل استهلاكي سريع معناته
+
+150
+00:15:01,290 --> 00:15:05,130
+I need more power بدي أستهلك الطاقة بشكل سريع إذا
+
+151
+00:15:05,130 --> 00:15:09,740
+كان معدل استهلاكي بطيء معناتهال power هتكون اقل
+
+152
+00:15:09,740 --> 00:15:14,640
+عشان ذلك اذا بدي عزم كبير بروح بيحطه gearbox بيبطق
+
+153
+00:15:14,640 --> 00:15:19,720
+فبصير معدل استهلاك على output اقل فبستاخدك انا انا
+
+154
+00:15:19,720 --> 00:15:22,440
+بدي في الأخر عزم بستهلك طاقة ب .. ب .. ب .. ببطء
+
+155
+00:15:22,440 --> 00:15:30,800
+وبتالي بدي power اقل في
+
+156
+00:15:30,800 --> 00:15:39,120
+الممارسة العملية ال engine بيمارس او بيشتغلضد ال
+
+157
+00:15:39,120 --> 00:15:41,920
+mean resisting torque انا عندي mean resisting
+
+158
+00:15:41,920 --> 00:15:47,500
+torque المطلوب من ال engine انه يقاوم هذا او يتغلب
+
+159
+00:15:47,500 --> 00:15:51,540
+عليه و احنا حكينا ال resisting torque جاي من
+
+160
+00:15:51,540 --> 00:15:54,060
+الأحمال على السيارة الأحمال على السيارة ايش؟
+
+161
+00:15:54,060 --> 00:15:59,060
+الأحمال على السيارة الوزن .. وزنها ووزن اللي فيها
+
+162
+00:15:59,060 --> 00:16:03,500
+ايش كمان أحمال؟ الهواء الاحتكاك
+
+163
+00:16:07,590 --> 00:16:10,490
+اذى طالع اللى حكينا الوزن اللى انا فى عندى
+
+164
+00:16:10,490 --> 00:16:14,230
+rotating masses جوا انا بكون عندك ال .. ال crank
+
+165
+00:16:14,230 --> 00:16:16,990
+نفسها بتدور بعدين ال crank بتسلم ال clutch ال
+
+166
+00:16:16,990 --> 00:16:19,530
+clutch بيسلم gearbox ال gearbox بيسلم هو
+
+167
+00:16:19,530 --> 00:16:22,810
+differential فهيش شغلات بتدور عشان ادورها محتاج
+
+168
+00:16:22,810 --> 00:16:27,990
+لياش ل power او ل energy وفى شغلاء برضه الاحتكاك
+
+169
+00:16:27,990 --> 00:16:31,670
+بيكون العملية مش انه يعني مافيش احتكاك فى احتكاك
+
+170
+00:16:31,670 --> 00:16:36,810
+بيدا قام الاحتكاك فكل هذه أحمال يجب على المحرك انه
+
+171
+00:16:37,770 --> 00:16:42,890
+يقومها او يشيلها فال total resisting torque ناتج
+
+172
+00:16:42,890 --> 00:16:46,190
+عن هذه الأحمال وزي السيارة اذا انا طالع اطلع من
+
+173
+00:16:46,190 --> 00:16:50,270
+مقاومة الريح اللي هو ال energy to rotate masses و
+
+174
+00:16:50,270 --> 00:16:56,450
+ال friction المساحة
+
+175
+00:16:56,450 --> 00:17:02,430
+اللي هي هذه a small a capital F capital a اللي هي
+
+176
+00:17:02,430 --> 00:17:08,560
+اقل عن ال T meanتيمين في إياش في الزاوية اللي هو
+
+177
+00:17:08,560 --> 00:17:12,380
+ال torque في الزاوية بيعطينا إياش شغل هذا يمثل
+
+178
+00:17:12,380 --> 00:17:17,720
+الشغل المفذول against ال load against ال resisting
+
+179
+00:17:17,720 --> 00:17:21,300
+torque معناته ال load جاي من ال resisting torque
+
+180
+00:17:21,300 --> 00:17:27,220
+طبعا
+
+181
+00:17:27,220 --> 00:17:30,560
+هذا اللي جاي هذا ال resisting torque هذا ال
+
+182
+00:17:30,560 --> 00:17:32,360
+resisting torque
+
+183
+00:17:34,110 --> 00:17:41,170
+و هذا اللي جاي من عندى ال piston ل ال crank هذا ال
+
+184
+00:17:41,170 --> 00:17:46,090
+torque as a function of theta معناته لاحظوا فى بعض
+
+185
+00:17:46,090 --> 00:17:52,310
+الأحيان بيكون ال torque احنا حاكينا بيكون اعلى من
+
+186
+00:17:52,310 --> 00:17:57,890
+ال mean resisting اذا اعلى معناته انا ال engine او
+
+187
+00:17:57,890 --> 00:18:01,110
+ال crank موصلة ب flywheel ال engine موصلة ب
+
+188
+00:18:01,110 --> 00:18:01,570
+flywheel
+
+189
+00:18:13,400 --> 00:18:23,020
+عند هذه ال piston في
+
+190
+00:18:23,020 --> 00:18:26,460
+الآخر عند ال power جاية من عند ال piston هتتحول ل
+
+191
+00:18:26,460 --> 00:18:38,420
+torque على ال crank فيه انا بحط flywheel flywheel
+
+192
+00:18:38,420 --> 00:18:45,800
+flywheel عبارة عن جسم كتره كبير كترهكبير ال energy
+
+193
+00:18:45,800 --> 00:18:52,420
+بشكل عام بيستوى نص عند صورة معينة نص I Omega
+
+194
+00:18:52,420 --> 00:18:56,240
+تربيه صح معناته
+
+195
+00:18:56,240 --> 00:18:59,720
+انا بتحكم في كمية ال energy اللي بخزنها في ال
+
+196
+00:18:59,720 --> 00:19:07,640
+flywheel من خلال ال I ال I بتعتمد is a function of
+
+197
+00:19:07,640 --> 00:19:15,600
+mass و نص في القطر صحمعناته عشان ارفع قدرة ال
+
+198
+00:19:15,600 --> 00:19:19,980
+flywheel على التخزين يعني يا بزود طبعا تتناسب مع
+
+199
+00:19:19,980 --> 00:19:26,840
+ال mass و ال R تربية طبعا يا بزود ال mass او بزود
+
+200
+00:19:26,840 --> 00:19:33,580
+ال R او بزود التنين طبعا ال effect بتاعة تكبير نصف
+
+201
+00:19:33,580 --> 00:19:42,370
+القطر اعلى من ال massيعني لو كان ال radius عندي
+
+202
+00:19:42,370 --> 00:19:49,070
+خيار يعني ال radius بيكون عندى مثلا اتنين انش و
+
+203
+00:19:49,070 --> 00:19:55,050
+radius تاني اربعة انش مقدار هذه راح تكون اربعة على
+
+204
+00:19:55,050 --> 00:20:07,120
+اتنين تربيع اربعة يعني مجرد ان ضعفة ال radiusصارت
+
+205
+00:20:07,120 --> 00:20:10,240
+ال moment of inertia أربعة ضعف مجرد أن ضعف ال
+
+206
+00:20:10,240 --> 00:20:15,220
+radius صارت ال moment of inertia أربعة ضعف لكن لو
+
+207
+00:20:15,220 --> 00:20:20,300
+ضعفت ال mass بيصير انا ضعفت ال .. ال .. ال .. ال
+
+208
+00:20:20,300 --> 00:20:25,940
+energy بتاعة ال .. ال flywheel اضعف فانت تأثير نص
+
+209
+00:20:25,940 --> 00:20:34,940
+القطر ضعف تأثير او .. او ضعف تأثير ال .. بنفعش
+
+210
+00:20:34,940 --> 00:20:42,370
+احكي ضعفيعني ال I تتناسب
+
+211
+00:20:42,370 --> 00:20:52,930
+ترضي مع ال mass وال I تتناسب ترضي مع ال R² لأن
+
+212
+00:20:52,930 --> 00:21:01,530
+لو خلّيت نصف القطر تلت أضعاف تسعة الكتلة تلت أضعاف
+
+213
+00:21:01,530 --> 00:21:07,430
+تلتة تسعة تلتةفبنفعش احكي الضعيف انت اخدته حالة
+
+214
+00:21:07,430 --> 00:21:11,430
+خاصة فالصح انه بحكي ان ال R تتنسو تتنسو ترضي مع ال
+
+215
+00:21:11,430 --> 00:21:18,210
+M تتنسو تتنسو ترضي مع ال R ترضي يعني لما تكون ال
+
+216
+00:21:18,210 --> 00:21:22,410
+turning moment عندي is
+
+217
+00:21:22,410 --> 00:21:26,350
+positive يعني
+
+218
+00:21:26,350 --> 00:21:29,630
+عندي ال turning moment اللي جاء من ال engine هذي
+
+219
+00:21:29,630 --> 00:21:35,630
+أعلى من ال resisting torqueزي ما هو بين B وC بيكون
+
+220
+00:21:35,630 --> 00:21:41,050
+في عندي طاقة زيادة الطاقة الزيادة هتاخدها ال
+
+221
+00:21:41,050 --> 00:21:46,230
+flywheel معناته سرعتها هتزيد صح؟ سرعة ال flywheel
+
+222
+00:21:46,230 --> 00:21:50,930
+هتزيد في الحالة هذه ال crank shaft اكسلريات
+
+223
+00:21:50,930 --> 00:21:56,070
+هيتسارع و ال work is done by the steam or by the
+
+224
+00:21:56,070 --> 00:22:00,910
+fuel انا في شغل موضول من الوقود او من ال steam
+
+225
+00:22:05,430 --> 00:22:12,310
+لما في منطقة زي بين C و D الشغل او ال torque اللي
+
+226
+00:22:12,310 --> 00:22:18,250
+جاي من ال engine اقل من ال resisting طب
+
+227
+00:22:18,250 --> 00:22:24,430
+انا كيف هعوضه؟ من ون هاخده؟ من المخزن عندى في ال
+
+228
+00:22:24,430 --> 00:22:26,710
+flywheel معناه اتصارات ال flywheel لما اخد منها
+
+229
+00:22:26,710 --> 00:22:31,190
+هتقل فبصير retardation او بصير deceleration لل
+
+230
+00:22:31,190 --> 00:22:35,390
+crank shaftو ال work is done on the steam يعني ال
+
+231
+00:22:35,390 --> 00:22:39,590
+steam في الأول كان في ال .. بين B و C بيعمل شغل
+
+232
+00:22:39,590 --> 00:22:43,790
+بيعمل شغل بين C و D احنا بيعمل شغل على ال steam
+
+233
+00:22:43,790 --> 00:22:48,550
+طيب
+
+234
+00:22:48,550 --> 00:22:53,530
+خلنا
+
+235
+00:22:53,530 --> 00:23:00,680
+نعرف نعمل .. نعرف نبدأ نعمل شوية معدلاتT هو torque
+
+236
+00:23:00,680 --> 00:23:05,600
+on the crankshaft at any instant اللي جاي من إيش؟
+
+237
+00:23:05,600 --> 00:23:10,800
+من ال engine جاي من عندي ال piston هذا ال T ال T
+
+238
+00:23:10,800 --> 00:23:12,820
+يعني ال main resisting torque هذا ال main
+
+239
+00:23:12,820 --> 00:23:16,480
+resisting torque اللي هو اللي جاي عن الأحمال اللي
+
+240
+00:23:16,480 --> 00:23:21,100
+على ال engine أو على السيارة يعني نفترض اندي هذا
+
+241
+00:23:21,100 --> 00:23:24,560
+بيشغل سيارة ممكن يكون شغل إشي تاني صح؟بس على فرض
+
+242
+00:23:24,560 --> 00:23:28,980
+انه بيشغل سيارة بتكون ال teaming جاي من الأحمال
+
+243
+00:23:28,980 --> 00:23:33,060
+على السيارة اللي هي اللي هي جاي من مقامة الهواء من
+
+244
+00:23:33,060 --> 00:23:43,520
+الوزن من تحريك الكتل الدوارة من الاحتكاك نعم طبعا
+
+245
+00:23:43,520 --> 00:23:48,040
+في اللي هو ال axel الملحقات بتاعة السيارة الإضاءة
+
+246
+00:23:48,040 --> 00:23:52,520
+برضه تمثل ايش أحمال التبريد والتكييف يمثل برضه
+
+247
+00:23:52,520 --> 00:23:56,080
+أحمالفكل هذه كلها إيش؟ أحمال، يعني لما أنا أشغل
+
+248
+00:23:56,080 --> 00:24:00,360
+السيارة على التكييفيستي تسحب بنزين أكتر لأن الحمل
+
+249
+00:24:00,360 --> 00:24:03,980
+زاد، إذا أنا أشغال في الليل في إضاءة بقى، بكون
+
+250
+00:24:03,980 --> 00:24:07,780
+أشحن، بكون أسحب energy من البطارية، و البطارية إيش
+
+251
+00:24:07,780 --> 00:24:15,160
+بتكون؟ تشحن، مظبوط؟ طبعا، وزن، مع أن وزن السيارة،
+
+252
+00:24:15,160 --> 00:24:20,740
+وزن السيارة كلها بالحمل الحملاءإذا كان الفرق بين
+
+253
+00:24:20,740 --> 00:24:27,620
+ال T و ال T main positive فال flywheel تتسارع إذا
+
+254
+00:24:27,620 --> 00:24:31,380
+كانت T ناقص ال T main negative يعني ال torque اللي
+
+255
+00:24:31,380 --> 00:24:34,940
+جام ال engine أقل من الأحمال بيكون أن دي أنا بصير
+
+256
+00:24:34,940 --> 00:24:38,400
+أسحب من ال flywheel فال flywheel تتراجع بيصير ت
+
+257
+00:24:38,400 --> 00:24:44,980
+decelerate هذا ال turning moment diagram ل four
+
+258
+00:24:44,980 --> 00:24:49,540
+stroke internal combustion engineinternal
+
+259
+00:24:49,540 --> 00:24:54,300
+combustion engine
+
+260
+00:24:54,300 --> 00:24:57,120
+احنا حكينا في ال four stroke engine فيه أربع
+
+261
+00:24:57,120 --> 00:25:03,530
+strokes في السحبcompression بعدين هين بيصير ايش
+
+262
+00:25:03,530 --> 00:25:08,290
+اللي اللي هو ال working او ال ال ال power stroke
+
+263
+00:25:08,290 --> 00:25:12,890
+او ال expansion stroke كذا اسم ال power stroke او
+
+264
+00:25:12,890 --> 00:25:16,070
+ال working stroke او ال expansion stroke بعدين هين
+
+265
+00:25:16,070 --> 00:25:20,170
+بطرد الغازات المحترقة يعني اولش بسحب وقود و غاز
+
+266
+00:25:20,170 --> 00:25:25,950
+بعدين compression بعدين expansion بصير احتراق
+
+267
+00:25:25,950 --> 00:25:31,730
+بعدين بطرد الغازات لحظة ال power وين جايةفي ال
+
+268
+00:25:31,730 --> 00:25:34,250
+working هذه ال power المناطق ال power هذه لازم
+
+269
+00:25:34,250 --> 00:25:38,370
+تكون كافية عشان تغطي احتياجات ال other strokes
+
+270
+00:25:38,370 --> 00:25:45,250
+لازم تكون .. اه تفضل فليه كافي ال power يعني؟ اه
+
+271
+00:25:45,250 --> 00:25:51,650
+طبعا لازم تكون كافية تغطي كل الأربع strokes عشانك
+
+272
+00:25:51,650 --> 00:25:56,830
+انا بحط flywheel عشان اخزن واستفيد منها بقياش ايوة
+
+273
+00:25:56,830 --> 00:25:59,010
+انت اول ما تشغل السيارة ايش بتسويه؟
+
+274
+00:26:01,680 --> 00:26:04,520
+أول الشخصية اللى بتستعمل ال switch ال switch إيش
+
+275
+00:26:04,520 --> 00:26:11,520
+بيسوي؟ كيف بيحركها في الأول؟ في ال starter في مطور
+
+276
+00:26:11,520 --> 00:26:14,260
+على الكهربا بيلفها في الأول عشان يبدأ العملية
+
+277
+00:26:14,260 --> 00:26:18,660
+فبيسموها إيش starting up مستحيل تبدأ بدون ال
+
+278
+00:26:18,660 --> 00:26:22,760
+starter لأنه بدك في الأول تتحركها فانت اللى بتهدي
+
+279
+00:26:22,760 --> 00:26:28,600
+لثوانى بتشغل ال engine باستخدام مطور كهربا DC
+
+280
+00:26:28,600 --> 00:26:29,100
+motor
+
+281
+00:26:36,790 --> 00:26:42,290
+طيب لأن في حالة ال
+
+282
+00:26:42,290 --> 00:26:48,710
+suction stroke انا بكون أسحب شفط معناته هصير
+
+283
+00:26:48,710 --> 00:26:52,650
+negative pressure و الدليل انه بندفع الوقود و
+
+284
+00:26:52,650 --> 00:26:54,150
+الهواء لو مافيش negative pressure انا مابدخلش
+
+285
+00:26:54,150 --> 00:26:58,570
+الوقود و الهواء صح فبنزل تحت ال zero فبصير عندى
+
+286
+00:26:58,570 --> 00:26:59,130
+vacuum
+
+287
+00:27:01,690 --> 00:27:06,090
+في ال compression stroke انا بعمل شغل على مين؟
+
+288
+00:27:06,090 --> 00:27:13,670
+بعمل شغل على الوقود و الهواء، معناته انا بستنفذ من
+
+289
+00:27:13,670 --> 00:27:17,790
+الشغل، مظبوط؟ معناته بخش في ال negative برضه، في
+
+290
+00:27:17,790 --> 00:27:24,790
+ال power stroke الوقود هو بشتعل و بيعمللي اش،
+
+291
+00:27:24,790 --> 00:27:28,590
+بيعمللي شغل، بيعمل شغل على ال piston عشانك بيصير
+
+292
+00:27:28,590 --> 00:27:33,590
+في اش positive loop، بيصير في الموجةفي حالة ال
+
+293
+00:27:33,590 --> 00:27:38,690
+exhaust اللي هو طرد الغازات انا بعمل شغل على
+
+294
+00:27:38,690 --> 00:27:47,210
+الغازات فبقى طردها فبتكون دي negative loop نرجع
+
+295
+00:27:47,210 --> 00:27:49,970
+لل turning moment diagram بتاع اللي هو turning
+
+296
+00:27:49,970 --> 00:27:56,330
+moment diagram for two stroke engine اللي هو
+
+297
+00:27:56,330 --> 00:28:00,770
+double acting steam engine double acting steam
+
+298
+00:28:00,770 --> 00:28:01,110
+engine
+
+299
+00:28:07,780 --> 00:28:13,680
+طبعا في حالة ال steam engine عندى two strokes يعني
+
+300
+00:28:13,680 --> 00:28:18,940
+الدورة كاملة تلاتمية و ستين درجة في حالة ال four
+
+301
+00:28:18,940 --> 00:28:23,160
+stroke engine الدورة كاملة سبعمية و عشرين دورتين
+
+302
+00:28:23,160 --> 00:28:28,500
+كاملات تلاتمية و ستين درجة مقسمين لاربع كل واحدة
+
+303
+00:28:28,500 --> 00:28:34,960
+مية و تمانية درجةintake compression expansion
+
+304
+00:28:34,960 --> 00:28:41,240
+exhaust في حالة ال steam engine يكون عندى الدورة
+
+305
+00:28:41,240 --> 00:28:46,640
+360 درجة طيب
+
+306
+00:28:46,640 --> 00:28:56,000
+نتبع double acting steam engine نتبع بين نقطة a a
+
+307
+00:28:56,000 --> 00:28:56,440
+small
+
+308
+00:28:59,170 --> 00:29:06,370
+و P A و P من هنا لهنا لاحظوا
+
+309
+00:29:06,370 --> 00:29:11,870
+من A ل P ال
+
+310
+00:29:11,870 --> 00:29:16,750
+torque اللي جاي من ال engine أقل من ال torque
+
+311
+00:29:16,750 --> 00:29:21,910
+المطلوبأقل من ال torque المطلوب الشغل ال energy
+
+312
+00:29:21,910 --> 00:29:27,750
+المطلوب عشان اغطي ال T mean هتكون مساحة المستطيل A
+
+313
+00:29:27,750 --> 00:29:33,970
+small A capital B capital P small لكن الطاقة اللي
+
+314
+00:29:33,970 --> 00:29:40,230
+جاء من ال engine هي مساحة اللي هي بين A,B,P اللي
+
+315
+00:29:40,230 --> 00:29:45,610
+هو هذه المساحةبالظبط العجز عندي ايش المساحة هادئ
+
+316
+00:29:45,610 --> 00:29:52,170
+اللي هي a small a capital B هذا العجز لأن العجز
+
+317
+00:29:52,170 --> 00:29:59,070
+هاتبون هحصله ال engine شغال حاليا يعني تخطر موضوع
+
+318
+00:29:59,070 --> 00:30:03,110
+ال starting من ال flywheel معناته في المرحلة هادئ
+
+319
+00:30:03,110 --> 00:30:06,230
+اذا هاخد ال flywheel معناته سرعة ال flywheel هتمزل
+
+320
+00:30:06,230 --> 00:30:08,210
+طيب
+
+321
+00:30:09,990 --> 00:30:20,610
+في الفترة من P ل Q الطاقة المطلوبة اللي هي الطاقة
+
+322
+00:30:20,610 --> 00:30:28,090
+المطلوبة هي مساحة المستطيل P,B,C,Q هذا المطلوب انا
+
+323
+00:30:28,090 --> 00:30:32,430
+اكم باعطيه ال engine باعطيه المساحة هذه في زيادة
+
+324
+00:30:32,430 --> 00:30:39,940
+اللي هي المساحة P,B,C هذا زيادةبتخز ال flywheel
+
+325
+00:30:39,940 --> 00:30:44,640
+بتتصارع ال flywheel من
+
+326
+00:30:44,640 --> 00:30:50,760
+Q ل R الطاقة
+
+327
+00:30:50,760 --> 00:30:55,120
+المطلوبة عشان اغطي ال load مساحة المساطيل Q,C,D,R
+
+328
+00:30:55,120 --> 00:30:59,120
+اللي جامع ال engine المتاح عندي اللي هو المساحة
+
+329
+00:30:59,120 --> 00:31:04,740
+هذه والمساحة هذه العجز اللي هي المساحة اللي هي C,C
+
+330
+00:31:04,740 --> 00:31:11,030
+,Dباخد من flywheel ال flywheel هتت بطأ سرعتها من R
+
+331
+00:31:11,030 --> 00:31:19,470
+ل S الطاقة المطلوبة مساحة موسطيل D E S R المتاح من
+
+332
+00:31:19,470 --> 00:31:25,750
+ال engine اللي هو جاية R D D E S مع ان انا فيه
+
+333
+00:31:25,750 --> 00:31:32,910
+زيادة عن دي ايش D D Eبتخزين الفلاويل تتسارع كمان
+
+334
+00:31:32,910 --> 00:31:39,790
+مرة بعدين بين ال S و ال E بيكون الطاقة المطلوبة
+
+335
+00:31:39,790 --> 00:31:46,410
+اللي هي مساحة مستوطين S E F E الشغل المتاح من ال
+
+336
+00:31:46,410 --> 00:31:50,390
+engine اللي هو المساحة S E E اللي هي هذه العجز
+
+337
+00:31:50,390 --> 00:31:56,490
+اللي هو E F E فباخد الفلاويل ترجع تتباطئ الفلاويل
+
+338
+00:32:03,130 --> 00:32:07,490
+الان في واضح في تذبذب في الطاقة في fluctuation of
+
+339
+00:32:07,490 --> 00:32:12,590
+energy حوالين ال mean resisting torque طبعا في
+
+340
+00:32:12,590 --> 00:32:15,390
+fluctuation up and down يعني ال energy اللي جاي ال
+
+341
+00:32:15,390 --> 00:32:19,830
+energy بتكون بعض احيان تحت تحتالـ torque اللي جاي
+
+342
+00:32:19,830 --> 00:32:22,170
+من ال engine تحت ال resisting و بعض احيان بيكون
+
+343
+00:32:22,170 --> 00:32:27,630
+اعلى هنا اقل هنا اعلى هنا اقل ففي عندي fluctuation
+
+344
+00:32:27,630 --> 00:32:32,090
+او تذبذب لل torque اللي جاي من ال engine حوالين ال
+
+345
+00:32:32,090 --> 00:32:36,050
+main resisting torque او ال torque اللي جاي من ال
+
+346
+00:32:36,050 --> 00:32:41,250
+load فالمساحات
+
+347
+00:32:41,250 --> 00:32:48,950
+المساحات ناخد المساحة ديAAB عبارة عن energy
+
+348
+00:32:48,950 --> 00:32:57,830
+fluctuation of energy below المساحة BBC above CCD
+
+349
+00:32:57,830 --> 00:33:07,870
+below DDE above EEF below طبعا
+
+350
+00:33:07,870 --> 00:33:15,600
+متوقع متوقع احنا حكينا في المنطقة ها بين B و Cال
+
+351
+00:33:15,600 --> 00:33:18,580
+energy اللي جاية من ال engine في عندي زيادة في
+
+352
+00:33:18,580 --> 00:33:22,280
+الطاقة متوقع ان يكون ال engine أسرع سرعة يكون أكبر
+
+353
+00:33:22,280 --> 00:33:28,400
+سرعة عند Q عند Q متوقع لأن انا بضيف يعدي فهي تسارع
+
+354
+00:33:28,400 --> 00:33:32,720
+ال engine متوقع تكون السرعة أعلي عشان عند Q او عند
+
+355
+00:33:32,720 --> 00:33:39,620
+S برضه هين بضيف يا عند Q او عند S الآن
+
+356
+00:33:43,730 --> 00:33:50,950
+طبعا واضح بين P و Q انا بخزن بضيف لل energy ل ال
+
+357
+00:33:50,950 --> 00:33:55,070
+fly whale و بين R و S برضه انا بضيف energy لل fly
+
+358
+00:33:55,070 --> 00:34:01,210
+whale عند
+
+359
+00:34:01,210 --> 00:34:11,070
+P او R P ناخد R R واضح عندى لحظة من C ل Dعند هذا
+
+360
+00:34:11,070 --> 00:34:15,410
+فيه عجزة من اين هسحبه ال flywheel متوقع معناته
+
+361
+00:34:15,410 --> 00:34:18,610
+السرعة ان ال flywheel تكون minimum عند R تكون
+
+362
+00:34:18,610 --> 00:34:23,410
+minimum عند R او عند P P لانه جاية ادربالكوا هذا
+
+363
+00:34:23,410 --> 00:34:27,210
+دورة كاملة يعني هي تكمل يعني هذا C مع A بتكمل يعني
+
+364
+00:34:27,210 --> 00:34:31,690
+كأنا جاية من هنا C وA فهتكون minimum عند P او عند
+
+365
+00:34:31,690 --> 00:34:34,730
+R اللي هي ال flywheel speed
+
+366
+00:34:40,770 --> 00:34:43,090
+طبعا فى عندى ال maximum fluctuation of energy هو
+
+367
+00:34:43,090 --> 00:34:45,430
+difference between maximum and minimum energies ال
+
+368
+00:34:45,430 --> 00:34:47,590
+maximum fluctuation of energy هو الفرق بين ال
+
+369
+00:34:47,590 --> 00:34:53,310
+maximum و ال minimum انا
+
+370
+00:34:53,310 --> 00:34:57,350
+عندهين turning moment diagram ل some engine هدى
+
+371
+00:34:57,350 --> 00:35:02,230
+طبعا turning moment افترضية هذا هو الخط يمثل ال
+
+372
+00:35:02,230 --> 00:35:07,350
+main resisting torque وهذا يمثل ال fluctuation of
+
+373
+00:35:07,350 --> 00:35:10,050
+torque اللى جاى من ال engine
+
+374
+00:35:13,690 --> 00:35:22,410
+فالان المساحات اللي هي A1 وA2 وA3 وA4 وA5 تتمثل
+
+375
+00:35:22,410 --> 00:35:26,110
+تذبذب للطاقة above and below ال mean resisting
+
+376
+00:35:26,110 --> 00:35:33,250
+torque اللي هي A1 وA2 وA3 وA4 وA5 وA6 تتمثل تذبذب
+
+377
+00:35:33,250 --> 00:35:38,470
+للطاقة حوالين ال mean torque line
+
+378
+00:35:45,390 --> 00:35:53,690
+طبعا ال areas a1 و a3 و a5 تمثل تذبذب أعلى ال mean
+
+379
+00:35:53,690 --> 00:36:02,710
+resisting و ال a2 و ال a4 و ال a6 below خليني
+
+380
+00:36:02,710 --> 00:36:05,850
+افترض ان ال energy اللي في ال flywheel لما كان عند
+
+381
+00:36:05,850 --> 00:36:09,590
+نقطة a كانت تساوي E capital ال energy اللي كانت
+
+382
+00:36:09,590 --> 00:36:14,530
+الطاقة المخزنة في flywheelلما كنا عند A كانت
+
+383
+00:36:14,530 --> 00:36:20,770
+قيمتها E طيب عند B إيش هكون ساوى طاقتك؟ هتزود
+
+384
+00:36:20,770 --> 00:36:30,200
+عليها A واحدعند C هتطرح منها A2 عند D A3 عند E
+
+385
+00:36:30,200 --> 00:36:36,260
+هتطرح منها A4 عند F هتطرح منها A5 عند G هتطرح منها
+
+386
+00:36:36,260 --> 00:36:41,420
+A6 المعناته ال energy at B هي E زاد A1 عند C E زاد
+
+387
+00:36:41,420 --> 00:36:47,740
+A1 ناقص A2 عند D E زاد A1 معناه A2 زاد A3 و هكذا
+
+388
+00:36:47,740 --> 00:36:51,220
+طبعا ال cycle تتكرر بعد ذلك
+
+389
+00:36:54,250 --> 00:37:00,530
+لأ خد عمل فرضية أن ال energy عند B كانت maximum ال
+
+390
+00:37:00,530 --> 00:37:04,710
+maximum energy كانت عند B و ال minimum energy كانت
+
+391
+00:37:04,710 --> 00:37:12,850
+عند E يعني ال E max هي عند B و ال E minimum كانت
+
+392
+00:37:12,850 --> 00:37:16,790
+عند E هي ال energy عند B اللي هي ال maximum و ال
+
+393
+00:37:16,790 --> 00:37:23,030
+energy عند E هي ال minimumبعد ذاته انا فى عندى
+
+394
+00:37:23,030 --> 00:37:25,290
+maximum value و فى minimum value المعنى هو ال
+
+395
+00:37:25,290 --> 00:37:28,590
+maximum fluctuation هيكون ال maximum minus ال
+
+396
+00:37:28,590 --> 00:37:32,090
+minimum هتكون ال maximum fluctuation of energy E
+
+397
+00:37:32,090 --> 00:37:34,530
+بيستوى ال maximum energy minus ال minimum energy
+
+398
+00:37:34,530 --> 00:37:38,390
+اللى هى ال maximum اللى هى E زيادة A1 minus E
+
+399
+00:37:38,390 --> 00:37:42,610
+زيادة A1 minus A2 زيادة A3 minus A4 بتطلع A2 minus
+
+400
+00:37:42,610 --> 00:37:45,150
+A3 زيادة A4 طبعا هذا ايش افتراض لحتى اللحظة
+
+401
+00:37:48,720 --> 00:37:52,200
+هنعرف ما هو coefficient of fluctuation of energy
+
+402
+00:37:52,200 --> 00:37:57,020
+معامل التذبذب في الطاقة معامل التذبذب في الطاقة
+
+403
+00:37:57,020 --> 00:38:02,700
+بيساوي ال maximum fluctuation of energy على ال
+
+404
+00:38:02,700 --> 00:38:09,300
+work done per cycle ال work done per cycle بيمثل
+
+405
+00:38:09,300 --> 00:38:12,620
+مساحة المستطيل اللي تحت ال mean resisting curve
+
+406
+00:38:12,620 --> 00:38:23,030
+اللي هي T mean في ال thetaهذا هو المساحة هذه بتمثل
+
+407
+00:38:23,030 --> 00:38:28,310
+ال work done during the cycle المعامل التذبذب في
+
+408
+00:38:28,310 --> 00:38:31,450
+الطاقة بالساوية ال maximum fluctuation of energy
+
+409
+00:38:31,450 --> 00:38:33,690
+على ال work done per cycle ال work done per cycle
+
+410
+00:38:33,690 --> 00:38:38,990
+هو T mean في theta ال theta ال angle turned in one
+
+411
+00:38:38,990 --> 00:38:42,740
+revolutionطبعا ال theta بتكون سوى اتنين باى يعني
+
+412
+00:38:42,740 --> 00:38:46,440
+تلت مية و ستين درجة في حالة two stroke engine او
+
+413
+00:38:46,440 --> 00:38:49,760
+steam engine ال theta بتكون سوى اربع باى سبع مية و
+
+414
+00:38:49,760 --> 00:38:53,900
+عشرين درجة في حالة four stroke engine اربع stroke
+
+415
+00:38:53,900 --> 00:38:56,920
+و واحدة مية و تمانية مية و تمانية و اربعة سبع مية
+
+416
+00:38:56,920 --> 00:39:03,560
+و عشرين في النهاية ال power ايش بتساوي torque فى
+
+417
+00:39:03,560 --> 00:39:08,570
+omega ال power بتساوي torqueفى omega يعني ال
+
+418
+00:39:08,570 --> 00:39:15,810
+torque ايش يساوي power على omega ال T mean بيساوي
+
+419
+00:39:15,810 --> 00:39:21,830
+ال power بتاعة ال engine ال
+
+420
+00:39:21,830 --> 00:39:28,390
+T mean بيساوي ال power لل engine على omega بيساوي
+
+421
+00:39:28,390 --> 00:39:36,040
+ال power لل engine ال omega عبارة عن اتنين باىفي
+
+422
+00:39:36,040 --> 00:39:41,720
+عدد دورات اللي هي على ستين يعني
+
+423
+00:39:41,720 --> 00:39:47,080
+سيكون يساوي ستين سيصبح في ال bus ستين ال power على
+
+424
+00:39:47,080 --> 00:39:56,500
+اتنين باى فعلا اللي هي المعادلة دي هو
+
+425
+00:39:56,500 --> 00:40:01,380
+حاطط general equation ال work done per cycle بسواة
+
+426
+00:40:01,380 --> 00:40:08,010
+P في ستين على N smallان small بيستوى ال number of
+
+427
+00:40:08,010 --> 00:40:14,490
+working strokes per minute الان بيستوى ان capital
+
+428
+00:40:14,490 --> 00:40:21,830
+في حالة steam engine او two stroke engine الان
+
+429
+00:40:21,830 --> 00:40:24,930
+small بيستوى ان على اتنين in case of four stroke
+
+430
+00:40:24,930 --> 00:40:31,890
+engine لان في حالة ال two stroke engine بيصير عندي
+
+431
+00:40:31,890 --> 00:40:40,010
+power ضعفال four stroke صح؟ في حالة ال ال ال ال ال
+
+432
+00:40:40,010 --> 00:40:40,430
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+433
+00:40:40,430 --> 00:40:41,010
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+434
+00:40:41,010 --> 00:40:41,850
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+435
+00:40:41,850 --> 00:40:42,330
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+436
+00:40:42,330 --> 00:40:44,670
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+437
+00:40:44,670 --> 00:40:47,170
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+438
+00:40:47,170 --> 00:40:47,510
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+439
+00:40:47,510 --> 00:40:47,510
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+440
+00:40:47,510 --> 00:40:47,510
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+441
+00:40:47,510 --> 00:40:47,510
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+442
+00:40:47,510 --> 00:40:47,510
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+443
+00:40:47,510 --> 00:40:47,510
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+444
+00:40:47,510 --> 00:40:52,790
+ال ال ال ال
+
+445
+00:40:52,790 --> 00:40:52,790
+ال
+
+446
+00:40:56,850 --> 00:41:00,370
+في حالة two stroke internal combustion engine او
+
+447
+00:41:00,370 --> 00:41:04,010
+في حالة steam engine بستوي N capital اللي هي ال
+
+448
+00:41:04,010 --> 00:41:07,830
+RPM على اتنين في حالة four stroke internal
+
+449
+00:41:07,830 --> 00:41:13,650
+combustion engine طبعا
+
+450
+00:41:13,650 --> 00:41:18,510
+متوقع كل ما زود ال number of cylinders التذبذب
+
+451
+00:41:18,510 --> 00:41:20,510
+حوالين ال main line يقل ولا يزيد
+
+452
+00:41:26,530 --> 00:41:31,210
+كل مزود قعدة ال cylinders تذبذب
+
+453
+00:41:31,210 --> 00:41:35,690
+و حتزيد ولا هتقل يعني
+
+454
+00:41:35,690 --> 00:41:38,090
+انا ممكن اعتبر اجابتكوا صحيح انا ممكن اعتبرها خطأ
+
+455
+00:41:38,090 --> 00:41:41,110
+حسب انتوا ما اعتبروها صحيح علي اسم اللي حكيته انه
+
+456
+00:41:41,110 --> 00:41:49,490
+حتزيد اذا
+
+457
+00:41:49,490 --> 00:41:55,790
+والله انا حكيت انه بدي اشغل الاربع cylindersو
+
+458
+00:41:55,790 --> 00:41:59,490
+ترتيب ال strokes نفسهم في الأربعة يعني يعني ال
+
+459
+00:41:59,490 --> 00:42:02,490
+power stroke هي نفسها نفس بيصير عند نفس اللحظة ال
+
+460
+00:42:02,490 --> 00:42:05,210
+power stroke في الأربعة معناته بيكون ال variation
+
+461
+00:42:05,210 --> 00:42:09,610
+تذبد في ال energy عالي جدا و هذا سيء جدا صح؟ لكن
+
+462
+00:42:09,610 --> 00:42:13,330
+لو خلت زاوية مش كلهم بيصير ال power stroke مع بعض
+
+463
+00:42:13,330 --> 00:42:18,410
+يعني بخلي زاوية بينهم معناته انا بوزع ال power و
+
+464
+00:42:18,410 --> 00:42:21,530
+بالتالي بقلل ايش ال fluctuation او تذبده
+
+465
+00:42:25,410 --> 00:42:28,850
+على أرض الواقع أنا بخليه زاوية، بخليهش كل .. يعني
+
+466
+00:42:28,850 --> 00:42:32,230
+عندي .. عندي مثلا أربعة سيلندر، بخليهش ال power
+
+467
+00:42:32,230 --> 00:42:35,850
+stroke لسيلندر أول والتان والتاتر و الرابع مع بعض
+
+468
+00:42:36,760 --> 00:42:40,780
+بخلي واحدة .. واحدة مثلا يعني هي stroke، التانية
+
+469
+00:42:40,780 --> 00:42:44,140
+stroke، التانية stroke، فانا بوزع .. بفرد ال power
+
+470
+00:42:44,140 --> 00:42:47,680
+على الأربع cycles عشان كل ما بزيد ال number of
+
+471
+00:42:47,680 --> 00:42:51,180
+cylinders كل ما ال coefficient of fluctuation of
+
+472
+00:42:51,180 --> 00:42:54,860
+energy بقل، انا بهمن يكون ال coefficient of
+
+473
+00:42:54,860 --> 00:43:00,880
+fluctuation of energy as minimum as I canفي حال
+
+474
+00:43:00,880 --> 00:43:03,780
+single cylinder double acting steam engine ال CE
+
+475
+00:43:03,780 --> 00:43:09,720
+بيساوي 0.21 طبعا هذه الارقام typical ال cross
+
+476
+00:43:09,720 --> 00:43:14,000
+compound steam engine 0.096 single cylinder single
+
+477
+00:43:14,000 --> 00:43:19,520
+acting four stroke gas engine 1.93 هذا سلندر واحدة
+
+478
+00:43:19,520 --> 00:43:26,980
+four stroke single acting 0.066 six cylinder يعني
+
+479
+00:43:26,980 --> 00:43:29,260
+صار من six cylinder single acting four stroke
+
+480
+00:43:29,260 --> 00:43:32,600
+لاحظوا أيشpoint O تلاتة واحد يعني كان عندي هين
+
+481
+00:43:32,600 --> 00:43:37,160
+cylinder واحدة كان ال coefficient of fluctuation
+
+482
+00:43:37,160 --> 00:43:40,500
+energy واحد point ستة تلاتة هين اربع cylinder
+
+483
+00:43:40,500 --> 00:43:43,580
+point O ستة ستة ستة ستة cylinder point O تلاتة
+
+484
+00:43:43,580 --> 00:43:48,560
+واحد لو عملت تمانى cylinder بيختلف بنزل اكتر برضه
+
+485
+00:43:48,560 --> 00:43:52,040
+لو عملت اتناشه انك السيارات مثلا كدلك السيارات ال
+
+486
+00:43:52,040 --> 00:44:00,040
+Toyota و Toyota ZX بتسمعش صوتهالأن بيكون عادة ال
+
+487
+00:44:00,040 --> 00:44:06,680
+cylinders كبير فيها، مافيش فيها fluctuation double
+
+488
+00:44:06,680 --> 00:44:12,020
+acting steam
+
+489
+00:44:12,020 --> 00:44:18,620
+engine في أنواع تانية، ماحكيتك هي single cylinder،
+
+490
+00:44:18,620 --> 00:44:22,210
+single acting، four strokeيعني بيصير الضغط في
+
+491
+00:44:22,210 --> 00:44:25,270
+اتجاه واحد double acting في اتجاه هنا فهمت على اي
+
+492
+00:44:25,270 --> 00:44:27,630
+كده يعني بيعمل power يعني بيزيد ال power في الحالة
+
+493
+00:44:27,630 --> 00:44:32,170
+هذه ال air compression engine معظمها بيكون single
+
+494
+00:44:32,170 --> 00:44:36,410
+acting خش على اليوتيوب هتشوف animations شوف single
+
+495
+00:44:36,410 --> 00:44:41,030
+cylinder single acting وشوف single cylinder double
+
+496
+00:44:41,030 --> 00:44:46,750
+acting for stroke هتشوف فيديوهات عليها compound خش
+
+497
+00:44:46,750 --> 00:44:49,690
+برضه على اليوتيوب شوف هتشوف فيديوهات كتير عن ال
+
+498
+00:44:49,690 --> 00:44:59,840
+compoundcross compound steam engine في
+
+499
+00:44:59,840 --> 00:45:02,720
+اي سؤال؟ اعطيكوا العافية
+
diff --git a/PL9fwy3NUQKwa0nXiCdyQcTW4hWDLTGpDb/Zy0B1BX3PHA_postprocess.srt b/PL9fwy3NUQKwa0nXiCdyQcTW4hWDLTGpDb/Zy0B1BX3PHA_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..830e07895cb32780a9b1a584bda23fdb957a278f
--- /dev/null
+++ b/PL9fwy3NUQKwa0nXiCdyQcTW4hWDLTGpDb/Zy0B1BX3PHA_postprocess.srt
@@ -0,0 +1,2048 @@
+1
+00:00:05,260 --> 00:00:07,800
+بسم الله الرحمن الرحيم السلام عليكم ورحمة الله
+
+2
+00:00:07,800 --> 00:00:12,240
+وبركاته، اليوم هنكمل في مادة نظرية الألات،
+
+3
+00:00:12,240 --> 00:00:15,220
+المحاضرات السابقة كنا نحكي عن ال cams and
+
+4
+00:00:15,220 --> 00:00:21,200
+followers، اتعلمنا كيف نرسم ال profile ال cam من
+
+5
+00:00:21,200 --> 00:00:25,260
+خلال معرفتنا لحركة ال followerده أصلا الحركات اللي
+
+6
+00:00:25,260 --> 00:00:29,520
+هي ال follower بتتحرك ب uniform velocity و simple
+
+7
+00:00:29,520 --> 00:00:33,400
+harmonic motion يعني باختصار معرفتك لحركة ال
+
+8
+00:00:33,400 --> 00:00:37,860
+follower ممكن تعرف شكل الكامة اللي هتحرك ال
+
+9
+00:00:37,860 --> 00:00:41,640
+follower اليوم في كامات اللي لها أشكال خاصة اللي
+
+10
+00:00:41,640 --> 00:00:44,440
+هندرسها أول واحدة اللي هي tangent cam with
+
+11
+00:00:44,440 --> 00:00:49,700
+reciprocating roller follower الكام
+
+12
+00:00:49,700 --> 00:00:51,180
+هذه هي الكام
+
+13
+00:01:19,920 --> 00:01:27,120
+هذا مركز دوران الكم هو
+
+14
+00:01:27,120 --> 00:01:30,400
+الكم
+
+15
+00:01:30,400 --> 00:01:33,280
+مكونة من يعني طبعا هذا هو ده هذا ال minimum radius
+
+16
+00:01:33,280 --> 00:01:44,740
+للكم في الفترة من نقطة P ل E بيكون الكامة في حالة
+
+17
+00:01:44,740 --> 00:01:50,820
+dwellمن P ل A بتكون الدول يعني لو افرضنا بتدور ال
+
+18
+00:01:50,820 --> 00:01:55,720
+cam بالشكل هذا هذا
+
+19
+00:01:55,720 --> 00:02:04,320
+ال nose ال minimum radius لل cam اللي هو R1 هذا ال
+
+20
+00:02:04,320 --> 00:02:13,240
+minimum radius لل cam وفي ال nose radius R3
+
+21
+00:02:15,070 --> 00:02:19,150
+طبعا انا هنا عندي follower من النوع roller type
+
+22
+00:02:19,150 --> 00:02:23,470
+follower ال follower في البداية يبدأ مثلا من
+
+23
+00:02:23,470 --> 00:02:29,330
+النقطة هذه ال
+
+24
+00:02:29,330 --> 00:02:33,030
+radius بتاعه R2
+
+25
+00:02:49,950 --> 00:02:55,210
+الزاوية Alpha لحد
+
+26
+00:02:55,210 --> 00:03:10,350
+هنا الكتير اصلا ما غلط هذا الزاوية Alpha طبعا
+
+27
+00:03:10,350 --> 00:03:13,900
+هذا ال radial lineهذه تاني الطين وهذه الزاوية
+
+28
+00:03:13,900 --> 00:03:24,240
+العمودية هذه
+
+29
+00:03:24,240 --> 00:03:31,060
+برضه هتكون الزاوية الفة
+
+30
+00:03:31,060 --> 00:03:35,560
+طبعا ال profile بتاعها قطع دائري نصف قطر R واحد
+
+31
+00:03:35,560 --> 00:03:42,000
+قطع مستقيمة قطع دائري نصف قطر R تلاتة قطع عيش
+
+32
+00:03:42,750 --> 00:03:49,610
+مستقيمة يعني مكون من واحدة تنتين تلاتة اربع قطع
+
+33
+00:03:49,610 --> 00:03:54,910
+الزاوية
+
+34
+00:03:54,910 --> 00:04:03,030
+في ال roller عند النقطة هذه
+
+35
+00:04:11,640 --> 00:04:19,060
+اللي هنا هي نهاية .. نهاية القطع المستقيمة هذه
+
+36
+00:04:19,060 --> 00:04:23,020
+نهاية القطع المستقيمة يعني بيكون هت تنجل لنهاية
+
+37
+00:04:23,020 --> 00:04:30,240
+القطع المستقيمة هنا نقطة دي الزاوية هذه هتكون اللي
+
+38
+00:04:30,240 --> 00:04:36,460
+جاي من مركز ال roller اسمه
+
+39
+00:04:36,460 --> 00:04:36,980
+الزاوية
+
+40
+00:04:50,000 --> 00:04:58,660
+five طبعا ال tip ده
+
+41
+00:04:58,660 --> 00:05:04,700
+لأن الحركة اللي ممكن نجلسها مرحلتين او او نحكي هي
+
+42
+00:05:04,700 --> 00:05:05,160
+مرحلة
+
+43
+00:05:08,240 --> 00:05:12,800
+اللي هي بيكون دي dwell ال roller او ال floor مابت
+
+44
+00:05:12,800 --> 00:05:19,560
+برتفاع بعدين هيتحرك على قطع مستقيم هاتنين بعدين
+
+45
+00:05:19,560 --> 00:05:24,000
+على قطع دائرية ال nose تلاتة بعدين على قطع مستقيم
+
+46
+00:05:24,000 --> 00:05:30,980
+بعدين تتكرر ال دورة at
+
+47
+00:05:30,980 --> 00:05:33,960
+any location بين بداية الحركة على القطع المستقيم
+
+48
+00:05:33,960 --> 00:05:36,640
+بين E و G
+
+49
+00:05:42,920 --> 00:05:49,460
+هذا any location هاي ال floor any location على
+
+50
+00:05:49,460 --> 00:05:58,140
+المنطقة المستقيمة هذا نقطة c الزاوية
+
+51
+00:05:58,140 --> 00:06:03,140
+هذه هتكون
+
+52
+00:06:03,140 --> 00:06:06,660
+theta
+
+53
+00:06:06,660 --> 00:06:10,240
+الزاوية theta
+
+54
+00:06:16,870 --> 00:06:28,910
+هذه نقطة K هذه H هذه O هذه Q
+
+55
+00:06:28,910 --> 00:06:35,830
+هذه
+
+56
+00:06:35,830 --> 00:06:40,610
+F المهم
+
+57
+00:06:40,610 --> 00:06:48,150
+هو احنا هندرس الحركةع القطع المستقيمة، هذه أول
+
+58
+00:06:48,150 --> 00:06:53,930
+دراسة، بعدين حنص الحركة على ال nose، حنص الحركة
+
+59
+00:06:53,930 --> 00:07:00,410
+على ال nose، بعدين طبعا إذا كان هو صعود من هنا ل
+
+60
+00:07:00,410 --> 00:07:03,750
+هنا، صعود، نفس الشي هكوناش؟ هبوط
+
+61
+00:07:11,400 --> 00:07:17,400
+ال X هتكون OC-OB
+
+62
+00:07:17,400 --> 00:07:21,540
+الان
+
+63
+00:07:21,540 --> 00:07:26,780
+احنا حكينا في الفترة من P ل E مافي له حركة ال
+
+64
+00:07:26,780 --> 00:07:30,760
+follower بيكون في حالة dual معناته ال reference
+
+65
+00:07:30,760 --> 00:07:39,350
+عنده معناته لما صار هنا المسافة هذه أشملهازادت
+
+66
+00:07:39,350 --> 00:07:47,470
+..معناته ال X هتساوي OC-
+
+67
+00:07:47,470 --> 00:07:54,390
+OB ال
+
+68
+00:07:54,390 --> 00:08:04,370
+X هتساوي OC- OB لأن
+
+69
+00:08:04,370 --> 00:08:06,650
+طبعا ال OB هتكون
+
+70
+00:08:10,500 --> 00:08:19,660
+R واحد زاد R اتنين ال
+
+71
+00:08:19,660 --> 00:08:28,740
+O C زي ما انتوا شايفين شايف المثلث O B C ال
+
+72
+00:08:28,740 --> 00:08:32,760
+O C ايش يستوي O
+
+73
+00:08:32,760 --> 00:08:40,390
+B على cosine theta صح؟هذا المثلث هذا قائم الزاوية
+
+74
+00:08:40,390 --> 00:08:47,410
+OB بيستوى OC Cos θ صح؟ معناته OC بيستوى OB على Cos
+
+75
+00:08:47,410 --> 00:08:55,270
+θ هتكون هذه تستوى OB على Cos θ minus OB يعني هتكون
+
+76
+00:08:55,270 --> 00:09:02,610
+سواء OB في واحد على Cos θ minus واحد ال OB اللي
+
+77
+00:09:02,610 --> 00:09:05,970
+احنا حاولينه R واحد زاد R اتنين
+
+78
+00:09:09,110 --> 00:09:19,630
+فى cos θ على 1 minus cos θ هدى
+
+79
+00:09:19,630 --> 00:09:22,990
+ال displacement للفلور معناه السرعة بتاعة الفلور
+
+80
+00:09:22,990 --> 00:09:33,210
+شو تساوي ذى دي اكس by دى تى ال chain rule دى اكس
+
+81
+00:09:33,210 --> 00:09:39,740
+by دى ثيتا فى دى ثيتا by دى تىالـ θ بتحكي عن ال
+
+82
+00:09:39,740 --> 00:09:43,660
+rotation بتاع الكم دي ثتا بتحكي عن أمجا بتاعة الكم
+
+83
+00:09:43,660 --> 00:09:51,580
+يعني هتكون أمجا في dx دي ثتا هاي اكس بيبقى دي اكس
+
+84
+00:09:51,580 --> 00:09:55,980
+بيبقى دي ثتا وان هو جيه بقياش ال V بعد ال
+
+85
+00:09:55,980 --> 00:10:04,400
+acceleration هتكون سوى dv على dt سوى dv على d
+
+86
+00:10:04,400 --> 00:10:16,100
+thetaفى d θ على d t اللى هى هتكون omega dv by d θ
+
+87
+00:10:16,100 --> 00:10:24,520
+بعمل الاشتقاق وبحسب ال V وبحسب ال A وبحسبه على
+
+88
+00:10:24,520 --> 00:10:29,800
+المعادلات التارية هى
+
+89
+00:10:29,800 --> 00:10:30,600
+ال V هتكون
+
+90
+00:10:33,620 --> 00:10:41,700
+وميجا في R واحد زي R اتنين في sin ثتا على cos
+
+91
+00:10:41,700 --> 00:10:47,460
+تربيع ثتا و ال acceleration هتكون omega square
+
+92
+00:10:47,460 --> 00:10:56,800
+هتكون
+
+93
+00:10:56,800 --> 00:11:03,020
+سواء omega square في R واحد زي R اتنين
+
+94
+00:11:23,290 --> 00:11:29,450
+طبعا طول ما في ال دول
+
+95
+00:11:33,590 --> 00:11:37,530
+بتحركش ال follower صح؟ معناته السرعة بتكون zero
+
+96
+00:11:37,530 --> 00:11:42,230
+يعني معناته كل ما لها بتزيد بتكون maximum في نهاية
+
+97
+00:11:42,230 --> 00:11:49,570
+القطر المستقيم لما theta ساوة five معناته V بيساوة
+
+98
+00:11:49,570 --> 00:12:04,620
+V max when theta بتساوة five يعني V maxهتكون Omega
+
+99
+00:12:04,620 --> 00:12:13,980
+في R واحد زاد R اتنين في Sine فيه على Cos Square
+
+100
+00:12:13,980 --> 00:12:20,080
+فيه اصلا في البداية لو حطت ثتا سفر يكون الصراحي
+
+101
+00:12:20,080 --> 00:12:28,760
+يستوى صفر Sine Zero Zero و Cos واحد ال
+
+102
+00:12:28,760 --> 00:12:29,340
+acceleration
+
+103
+00:12:34,140 --> 00:12:40,700
+الـ acceleration اللي
+
+104
+00:12:40,700 --> 00:12:47,600
+عند ال a minimum عند
+
+105
+00:12:47,600 --> 00:12:55,520
+ال a minimum ال
+
+106
+00:12:55,520 --> 00:12:58,760
+a minimum هتكون ساوية لو أعوضت عند theta
+
+107
+00:13:04,570 --> 00:13:10,390
+بزيرو اتنين ناقص واحد واحد على واحد كمسة omega
+
+108
+00:13:10,390 --> 00:13:14,770
+square في
+
+109
+00:13:14,770 --> 00:13:23,310
+R واحد زائد R اتنين و A max لما نتعود عن theta
+
+110
+00:13:23,310 --> 00:13:27,850
+بفاي نعم
+
+111
+00:13:30,860 --> 00:13:33,300
+لأ ال .. ال .. ال .. ال five مش في ضروره تكون ناشي
+
+112
+00:13:33,300 --> 00:13:37,240
+اسمه اه هتكون ال a max او a minus of r واحد زرعه
+
+113
+00:13:37,240 --> 00:13:41,540
+اتنين واضح انه هذه اكبر ان هذه لأن ده ال cosine ال
+
+114
+00:13:41,540 --> 00:13:47,600
+bound بتاعتها ايش اكتر اشي واحد بيجيب صح كبيرها
+
+115
+00:13:47,600 --> 00:13:52,040
+واحد فمعناته في أسوأ الاحتمال هتكون نفس هذه اي ..
+
+116
+00:13:52,040 --> 00:13:56,160
+اي شي تاني بالول واحد هتكون هذه اكبر ان واحد وهذا
+
+117
+00:13:56,160 --> 00:13:58,740
+زرعه واحد معناته هذه ايش ال max
+
+118
+00:14:03,070 --> 00:14:09,110
+هذا الحركة على القطع المستقيم الحركة على القطع على
+
+119
+00:14:09,110 --> 00:14:23,690
+الـ nose أنا
+
+120
+00:14:23,690 --> 00:14:32,350
+عندي هذه نقطة A هذه
+
+121
+00:14:32,350 --> 00:14:51,800
+Eهذه P طبعا هذه R1 طبعا
+
+122
+00:14:51,800 --> 00:14:57,040
+ال alpha زي هذه ال alpha لحد هنا هذه alpha
+
+123
+00:15:05,380 --> 00:15:09,300
+هو بعد ال reference عنده بعد ال reference من قمة
+
+124
+00:15:09,300 --> 00:15:16,300
+ال nodes مسمى ال variable عنده مسمى theta 1 هذا
+
+125
+00:15:16,300 --> 00:15:22,280
+theta 1 يعني theta 1 بالساوية zero لما نكون ال
+
+126
+00:15:22,280 --> 00:15:27,360
+roller عند قمة ال nodes من هنا ل هنا طبعا ال theta
+
+127
+00:15:27,360 --> 00:15:30,740
+تتغير من هنا ل هنا يعني هتكون
+
+128
+00:15:33,450 --> 00:15:40,610
+ثتا واحد لأ انا هاكول عن دي المعنى هو ال X لحظة
+
+129
+00:15:40,610 --> 00:15:47,990
+ال reference عندي اللي هو OG OG وهو
+
+130
+00:15:47,990 --> 00:15:59,750
+اي value تانية O D ال X بتاعتها ايش هتكون OG minus
+
+131
+00:15:59,750 --> 00:16:07,990
+O D واضح ان O Dشكلها أقل من ال OG صح؟
+
+132
+00:16:07,990 --> 00:16:12,630
+الان ال OG بين ال center و ال center هذه بسميها
+
+133
+00:16:12,630 --> 00:16:22,690
+المسافة R هذه
+
+134
+00:16:22,690 --> 00:16:30,110
+R ال OG بالساوية
+
+135
+00:16:30,110 --> 00:16:38,580
+اللي هو ال OKزاد ال KG ال OK زاد
+
+136
+00:16:38,580 --> 00:16:46,740
+ال KG ال OK اللي هي HR وال
+
+137
+00:16:46,740 --> 00:16:51,320
+KG ال nose radius زاد ال radius بتاع ال roller
+
+138
+00:16:51,320 --> 00:16:57,460
+يعني هيكون R2 زاد R2 .. R2 زاد
+
+139
+00:16:57,460 --> 00:17:07,740
+R3 هو بيسميهم هدولبسميه L اللي هي المسافة في هذه
+
+140
+00:17:07,740 --> 00:17:18,820
+اللي
+
+141
+00:17:18,820 --> 00:17:26,780
+احنا عبارنا عن OJ ضارل عندي ال O D ال O D راح عمل
+
+142
+00:17:26,780 --> 00:17:27,220
+عمودي
+
+143
+00:17:47,260 --> 00:17:52,140
+الـ O D بالساوية
+
+144
+00:17:52,140 --> 00:17:58,380
+الـ O A زائد
+
+145
+00:17:58,380 --> 00:18:06,080
+الـ A D طيب
+
+146
+00:18:06,080 --> 00:18:10,600
+حاجة زاوية ثتا واحد اخد المثلث
+
+147
+00:18:14,950 --> 00:18:22,070
+oak اللي هو الوطر بتاعه ok و عند الضلع oa ال oa
+
+148
+00:18:22,070 --> 00:18:33,610
+بيشو يساوي ال oa بيساوي ال R cos θ 1 صح هذا الوطر
+
+149
+00:18:33,610 --> 00:18:42,250
+هذا oa بيساوي ال R cos θ 1 زاد
+
+150
+00:18:45,170 --> 00:18:51,510
+الـ A D أخد المثلث هذا يسوى
+
+151
+00:18:51,510 --> 00:19:05,250
+D K Cos Beta يعني هتكون R Cos Theta 1 زاد D K مو
+
+152
+00:19:05,250 --> 00:19:11,490
+هذا زاد هذا اللي هي L هتكون صح اللي هي R 2 زاد R 2
+
+153
+00:19:11,490 --> 00:19:18,410
+اللي هي L Cosبيتا الان ممكن نوجه علاقة بين بيتا
+
+154
+00:19:18,410 --> 00:19:24,430
+وثيتا واحد اتضلع
+
+155
+00:19:24,430 --> 00:19:29,950
+اك مع
+
+156
+00:19:29,950 --> 00:19:37,310
+وجه مثلث هذا بيكون ابقى عن R sin theta واحد صح و
+
+157
+00:19:37,310 --> 00:19:44,190
+برضه بيكون ساوي L sin beta معناته sin beta
+
+158
+00:19:47,360 --> 00:19:58,160
+بتساوي R على L Sine Theta واحد هدق أنا شي تاني نفس
+
+159
+00:19:58,160 --> 00:20:06,800
+الفكرة يعني طيب معناته Cos Beta Sine تربيع زي Cos
+
+160
+00:20:06,800 --> 00:20:14,580
+تربيع ساو واحد معناته Cos Beta هتكون جدر التربيعي
+
+161
+00:20:17,530 --> 00:20:24,830
+لواحد minus R squared عالي square Sine square ثتا
+
+162
+00:20:24,830 --> 00:20:34,170
+واحد يعني هيكون عندي ال O D ال
+
+163
+00:20:34,170 --> 00:20:44,090
+O D هيكون اللي هو ال O A اللي هو R cosine ثتا واحد
+
+164
+00:20:44,090 --> 00:20:45,790
+زائد
+
+165
+00:20:52,130 --> 00:20:58,650
+L يعني ممكن دخلتها جذر سواء جذر التربيع لL تربيع
+
+166
+00:20:58,650 --> 00:21:04,410
+ثتا
+
+167
+00:21:04,410 --> 00:21:13,630
+واحد مظبوط هذه اللي هي ال O دي معناته ال X هتكون
+
+168
+00:21:13,630 --> 00:21:18,650
+OG اللي هي R زائد L
+
+169
+00:21:23,030 --> 00:21:35,410
+زائد R زائد L في ناقص ناقص
+
+170
+00:21:35,410 --> 00:21:41,850
+بالظبط
+
+171
+00:21:41,850 --> 00:21:55,290
+خدمة عشان نسهّل الحالة ناقص ال ODEاللي هو R Cos θ
+
+172
+00:21:55,290 --> 00:22:00,190
+1 زائد
+
+173
+00:22:00,190 --> 00:22:06,670
+L جزر التربيع إلى 1 minus R squared على L squared
+
+174
+00:22:06,670 --> 00:22:15,620
+Sin تربيع θ 1 خلاص وانت عرفنا X بنعرف ال Vالـ V
+
+175
+00:22:15,620 --> 00:22:27,100
+هتكون DX by DT سواء DX by Dθ واحد في Dθ واحد DT
+
+176
+00:22:27,100 --> 00:22:31,660
+اللي هي Omega صح برضه Omega اللي هتكون مش Omega
+
+177
+00:22:31,660 --> 00:22:34,260
+واحد ما هي Omega واحد هتكون سواء Omega برضه فانت
+
+178
+00:22:34,260 --> 00:22:38,060
+بتعب على ال rotational كامة في كل أحوال هتكون
+
+179
+00:22:38,060 --> 00:22:49,390
+Omegaفى dx by d theta واحد و ال a هتكون omega dv
+
+180
+00:22:49,390 --> 00:23:01,810
+by d theta واحد تعمل اشتقاق و بنطلع معادلات ل ال v
+
+181
+00:23:01,810 --> 00:23:05,510
+هذه معادلة ال v و معادلة ال acceleration
+
+182
+00:23:23,440 --> 00:23:27,540
+نشوف مثال in
+
+183
+00:23:27,540 --> 00:23:30,420
+a symmetrical tangent cam operating a roller
+
+184
+00:23:30,420 --> 00:23:35,840
+follower, the least radius of the cam is 30, least
+
+185
+00:23:35,840 --> 00:23:49,520
+radius يعني R1 صح؟ R1 بالساوية تلاتين مليمتر and
+
+186
+00:23:49,520 --> 00:23:53,720
+the roller radius is seventeen point fiveو ال R2
+
+187
+00:23:53,720 --> 00:24:03,500
+سبعتاشر و نص ملي متر ال angle of ascent و ذات
+
+188
+00:24:03,500 --> 00:24:08,400
+الصعود اللي هي Alpha اللي
+
+189
+00:24:08,400 --> 00:24:15,100
+هي قاعدة ثابتة خمس سبعية درجة ال
+
+190
+00:24:15,100 --> 00:24:20,720
+total lift هتكون سبعتاشر و نص ملي متر total lift
+
+191
+00:24:23,570 --> 00:24:29,790
+السبعتاشر و نص يعني من لحد ما اصل ال nose هيكون
+
+192
+00:24:29,790 --> 00:24:35,050
+رتفع السبعتاشر و نص ملي متر ال speed of the
+
+193
+00:24:35,050 --> 00:24:41,250
+camshaft اللي هي omega معطيني
+
+194
+00:24:41,250 --> 00:24:47,490
+ستمين rpm radian
+
+195
+00:24:47,490 --> 00:24:49,530
+per second
+
+196
+00:24:54,010 --> 00:24:59,690
+طيب هذه ايش ال omega بدو ال dimensions of the cam
+
+197
+00:24:59,690 --> 00:25:12,950
+انا عندي هاي ال cam هاي شكل ال cam هذه
+
+198
+00:25:12,950 --> 00:25:17,950
+alpha هذه
+
+199
+00:25:17,950 --> 00:25:21,770
+alpha طيب
+
+200
+00:25:21,770 --> 00:25:26,060
+ال tot اللي انا عندي اناال total left ايش بتساوي
+
+201
+00:25:26,060 --> 00:25:29,240
+17
+
+202
+00:25:29,240 --> 00:25:33,260
+.5 عبارة
+
+203
+00:25:33,260 --> 00:25:42,620
+عن أقصى مسافة اللي هي O OJ هي دي J صح؟
+
+204
+00:25:42,620 --> 00:25:47,720
+OJ minus
+
+205
+00:25:47,720 --> 00:25:51,820
+OB صح؟
+
+206
+00:25:57,510 --> 00:26:04,790
+لأنه على الدائرة هذه مافيش حركة الان هيصل اقصر
+
+207
+00:26:04,790 --> 00:26:09,250
+تفاهي عن جيه جيه اقصر اقصر تفاهي عن جيه جيه اقصر
+
+208
+00:26:09,250 --> 00:26:09,270
+عن جيه اقصر تفاهي عن جيه اقصر تفاهي عن جيه اقصر
+
+209
+00:26:09,270 --> 00:26:09,290
+تفاهي عن جيه اقصر تفاهي عن جيه اقصر تفاهي عن جيه
+
+210
+00:26:09,290 --> 00:26:19,290
+اقصر تفاهي عن جيه اقصر تفاهي عن جيه اقصر
+
+211
+00:26:19,290 --> 00:26:22,190
+تفاهي عن جيه ا
+
+212
+00:26:28,890 --> 00:26:45,550
+زاد كي جي minus ال OB عبارة عن R1 زاد R2 يعني
+
+213
+00:26:45,550 --> 00:26:51,730
+حاسيب عندي السبعتاشر و نص بيساوي ال okay الاسئلة
+
+214
+00:26:51,730 --> 00:26:57,530
+مش عارفه صح okay اللي هي عبارة عن ال R
+
+215
+00:27:03,980 --> 00:27:15,440
+زاد ال KG اقل عن R2 زاد R3 زاد
+
+216
+00:27:15,440 --> 00:27:27,740
+R2 زاد R3 minus R1 minus R2 صح هذه بتروح مع هذه
+
+217
+00:27:27,740 --> 00:27:40,740
+يعني السبعتاش و نصبتساوى R R زي .. اه
+
+218
+00:27:40,740 --> 00:27:43,780
+.. اه .. اه .. اه .. اه .. اه .. اه .. اه .. اه ..
+
+219
+00:27:43,780 --> 00:27:43,960
+اه .. اه .. اه .. اه .. اه .. اه .. اه .. اه .. اه
+
+220
+00:27:43,960 --> 00:27:44,760
+.. اه .. اه .. اه .. اه .. اه .. اه .. اه .. اه ..
+
+221
+00:27:44,760 --> 00:27:46,220
+اه .. اه .. اه .. اه .. اه .. اه .. اه .. اه .. اه
+
+222
+00:27:46,220 --> 00:27:47,220
+.. اه .. اه .. اه .. اه .. اه .. اه .. اه .. اه ..
+
+223
+00:27:47,220 --> 00:27:47,280
+.. اه .. اه .. اه .. اه .. اه .. اه .. اه .. اه ..
+
+224
+00:27:47,280 --> 00:27:52,900
+.. اه .. اه ..
+
+225
+00:27:58,350 --> 00:28:09,410
+معناته R زاد R تلاتة سبعة واربعين و نص هذه
+
+226
+00:28:09,410 --> 00:28:16,950
+معادلة واحد صح؟ ماعطيني
+
+227
+00:28:16,950 --> 00:28:22,910
+ال alpha ماعطيني ال alpha
+
+228
+00:28:26,740 --> 00:28:32,880
+اللي هي خمس و سبعين درجة الخمس و سبعين درجة
+
+229
+00:28:32,880 --> 00:28:35,980
+الالف
+
+230
+00:28:35,980 --> 00:28:42,280
+الساوي خمس و سبعين درجة
+
+231
+00:28:42,280 --> 00:28:48,900
+اه طيب انا هسخدم المثلثات
+
+232
+00:28:56,640 --> 00:29:08,040
+لو انازل عمودي انازل
+
+233
+00:29:08,040 --> 00:29:14,940
+عمودي عند
+
+234
+00:29:14,940 --> 00:29:23,200
+هذه هتكون عمودية هذه المسافة مش هتكون اللي
+
+235
+00:29:23,200 --> 00:29:37,630
+هي هتكون Rcos α وهذه R sin α مظبوط؟ ال okay هذه
+
+236
+00:29:37,630 --> 00:29:47,450
+ستكون تساوي طيب
+
+237
+00:29:47,450 --> 00:29:56,150
+هذه ستكون ايه كمتها؟ R2 هذي R3 وR2
+
+238
+00:29:57,880 --> 00:30:02,760
+خلّيني أسمي هذه OB فش
+
+239
+00:30:02,760 --> 00:30:06,620
+أف عندي هذه
+
+240
+00:30:06,620 --> 00:30:19,160
+O ال OF عشان حتساوي حتساوي OB minus
+
+241
+00:30:19,160 --> 00:30:26,860
+BF صح ال OB اللي هو R1
+
+242
+00:30:29,550 --> 00:30:44,350
+زاد R2 minus ال BF R2 يعني
+
+243
+00:30:44,350 --> 00:30:54,570
+هتكون R1 زاد R2 minus R2 minus R3 يعني هتكون لل OF
+
+244
+00:30:57,870 --> 00:31:09,510
+هتكون R واحد اللي هي تلاتين minus R تلاتة صح بتسوء
+
+245
+00:31:09,510 --> 00:31:14,390
+R Cos
+
+246
+00:31:14,390 --> 00:31:28,470
+Alpha يعني هكون تلاتين minus R تلاتةبالسواء R Cos
+
+247
+00:31:28,470 --> 00:31:50,470
+75 يعني R سواء 30-R 3 على Cos 75 عوض هنا سواء 30-R
+
+248
+00:31:50,470 --> 00:32:04,440
+3 على Cos 75الخمسة سبعين زائد R تلاتة بتساوي سبعة
+
+249
+00:32:04,440 --> 00:32:12,060
+واربعين ونص ومنها بتحسب R
+
+250
+00:32:12,060 --> 00:32:12,580
+تلاتة
+
+251
+00:32:27,740 --> 00:32:30,840
+يعني أحسن ان اشتغل بالطرفين الـ cos 75 هيكون لي 30
+
+252
+00:32:30,840 --> 00:32:34,120
+30
+
+253
+00:32:34,120 --> 00:32:37,640
+زائد
+
+254
+00:32:37,640 --> 00:32:49,760
+cos 75 ناقص 1 في R3 بتساوي
+
+255
+00:32:49,760 --> 00:32:55,580
+47.5 cos 75
+
+256
+00:32:57,530 --> 00:33:02,890
+و منها بتحسب اكم طلع ال R تلاتة تلاتة
+
+257
+00:33:02,890 --> 00:33:08,110
+و عشرين ميلي
+
+258
+00:33:08,110 --> 00:33:16,690
+متر و منها بتحسب عشر ال R اللي هي تلاتين نقل تلاشر
+
+259
+00:33:16,690 --> 00:33:18,290
+بون تسعة على كسايم خمس سبعين
+
+260
+00:33:26,430 --> 00:33:36,430
+23.6 مليمتر
+
+261
+00:33:36,430 --> 00:33:42,670
+احنا لما تحسبنا كل ال geometric parameters للكام
+
+262
+00:33:42,670 --> 00:33:47,830
+المعنى بتبقى اقدر ارسمها حاليا صح؟ اعرف ال R واحد
+
+263
+00:33:47,830 --> 00:33:55,780
+اعرف ال R تلاتةوعارف المسافة بينهم بعد برسم two
+
+264
+00:33:55,780 --> 00:34:01,260
+tangent lines هي tangent و tangent بصمنا الكامر
+
+265
+00:34:01,260 --> 00:34:10,080
+نعم
+
+266
+00:34:10,080 --> 00:34:14,900
+دخلوا
+
+267
+00:34:14,900 --> 00:34:18,900
+كل أرقام نعم
+
+268
+00:34:21,670 --> 00:34:28,230
+أصغر من اك واحد و اصغر من .. اه ايش المشكلة ؟ نصف
+
+269
+00:34:28,230 --> 00:34:32,610
+قطر بتحكي ايوه هذا مش ضروري تكون .. ممكن تكون اصغر
+
+270
+00:34:32,610 --> 00:34:37,750
+من هذه .. ممكن تكون .. اه
+
+271
+00:34:37,750 --> 00:34:43,610
+واضح انه اقل من التلاتين هذه
+
+272
+00:34:48,900 --> 00:34:55,120
+طيب هذا المطلوب الأول المطلوب التاني accelerations
+
+273
+00:34:55,120 --> 00:35:00,320
+of the follower at the beginning of lift where
+
+274
+00:35:00,320 --> 00:35:05,420
+straight line where straight flank merges into the
+
+275
+00:35:05,420 --> 00:35:10,360
+circular nose and
+
+276
+00:35:10,360 --> 00:35:14,860
+at the apex of the circular nose assume that there
+
+277
+00:35:14,860 --> 00:35:21,370
+is no dwell betweenascent and descent مغير ما تحكي
+
+278
+00:35:21,370 --> 00:35:24,210
+اسمه مافيش دول بينهم بيده ال acceleration هو at
+
+279
+00:35:24,210 --> 00:35:28,490
+the beginning of left where straight flank merges
+
+280
+00:35:28,490 --> 00:35:32,390
+into the circle nose and at the apex of the circle
+
+281
+00:35:32,390 --> 00:35:41,230
+nose يعني هاد انا يعني بيده ال acceleration عند
+
+282
+00:35:41,230 --> 00:35:46,430
+بداية ال nose عند نقطة هادة و عند نقطة هادةالـ
+
+283
+00:35:46,430 --> 00:35:52,610
+acceleration بتكون
+
+284
+00:35:52,610 --> 00:36:01,890
+نهاية الحركة على القطعة المستقيمة يعني هتكون نهاية
+
+285
+00:36:01,890 --> 00:36:05,370
+الحركة على القطعة المستقيمة هتكون اللي هي a max
+
+286
+00:36:05,370 --> 00:36:13,130
+لما نزوّت سواش فاي هتكون a اللي
+
+287
+00:36:13,130 --> 00:36:25,340
+هي omega squareفى R1 زاد R2 فى 2 minus cosine
+
+288
+00:36:25,340 --> 00:36:36,740
+تربيع فاي على cosine تكييب الفاي احنا
+
+289
+00:36:36,740 --> 00:36:41,120
+الفاي لألف و خمس و سبعين
+
+290
+00:36:45,070 --> 00:36:52,330
+هذه الألفة وهذه
+
+291
+00:36:52,330 --> 00:37:07,870
+الفاية
+
+292
+00:37:07,870 --> 00:37:12,450
+الخط
+
+293
+00:37:12,450 --> 00:37:19,650
+المستقيمنزلنا ايش؟ عمودي صح؟ يعني هذا هيكون طول
+
+294
+00:37:19,650 --> 00:37:27,330
+ايه؟ شو يساوي؟ R sin α صح؟
+
+295
+00:37:27,330 --> 00:37:33,270
+و هذا طوله أكام؟
+
+296
+00:37:33,270 --> 00:37:40,530
+R واحد زاد R اتنين زاد R اتنين معناته تاني الفاية
+
+297
+00:37:40,530 --> 00:37:43,970
+شو يساوي؟ تاني الفاية
+
+298
+00:37:48,220 --> 00:37:54,000
+بالساوية R sin α على
+
+299
+00:37:54,000 --> 00:37:58,600
+R واحد زاد R اتنين ال
+
+300
+00:37:58,600 --> 00:38:06,160
+R احنا كما حكينا تلات و عشرين sin
+
+301
+00:38:06,160 --> 00:38:09,960
+خمس
+
+302
+00:38:09,960 --> 00:38:13,920
+سبعين على
+
+303
+00:38:15,610 --> 00:38:20,530
+أروح التلاتين هات
+
+304
+00:38:20,530 --> 00:38:27,150
+الرقم صح؟ بون ستة
+
+305
+00:38:27,150 --> 00:38:38,650
+من هنا بتحسب اش الفاية بعدها هتحسب ال a اللي هو
+
+306
+00:38:38,650 --> 00:38:44,030
+بده أحكي beginning ل nose نعم
+
+307
+00:38:44,990 --> 00:38:50,330
+خمسة و عشرين فاية ستة و ستة ثلاثة ال ايش الفاية؟
+
+308
+00:38:50,330 --> 00:38:56,990
+هذا
+
+309
+00:38:56,990 --> 00:39:13,910
+رسم عامة الرسم بتاعتها هيها؟ واضح
+
+310
+00:39:13,910 --> 00:39:25,530
+انها ايش؟أصغر نعم لأ طبعا مش ادول بقي على أي قاعدة
+
+311
+00:39:25,530 --> 00:39:32,170
+هي هين هي ادول بعدين بيبدأ يطلع يطلع يطلع يطلع
+
+312
+00:39:32,170 --> 00:39:34,850
+يطلع يطلع يطلع يطلع يطلع يطلع يطلع يطلع يطلع يطلع
+
+313
+00:39:34,850 --> 00:39:35,350
+يطلع يطلع يطلع يطلع يطلع يطلع يطلع يطلع يطلع يطلع
+
+314
+00:39:35,350 --> 00:39:35,810
+يطلع يطلع يطلع يطلع يطلع يطلع يطلع يطلع يطلع يطلع
+
+315
+00:39:35,810 --> 00:39:40,550
+يطلع يطلع يطلع يطلع يطلع يطلع يطلع يطلع يطلع يطلع
+
+316
+00:39:40,550 --> 00:39:42,890
+يطلع يطلع يطل
+
+317
+00:39:45,890 --> 00:39:53,490
+بعد مده ال .. ال .. ال extension عند ال nose هتكون
+
+318
+00:39:53,490 --> 00:40:00,550
+ال theta واحد شو ساوي؟ صفر يعني هتكون عند ايه؟ ال
+
+319
+00:40:00,550 --> 00:40:06,790
+a واحد ال a عند ال nose هتكون ال theta واحد شو
+
+320
+00:40:06,790 --> 00:40:11,690
+ساوي؟ صفر يعني هتكون cosine الصفر omega square R
+
+321
+00:40:16,480 --> 00:40:30,540
+cos θ الصفر ايش؟ واحد زاد L تربيع في R اللي هي cos
+
+322
+00:40:30,540 --> 00:40:41,060
+الصفر واحد زاد R تكييب الصين الصفر صفر هذا هتكون
+
+323
+00:40:41,060 --> 00:40:44,600
+صفر هتكون على L تربيع وصفر تكييب يعني L تكييب على
+
+324
+00:40:44,600 --> 00:40:46,000
+L تكييب
+
+325
+00:40:50,480 --> 00:40:59,120
+يعني هتكون omega squared R في واحد زاد R على L
+
+326
+00:40:59,120 --> 00:41:04,580
+يعني هتكون اتنين و ستين point تمانية تلاتة تربيع
+
+327
+00:41:04,580 --> 00:41:12,520
+في ال R اللي هي تلاتة و عشرين point ستة في
+
+328
+00:41:14,360 --> 00:41:20,600
+واحد زائد R التي هي تلاتة وعشرين point ستة على L
+
+329
+00:41:20,600 --> 00:41:35,020
+ال L هي عبارة عن R اتنين زائد R تلاتة ومن
+
+330
+00:41:35,020 --> 00:41:37,100
+هنا تحسب ال A عند
+
+331
+00:41:54,350 --> 00:42:01,610
+لأ منطقي millimeter per second square هتكون مائة و
+
+332
+00:42:01,610 --> 00:42:07,230
+تسعة و تلاتين معناته point أربع خمس تسعة meter
+
+333
+00:42:09,410 --> 00:42:14,530
+per second square يعني
+
+334
+00:42:14,530 --> 00:42:23,930
+هذه المثلة نفس الأشياء تقريبا لأن
+
+335
+00:42:23,930 --> 00:42:29,390
+في نوع تاني من ال cams
+
+336
+00:42:29,390 --> 00:42:34,790
+الجزء اللي كان في النوع الأولاني كان خط مستقيم لأ
+
+337
+00:42:34,790 --> 00:42:42,840
+هنا arcTangent للنوز و Minimum Radius Arc Tangent
+
+338
+00:42:42,840 --> 00:42:52,800
+للنوز و Minimum Radius Minimum Radius R1 طبعا
+
+339
+00:42:52,800 --> 00:42:55,780
+الاشتقاء كما نفعله ل Flat-Faced Follower Flat
+
+340
+00:42:55,780 --> 00:43:03,720
+-Faced Follower R1
+
+341
+00:43:03,720 --> 00:43:12,190
+Minimum Radiusالار اتنين ال nose radius الار
+
+342
+00:43:12,190 --> 00:43:18,190
+كابيتال هو ال radius لهذا الارك اللي هو الار
+
+343
+00:43:18,190 --> 00:43:25,070
+كابيتل او الارك هذا يعني هذه المسافة او هذه
+
+344
+00:43:25,070 --> 00:43:30,310
+المسافة طبعا ال two arc دولالـ cam is symmetrical
+
+345
+00:43:30,310 --> 00:43:33,310
+يعني هاد ال tangent to the nose and the minimum
+
+346
+00:43:33,310 --> 00:43:42,690
+radius tangent to the nose and minimum radius ال
+
+347
+00:43:42,690 --> 00:43:46,610
+angle of action اللي هي عندي إيش عندي هين tangency
+
+348
+00:43:46,610 --> 00:43:49,730
+point معناه إذا عملت tangent هتكون إيش الزاوية
+
+349
+00:43:49,730 --> 00:43:51,510
+تسعين درجة
+
+350
+00:44:01,460 --> 00:44:08,320
+هو عملت tangent هنا هاي ال tangent معناته
+
+351
+00:44:08,320 --> 00:44:15,940
+هدف ده هو هدف النص جاي لحد مركز ال نوز عندي هيكون
+
+352
+00:44:15,940 --> 00:44:21,900
+Alpha و
+
+353
+00:44:21,900 --> 00:44:22,220
+Alpha
+
+354
+00:44:33,420 --> 00:44:38,200
+طيب ال file angle of action of cam on the circle
+
+355
+00:44:38,200 --> 00:44:47,340
+of length الفاى عندهين
+
+356
+00:44:47,340 --> 00:44:54,720
+الفاى هذه الفاى هذا
+
+357
+00:44:54,720 --> 00:45:03,310
+مركز ال circle archive بدايته وهذه نهايتههذه بداية
+
+358
+00:45:03,310 --> 00:45:14,070
+ال arc هذه نهاية ال arc الزاوية في بتمثل هذه
+
+359
+00:45:14,070 --> 00:45:21,090
+الزاوية في
+
+360
+00:45:21,090 --> 00:45:24,130
+لو
+
+361
+00:45:24,130 --> 00:45:31,140
+بنرسم الحركة على ال circle arc هعتبر هذه البدايةو
+
+362
+00:45:31,140 --> 00:45:34,860
+هاخد اي position منها يعني هاخد هذه الزاوية هتكون
+
+363
+00:45:34,860 --> 00:45:40,000
+هذه
+
+364
+00:45:40,000 --> 00:45:46,340
+الزاوية ثتا في البداية ثتا بيكون سواء صفر و في
+
+365
+00:45:46,340 --> 00:45:48,340
+نهاية ثتا بيكون سواء five
+
+366
+00:46:02,730 --> 00:46:09,250
+طيب بنفس المنطق السابق نوجد معدل ل X يعني هكون
+
+367
+00:46:09,250 --> 00:46:17,650
+عندي معدلتين معدلة على ال circular arc و معدلة ل
+
+368
+00:46:17,650 --> 00:46:25,350
+ال nose او
+
+369
+00:46:25,350 --> 00:46:27,910
+حتى معدلة لنص ال nose لأن هو بيصير .. يعني هو
+
+370
+00:46:27,910 --> 00:46:32,530
+symmetric يعني معدل من هنا ل هنامعدلة من بداية ال
+
+371
+00:46:32,530 --> 00:46:36,890
+nose لنص ال nose طبعا على ال minimum radius بيكون
+
+372
+00:46:36,890 --> 00:46:42,410
+عنده ايش اتول .. بيكون عنده اتول يعني مافيش motion
+
+373
+00:46:42,410 --> 00:46:48,070
+ال motion من بداية ال circle arc لنهايته اللي هي
+
+374
+00:46:48,070 --> 00:46:52,610
+بداية ال nose بصل اكثر ارتفاع من منتصف ال nose و
+
+375
+00:46:52,610 --> 00:46:55,510
+بعدين ماببدأش ينزل و بعدين اتول
+
+376
+00:47:02,730 --> 00:47:09,770
+يعني ال X ال X اللي
+
+377
+00:47:09,770 --> 00:47:21,530
+هي معتبر هاي ال طبعا هو يعني هذا position data هاي
+
+378
+00:47:21,530 --> 00:47:25,510
+ال follower هو
+
+379
+00:47:25,510 --> 00:47:31,090
+ال tangent هنا لكن ال X هتكون المسافة المسافة هذه
+
+380
+00:47:35,270 --> 00:47:38,730
+با مش هنخش في ال derivation ال بي إيه هنخش يعني ال
+
+381
+00:47:38,730 --> 00:47:43,970
+derivation موجود بحسب ال X تطلع ال X يستوي R minus
+
+382
+00:47:43,970 --> 00:47:48,350
+R واحد في واحد minus cosine theta theta measured
+
+383
+00:47:48,350 --> 00:47:53,510
+from this line وبعدين بيحسب بحكي V بيستوي DX by DT
+
+384
+00:47:53,510 --> 00:47:58,300
+بيستوي DX by D theta في D theta علىdt هي omega dx
+
+385
+00:47:58,300 --> 00:48:03,080
+by d theta و نفس الأشياء ال acceleration بيستوى dv
+
+386
+00:48:03,080 --> 00:48:06,640
+by dt بيستوى dv by d theta في d theta by dt يعني
+
+387
+00:48:06,640 --> 00:48:16,760
+omega في dv by d theta بيطلع معدلة ل ال V الآن في
+
+388
+00:48:16,760 --> 00:48:20,200
+بداية الحركة لما انتهيت سوى صفر هو خارج من ال دول
+
+389
+00:48:20,200 --> 00:48:26,480
+ماكانش عنده سرعة صح؟ بتكون صفربعدين بيصير maximum
+
+390
+00:48:26,480 --> 00:48:32,140
+عند نقطة هذي لما ثتر ساوية ايش؟ فاي.معنى انت V
+
+391
+00:48:32,140 --> 00:48:35,040
+maximum ساوية Omega في R capital معناه R واحد ساين
+
+392
+00:48:35,040 --> 00:48:43,660
+الفاية معادة ال acceleration ال A بساوية Omega في
+
+393
+00:48:43,660 --> 00:48:48,920
+R Omega square في R capital معناه R واحد كساين ثتا
+
+394
+00:48:48,920 --> 00:48:53,000
+في بداية الحركة من الخروج من الدول بتكون ال .. ال
+
+395
+00:48:53,000 --> 00:48:57,370
+.. ال ..بتكون ال cosine maximum بتكون maximum لما
+
+396
+00:48:57,370 --> 00:49:02,070
+انتهيت ايش الساوية zero هتكون omega square في R و
+
+397
+00:49:02,070 --> 00:49:06,990
+R منص R واحد و بتكون minimum في نهاية ال arc لما
+
+398
+00:49:06,990 --> 00:49:10,930
+انتهيت الساوية ايش five ايه minimum الساوية omega
+
+399
+00:49:10,930 --> 00:49:22,310
+square في R كتر منص R one في cosine ال five طبعا
+
+400
+00:49:22,310 --> 00:49:29,940
+ال دولledwell يعني
+
+401
+00:49:29,940 --> 00:49:36,260
+ممكن اعتبرها فترة اغلاق للصمام لو هد في ال .. في
+
+402
+00:49:36,260 --> 00:49:44,040
+ال camshaft بتاع السيارة و هد فترة ايش؟ فتح الصمام
+
+403
+00:49:46,690 --> 00:49:51,170
+الفتحة بتبدأ من zero مثلا zero cross sectional
+
+404
+00:49:51,170 --> 00:49:58,870
+area و بتزيد بصل maximum هنا وبعدين بفتح تدريجي و
+
+405
+00:49:58,870 --> 00:50:08,150
+بسكر تدريجي و بظل مسكر بعدين فبيعرفتك
+
+406
+00:50:08,150 --> 00:50:15,830
+للزاوية omega بتقدر تحسب زمن
+
+407
+00:50:19,580 --> 00:50:28,140
+الإغلاق و زمن من بداية ما فتح لحد ما سكر الصمم اذا
+
+408
+00:50:28,140 --> 00:50:37,220
+انا كنت حاكم صمم طبعا
+
+409
+00:50:37,220 --> 00:50:40,060
+منطقي يعني في حياتي الكام شركة تشتغل بالشكل هذا
+
+410
+00:50:40,060 --> 00:50:46,660
+انه يعني بيعملش اشي مفاجئ بدخل وقود و وقود و هو
+
+411
+00:50:46,660 --> 00:50:54,450
+مثلامقود و هواء فجأة بدخل شويه شويه لحد نص ال
+
+412
+00:50:54,450 --> 00:51:06,970
+maximum و بعدين يخفف طبعا
+
+413
+00:51:06,970 --> 00:51:13,690
+هذه المعادلات السابقة كانت في حالة ايش في حالة لل
+
+414
+00:51:13,690 --> 00:51:20,680
+arc هذا لأن في جزء من الحركة جاي وينعلى ال nose
+
+415
+00:51:20,680 --> 00:51:32,200
+جاي على ال nose طبعا
+
+416
+00:51:32,200 --> 00:51:41,660
+ال reference عنده عكينا
+
+417
+00:51:41,660 --> 00:51:42,380
+هذه هي alpha
+
+418
+00:51:52,090 --> 00:51:55,490
+هيكون اللي هيحكي هو الان ال reference عنده أقصر
+
+419
+00:51:55,490 --> 00:51:58,970
+اتفاع زي ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+420
+00:51:58,970 --> 00:52:00,070
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+421
+00:52:00,070 --> 00:52:00,490
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+422
+00:52:00,490 --> 00:52:01,070
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+423
+00:52:01,070 --> 00:52:03,710
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+424
+00:52:03,710 --> 00:52:05,050
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+425
+00:52:05,050 --> 00:52:09,570
+ال
+
+426
+00:52:09,570 --> 00:52:09,630
+ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+427
+00:52:20,280 --> 00:52:28,940
+و ال V هتكون DX by Dθ في Omega طبعا ال OQ هي
+
+428
+00:52:28,940 --> 00:52:33,660
+المسافة بين Center ال minimum radius وال Center
+
+429
+00:52:33,660 --> 00:52:41,500
+تعيش ال nose اللي كان يسميه في ال cam السابقة R صح
+
+430
+00:52:41,500 --> 00:52:44,100
+هذا هي ال OQ
+
+431
+00:52:47,050 --> 00:52:51,170
+فهتكون ال V بيستوى Omega في OQ Sine Alpha Minus
+
+432
+00:52:51,170 --> 00:52:56,270
+Theta وال A بيستوى Omega DV بعدي Theta بيستوى
+
+433
+00:52:56,270 --> 00:53:02,270
+Minus Omega Square في OQ Cosine Alpha Minus Theta
+
+434
+00:53:02,270 --> 00:53:06,690
+ال maximum retardation يعني ال dissertation يكون
+
+435
+00:53:06,690 --> 00:53:11,760
+عندي Omega Square في OQوالـ minimum retardation
+
+436
+00:53:11,760 --> 00:53:16,380
+سيكون omega squared في OQ cos α ناقصه يعني لما ..
+
+437
+00:53:16,380 --> 00:53:22,480
+لما .. هي لما θ تتسوا ألفة بيصير cosine ال zero
+
+438
+00:53:22,480 --> 00:53:27,800
+بيصيرها ده ايش المقدار maximum ولأن هندي هنا minus
+
+439
+00:53:27,800 --> 00:53:33,080
+يعتبر retardation يعني في ايش يعني تغير في السرعة
+
+440
+00:53:33,080 --> 00:53:40,920
+بمعدل متناقص يعني ممكن السرعة تزيدبمعدل متناقص
+
+441
+00:53:40,920 --> 00:53:45,340
+اضغط الزيادة
+
+442
+00:53:45,340 --> 00:53:52,500
+لاتعني انه في acceleration يعني هنا السرعة بتزيد
+
+443
+00:53:52,500 --> 00:53:58,300
+في معدل متناقص و ال minimum retardation سواء omega
+
+444
+00:53:58,300 --> 00:54:03,800
+square لما سير عندي في OQ cosine Alpha minus Phi
+
+445
+00:54:14,730 --> 00:54:21,430
+هي عندك حالة هذا
+
+446
+00:54:21,430 --> 00:54:36,490
+الاشي هاي Y هاي X بتزيد بمعدل متزايد هذا بتزيد
+
+447
+00:54:36,490 --> 00:54:45,360
+بمعدل متناقصهذا يزيد وهذا يزيد بصير ولا بصيراش؟
+
+448
+00:54:45,360 --> 00:54:55,480
+عشان
+
+449
+00:54:55,480 --> 00:55:04,840
+هيك في الحالة هذه ما هو لازم هذه تزيد بمعدل متناقص
+
+450
+00:55:04,840 --> 00:55:16,190
+عشان تصل maximum بعدين تنزلإذا صار زي هيك لازم ال
+
+451
+00:55:16,190 --> 00:55:33,370
+curve يكون جزئين لازم يكون في انقلاب نقطة
+
+452
+00:55:33,370 --> 00:55:35,510
+انقلاب واضح؟
+
+453
+00:55:37,650 --> 00:55:40,890
+هذه المفهوم ممكن انقلاب ممكن انقلاب انا بدي انتقل
+
+454
+00:55:40,890 --> 00:55:46,750
+من .. من اشي اقل ما يمكن لعلى ما يمكن لا يمكن اللي
+
+455
+00:55:46,750 --> 00:55:50,810
+يصير انقلاب يعني اذا كنت minimum و بدي اروح ل
+
+456
+00:55:50,810 --> 00:55:58,650
+maximum اذا كنت maximum و بدي اروح ل minimum لكن
+
+457
+00:55:58,650 --> 00:56:02,290
+ممكن اصل maximum بدون انقلاب اذا كنت بمعدل متنقص
+
+458
+00:56:02,290 --> 00:56:05,090
+يعني هيك انا طالع هيك
+
+459
+00:56:17,360 --> 00:56:22,540
+واضح؟ مانا تبل فأزيد السرعة بمعدل متناطس
+
+460
+00:56:31,700 --> 00:56:37,100
+طيب نشوف مثال a symmetric circle cam operating a
+
+461
+00:56:37,100 --> 00:56:40,360
+flat-faced follower has the following particulars
+
+462
+00:56:40,360 --> 00:56:47,800
+عندك ال minimum radius of cam اللي هي R13 و
+
+463
+00:56:47,800 --> 00:56:52,400
+ال
+
+464
+00:56:52,400 --> 00:56:56,380
+total lift عشرين
+
+465
+00:56:56,380 --> 00:56:57,720
+نفس المثل صحيح تقريبا
+
+466
+00:57:02,050 --> 00:57:09,030
+الـ Angle of Lift ألفة والـ
+
+467
+00:57:09,030 --> 00:57:19,590
+Nose Radius R2 يساوي خمسة ملي متر ومعطيني
+
+468
+00:57:19,590 --> 00:57:23,610
+ال speed نفس
+
+469
+00:57:23,610 --> 00:57:28,170
+المثال السابق تماما تحسب ال total lift
+
+470
+00:57:31,240 --> 00:57:36,260
+منها تطلع one تطلع total left اللي عندي أكم عشرين
+
+471
+00:57:36,260 --> 00:57:39,520
+بتساوي
+
+472
+00:57:39,520 --> 00:57:50,940
+أنا أجلس الشكل العام total left هيكون O
+
+473
+00:57:50,940 --> 00:57:54,940
+K
+
+474
+00:57:54,940 --> 00:58:00,240
+minus O E أو O G صح؟
+
+475
+00:58:02,510 --> 00:58:09,730
+Okay عبارة
+
+476
+00:58:09,730 --> 00:58:17,930
+عن اللي هي OQ زائد
+
+477
+00:58:17,930 --> 00:58:24,890
+R2 صح؟ minus OE R1
+
+478
+00:58:27,940 --> 00:58:38,060
+تتلف عن دقة كم؟ عشرين بالساوية OQ زائد R2 خمسة
+
+479
+00:58:38,060 --> 00:58:46,480
+minus R1 تلاتين معناة OQ بالساوية
+
+480
+00:58:46,480 --> 00:58:52,220
+خمس و أربعين ملي صح؟ طلعنا
+
+481
+00:58:52,220 --> 00:59:04,770
+إيش؟ ال OQهيتأثّل خلّصنا بدّوا
+
+482
+00:59:04,770 --> 00:59:09,170
+acceleration floor at the beginning of left at the
+
+483
+00:59:09,170 --> 00:59:15,890
+end of contact with the circle of flank at the
+
+484
+00:59:15,890 --> 00:59:19,050
+beginning of contact with nose and at the apex of
+
+485
+00:59:19,050 --> 00:59:21,350
+the nose يعني بدّوا ال acceleration
+
+486
+00:59:26,340 --> 00:59:37,080
+بدو هنا و هنا و هنا طيب ال low key و عرفناها خمس و
+
+487
+00:59:37,080 --> 00:59:45,720
+أربعين يعني
+
+488
+00:59:45,720 --> 00:59:53,920
+بده ال a هاي ال theta هستخدم النقطة هذه ال point
+
+489
+01:00:02,590 --> 01:00:08,150
+عند E و F و K E و
+
+490
+01:00:08,150 --> 01:00:19,330
+F و K هتكون ثتا سفر فاي و ثتا التاني هدل بالك و
+
+491
+01:00:19,330 --> 01:00:23,710
+عند K ثتا التاني انا خدشت عن نوز مالاش خاص في ثتا
+
+492
+01:00:23,710 --> 01:00:31,590
+إياش التاني هتكون إياش سفر صح؟ هتكون معناتههتكون
+
+493
+01:00:31,590 --> 01:00:41,510
+omega square هنا في R capital minus R واحد cosine
+
+494
+01:00:41,510 --> 01:00:47,950
+خلصنا من ال cosine التاني
+
+495
+01:00:47,950 --> 01:00:55,170
+هتكون omega square في R capital minus R واحد
+
+496
+01:00:55,170 --> 01:00:58,910
+cosine الفاي
+
+497
+01:01:01,250 --> 01:01:13,670
+التالتة توقعني بس التالتة
+
+498
+01:01:13,670 --> 01:01:19,170
+هتكون
+
+499
+01:01:19,170 --> 01:01:24,510
+minus omega square
+
+500
+01:01:24,510 --> 01:01:28,810
+OQ
+
+501
+01:01:42,170 --> 01:01:46,570
+في alpha minus theta فيه الف ناقص
+
+502
+01:01:46,570 --> 01:01:53,070
+تيتا فيه الف ناقص
+
+503
+01:01:53,070 --> 01:02:00,590
+تيتا فيه الف ناقص تيتا فيه الف ناقص تيتا فيه الف
+
+504
+01:02:00,590 --> 01:02:01,850
+ناقص تيتا فيه الف ناقص تيتا فيه الف ناقص تيتا فيه
+
+505
+01:02:01,850 --> 01:02:08,120
+فيه الف ناقص تيتاعارفها بنفس الطريقة هتكون ..يعني
+
+506
+01:02:08,120 --> 01:02:12,580
+هتكون omega square OQ
+
+507
+01:02:12,580 --> 01:02:19,400
+omega square ف OQ و بس احنا
+
+508
+01:02:19,400 --> 01:02:26,600
+حسبنا ال .. ال .. ال OQ صح؟ ال OQ انحسبت و ضال
+
+509
+01:02:26,600 --> 01:02:36,040
+عندك اللي هو اللي هي ال Phiو ال R capital ال R
+
+510
+01:02:36,040 --> 01:02:42,060
+واحد معروفة ال R كده
+
+511
+01:02:42,060 --> 01:02:48,560
+حسبوها عادى حسبوها لحالكوا و كملوا حل السؤال هيك
+
+512
+01:02:48,560 --> 01:02:53,560
+يكون خلصنا ال cams في أي سؤال؟
+
diff --git a/PL9fwy3NUQKwa0nXiCdyQcTW4hWDLTGpDb/dfpCMzWBnD0_postprocess.srt b/PL9fwy3NUQKwa0nXiCdyQcTW4hWDLTGpDb/dfpCMzWBnD0_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..a1348eebebf433cc980e8ce86800f88035ac13bc
--- /dev/null
+++ b/PL9fwy3NUQKwa0nXiCdyQcTW4hWDLTGpDb/dfpCMzWBnD0_postprocess.srt
@@ -0,0 +1,1876 @@
+1
+00:00:05,500 --> 00:00:08,440
+بسم الله الرحمن الرحيم السلام عليكم ورحمة الله
+
+2
+00:00:08,440 --> 00:00:13,720
+وبركاته اليوم هنكمل في chapter 15 من مادة نظرية
+
+3
+00:00:13,720 --> 00:00:17,080
+الألات اللي هي inertia forces and reciprocating
+
+4
+00:00:17,080 --> 00:00:22,920
+parts في البداية هنعمل مراجعة سريعة للمحاضرة
+
+5
+00:00:22,920 --> 00:00:27,860
+الفاتتة المرة الفاتة عملنا kinematic analysis
+
+6
+00:00:27,860 --> 00:00:32,860
+لslider crank mechanismاللي هي قلب المحرك بتاع
+
+7
+00:00:32,860 --> 00:00:37,000
+السيارة عملنا displacement velocity و acceleration
+
+8
+00:00:37,000 --> 00:00:40,740
+analysis كانت ال displacement اللي علاقة اللي هي
+
+9
+00:00:40,740 --> 00:00:45,620
+ان انتوا شايفينها X بساوي R اللي طبعا X بتاعة ال
+
+10
+00:00:45,620 --> 00:00:49,400
+piston R في واحد minus cosine theta زد N في واحد
+
+11
+00:00:49,400 --> 00:00:57,220
+minus cosine Pi بالنسبة ل .. لل
+
+12
+00:00:57,220 --> 00:01:01,330
+velocity of the pistonالـ V بتاعة البسطون كانت
+
+13
+00:01:01,330 --> 00:01:04,930
+Omega R Sine Theta زي Sine Two Theta على اتنين N
+
+14
+00:01:04,930 --> 00:01:09,050
+والاكسليريشي للبسطون كانت Omega Square R في Cos
+
+15
+00:01:09,050 --> 00:01:14,230
+Theta زي Cos Two Theta على N بعد ان جيبنا ال anger
+
+16
+00:01:14,230 --> 00:01:16,070
+of velocity وال anger of acceleration لل
+
+17
+00:01:16,070 --> 00:01:21,030
+connecting rod ال anger of velocity كانت النهائية
+
+18
+00:01:21,030 --> 00:01:28,940
+بعد التقريبات Omega لل connecting rod بساويةوميجا
+
+19
+00:01:28,940 --> 00:01:32,840
+كوسينث تيتا على N و ال angle acceleration لل
+
+20
+00:01:32,840 --> 00:01:36,520
+connecting rod كان يسوى minus omega square sin
+
+21
+00:01:36,520 --> 00:01:40,000
+theta على N طبعا المعادلات هذه معادلات تقريبيا
+
+22
+00:01:40,000 --> 00:01:43,920
+لأننا عملنا بعض الفرضيات فصار بعض التقريبات يعني
+
+23
+00:01:43,920 --> 00:01:52,540
+معادلات مش exact مش طيب حلنا مثال خمساش تلاتة
+
+24
+00:01:52,540 --> 00:02:06,010
+حلناه مظبوططب خلينا نحل ال example و نكمل if
+
+25
+00:02:06,010 --> 00:02:12,030
+the crank نقرأ المثال if the crank and connecting
+
+26
+00:02:12,030 --> 00:02:15,850
+rod are three hundred millimeter and one thousand
+
+27
+00:02:15,850 --> 00:02:19,910
+millimeter long respectively ومعطيني الطول ل crank
+
+28
+00:02:19,910 --> 00:02:23,110
+معطيني
+
+29
+00:02:23,110 --> 00:02:24,030
+الطول ل crank are
+
+30
+00:02:28,650 --> 00:02:32,730
+تلاتمية ملي تلاتمية ملي تلاتمية ملي تلاتمية ملي
+
+31
+00:02:32,730 --> 00:02:36,410
+تلاتمية ملي تلاتمية ملي تلاتمية ملي تلاتمية ملي
+
+32
+00:02:36,410 --> 00:02:40,530
+تلاتمية ملي تلاتمية ملي تلاتمية ملي تلاتمية ملي
+
+33
+00:02:40,530 --> 00:02:43,210
+تلاتمية ملي تلاتمية ملي تلاتمية ملي تلاتمية ملي
+
+34
+00:02:43,210 --> 00:02:43,230
+تلاتمية ملي تلاتمية ملي تلاتمية ملي تلاتمية ملي
+
+35
+00:02:43,230 --> 00:02:43,310
+تلاتمية ملي تلاتمية ملي تلاتمية ملي تلاتمية ملي
+
+36
+00:02:43,310 --> 00:02:48,890
+تلاتمية ملي تلاتمية
+
+37
+00:02:48,890 --> 00:02:56,950
+ملي تلاتمية ملي تلاتمية
+
+38
+00:02:56,950 --> 00:02:57,430
+ملي
+
+39
+00:03:02,030 --> 00:03:06,470
+تسعة سبعة تسعة
+
+40
+00:03:06,470 --> 00:03:13,670
+اربعة radians per second
+
+41
+00:03:13,670 --> 00:03:16,790
+determine
+
+42
+00:03:16,790 --> 00:03:21,050
+crank angle at which maximum velocity okay يعني
+
+43
+00:03:21,050 --> 00:03:28,150
+بده زاوية زاوية ملانة crank لما تكون ال velocity
+
+44
+00:03:28,150 --> 00:03:30,250
+maximum متى ال velocity تكون maximum
+
+45
+00:03:33,150 --> 00:03:40,290
+لما الاكسليريشن max او zero صح؟ يعني V يكون سوى
+
+46
+00:03:40,290 --> 00:03:48,470
+max او minimum لما الاكسليريشن سوى zero
+
+47
+00:03:59,970 --> 00:04:02,810
+لأ مش في الضروري عندي التوقف يكون acceleration سفر
+
+48
+00:04:02,810 --> 00:04:06,430
+و احنا في ال dynamica كمان هروح نتبه الطولة لان
+
+49
+00:04:06,430 --> 00:04:12,250
+when
+
+50
+00:04:12,250 --> 00:04:16,470
+you accelerate يعني مثلا انا زي ما حكيتلك انا ماشي
+
+51
+00:04:16,470 --> 00:04:24,410
+باتجاه معين ماشي يعني high particle السرعة
+
+52
+00:04:24,410 --> 00:04:25,770
+بتاعته بتتغير بالشكل هذا
+
+53
+00:04:29,040 --> 00:04:35,580
+مثلا نحكي sine wave هاي ال ballistic wave particle
+
+54
+00:04:35,580 --> 00:04:42,560
+معين ماشي على خط مستقيم ماشي على خط مستقيم وهذا
+
+55
+00:04:42,560 --> 00:04:50,260
+الزمن يعني مع الزمن مثلا نحكي هاي السفر خمس ثواني
+
+56
+00:04:50,260 --> 00:04:57,380
+عشر ثواني خمستاشر عشرين يعني أنا كنت في الموقع هذا
+
+57
+00:04:59,720 --> 00:05:02,680
+وبديت أسرع .. أسرع .. أسرع .. أسرع .. أسرع .. أسرع
+
+58
+00:05:02,680 --> 00:05:04,160
+.. أسرع .. أسرع .. أسرع .. أسرع .. أسرع .. أسرع ..
+
+59
+00:05:04,160 --> 00:05:05,920
+أسرع .. أسرع .. أسرع .. أسرع .. أسرع .. أسرع ..
+
+60
+00:05:05,920 --> 00:05:07,600
+أسرع .. أسرع .. أسرع .. أسرع .. أسرع .. أسرع ..
+
+61
+00:05:07,600 --> 00:05:09,380
+أسرع .. أسرع .. أسرع .. أسرع .. أسرع .. أسرع ..
+
+62
+00:05:09,380 --> 00:05:09,480
+أسرع .. أسرع .. أسرع .. أسرع .. أسرع .. أسرع ..
+
+63
+00:05:09,480 --> 00:05:17,400
+أسرع .. أسرع .. أسرع .. أسرع .. أسرع .. أسرع ..
+
+64
+00:05:17,400 --> 00:05:23,020
+أسرع
+
+65
+00:05:23,020 --> 00:05:26,200
+.. أسرع
+
+66
+00:05:26,200 --> 00:05:32,970
+.. أmeter per second per second لان هي بتعبر عن
+
+67
+00:05:32,970 --> 00:05:37,650
+تغير في السرعة فانا امشي التسارعة لحد ما اصلت
+
+68
+00:05:37,650 --> 00:05:42,830
+لأقصى السرعة بعدين
+
+69
+00:05:42,830 --> 00:05:49,970
+عشان اصل السفر لازم ابدأ اخفف سرعتى الان انا عندي
+
+70
+00:05:49,970 --> 00:05:53,330
+تسارعة كان في معدل تغير في السرعة موجب
+
+71
+00:05:55,980 --> 00:05:59,380
+عشان التغير بقعد يصير ملوعات السالب لازم أصل ل
+
+72
+00:05:59,380 --> 00:06:02,400
+zero في ال acceleration لازم أصل ل zero في ال
+
+73
+00:06:02,400 --> 00:06:06,900
+acceleration عشان هيك عند ال maximum speed عشان
+
+74
+00:06:06,900 --> 00:06:10,160
+أفكر بتكون acceleration زير و ال acceleration
+
+75
+00:06:10,160 --> 00:06:14,160
+الأخر هي ال slope هي ال slope يبدأ maximum مثلا
+
+76
+00:06:14,160 --> 00:06:17,780
+بقل شوية شوية شوية شوية شوية شوية شوية شوية لحد ما
+
+77
+00:06:17,780 --> 00:06:22,440
+يسافر ال slope قضا بعض مش هصير يعني physically مش
+
+78
+00:06:22,440 --> 00:06:36,440
+هصيرالجواب تاك على سؤالك؟ بدنا
+
+79
+00:06:36,440 --> 00:06:39,200
+نحسب ال crank angle اللى بتكون عندها سرعة maximum
+
+80
+00:06:39,200 --> 00:06:43,200
+يعني بتكون ال acceleration بتساوي zero احنا حكينا
+
+81
+00:06:43,200 --> 00:06:50,460
+ال acceleration لل piston ال
+
+82
+00:06:50,460 --> 00:06:54,340
+a بتساوي
+
+83
+00:07:13,700 --> 00:07:20,140
+الان شو ساوي؟
+
+84
+00:07:20,140 --> 00:07:22,660
+عشر ع تلاتة
+
+85
+00:07:26,870 --> 00:07:33,390
+هذه تساوي Zero معناه تحكم اندي Cos Theta زائد
+
+86
+00:07:33,390 --> 00:07:42,970
+تلاتة على عشرة Cos Two Theta بساوي Zero
+
+87
+00:07:42,970 --> 00:07:48,250
+Solve
+
+88
+00:07:48,250 --> 00:07:51,690
+for
+
+89
+00:07:51,690 --> 00:07:55,290
+Theta
+
+90
+00:07:57,730 --> 00:08:03,010
+هو كنت استخدم software Math
+
+91
+00:08:03,010 --> 00:08:06,930
+Lab او
+
+92
+00:08:06,930 --> 00:08:16,650
+Mathematica مثلا هحاول
+
+93
+00:08:16,650 --> 00:08:19,030
+نزل Mathematica على الجهاز هذا عشان المرة الجاية
+
+94
+00:08:19,030 --> 00:08:23,550
+اذا احتجناه نورجيكوا فالطرق دفته في الكتاب حالة
+
+95
+00:08:23,550 --> 00:08:29,840
+بالتحليقاللي هو بيحولك
+
+96
+00:08:29,840 --> 00:08:33,420
+معادلة أربعية و بعدين .. ماشي ماشي انا بعطيلك
+
+97
+00:08:33,420 --> 00:08:37,560
+طريقة مختلفة انا شايف من طلع الكتاب الان انت عندك
+
+98
+00:08:37,560 --> 00:08:41,380
+في المحاضرة هنا انا بعطيلك فرصة تانية عندك فرصة
+
+99
+00:08:41,380 --> 00:08:45,940
+انك تشوف أناشي الأفكار بتراها و عندك الكتاب أفكار
+
+100
+00:08:45,940 --> 00:08:51,180
+تانية فعندك فرصتين متاحة عندك يعني الكتاب اللي
+
+101
+00:08:51,180 --> 00:08:54,020
+عمله برضه صح يعني هو ممكن اشعر من الزمن حكاية
+
+102
+00:08:54,020 --> 00:09:01,470
+تلاتة على عشرةتلاتة عشرة تلاتة عشرة تلاتة عشرة
+
+103
+00:09:01,470 --> 00:09:03,610
+تلاتة عشرة تلاتة عشرة تلاتة عشرة تلاتة عشرة تلاتة
+
+104
+00:09:03,610 --> 00:09:03,870
+عشرة تلاتة عشرة تلاتة عشرة تلاتة عشرة تلاتة عشرة
+
+105
+00:09:03,870 --> 00:09:03,990
+تلاتة عشرة تلاتة عشرة تلاتة عشرة تلاتة عشرة تلاتة
+
+106
+00:09:03,990 --> 00:09:04,030
+عشرة تلاتة عشرة تلاتة عشرة تلاتة عشرة تلاتة عشرة
+
+107
+00:09:04,030 --> 00:09:06,450
+تلاتة عشرة تلاتة عشرة تلاتة عشرة تلاتة عشرة تلاتة
+
+108
+00:09:06,450 --> 00:09:09,210
+عشرة تلاتة عشرة تلاتة عشرة تلاتة عشرة تلاتة عشرة
+
+109
+00:09:09,210 --> 00:09:20,270
+تلاتة عشرة تلاتة
+
+110
+00:09:20,270 --> 00:09:24,850
+عشرة
+
+111
+00:09:25,600 --> 00:09:31,700
+بتساوي cos تربيع θ minus 1 minus cos تربيع ثتا
+
+112
+00:09:31,700 --> 00:09:41,900
+بتساوي اتنين cos تربيع ثتا minus واحد معناته هذه
+
+113
+00:09:41,900 --> 00:09:50,900
+مش هتكون الساوية cos ثتا زائد تلاتة عشرة في اتنين
+
+114
+00:09:50,900 --> 00:09:59,230
+cos تربيعCos تربيع θ minus واحد بساوي صفر يعني
+
+115
+00:09:59,230 --> 00:10:10,570
+هتصير ستة من عشرة Cos تربيع ثتا زاد Cos ثتا
+
+116
+00:10:10,570 --> 00:10:19,770
+ناقص تلاتة من عشرة بساوي عشر صفر
+
+117
+00:10:22,350 --> 00:10:25,470
+اكس من الطرفين على ستة من عشرة باسم ده cosine
+
+118
+00:10:25,470 --> 00:10:35,770
+تربيه ثتا زاد واحد cosine ثتا على ستة من عشرة
+
+119
+00:10:35,770 --> 00:10:43,370
+minus نص ساعة سفر اعتبر cosine ثتا هي ال variable
+
+120
+00:10:43,370 --> 00:10:49,690
+تاعك اعتبرها كأنها Xيعني بيصير عندك X تربيع زائد B
+
+121
+00:10:49,690 --> 00:10:55,810
+في X زائد C فانت على القانون اللي هو بتحكي Cos
+
+122
+00:10:55,810 --> 00:11:02,870
+Theta Cos Theta هتكون
+
+123
+00:11:02,870 --> 00:11:09,750
+سواء minus B هي minus واحد ستون عشرة زاد
+
+124
+00:11:09,750 --> 00:11:13,630
+او ناقص الجزر التربيعي ل B تربيع
+
+125
+00:11:16,260 --> 00:11:22,980
+زائد minus minus plus زائد أربعة في نص اتنين على
+
+126
+00:11:22,980 --> 00:11:33,420
+اتنين بعدين solve for theta هكون عندى two
+
+127
+00:11:33,420 --> 00:11:40,890
+solutions مرة فرصة هتكون maximum في اتجاه معينو
+
+128
+00:11:40,890 --> 00:11:44,890
+مرة تكون maximum في اتجاه تاني المعاكس و هو يعني
+
+129
+00:11:44,890 --> 00:11:50,050
+ان ال piston هو طالع بيصل maximum و هو راجعاش بيصل
+
+130
+00:11:50,050 --> 00:11:56,830
+maximum الان رياضيا تنفهم maximum و minimum بس و
+
+131
+00:11:56,830 --> 00:11:59,290
+في الآخر اذا انا ماشي بالاتجاه هذا يعني انا مقاعد
+
+132
+00:11:59,290 --> 00:12:05,530
+على صمت الصرف زي ذلك انا ممكن افكر بالاتجاهات اذا
+
+133
+00:12:05,530 --> 00:12:10,440
+انا ماشي بالاتجاه هذاهذا اعتبرها maximum اذا ماشي
+
+134
+00:12:10,440 --> 00:12:15,960
+باتجاه هذا اعتبر هذه maximum واضح فهي ال maximum
+
+135
+00:12:15,960 --> 00:12:23,520
+هي minimum في الآخر بس التجاهات واضح فبتحصل cosine
+
+136
+00:12:23,520 --> 00:12:27,700
+theta اي theta solve for theta بقى اللي بتعرفه
+
+137
+00:12:27,700 --> 00:12:38,350
+عدلة ال V ال V اللي هي ال V بيستوى Omega Rبس هو
+
+138
+00:12:38,350 --> 00:12:48,450
+omega r في sin theta اللي حسبته انا زائد sin two
+
+139
+00:12:48,450 --> 00:12:54,550
+theta على اتنين N واضح
+
+140
+00:12:54,550 --> 00:13:01,310
+اللي سوينها دايما
+
+141
+00:13:01,310 --> 00:13:05,170
+في ال geometric relationship في الشداء تحفظ كتير
+
+142
+00:13:05,170 --> 00:13:14,320
+علاقاتانت تحفظ الشغلات الأساسية و بتشتق
+
+143
+00:13:14,320 --> 00:13:17,260
+كل الشغلات بتعرفها في ال sign و ال cosine ال sign
+
+144
+00:13:17,260 --> 00:13:21,380
+تربيع بيساوي نص في واحد minus cosine two theta هذه
+
+145
+00:13:21,380 --> 00:13:24,940
+كلها مشتقة من الأساس اللي هي sin تربيع زي cos
+
+146
+00:13:24,940 --> 00:13:29,370
+تربيع بيساوي واحدواللقاة التانية اللي هي cosine
+
+147
+00:13:29,370 --> 00:13:32,050
+two theta اللي هي cosine تربيع معناه sin تربيع sin
+
+148
+00:13:32,050 --> 00:13:35,630
+two theta اللي هي اتنين sin theta cosine theta بس
+
+149
+00:13:35,630 --> 00:13:40,530
+اكتر من علاقة احفظهم تشتقوا للقات التانية طيب the
+
+150
+00:13:40,530 --> 00:13:46,350
+crank and conrod انا استخدم مصطلح هذا انا استغلت
+
+151
+00:13:46,350 --> 00:13:51,730
+فترة في شركات سيارات في أمريكا كان خلاص conrod
+
+152
+00:13:51,730 --> 00:13:54,790
+معروف عندهم بيحكيش connecting rod conrod يعني
+
+153
+00:13:54,790 --> 00:13:58,570
+connecting rodThe crank and connecting rod of a
+
+154
+00:13:58,570 --> 00:14:01,430
+steam engine are 0.3 meters and 1.5 meters in
+
+155
+00:14:01,430 --> 00:14:06,430
+length يعني ماعطين ال R و ال L R التي هي تلاتة و
+
+156
+00:14:06,430 --> 00:14:12,210
+عشرة متر و ال L واحد و نص متر يعني الأن كم تساوي
+
+157
+00:14:12,210 --> 00:14:23,530
+خمسة صح خمس عشرة تلاتة خمسة The crank rotates at
+
+158
+00:14:23,530 --> 00:14:24,450
+omega
+
+159
+00:14:26,550 --> 00:14:32,530
+بالساوة مية و تمانين ر بي ام الها الساوة تمانتاش
+
+160
+00:14:32,530 --> 00:14:44,210
+point سبعة تمانية تمانية سبعة و سبعة يعني
+
+161
+00:14:44,210 --> 00:14:49,290
+طاقة كان راديوس
+
+162
+00:14:49,290 --> 00:14:51,910
+per second
+
+163
+00:14:56,240 --> 00:14:58,780
+Velocity determines velocity and acceleration of
+
+164
+00:14:58,780 --> 00:15:01,280
+the piston when the crank is at four degrees from
+
+165
+00:15:01,280 --> 00:15:08,420
+inner that center يعني هاي عندى ال crank هاي
+
+166
+00:15:08,420 --> 00:15:14,020
+ال piston هاي
+
+167
+00:15:14,020 --> 00:15:20,440
+ال theta لما كان ال theta بالسواء أربعين درجة أحسب
+
+168
+00:15:20,440 --> 00:15:22,480
+ال velocity و ال acceleration بتحصل في معادلات
+
+169
+00:15:22,480 --> 00:15:38,430
+مظهورة LVوميجا فى ار صين ثيتا زاد صين
+
+170
+00:15:38,430 --> 00:15:46,490
+تى ثيتا على اتنين ان بتعود
+
+171
+00:15:46,490 --> 00:15:48,450
+عن ثيتا اربعين درجة والان خمسة
+
+172
+00:16:14,950 --> 00:16:20,600
+مطلوب التانيFind the position of the crank for
+
+173
+00:16:20,600 --> 00:16:23,620
+zero acceleration of the piston نفس ال example
+
+174
+00:16:23,620 --> 00:16:29,980
+السابق او theta يعني
+
+175
+00:16:29,980 --> 00:16:32,840
+hold position تحسب theta at which acceleration is
+
+176
+00:16:32,840 --> 00:16:37,320
+zero يعني ال velocity is maximum بعدين تحسب x at
+
+177
+00:16:37,320 --> 00:16:44,340
+this theta تحسب ال x اللي هي x شو الساوية ساوية
+
+178
+00:16:55,470 --> 00:17:00,090
+بالظبط لفستون هو طالب يحكي لك احسب ال position at
+
+179
+00:17:00,090 --> 00:17:03,790
+which ال acceleration is zeroفبتحسب ال .. اولش
+
+180
+00:17:03,790 --> 00:17:06,190
+بتحسب ال theta اللى بتكون عندك ال acceleration
+
+181
+00:17:06,190 --> 00:17:11,090
+zero و بعدين بتعود و بتحسب ال X موقع ال wisdom
+
+182
+00:17:11,090 --> 00:17:14,730
+بالطبع يعني دلوقت لو شيلنا من القانون ال X لواحد
+
+183
+00:17:14,730 --> 00:17:19,210
+نفسي cosine فاي عدناها cosine square theta اتنين
+
+184
+00:17:19,210 --> 00:17:23,650
+and square I بعدي يعني هذا تقريب لأن انت .. انت ال
+
+185
+00:17:23,650 --> 00:17:28,450
+cosine فاي قربتها باستخدام اللى هو Taylor
+
+186
+00:17:28,450 --> 00:17:35,000
+expansion انتوا كتير انا حكيتلكم بيرحإذا التقريب
+
+187
+00:17:35,000 --> 00:17:39,240
+بناء على expansion ممكن تعمله و حتى تشتق عادي
+
+188
+00:17:39,240 --> 00:17:45,940
+بعدها بس إذا كان بناء على فرضية بتعمل التقريبات
+
+189
+00:17:45,940 --> 00:17:48,960
+بعد ما تعمل كل اشتقاقات طلعت معناه بالصدفة مثلا
+
+190
+00:17:48,960 --> 00:17:53,760
+طلعت نفس المعادلة بس مش دايما يعني طلعت صدفة اه
+
+191
+00:17:53,760 --> 00:17:57,360
+تبقى لنا نقطة كتير هذه عادي اتحاليل التقريب عادي
+
+192
+00:17:57,360 --> 00:18:05,590
+اه طب نكمل موضوع جديدنعمل في ال machines انت في
+
+193
+00:18:05,590 --> 00:18:10,190
+الأول تعمل kinematic analysis بعدين تعمل kinetic
+
+194
+00:18:10,190 --> 00:18:13,310
+analysis اللي هو force analysis kinematic analysis
+
+195
+00:18:13,310 --> 00:18:19,250
+بتعمل توجد الهندسة الحركة بدون الرجولة المؤثر اللي
+
+196
+00:18:19,250 --> 00:18:24,270
+هي أياش ال forces أو القوة لكن في الkinetics بتربط
+
+197
+00:18:24,270 --> 00:18:32,500
+بين المؤثر والحركة نفسهاالخطوة التانية هي force
+
+198
+00:18:32,500 --> 00:18:35,660
+analysis او kinetic analysis انا عندي هذه الكرانك
+
+199
+00:18:35,660 --> 00:18:39,920
+عندي
+
+200
+00:18:39,920 --> 00:18:46,200
+هنا revolute joint وعندي هنا revolute joint هذا
+
+201
+00:18:46,200 --> 00:18:56,100
+النقطة O C P الان
+
+202
+00:18:56,100 --> 00:19:00,980
+في ال engineال input يبدو أنه عند ال piston
+
+203
+00:19:00,980 --> 00:19:04,660
+الاحتراط
+
+204
+00:19:04,660 --> 00:19:10,480
+يحدث في الأسطوانة وبتحول الحركة من حركة خطية
+
+205
+00:19:10,480 --> 00:19:13,800
+متدبدة إلى حركة دورانية عند الكرانك هنشوف كيف ال
+
+206
+00:19:13,800 --> 00:19:20,820
+force تنتقل لأن ال piston هيكون
+
+207
+00:19:20,820 --> 00:19:25,360
+عليها forces في
+
+208
+00:19:25,360 --> 00:19:31,230
+أن ال هو الوزنطبعا هان بدرس engine إيش أفوكي يعني
+
+209
+00:19:31,230 --> 00:19:34,410
+هاي .. هاي ال crank وهي ال connecting rod وهي ال
+
+210
+00:19:34,410 --> 00:19:43,010
+slider يعني ال slide مش رأسي .. رأسي بيختلف طيب
+
+211
+00:19:43,010 --> 00:19:48,130
+و هأهم الوزن ال connecting rod .. ههم الوزن ال
+
+212
+00:19:48,130 --> 00:19:52,110
+connecting rod لأن وزنه مهما يكون أقل بكتير من ال
+
+213
+00:19:52,110 --> 00:19:57,580
+force الموجودة التانيةال pesto عليه force اللي هو
+
+214
+00:19:57,580 --> 00:20:07,500
+وزنه و في عنده normal force ل F normal على فرض انه
+
+215
+00:20:07,500 --> 00:20:15,340
+احنا كنا متحركين بهذا الاتجاه يعني
+
+216
+00:20:15,340 --> 00:20:21,200
+كان متسارب بهذا الاتجاه هيكون
+
+217
+00:20:21,200 --> 00:20:27,130
+يعني هيكون في احتكاك هناresistance من ال friction
+
+218
+00:20:27,130 --> 00:20:30,290
+وفيه
+
+219
+00:20:30,290 --> 00:20:34,710
+.. وفيه
+
+220
+00:20:34,710 --> 00:20:38,110
+اللي هي ال load اللي جاي من ال pressure بتاع
+
+221
+00:20:38,110 --> 00:20:44,430
+الاحتراق نسمي FL مثلا هذا
+
+222
+00:20:44,430 --> 00:20:53,110
+في ال .. هذا بيساوي بيساوي اذا
+
+223
+00:20:53,110 --> 00:21:00,690
+حسي أكسيراشن كان من موتر سيارةحسين ال MR في ال A
+
+224
+00:21:00,690 --> 00:21:11,210
+تاع ال reciprocating parts الكتلة
+
+225
+00:21:11,210 --> 00:21:16,050
+بتاعته هو الكتلة بتاعة ال piston و ملحقاتها في
+
+226
+00:21:16,050 --> 00:21:20,230
+التسارة تبعهم هذه طريقة التعبير ممكن احكي زي هيك
+
+227
+00:21:20,230 --> 00:21:24,930
+هذه
+
+228
+00:21:24,930 --> 00:21:37,220
+ال forcesهي وزن ال piston هاي ال friction هاي
+
+229
+00:21:37,220 --> 00:21:43,420
+ال load وهاي ال inertia force inertia force شو
+
+230
+00:21:43,420 --> 00:21:51,140
+يساوي عكس هذه اللي هتكون نسميها هذه FI
+
+231
+00:21:58,490 --> 00:22:12,770
+fi الآن هسمي هدول يسمي
+
+232
+00:22:12,770 --> 00:22:22,630
+ال piston effort الجهد ال piston piston effort ال
+
+233
+00:22:22,630 --> 00:22:33,420
+piston effort هو محصلة ال forceاللي جاية من ال
+
+234
+00:22:33,420 --> 00:22:37,960
+load وال
+
+235
+00:22:37,960 --> 00:22:44,060
+friction وال acceleration
+
+236
+00:22:44,060 --> 00:22:47,720
+طبعا
+
+237
+00:22:47,720 --> 00:22:52,900
+إذا كان ال piston في حالة تسارع هتكون ال inertia
+
+238
+00:22:52,900 --> 00:22:56,200
+بتعكسنا ال inertia بتعكسنا
+
+239
+00:22:57,370 --> 00:23:01,510
+إذا كان في حالة retardation يعني تناقص في الرجعة
+
+240
+00:23:01,510 --> 00:23:07,530
+بتكون ال inertia force بتصدر بتكون ايش بتصدر
+
+241
+00:23:07,530 --> 00:23:15,390
+فهيكون ال piston effort اللي هو F P بيسوء
+
+242
+00:23:15,390 --> 00:23:24,910
+F load minus ال friction minus plus ال inertia
+
+243
+00:23:24,910 --> 00:23:29,800
+forceminus في حالة انه كان ال .. ال .. ال piston
+
+244
+00:23:29,800 --> 00:23:34,000
+متسارع، اذا كان هندي ال piston متسارع بتكون minus،
+
+245
+00:23:34,000 --> 00:23:38,960
+اذا كان ال piston متباطق، يعني متباطق بيحاول يعني
+
+246
+00:23:38,960 --> 00:23:43,460
+.. يعني .. يعني .. يعني يرجع لوراي، يساعدني اللي
+
+247
+00:23:43,460 --> 00:23:48,380
+انا .. انا عشان اسرع اشي لما انا شغل السيارة، شغل
+
+248
+00:23:48,380 --> 00:23:57,600
+السيارة و بدي اسرعها، اش بحتاج؟ اعطيها؟بدي اعطيها
+
+249
+00:23:57,600 --> 00:24:01,720
+بنزين اكتر يعني بدي طاقة اكتر معناته هي بتقاومني
+
+250
+00:24:01,720 --> 00:24:06,020
+لما بسرع السيارة بتقاومني و الدليل انا بعطيها طاقة
+
+251
+00:24:06,020 --> 00:24:11,460
+اكتر صح؟ صح فهي بتكون مقاومة يعني لما انا بدي ابطق
+
+252
+00:24:11,460 --> 00:24:16,980
+بشيرجلي بشيرجلي يعني احسر الظروف بشيرجلي اظلوط
+
+253
+00:24:16,980 --> 00:24:20,720
+معناته بتساعدني في الحالة هذه تملياش مساعدة
+
+254
+00:24:24,740 --> 00:24:28,660
+فبصف عندى حكى ان ال piston effort هو ال net force
+
+255
+00:24:28,660 --> 00:24:33,980
+اللى بتأثر باتجاه ال line و ال stroke ناتجة عن ال
+
+256
+00:24:33,980 --> 00:24:35,920
+load اللى جاية من ال pressure ناتجة عن عملة
+
+257
+00:24:35,920 --> 00:24:39,920
+الاحتراق و ال friction و ال resistance و ال
+
+258
+00:24:39,920 --> 00:24:43,340
+inertia force اللى جاية من ال piston إذا كان في
+
+259
+00:24:43,340 --> 00:24:47,660
+حالة تسارق بتحاول تقلل ال net effort لإن أنا محتاج
+
+260
+00:24:47,660 --> 00:24:51,760
+أبدل طاقة عشان أعطيها acceleration مظبوط؟
+
+261
+00:25:00,750 --> 00:25:04,210
+طبعا من ال section السابق احنا حسبنا ال
+
+262
+00:25:04,210 --> 00:25:07,890
+acceleration بتاعة ال piston من علاقة هذه omega
+
+263
+00:25:07,890 --> 00:25:10,950
+square r في كوسينت ثتا زي كوسينت وثيتا على n
+
+264
+00:25:10,950 --> 00:25:16,350
+وبالتالي هتكون قيمة ال inertia force ال mass بتاعة
+
+265
+00:25:16,350 --> 00:25:18,090
+ال reciprocating part طبعا ال mass بتاعة ال
+
+266
+00:25:18,090 --> 00:25:23,300
+reciprocating part ليس فقط ال piston فقطفي جزء
+
+267
+00:25:23,300 --> 00:25:26,640
+هندرسه في آخر الشبطة جزء جاي من .. من .. من ال
+
+268
+00:25:26,640 --> 00:25:28,900
+connecting rod ال connecting rod انا ال effect
+
+269
+00:25:28,900 --> 00:25:33,800
+بتاع ال force اللي الوزن بتاعه ممكن اوزعه على
+
+270
+00:25:33,800 --> 00:25:38,140
+الأطراف يعني ممكن اخل جزء بطريقة ما جزء من ال
+
+271
+00:25:38,140 --> 00:25:43,520
+connecting rod اللي اتأثر عند ال piston وجزء احطه
+
+272
+00:25:43,520 --> 00:25:48,650
+عندين ال pin اللي عند ال crankفإله قالية للتوزيع
+
+273
+00:25:48,650 --> 00:25:52,570
+على أي حال فال inertia force هتكون الماية بتاعة ال
+
+274
+00:25:52,570 --> 00:25:58,210
+piston في ال isolation بتاعة ال piston
+
+275
+00:25:58,210 --> 00:26:05,530
+زي ما حكينا في حالة engine أفقي بيصير
+
+276
+00:26:05,530 --> 00:26:13,230
+عملية تسارع لل piston من السكون لما ال piston
+
+277
+00:26:13,230 --> 00:26:16,430
+اتحرك من ال inner dead center لل outer dead center
+
+278
+00:26:16,430 --> 00:26:24,180
+يعنيهذا الميكانيزم اللي عنده
+
+279
+00:26:24,180 --> 00:26:37,020
+الان
+
+280
+00:26:37,020 --> 00:26:41,020
+هذا
+
+281
+00:26:41,020 --> 00:26:41,940
+ال inner dead center
+
+282
+00:26:48,170 --> 00:26:50,770
+بالحركة من ال inner dead center لل outer dead
+
+283
+00:26:50,770 --> 00:26:57,130
+center بيكون في حالة اتسارة من ال outer dead
+
+284
+00:26:57,130 --> 00:26:59,790
+center لل inner dead center بيكون خلاص راجع رجوع
+
+285
+00:26:59,790 --> 00:27:03,410
+بالاتجاه التاني راجع رجوع بالاتجاه التاني فبيكون
+
+286
+00:27:03,410 --> 00:27:14,670
+في حالة ايش deceleration او retardation طبعا
+
+287
+00:27:14,670 --> 00:27:17,470
+في حالة اتسارة ال inertia force
+
+288
+00:27:19,890 --> 00:27:22,350
+بتقل من ال net effort .. من ال net effort يعني جزء
+
+289
+00:27:22,350 --> 00:27:24,230
+من ال effort اللي بدي أبزله .. اللي بدي أبزله من
+
+290
+00:27:24,230 --> 00:27:28,370
+عملية الاحتراك بدي أخليه يسرع فيستهلك جزء من
+
+291
+00:27:28,370 --> 00:27:31,730
+الطاقة في عملية التسريع عشان كده بتكون بال minus
+
+292
+00:27:31,730 --> 00:27:36,790
+فجزء الرجوع لأ لإيه راجع بتساعد
+
+293
+00:27:42,020 --> 00:27:44,640
+لو جيت انا بقول انه بيه ال acceleration، ال
+
+294
+00:27:44,640 --> 00:27:48,180
+fingers بيه راجع، ال fingers سان اتجاه اللي هي
+
+295
+00:27:48,180 --> 00:27:49,720
+تتعالي نفس السرعة بس بيه راجع
+
+296
+00:27:54,960 --> 00:27:58,440
+يعني عشان توضح الصورة أكتر، بدك تعرف اللي هي دورة
+
+297
+00:27:58,440 --> 00:28:03,540
+ال engine، دورة إياش؟ ال engine، لو أخدت four
+
+298
+00:28:03,540 --> 00:28:08,440
+stroke engine، مظبوط؟ four stroke engine أكم shot
+
+299
+00:28:08,440 --> 00:28:13,800
+في ال four stroke؟ أربعة، إيش ال shot الأول؟ أولش
+
+300
+00:28:13,800 --> 00:28:21,350
+إيش؟ إيش تسحب؟تسحب هوا مع وقود يعني تفتح صمام
+
+301
+00:28:21,350 --> 00:28:26,330
+الوقود وبتفتح نحكي 180 درجة تسحب هاي أول ال stroke
+
+302
+00:28:26,330 --> 00:28:32,910
+ال stroke التاني هي compression طبعا انت لحد تاني
+
+303
+00:28:32,910 --> 00:28:38,590
+ما طلعتش طاقة انت بتطلعش طاقة تستنفذ طاقة انت أول
+
+304
+00:28:38,590 --> 00:28:44,370
+شفطت هوا مع وقود وانزلت ل 180 درجة ال shot التاني
+
+305
+00:28:45,380 --> 00:28:47,720
+بعمل compression بضغط الهواء و القوة دي و لما أصبح
+
+306
+00:28:47,720 --> 00:28:54,260
+الأخر بيعطيه الشعلة بيعطيه الشعلة بنفجر يعني دافع
+
+307
+00:28:54,260 --> 00:28:59,660
+في ال shot التالت أعطاني power في ال shot ترى لإن
+
+308
+00:28:59,660 --> 00:29:03,560
+بنفجر بننزل لتحت بعدين أنا بدي أخرج الدخنة بيطلع
+
+309
+00:29:03,560 --> 00:29:08,640
+إيش exhaust معناته الفترة اللي صار فيها power و
+
+310
+00:29:08,640 --> 00:29:14,460
+فيها energy shot واحد من أربعةعشان انا بكون راكب
+
+311
+00:29:14,460 --> 00:29:18,540
+على ال engine ال flywheel عشان اخزن الطاقة هذه في
+
+312
+00:29:18,540 --> 00:29:22,540
+ال shot هذا و استخدمه في الأشواط التانية اوزعها
+
+313
+00:29:22,540 --> 00:29:26,160
+عشان اول ما اتشغل ال engine بكون .. بكونش .. بكون
+
+314
+00:29:26,160 --> 00:29:29,060
+عندك ايش starter starter على الكهربع البطارية يكون
+
+315
+00:29:29,060 --> 00:29:34,100
+يشتغل عشان تبدأ العملية once بدت خلاص بيصير ايش ال
+
+316
+00:29:34,100 --> 00:29:39,760
+flywheel جهاز لتخزين الطاقة على شكل طاقة حركتها
+
+317
+00:29:39,760 --> 00:29:43,810
+شبكة رجاية هتحكي فيهامارت جاوبتك ولا انا اطلعت على
+
+318
+00:29:43,810 --> 00:29:51,450
+الموضوع؟ اجاوبتك بصورة مباشرة انا ان انا حكيتلك في
+
+319
+00:29:51,450 --> 00:29:58,690
+ال stroke الأولانية باشفط فى stroke التانية اضغط
+
+320
+00:29:58,690 --> 00:30:02,490
+خلنا ناخد التالتة وراها فى التالتة بسير ال power
+
+321
+00:30:02,490 --> 00:30:08,420
+بسير تسارعفى التالتة فى التالتة فى الرابع انا بصير
+
+322
+00:30:08,420 --> 00:30:14,140
+راجع بفتحله الصمام بتاع ال exhaust و بصير
+
+323
+00:30:14,140 --> 00:30:18,260
+بالاندفاع بتاعته بيصير retardation و هو راجع يعني
+
+324
+00:30:18,260 --> 00:30:22,700
+ال shotgun اندي احنا الدورة تلت و ستين درجة اول
+
+325
+00:30:22,700 --> 00:30:24,260
+مائة و اتونين درجة ده اخد التالتة و الرابع اول
+
+326
+00:30:24,260 --> 00:30:27,780
+مائة و اتونين درجة كان عندي power اكسلاريت دفعته
+
+327
+00:30:27,780 --> 00:30:33,020
+بعدين هيرجع يطرد هذه الفترة التانية هي ال
+
+328
+00:30:33,020 --> 00:30:33,640
+retardation
+
+329
+00:30:37,480 --> 00:30:42,220
+طيب معناته ال net effort هو ال net effect along
+
+330
+00:30:42,220 --> 00:30:48,380
+the line of stroke لل engine فى
+
+331
+00:30:48,380 --> 00:30:50,760
+positive effect جا من ال load من ال pressure بتاع
+
+332
+00:30:50,760 --> 00:30:53,940
+ال engine ممكن يكون ماضحان و العكس اذا بطلت بيكون
+
+333
+00:30:53,940 --> 00:31:02,410
+يعني يعني في ال power stroke بيكون الال working
+
+334
+00:31:02,410 --> 00:31:05,670
+fluid اللي هو محترق بيعمل work على ال piston بساعد
+
+335
+00:31:05,670 --> 00:31:09,970
+بيعمل work على ال piston في ال exhaust stroke انا
+
+336
+00:31:09,970 --> 00:31:14,990
+بعمل شغل ال piston بيعمل شغل على الداخل عشان
+
+337
+00:31:14,990 --> 00:31:19,850
+نطردها من ال negative فانت بيكون عندك fl minus
+
+338
+00:31:19,850 --> 00:31:24,230
+plus fi اللي هي ناشر force minus اذا كان متسارق في
+
+339
+00:31:24,230 --> 00:31:29,330
+ال power stroke plus في حالة ايه نحكي ال stroke
+
+340
+00:31:29,330 --> 00:31:30,110
+التاني اللي هي
+
+341
+00:31:33,720 --> 00:31:39,560
+minus the frictional resistance طبعا
+
+342
+00:31:39,560 --> 00:31:47,520
+هذه المعادلة هستغل ال 100% وهذه أهم ال what ال
+
+343
+00:31:47,520 --> 00:31:52,960
+friction نحكي بتكون هنا ال sign negative في حالة
+
+344
+00:31:52,960 --> 00:31:56,960
+ال piston is accelerating تكون positive في حالة ال
+
+345
+00:31:56,960 --> 00:32:00,060
+piston is retarding او decelerating
+
+346
+00:32:04,220 --> 00:32:08,060
+ال energy force عرفنا كيف نحسبها الان بدنا نشوف
+
+347
+00:32:08,060 --> 00:32:20,020
+كيف نحسب ال load لو كانت ال steam engine بيكون
+
+348
+00:32:20,020 --> 00:32:28,360
+فيه بخار من أمام الاستوانة و من خلفها يعني هو طالع
+
+349
+00:32:32,090 --> 00:32:35,550
+البخار بيضغط بيعطيني power و هو راجع بسكر صمام
+
+350
+00:32:35,550 --> 00:32:37,890
+بفتح صمام بيقعد بالفرق بال power يعني باخد power
+
+351
+00:32:37,890 --> 00:32:42,070
+على two strokes باخد power على two strokes معناته
+
+352
+00:32:42,070 --> 00:32:46,230
+ال piston بيكون متعرض لضغط على جانبي يعني في ضغط
+
+353
+00:32:46,230 --> 00:32:48,750
+هنا و في ضغط هنا و في ضغط هنا بس واحد بيكون أعلى
+
+354
+00:32:48,750 --> 00:32:53,930
+من التاني فالأفئل
+
+355
+00:32:53,930 --> 00:32:58,370
+في حالة steam engine بيساوي P1A1 للضغط على الجهة
+
+356
+00:32:58,370 --> 00:33:03,560
+الشمالمعينة speed 2 اي 2 الضغط و مساحة المقطع على
+
+357
+00:33:03,560 --> 00:33:08,520
+الجهة اليامين طبعا على الجهة اليامين بيكون عند هذه
+
+358
+00:33:08,520 --> 00:33:14,140
+ال piston بيكون فيه الرد فبتكون ال net area هنا
+
+359
+00:33:14,140 --> 00:33:20,460
+أصغر من هنا يعني هتكون net area ال area بتاعة
+
+360
+00:33:20,460 --> 00:33:25,180
+السلندر مانقس ال area بتاعة الرد اللي ماسك ال
+
+361
+00:33:25,180 --> 00:33:27,880
+piston من الجهة اليامين
+
+362
+00:33:35,330 --> 00:33:44,850
+هذا في حالة engine افضل في حالة engine رأسي
+
+363
+00:33:44,850 --> 00:33:49,690
+بتضيفي
+
+364
+00:33:49,690 --> 00:33:54,910
+ال component بتاعة الوزن ال piston هو
+
+365
+00:33:54,910 --> 00:34:01,750
+نازل الوزن بساعدني معناه ان ال piston effort بيعلى
+
+366
+00:34:02,570 --> 00:34:12,990
+و هو طالع بساعدني يعني بعكسني في ال minus نفس
+
+367
+00:34:12,990 --> 00:34:16,590
+المعايير بس دفت plus or minus الوزن تعرف
+
+368
+00:34:16,590 --> 00:34:22,530
+suffocating parts طيب
+
+369
+00:34:22,530 --> 00:34:26,030
+ال
+
+370
+00:34:26,030 --> 00:34:32,350
+piston effort اللي هو along the line of strokeوين
+
+371
+00:34:32,350 --> 00:34:36,610
+هيروح؟
+
+372
+00:34:36,610 --> 00:34:40,990
+صار anti-piston effort وين هيروح؟ من وين؟ كيف هو
+
+373
+00:34:40,990 --> 00:34:44,590
+هيصلق rank؟ على ال connecting rod ال connecting
+
+374
+00:34:44,590 --> 00:34:47,350
+rod انا عايش انا مهم الوزن neglecting weight of
+
+375
+00:34:47,350 --> 00:34:50,850
+connecting rod طبعا مهم الوزن بيصير ال connecting
+
+376
+00:34:50,850 --> 00:34:57,510
+rod to force member to force member ايش عن to
+
+377
+00:34:57,510 --> 00:35:03,730
+force member؟يعني جسم تحت أثير قوتين يعني بيكون ال
+
+378
+00:35:03,730 --> 00:35:07,810
+force بتأثر في اتجاه ال link يعني هتكون اندي هين
+
+379
+00:35:07,810 --> 00:35:11,710
+ال piston effort هنتقل ل force في ال connecting
+
+380
+00:35:11,710 --> 00:35:20,890
+rod هنتقل ع شكل ال force يسميها FQ طبعا
+
+381
+00:35:20,890 --> 00:35:26,130
+هاي
+
+382
+00:35:26,130 --> 00:35:26,770
+FQ
+
+383
+00:35:30,160 --> 00:35:39,940
+وهذا الزرعيش فاي وهذا ال piston effort فال
+
+384
+00:35:39,940 --> 00:35:45,700
+piston effort اللي هو F P هيكون سوى F Q cos فاي
+
+385
+00:35:45,700 --> 00:35:50,440
+صح؟
+
+386
+00:35:50,440 --> 00:35:58,310
+F Q cos فاي معناته F Q هيسوى F P على cos فاياللي
+
+387
+00:35:58,310 --> 00:36:02,010
+هي دلوقت fq بيسوي fp على cos فاي و احنا عرفنا
+
+388
+00:36:02,010 --> 00:36:11,850
+سابقا sin فاي ايش بيساوي sin θ على n و منها حسبنا
+
+389
+00:36:11,850 --> 00:36:17,190
+cos فاي اللي هي واحد minus sin square فاي اللي هي
+
+390
+00:36:17,190 --> 00:36:21,890
+واحد minus sin square θ على n تربية المنطقة ال
+
+391
+00:36:21,890 --> 00:36:27,090
+force او ال net piston effort انتقل
+
+392
+00:36:29,430 --> 00:36:36,030
+للـ Connecting Rod من خلال الـ FQ خلال الـ FQ
+
+393
+00:36:36,030 --> 00:36:48,090
+معناته هذه هي هذه الـ FQ الـ FQ بدي أحلله مركبتين
+
+394
+00:36:48,090 --> 00:36:52,730
+مركبة عمودية على ال crank هذه
+
+395
+00:36:58,670 --> 00:37:09,850
+هذا يسمى FT ومركب في اتجاه الكرانك FB لحظة هذه FQ
+
+396
+00:37:09,850 --> 00:37:12,850
+وهذه زاوية خارجها هذه ثتا وهذه فاي معناها هذه
+
+397
+00:37:12,850 --> 00:37:20,410
+زاوية كم؟ ثتا زائد فاي صح؟ هذه زاوية كلها تسعين
+
+398
+00:37:20,410 --> 00:37:28,340
+معناها هذه زاوية كم؟ تسعين minus theta زائد فايوها
+
+399
+00:37:28,340 --> 00:37:38,100
+دي تسعين minus theta الان ال FB بتعمل torque على
+
+400
+00:37:38,100 --> 00:37:42,440
+ال crank ال
+
+401
+00:37:42,440 --> 00:37:47,720
+FB لو بدي احسب ال moment حوالين او نتيجة تعملش لان
+
+402
+00:37:47,720 --> 00:37:53,480
+بتمر في المركز مين اللي بيعمل torque FT مركز FQ
+
+403
+00:37:53,480 --> 00:37:56,860
+العمودي على ال crank هي اللي بتعمل ال torque
+
+404
+00:37:56,860 --> 00:38:06,400
+العظيممعناته ال F T هذا الزاوية ال F B بيساوي F Q
+
+405
+00:38:06,400 --> 00:38:10,700
+ال F B بيساوي
+
+406
+00:38:10,700 --> 00:38:22,660
+F Q Cos Theta زائد Phi و ال F T بيساوي F Q Sin
+
+407
+00:38:22,660 --> 00:38:27,120
+Theta زائد Phi
+
+408
+00:38:31,450 --> 00:38:36,990
+الـ FB بتعمل load على ال bearing بتعمل load على ال
+
+409
+00:38:36,990 --> 00:38:40,610
+bearing اللي هنا المحور اللي هنا لكن مابتعمل عزل
+
+410
+00:38:40,610 --> 00:38:48,210
+العزل معناتهش هساوي ال torque هساوي
+
+411
+00:38:48,210 --> 00:38:57,250
+ال FT في ال radius فح؟ FT في
+
+412
+00:38:57,250 --> 00:39:01,550
+ال radiusبالطريقة اللى احنا شوفنا كيف ال piston
+
+413
+00:39:01,550 --> 00:39:06,290
+effort ينتقل عبر ال connecting rod و كيف بتحول ل
+
+414
+00:39:06,290 --> 00:39:10,110
+torque بلف
+
+415
+00:39:10,110 --> 00:39:11,150
+الكرانك
+
+416
+00:39:15,090 --> 00:39:18,690
+زي ما حكي ان ال F T بالساوية F Q Sine Theta Phi
+
+417
+00:39:18,690 --> 00:39:24,130
+هاي طبعا طبعا بعود عن F Q ال F Q اللي هي اياش F P
+
+418
+00:39:24,130 --> 00:39:28,570
+على Cos Phi F Q ليه F P على Cos Phi في Sine Theta
+
+419
+00:39:28,570 --> 00:39:32,190
+زائد Phi بفك Sine Theta زائد Phi Sine Theta Cos
+
+420
+00:39:32,190 --> 00:39:36,510
+Phi زائد Cos Theta Sine Phi و بعود عن Sine Phi و
+
+421
+00:39:36,510 --> 00:39:49,500
+Cos Phiو FB هكلمه تساوي FQ Cos FB FB
+
+422
+00:39:49,500 --> 00:39:54,900
+FB FB FB FB FB FB FB FB FB FB FB FB FB
+
+423
+00:40:03,170 --> 00:40:07,910
+طبعا ال cos فى التحت هنا بدخلها على كل term باسمه
+
+424
+00:40:07,910 --> 00:40:13,790
+هنا بس sin θ زاد cos θ sin فى على cos فى يعنى
+
+425
+00:40:13,790 --> 00:40:18,910
+هتكون FP sin θ زاد cos θ tan فى في أرض هذا ال
+
+426
+00:40:18,910 --> 00:40:24,810
+torque at the crank الان
+
+427
+00:40:24,810 --> 00:40:30,890
+احنا سابقا كنا نعرف ان sin فى بيساوي sin θ على N
+
+428
+00:40:30,890 --> 00:40:36,140
+مظبوطومن هنا حسبنا ال cos فى بيسوا واحد minus sin
+
+429
+00:40:36,140 --> 00:40:40,400
+square فى اللى بيسوا واحد minus sin square θ على n
+
+430
+00:40:40,400 --> 00:40:43,440
+square يعني واحدة ل n في n تربية minus sin تربية θ
+
+431
+00:40:43,440 --> 00:40:51,260
+ال tan فى sin فى على cos فى بعمل simplification و
+
+432
+00:40:51,260 --> 00:40:54,620
+بيصير هال علاقة ل tan فى برجع بعود في المعادلة
+
+433
+00:40:54,620 --> 00:41:00,340
+تاعة ال torque بيصير ال torque بيستواف P في R sin
+
+434
+00:41:00,340 --> 00:41:05,780
+θ زي sin 2 θ على 2في الجدر التربيعي لان تربية
+
+435
+00:41:05,780 --> 00:41:11,720
+minus sign تربية معناته انا استطعت ان احسب ال
+
+436
+00:41:11,720 --> 00:41:16,920
+torque الناتج عن piston effort at the piston و ال
+
+437
+00:41:16,920 --> 00:41:24,080
+piston effort ناتج عن ال pressure ناتج عن عملية
+
+438
+00:41:24,080 --> 00:41:24,700
+الاحتراق
+
+439
+00:41:27,390 --> 00:41:31,790
+هو ال inertia force و ال friction force هذا هو
+
+440
+00:41:31,790 --> 00:41:35,530
+الجهد الصافي اللي بياخد من ال piston و بيعمل فيه
+
+441
+00:41:35,530 --> 00:41:39,410
+عزم عند ال crank و اللي فيه بتلف ال crank هذه هي
+
+442
+00:41:39,410 --> 00:41:46,610
+المعادلة طيب
+
+443
+00:41:46,610 --> 00:41:49,710
+الآن
+
+444
+00:41:49,710 --> 00:41:56,170
+sin² صغيرة كتير بالمقارنة مع n²
+
+445
+00:41:59,640 --> 00:42:05,400
+ف ها دي بيصير لو صين سكوير اقل بكتير مقارنة هعمل
+
+446
+00:42:05,400 --> 00:42:10,380
+فرضية هنا ان الان سكوير ها دي بيصير تطلع تحت الصين
+
+447
+00:42:10,380 --> 00:42:18,620
+ثتا زي الصين تيو ثتا على اتنين ان بتصفى
+
+448
+00:42:18,620 --> 00:42:23,160
+المعادلة بالشكل هذا الكتاب بحل graphical method
+
+449
+00:42:31,260 --> 00:42:38,500
+هو بيحكي ان ال Fp ال torque at the crank بيستوي ال
+
+450
+00:42:38,500 --> 00:42:44,660
+piston effort في المسافة OM اللي هي هدف
+
+451
+00:43:16,410 --> 00:43:19,590
+Find the inertia force for the following data of
+
+452
+00:43:19,590 --> 00:43:23,210
+an internal combustion engineمعطيني ال bore بتاعة
+
+453
+00:43:23,210 --> 00:43:29,110
+السيلندر 175 ميلي معطيني ال stroke 200 ميلي معطيني
+
+454
+00:43:29,110 --> 00:43:35,070
+ال engine speed 500 rpm ومعطيني length of
+
+455
+00:43:35,070 --> 00:43:39,490
+connecting rod 400 ال crack angle 60 درجة افهم
+
+456
+00:43:39,490 --> 00:43:43,310
+inner dead center و ال mass of reciprocating parts
+
+457
+00:43:43,310 --> 00:43:49,010
+180 كيلو بيستون و ملحقاته 180 كيلو جرام بده ال
+
+458
+00:43:49,010 --> 00:43:51,230
+inertia force ال inertia force ايش بيستوي
+
+459
+00:43:58,320 --> 00:44:06,800
+م ر في ا ا ر وال ا ا ر ايش بتساوي عشان اوميجا
+
+460
+00:44:06,800 --> 00:44:15,860
+سكويت ا ر في كوسين تيتا زائد كوسين two theta على n
+
+461
+00:44:15,860 --> 00:44:22,840
+صح ال theta ات لما اعطينيها ستين
+
+462
+00:44:22,840 --> 00:44:26,600
+وال
+
+463
+00:44:26,600 --> 00:44:31,260
+اوميجاخمسمية بضرب اتنين بقى ع ستين بحول ال reading
+
+464
+00:44:31,260 --> 00:44:41,620
+بال second بالظبط و ال R كم معطينيها أكم
+
+465
+00:44:41,620 --> 00:44:46,840
+ال R معطيني ال stroke الشوط الشوط متين معناته ال R
+
+466
+00:44:46,840 --> 00:44:53,080
+كم مية ال stroke ع اتنين معناته ال R بيساوي متين ع
+
+467
+00:44:53,080 --> 00:45:01,370
+اتنين و ال N هتكون تساوي اربعميةعالمية يعني أكم هو
+
+468
+00:45:01,370 --> 00:45:08,470
+أربعة وبحسب ال AR بعدين بحسب ال inertia force هيكم
+
+469
+00:45:08,470 --> 00:45:11,450
+كمان خلصت محاضرة اليوم يعطيكوا العافية
+
diff --git a/PL9fwy3NUQKwa0nXiCdyQcTW4hWDLTGpDb/fI8Ana0_Uzg_raw.json b/PL9fwy3NUQKwa0nXiCdyQcTW4hWDLTGpDb/fI8Ana0_Uzg_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..6c0841af4a1498d5013a5895f19e9a0d8c4e348d
--- /dev/null
+++ b/PL9fwy3NUQKwa0nXiCdyQcTW4hWDLTGpDb/fI8Ana0_Uzg_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 2966, "start": 5.06, "end": 29.66, "text": "السلام عليكم ورحمة الله وبركاته اليوم هنكمل في مادة نظرية الألات هنبدأ بالشفتر جديد اللي هو balancing of rotating masses توزين الكتل الدوارة الكتل الدوارة زي ال crank بتاعة ال engine كتلة بتدور نتيجة انه في ال engine انا عند هاي ال crank", "tokens": [6027, 3794, 37440, 25894, 24793, 4032, 2288, 35571, 3660, 21984, 4032, 26890, 4117, 9307, 3224, 45595, 20498, 8032, 1863, 24793, 1211, 8978, 3714, 18513, 3660, 8717, 19913, 2288, 10632, 16247, 1211, 9307, 8032, 1863, 44510, 10721, 20666, 8592, 5172, 2655, 2288, 10874, 16254, 3215, 13672, 1829, 31439, 22495, 295, 19627, 23935, 33427, 11622, 9957, 33251, 2655, 1211, 32748, 2407, 9640, 3660, 33251, 2655, 1211, 32748, 2407, 9640, 3660, 30767, 1829, 2423, 21263, 39894, 995, 27884, 2423, 2848, 9122, 2655, 37977, 39894, 3215, 13063, 8717, 31371, 7435, 3660, 16472, 3224, 8978, 2423, 2848, 1975, 8315, 43242, 8032, 47302, 2423, 21263], "avg_logprob": -0.15625000342726708, 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1975, 1829, 8592, 4724, 1829, 3794, 995, 45865, 6055, 32640, 9957, 8978, 2423, 9725, 6055, 36081, 995, 1975, 24793, 43242, 8315, 1975, 2655, 1863, 9957, 538, 6055, 32640, 9957, 1975, 24793, 8608, 3555, 27884, 8608, 2655, 9957, 4032, 8717, 9381, 8978, 1975, 2655, 1863, 9957, 538, 13672, 1829, 39896, 29538, 2423, 1859, 20328, 5016, 22807], "avg_logprob": -0.33506945485160466, "compression_ratio": 1.4932432432432432, "no_speech_prob": 2.980232238769531e-07, "words": [{"start": 3023.29, "end": 3024.17, "word": "ال", "probability": 0.7080078125}, {"start": 3024.17, "end": 3024.47, "word": " work", "probability": 0.2266845703125}, {"start": 3024.47, "end": 3024.91, "word": " done", "probability": 0.82568359375}, {"start": 3024.91, "end": 3025.35, "word": " per", "probability": 0.95458984375}, {"start": 3025.35, "end": 3025.93, "word": " cycle", "probability": 0.91259765625}, {"start": 3025.93, "end": 3026.41, "word": " w", "probability": 0.1241455078125}, {"start": 3026.41, "end": 3026.97, "word": " cycle", "probability": 0.57958984375}, {"start": 3026.97, "end": 3028.25, "word": " ايش", "probability": 0.6106363932291666}, {"start": 3028.25, "end": 3028.67, "word": " بيساوي", "probability": 0.8353515625}, {"start": 3028.67, "end": 3030.03, "word": " تيمين", "probability": 0.58447265625}, {"start": 3030.03, "end": 3033.27, "word": " في", "probability": 0.74267578125}, {"start": 3033.27, "end": 3033.39, "word": " ال", "probability": 0.66943359375}, {"start": 3033.39, "end": 3033.67, "word": " theta", "probability": 0.451171875}, {"start": 3033.67, "end": 3034.07, "word": " تيتا", "probability": 0.6128336588541666}, {"start": 3034.07, "end": 3034.25, "word": " اكم", "probability": 0.6220703125}, {"start": 3034.25, "end": 3035.29, "word": " عندنا", "probability": 0.66015625}, {"start": 3035.29, "end": 3036.47, "word": " اتنين", "probability": 0.8828125}, {"start": 3036.47, "end": 3036.73, "word": " by", "probability": 0.398681640625}, {"start": 3036.73, "end": 3038.03, "word": " تيمين", "probability": 0.935546875}, {"start": 3038.03, "end": 3038.35, "word": " اكم", "probability": 0.908935546875}, {"start": 3038.35, "end": 3039.31, "word": " سبعة", "probability": 0.8572591145833334}, {"start": 3039.31, "end": 3039.61, "word": " ستين", "probability": 0.669189453125}, {"start": 3039.61, "end": 3039.71, "word": " و", "probability": 0.97998046875}, {"start": 3039.71, "end": 3039.93, "word": " نص", "probability": 0.913330078125}, {"start": 3039.93, "end": 3042.91, "word": " في", "probability": 0.87451171875}, {"start": 3042.91, "end": 3043.41, "word": " اتنين", "probability": 0.986572265625}, {"start": 3043.41, "end": 3043.79, "word": " by", "probability": 0.958984375}, {"start": 3043.79, "end": 3045.65, "word": " اللي", "probability": 0.772216796875}, {"start": 3045.65, "end": 3045.81, "word": " هي", "probability": 0.8037109375}, {"start": 3045.81, "end": 3046.13, "word": " هذه", "probability": 0.76611328125}, {"start": 3046.13, "end": 3046.37, "word": " ال", "probability": 0.921875}, {"start": 3046.37, "end": 3046.67, "word": " area", "probability": 0.9208984375}, {"start": 3046.67, "end": 3049.25, "word": " صح؟", "probability": 0.9187825520833334}], "temperature": 1.0}, {"id": 104, "seek": 307251, "start": 3051.91, "end": 3072.51, "text": "هي هتكون مية و خمس سلاتين by يعني ال delta E هتكون ال CE دلتة ايه اللي هي احداشر point سبعة تمانية", "tokens": [3224, 1829, 8032, 2655, 30544, 3714, 10632, 4032, 16490, 2304, 3794, 8608, 1211, 9307, 9957, 538, 37495, 22653, 2423, 8289, 462, 8032, 2655, 30544, 2423, 28109, 11778, 1211, 2655, 3660, 1975, 1829, 3224, 13672, 1829, 39896, 1975, 24401, 33599, 2288, 935, 8608, 3555, 27884, 46811, 7649, 10632], "avg_logprob": -0.4700520783662796, "compression_ratio": 1.28, "no_speech_prob": 0.0, "words": [{"start": 3051.91, "end": 3052.15, "word": "هي", "probability": 0.4066162109375}, {"start": 3052.15, "end": 3052.43, "word": " هتكون", "probability": 0.6789957682291666}, {"start": 3052.43, "end": 3052.59, "word": " مية", "probability": 0.5645751953125}, {"start": 3052.59, "end": 3052.75, "word": " و", "probability": 0.9189453125}, {"start": 3052.75, "end": 3052.79, "word": " خمس", "probability": 0.9326171875}, {"start": 3052.79, "end": 3053.35, "word": " سلاتين", "probability": 0.70367431640625}, {"start": 3053.35, "end": 3056.45, "word": " by", "probability": 0.1663818359375}, {"start": 3056.45, "end": 3058.75, "word": " يعني", "probability": 0.6192626953125}, {"start": 3058.75, "end": 3058.89, "word": " ال", "probability": 0.61181640625}, {"start": 3058.89, "end": 3059.11, "word": " delta", "probability": 0.59130859375}, {"start": 3059.11, "end": 3059.25, "word": " E", "probability": 0.54248046875}, {"start": 3059.25, "end": 3060.67, "word": " هتكون", "probability": 0.8961588541666666}, {"start": 3060.67, "end": 3063.07, "word": " ال", "probability": 0.7294921875}, {"start": 3063.07, "end": 3064.39, "word": " CE", "probability": 0.460205078125}, {"start": 3064.39, "end": 3066.79, "word": " دلتة", "probability": 0.61944580078125}, {"start": 3066.79, "end": 3067.13, "word": " ايه", "probability": 0.7561848958333334}, {"start": 3067.13, "end": 3069.35, "word": " اللي", "probability": 0.65576171875}, {"start": 3069.35, "end": 3069.51, "word": " هي", "probability": 0.82958984375}, {"start": 3069.51, "end": 3069.89, "word": " احداشر", "probability": 0.753265380859375}, {"start": 3069.89, "end": 3070.05, "word": " point", "probability": 0.212890625}, {"start": 3070.05, "end": 3070.63, "word": " سبعة", "probability": 0.9567057291666666}, {"start": 3070.63, "end": 3072.51, "word": " تمانية", "probability": 0.9794921875}], "temperature": 1.0}, {"id": 105, "seek": 309186, "start": 3073.48, "end": 3091.86, "text": "ع ال work done per person هي ال 135 by و بتحسبوها point o اين سبعة point o اين سبعة point o اين سبعة point o اين سبعة point o اين سبعة point o اين سبعة point o اين سبعة", "tokens": [3615, 2423, 589, 1096, 680, 954, 39896, 2423, 42652, 538, 4032, 39894, 5016, 35457, 2407, 11296, 935, 277, 1975, 9957, 8608, 3555, 27884, 935, 277, 1975, 9957, 8608, 3555, 27884, 935, 277, 1975, 9957, 8608, 3555, 27884, 935, 277, 1975, 9957, 8608, 3555, 27884, 935, 277, 1975, 9957, 8608, 3555, 27884, 935, 277, 1975, 9957, 8608, 3555, 27884, 935, 277, 1975, 9957, 8608, 3555, 27884], "avg_logprob": -0.33688446337526495, "compression_ratio": 2.532608695652174, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 3073.48, "end": 3073.72, "word": "ع", "probability": 0.884765625}, {"start": 3073.72, "end": 3073.84, "word": " ال", "probability": 0.765625}, {"start": 3073.84, "end": 3074.06, "word": " work", "probability": 0.90576171875}, {"start": 3074.06, "end": 3074.28, "word": " done", "probability": 0.86474609375}, {"start": 3074.28, "end": 3074.52, "word": " per", "probability": 0.64794921875}, {"start": 3074.52, "end": 3074.7, "word": " person", "probability": 0.1396484375}, {"start": 3074.7, "end": 3074.98, "word": " هي", "probability": 0.2159423828125}, {"start": 3074.98, "end": 3075.04, "word": " ال", "probability": 0.4404296875}, {"start": 3075.04, "end": 3075.4, "word": " 135", "probability": 0.70751953125}, {"start": 3075.4, "end": 3077.34, "word": " by", "probability": 0.50244140625}, {"start": 3077.34, "end": 3077.84, "word": " و", "probability": 0.4833984375}, {"start": 3077.84, "end": 3078.6, "word": " بتحسبوها", "probability": 0.9619140625}, {"start": 3078.6, "end": 3079.22, "word": " point", "probability": 0.35888671875}, {"start": 3079.22, "end": 3079.52, "word": " o", "probability": 0.4462890625}, {"start": 3079.52, "end": 3081.46, "word": " اين", "probability": 0.267730712890625}, {"start": 3081.46, "end": 3082.16, "word": " سبعة", "probability": 0.9334309895833334}, {"start": 3082.16, "end": 3082.54, "word": " point", "probability": 0.45361328125}, {"start": 3082.54, "end": 3082.54, "word": " o", "probability": 0.76318359375}, {"start": 3082.54, "end": 3082.54, "word": " اين", "probability": 0.64599609375}, {"start": 3082.54, "end": 3082.54, "word": " سبعة", "probability": 0.9773763020833334}, {"start": 3082.54, "end": 3082.54, "word": " point", "probability": 0.71875}, {"start": 3082.54, "end": 3083.04, "word": " o", "probability": 0.8486328125}, {"start": 3083.04, "end": 3083.6, "word": " اين", "probability": 0.74658203125}, {"start": 3083.6, "end": 3084.42, "word": " سبعة", "probability": 0.984375}, {"start": 3084.42, "end": 3084.42, "word": " point", "probability": 0.70361328125}, {"start": 3084.42, "end": 3084.42, "word": " o", "probability": 0.9169921875}, {"start": 3084.42, "end": 3085.88, "word": " اين", "probability": 0.840087890625}, {"start": 3085.88, "end": 3086.88, "word": " سبعة", "probability": 0.9866536458333334}, {"start": 3086.88, "end": 3086.88, "word": " point", "probability": 0.83740234375}, {"start": 3086.88, "end": 3086.88, "word": " o", "probability": 0.943359375}, {"start": 3086.88, "end": 3086.88, "word": " اين", "probability": 0.874755859375}, {"start": 3086.88, "end": 3086.92, "word": " سبعة", "probability": 0.9871419270833334}, {"start": 3086.92, "end": 3089.38, "word": " point", "probability": 0.880859375}, {"start": 3089.38, "end": 3089.54, "word": " o", "probability": 0.95263671875}, {"start": 3089.54, "end": 3089.68, "word": " اين", "probability": 0.890625}, {"start": 3089.68, "end": 3090.1, "word": " سبعة", "probability": 0.9869791666666666}, {"start": 3090.1, "end": 3090.28, "word": " point", "probability": 0.89794921875}, {"start": 3090.28, "end": 3091.8, "word": " o", "probability": 0.95947265625}, {"start": 3091.8, "end": 3091.8, "word": " اين", "probability": 0.903564453125}, {"start": 3091.8, "end": 3091.86, "word": " سبعة", "probability": 0.9866536458333334}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 3091.7601875, "duration_after_vad": 2793.8531249999896}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwa0nXiCdyQcTW4hWDLTGpDb/gPBBfvb_0qE.srt b/PL9fwy3NUQKwa0nXiCdyQcTW4hWDLTGpDb/gPBBfvb_0qE.srt
new file mode 100644
index 0000000000000000000000000000000000000000..0a6e843146277d79baf7df5ec80dbe5dd52028b2
--- /dev/null
+++ b/PL9fwy3NUQKwa0nXiCdyQcTW4hWDLTGpDb/gPBBfvb_0qE.srt
@@ -0,0 +1,659 @@
+1
+00:00:05,080 --> 00:00:08,100
+بسم الله الرحمن الرحيم السلام عليكم ورحمة الله
+
+2
+00:00:08,100 --> 00:00:12,840
+وبركاته اليوم هنكمل محاضرات نماذج نظرية الآلات
+
+3
+00:00:12,840 --> 00:00:15,560
+بدأنا في الـ chapter اللي هو بيحكي عن الـ inertia
+
+4
+00:00:15,560 --> 00:00:21,640
+forces in reciprocating mechanisms ودرسنا حالة
+
+5
+00:00:21,640 --> 00:00:25,780
+اللي هي slider  cranking mechanism عملنا kinematic
+
+6
+00:00:25,780 --> 00:00:29,580
+analysis جبنا الـ displacement, velocity و الـ
+
+7
+00:00:29,580 --> 00:00:32,660
+acceleration للـ piston و جبنا الـ angle of
+
+8
+00:00:32,660 --> 00:00:36,140
+velocity و الـ angle of acceleration للـ connecting
+
+9
+00:00:36,140 --> 00:00:42,400
+rod بعدين عملنا force analysis حسبنا الـ piston
+
+10
+00:00:42,400 --> 00:00:47,300
+effort أو الـ effort عند الـ piston اللي هو محصلة الـ
+
+11
+00:00:47,300 --> 00:00:53,090
+load اللي جاء من الـ pressure forces مطروح منه الـ
+
+12
+00:00:53,090 --> 00:00:58,650
+frictional resistance مطروح منه الـ inertia force
+
+13
+00:00:58,650 --> 00:01:02,530
+في حالة كان الـ piston في حالة تسارع أو مضاف الـ
+
+14
+00:01:02,530 --> 00:01:08,430
+inertia force في حالة كان الـ piston في حالة تباطؤ
+
+15
+00:01:08,430 --> 00:01:14,150
+لأن الـ piston effort بينتقل إلى الـ connecting rod
+
+16
+00:01:14,150 --> 00:01:20,040
+من خلال الـ FQ و الـ FQ حلّيناها لمُركبتين، واحدة باتجاه
+
+17
+00:01:20,040 --> 00:01:26,440
+الكرانك، واحدة عمودية على الكرانك FT, الـ FT هي اللي
+
+18
+00:01:26,440 --> 00:01:32,180
+بتعمل العزم الدوراني حول الكرانك، حسبنا الـ torque
+
+19
+00:01:32,180 --> 00:01:39,420
+حسبنا الـ
+
+20
+00:01:39,420 --> 00:01:44,620
+FQ بعدين حسبنا الـ FT بعدين الـ FB, الـ force باتجاه
+
+21
+00:01:44,620 --> 00:01:50,530
+الكرانك بعدين الـ torque اللي
+
+22
+00:01:50,530 --> 00:01:54,330
+هو مُعطّب للواقع F, الـ torque بيساوي ال F P, الـ piston
+
+23
+00:01:54,330 --> 00:01:58,530
+effort في R sin θ زائد sin 2θ على اتنين
+
+24
+00:01:58,530 --> 00:02:05,270
+حلينا  examples خمسة أو ستة هنحل كمان example بعدين
+
+25
+00:02:05,270 --> 00:02:11,350
+نكمل The
+
+26
+00:02:11,350 --> 00:02:14,570
+crank of a horizontal engine is three hundred
+
+27
+00:02:14,570 --> 00:02:20,850
+millimeters معطيل طول الكرانك لآلة  أفقية اللي هي الـ
+
+28
+00:02:20,850 --> 00:02:25,110
+R بيساوي
+
+29
+00:02:25,110 --> 00:02:33,250
+ثلاث مية ملي متر الـ mass of reciprocating parts is
+
+30
+00:02:33,250 --> 00:02:40,350
+two hundred fifty kilogram, الـ MR اثنين
+
+31
+00:02:40,350 --> 00:02:43,090
+وخمسين kilogram
+
+32
+00:02:45,830 --> 00:02:48,770
+when the crank has traveled six degrees from the
+
+33
+00:02:48,770 --> 00:02:56,210
+inner dead center، ها عندي الـ crank 
+
+34
+00:02:56,210 --> 00:03:04,890
+ها
+
+35
+00:03:04,890 --> 00:03:09,150
+الـ piston والزاوية
+
+36
+00:03:09,150 --> 00:03:18,470
+دي كانت ستين درجة، يعني الـ θ بيساوي ستين درجة
+
+37
+00:03:18,470 --> 00:03:23,510
+when the crank has traveled six degrees from the 
+
+38
+00:03:23,510 --> 00:03:27,510
+inner dead center the difference between the
+
+39
+00:03:27,510 --> 00:03:31,670
+driving and back pressure، في عندي هنا في driving ع
+
+40
+00:03:31,670 --> 00:03:36,370
+الجهد pressure في عندي back pressure الفرق بينهم 
+
+41
+00:03:36,370 --> 00:03:41,010
+3.5 نيوتن/المليمتر مربع يعني 3.5 ميجا
+
+42
+00:03:41,010 --> 00:03:46,030
+باسكال يعني ΔP
+
+43
+00:03:49,330 --> 00:03:57,770
+إذا حد مشغل جوال يطفئه ماشي، Δ
+
+44
+00:03:57,770 --> 00:04:04,550
+P بيساوي 3.5 ميجا
+
+45
+00:04:04,550 --> 00:04:09,350
+باسكال الـ 
+
+46
+00:04:09,350 --> 00:04:12,670
+connecting rod length between centers is one point
+
+47
+00:04:12,670 --> 00:04:20,570
+two meters، طول الـ connecting rod 1.2 متر 
+
+48
+00:04:20,570 --> 00:04:30,190
+الـ L/R اللي هي 1200 على 300 
+
+49
+00:04:30,190 --> 00:04:38,270
+4 طيب 
+
+50
+00:04:38,270 --> 00:04:45,750
+الـ cylinder bore، قطر الـ cylinder دي
+
+51
+00:04:48,320 --> 00:04:55,040
+نصف متر، if the
+
+52
+00:04:55,040 --> 00:05:00,820
+engine runs at two hundred fifty rpm, الـ ω 250
+
+53
+00:05:00,820 --> 00:05:07,880
+rpm يعني هتكون 250 × 2π
+
+54
+00:05:07,880 --> 00:05:14,700
+26.18 radians
+
+55
+00:05:14,700 --> 00:05:16,600
+per second
+
+56
+00:05:24,230 --> 00:05:27,950
+and if the effect of the piston rod diameter
+
+57
+00:05:27,950 --> 00:05:32,570
+المهمل 
+
+58
+00:05:32,570 --> 00:05:38,150
+يعني واضح قطر الـ، قطر الـ cylinder نصف متر، معناه إن الـ 
+
+59
+00:05:38,150 --> 00:05:42,450
+piston rod هيكون صغير كتير بالمقارنة مع الـ piston
+
+60
+00:05:42,450 --> 00:05:46,270
+rod من هنا calculate
+
+61
+00:05:46,270 --> 00:05:47,890
+the piston effort
+
+62
+00:05:52,690 --> 00:06:01,730
+طبعاً احنا حكينا شو بيساوي الـ FL الـ
+
+63
+00:06:01,730 --> 00:06:05,890
+FL ناقص 
+
+64
+00:06:05,890 --> 00:06:09,570
+زائد
+
+65
+00:06:09,570 --> 00:06:19,850
+FI ناقص الـ frictional resistance احنا في اللحظة
+
+66
+00:06:19,850 --> 00:06:21,970
+… يعني في الـ … يعني احنا مش هنعمل علامة الـ
+
+67
+00:06:21,970 --> 00:06:28,170
+pressure resistance هنعملها هنكتبها RF
+
+68
+00:06:28,170 --> 00:06:39,570
+بيساوى Zero وما نقلش، هنحسب الـ load، الـ load الـ FL
+
+69
+00:06:39,570 --> 00:06:47,790
+هيساوى ΔV مساحة المقطع بتاع الـ cylinder صح؟ يعني
+
+70
+00:06:47,790 --> 00:06:59,130
+هيساوى الـ A بيساوى π/4 D<sup>2</sup> في ΔP يعني
+
+71
+00:06:59,130 --> 00:07:12,270
+عندي الـ π/4 موجود عندي، نص متر ×
+
+72
+00:07:12,270 --> 00:07:15,350
+×
+
+73
+00:07:15,350 --> 00:07:21,090
+3.5 × 10<sup>6</sup> عشان أحول الـ
+
+74
+00:07:21,090 --> 00:07:32,770
+نيوتن/المتر مربع 68722
+
+75
+00:07:32,770 --> 00:07:40,570
+نيوتن، الـ inertia
+
+76
+00:07:40,570 --> 00:07:41,690
+force بيساوي 
+
+77
+00:07:53,780 --> 00:07:59,260
+الـ inertia force FI بيساوي 
+
+78
+00:07:59,260 --> 00:08:06,960
+MR ω<sup>2</sup>، MR ω
+
+79
+00:08:06,960 --> 00:08:10,740
+<sup>2</sup>R 
+
+80
+00:08:10,740 --> 00:08:28,270
+(cos θ + cos 2θ / n)، يعني هيكون الـ MR 250
+
+81
+00:08:28,270 --> 00:08:43,350
+كيلو، ω 26.18 تربيع، R 300 cos
+
+82
+00:08:43,350 --> 00:08:47,790
+60 +
+
+83
+00:08:47,790 --> 00:08:52,950
+cos 120 / 4 
+
+84
+00:09:00,150 --> 00:09:10,190
+cos 60 كام؟ نص، ودي ناقص نص، ناقص نص سالب 8 كام
+
+85
+00:09:10,190 --> 00:09:22,170
+بتطلع الجواب 19000 نيوتن 
+
+86
+00:09:28,550 --> 00:09:35,250
+هيكون الـ effort اللي هو 68000 هذا
+
+87
+00:09:35,250 --> 00:09:42,470
+اللي جاء من احتراق الغازات جزء سوف يُستنفذ في تسريع
+
+88
+00:09:42,470 --> 00:09:51,150
+الـ piston عشان أسرّعه محتاج طاقة، أضغط عشان أضغط أو
+
+89
+00:09:51,150 --> 00:09:53,910
+هو وطيق هو بيتباطأ ما هو فيه طاقة ويقعد يخسرها
+
+90
+00:09:53,910 --> 00:09:59,410
+إليه، هتكون تماماً 60720
+
+91
+00:09:59,410 --> 00:10:09,550
+ناقص الـ FI 19076 49400
+
+92
+00:10:09,550 --> 00:10:13,890
+49445 نيوتن هذا الـ piston effort يعني حوالي 9 
+
+93
+00:10:18,400 --> 00:10:21,180
+و40 يعني لو قسمنا على 10 يعني حوالي … الـ
+
+94
+00:10:21,180 --> 00:10:26,980
+piston effort حوالي 5 طن وزن 5 طن اه piston 
+
+95
+00:10:26,980 --> 00:10:35,220
+ضخم، صحيح،  مواخر أو محطة التوليد أو جِزاهِير، في محرك 
+
+96
+00:10:35,220 --> 00:10:42,650
+الرشد؟ اه في قطار واحد؟ صحيح في حالة السفن الضخمة
+
+97
+00:10:42,650 --> 00:10:51,250
+أو في حالة محطات الكهرباء بيكون في الآلات هذه طيب
+
+98
+00:10:51,250 --> 00:10:54,970
+هذا المطلوب الأول، المطلوب الثاني
+
+99
+00:10:54,970 --> 00:11:00,150
+thrust in the connecting rod ايش يعني thrust in
+
+100
+00:11:00,150 --> 00:11:03,530
+the connecting rod؟ القوة اللي هي جاية من الـ FQ صح؟ الـ
+
+101
+00:11:03,530 --> 00:11:10,230
+FQ ايش بيساوي؟ 
+
+102
+00:11:10,230 --> 00:11:11,290
+الـ FQ ايش بيساوي؟
+
+103
+00:11:17,870 --> 00:11:23,070
+الـ Fq بيساوي
+
+104
+00:11:23,070 --> 00:11:35,690
+الـ piston effort على cos φ، طيب
+
+105
+00:11:35,690 --> 00:11:41,870
+الـ φ أنا عارفها هي φ صح؟ 
+
+106
+00:11:47,600 --> 00:11:55,700
+يعني هتكون ممكن مباشرة … مباشرة احكي أنا إن الـ 
+
+107
+00:11:55,700 --> 00:12:10,900
+sin φ بيساوي … n بيساوي r sin θ صح؟ و
+
+108
+00:12:10,900 --> 00:12:15,480
+sin φ بيساوي
+
+109
+00:12:15,480 --> 00:12:23,300
+sin θ على n أو مباشرة من المعادلة أعوض طاولة
+
+110
+00:12:23,300 --> 00:12:38,060
+مباشرة يعني هتكون sin 60 على 4 ومنها بحسب الـ φ كام؟ 
+
+111
+00:12:38,060 --> 00:12:44,520
+12.5 درجة هنا هحكي الـ piston effort اللي هو 
+
+112
+00:12:44,520 --> 00:12:50,490
+49445 على cos 
+
+113
+00:12:50,490 --> 00:12:57,230
+12.5 ها
+
+114
+00:12:57,230 --> 00:13:02,290
+هيطلع FQ كام؟ حاجة تطلع 50 
+
+115
+00:13:02,290 --> 00:13:07,410
+ألف نيوتن 
+
+116
+00:13:16,080 --> 00:13:20,160
+بدّي الـ tangential force on the crank pin بدّي الـ FT
+
+117
+00:13:20,160 --> 00:13:30,700
+صح، الـ FT الـ
+
+118
+00:13:30,700 --> 00:13:40,400
+FT ايش بيساوي؟ بيساوي
+
+119
+00:13:40,400 --> 00:13:41,060
+FQ 
+
+120
+00:13:44,210 --> 00:13:55,250
+sin (θ + φ) يعني الـ FQ اللي هي 50645
+
+121
+00:13:55,250 --> 00:14:02,910
+في sin (60 + 12.5)
+
+122
+00:14:13,160 --> 00:14:21,160
+48300 نيوتن، معناته العزم على 
+
+123
+00:14:21,160 --> 00:14:26,060
+الـ … العزم على الـ … على الـ crank ايش بيساوي؟ 
+
+124
+00:14:26,060 --> 00:14:33,660
+torque = R × FT, الـ R عندي 300 
+
+125
+00:14:36,280 --> 00:14:43,280
+× 48300 14490000 
+
+126
+00:14:43,280 --> 00:14:48,280
+نيوتن طيب لو بدي أحسن الـ power كيف بدي
+
+127
+00:14:48,280 --> 00:14:52,760
+أحسن الـ power في اللحظة هذه، power 
+
+128
+00:14:52,760 --> 00:15:03,670
+torque × ω صح؟ الـ power بيساوي الـ torque ×
+
+129
+00:15:03,670 --> 00:15:06,430
+الـ ω في اللحظة هذه، يعني الـ torque كانت 14490 
+
+130
+00:15:06,430 --> 00:15:15,450
+× الـ ω اللي هي 26.18
+
+131
+00:15:15,450 --> 00:15:22,010
+380000 سيبوها
+
+132
+00:15:22,010 --> 00:15:28,130
+379000 
+
+133
+00:15:28,130 --> 00:15:34,300
+و 379000 × 379000 × 
+
+134
+00:15:34,300 --> 00:15:40,200
+379000، أقسمها على 746، 746
+
+135
+00:15:40,200 --> 00:15:44,220
+أقسامها على 746 509
+
+136
+00:15:44,220 --> 00:15:52,060
+509 حصان
+
+137
+00:15:52,060 --> 00:15:59,020
+حصان، يعني موتور دخل لو
+
+138
+00:15:59,020 --> 00:16:09,060
+بدّي أجيب الـ FB الـ FB بيساوي بيساوي 
+
+139
+00:16:09,060 --> 00:16:14,040
+الـ FQ cos 
+
+140
+00:16:14,040 --> 00:16:17,340
+θ 
+
+141
+00:16:17,340 --> 00:16:25,740
+زائد φ، يعني هتكون الـ FQ اللي هي 50645
+
+142
+00:16:25,740 --> 00:16:30,640
+cos (60 + 12.5)
+
+143
+00:16:30,640 --> 00:16:30,980
+ونصف
+
+144
+00:16:33,940 --> 00:16:38,040
+هذا كام بتطلع لف فيه؟
+
+145
+00:16:38,040 --> 00:16:41,700
+لا
+
+146
+00:16:41,700 --> 00:16:47,320
+لأ
+
+147
+00:16:47,320 --> 00:16:54,390
+هذا منطقي أكثر لأن cos 12.5 كبيرة احسبها ثانية اش طنش هتكون أقل أكثر من 9 من 10
+
+148
+00:16:54,390 --> 00:16:56,650
+سبعمائة 
+
+149
+00:16:56,650 --> 00:17:00,690
+640
+
+150
+00:17:00,690 --> 00:17:07,090
+640 كل 740
+
+151
+00:17:07,090 --> 00:17:14,570
+640 واط، حصان، سيبك 
+
+152
+00:17:14,570 --> 00:17:17,230
+من القسمة التالية تعني الورشة
+
+153
+00:17:20,400 --> 00:17:24,140
+خليك ارجع للـ basic دايماً… 746
+
+154
+00:17:24,140 --> 00:17:32,840
+واط لحصان … اه اكتمل بتطلع … اكتش … FBI كام
+
+155
+00:17:32,840 --> 00:17:38,220
+بتطلع… 50645… 15
+
+156
+00:17:38,220 --> 00:17:48,340
+ألف و 296 نيوتن يعني حوالي تقريباً بتكون 
+
+157
+00:17:48,340 --> 00:17:56,660
+الخبط على الـ bearing بتحكي عن طن ونص يعني لو ماكانش
+
+158
+00:17:56,660 --> 00:18:02,060
+الـ crank موزّن هيكون كأنه ماسك شكوّش ووزنه كتلة و
+
+159
+00:18:02,060 --> 00:18:08,480
+طن ونص وبيقعد يخبط على الـ bearing بثواني هيكسرها الـ
+
+160
+00:18:08,480 --> 00:18:13,920
+bearing بتوزن
+
+161
+00:18:16,590 --> 00:18:21,870
+بتوزن؟ لأ بتوزن بحيث إن الـ cylinder مافيش force 
+
+162
+00:18:21,870 --> 00:18:26,490
+متغيرة بالضبط، بيوزنها بيحط كتلة معاكسة counter
+
+163
+00:18:26,490 --> 00:18:32,990
+weight، طيب
+
+164
+00:18:32,990 --> 00:18:38,210
+في أي سؤال؟ طيب اليوم نكون أنهينا المحاضرة، المحاضرة
+
+165
+00:18:38,210 --> 00:18:39,070
+الجاية بنكمل 
diff --git a/PL9fwy3NUQKwa0nXiCdyQcTW4hWDLTGpDb/gPBBfvb_0qE_postprocess.srt b/PL9fwy3NUQKwa0nXiCdyQcTW4hWDLTGpDb/gPBBfvb_0qE_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..5e8d2c43006f8799e2e7012284387bc378ac898e
--- /dev/null
+++ b/PL9fwy3NUQKwa0nXiCdyQcTW4hWDLTGpDb/gPBBfvb_0qE_postprocess.srt
@@ -0,0 +1,660 @@
+1
+00:00:05,080 --> 00:00:08,100
+بسم الله الرحمن الرحيم السلام عليكم ورحمة الله
+
+2
+00:00:08,100 --> 00:00:12,840
+وبركاته اليوم هنكمل محاضرات نماذج نظرية الألات
+
+3
+00:00:12,840 --> 00:00:15,560
+بدأنا في ال chapter اللي هو بيحكي عن ال inertia
+
+4
+00:00:15,560 --> 00:00:21,640
+forces in reciprocating mechanisms ودرسنا حالة
+
+5
+00:00:21,640 --> 00:00:25,780
+اللي هي slug reclining mechanismعملنا kinematic
+
+6
+00:00:25,780 --> 00:00:29,580
+analysis جيبنا ال displacement velocity و ال
+
+7
+00:00:29,580 --> 00:00:32,660
+acceleration لل piston و جيبنا ال angle of
+
+8
+00:00:32,660 --> 00:00:36,140
+velocity و ال angle of acceleration لل connecting
+
+9
+00:00:36,140 --> 00:00:42,400
+rod بعدين عملنا force analysis حسبنا ال piston
+
+10
+00:00:42,400 --> 00:00:47,300
+effort او ال effort عند ال piston اللي هو محصلة ال
+
+11
+00:00:47,300 --> 00:00:53,090
+load اللي جاء من ال pressure forcesومطروح منه ال
+
+12
+00:00:53,090 --> 00:00:58,650
+frictional resistance ومطروح منه ال inertia force
+
+13
+00:00:58,650 --> 00:01:02,530
+في حالة كان ال piston في حالة تسارع او مضاف ال
+
+14
+00:01:02,530 --> 00:01:08,430
+inertia force في حالة كان ال piston في حالة تباطؤ
+
+15
+00:01:08,430 --> 00:01:14,150
+لأن ال piston effort ينتقل الى ال connecting rod
+
+16
+00:01:14,150 --> 00:01:20,040
+من خلال ال FQوالـ FQ حلناها لمراكبتين واحدة باتجاه
+
+17
+00:01:20,040 --> 00:01:26,440
+الكرانك واحدة عمودية على الكرانك FT الـ FT هي اللي
+
+18
+00:01:26,440 --> 00:01:32,180
+بتعمل العزم الدوراني حول الكرانك حسبنا ال torque
+
+19
+00:01:32,180 --> 00:01:39,420
+حسبنا ال
+
+20
+00:01:39,420 --> 00:01:44,620
+FQ بعدين حسبنا ال FT بعدين ال FB ال force باتجاه
+
+21
+00:01:44,620 --> 00:01:50,530
+الكرانكبعدين ال torque اللى
+
+22
+00:01:50,530 --> 00:01:54,330
+هو مُعطّب للواقع F ال torque بيستوى F P ال piston
+
+23
+00:01:54,330 --> 00:01:58,530
+effort في R sine theta زى sine two theta على اتنين
+
+24
+00:01:58,530 --> 00:02:05,270
+M حلّين example خمساش ستة هنحل كمان example بعدين
+
+25
+00:02:05,270 --> 00:02:11,350
+نكمل The
+
+26
+00:02:11,350 --> 00:02:14,570
+crank of a horizontal engine is three hundred
+
+27
+00:02:14,570 --> 00:02:20,850
+millimetersمعطيل طولي كرانك لانجين أفقي اللى هى ال
+
+28
+00:02:20,850 --> 00:02:25,110
+R بستوى
+
+29
+00:02:25,110 --> 00:02:33,250
+تلت ميت ملي ميتر ال mass of reciprocating parts is
+
+30
+00:02:33,250 --> 00:02:40,350
+two hundred fifty kilogram ال MR متين
+
+31
+00:02:40,350 --> 00:02:43,090
+و خمسين kilogram
+
+32
+00:02:45,830 --> 00:02:48,770
+when the crank has traveled six degrees from the
+
+33
+00:02:48,770 --> 00:02:56,210
+inner dead center هاي عندي الكرانك
+
+34
+00:02:56,210 --> 00:03:04,890
+هاي
+
+35
+00:03:04,890 --> 00:03:09,150
+ال piston والزاوية
+
+36
+00:03:09,150 --> 00:03:18,470
+دي كانت ستين درجة يعني ال thetaبساوة ستين درجة
+
+37
+00:03:18,470 --> 00:03:23,510
+when the crank has traveled six degrees from the
+
+38
+00:03:23,510 --> 00:03:27,510
+inner dead center the difference between the
+
+39
+00:03:27,510 --> 00:03:31,670
+driving and back pressure في عندى هنا في driving ع
+
+40
+00:03:31,670 --> 00:03:36,370
+الجهد pressure في عندى back pressure الفرق بينهم
+
+41
+00:03:36,370 --> 00:03:41,010
+point تلاتة خمسة نيوتن ع الميلي متر يعني point
+
+42
+00:03:41,010 --> 00:03:46,030
+تلاتة خمسة ميجا بسكال يعني delta P
+
+43
+00:03:49,330 --> 00:03:57,770
+إذا حد مشغل جوال يطفئه ماشي Delta
+
+44
+00:03:57,770 --> 00:04:04,550
+P سوة point تلاتة خمسة ميجا
+
+45
+00:04:04,550 --> 00:04:09,350
+بسكال الـ
+
+46
+00:04:09,350 --> 00:04:12,670
+connecting rod length between centers is one point
+
+47
+00:04:12,670 --> 00:04:20,570
+two meters طول ال connecting rod واحد تم عشرةمعناة
+
+48
+00:04:20,570 --> 00:04:30,190
+الانش الساوية L على R اللي هي الف و متين ع تلت مية
+
+49
+00:04:30,190 --> 00:04:38,270
+أربع طيب
+
+50
+00:04:38,270 --> 00:04:45,750
+ال cylinder bore قطر ال cylinder دي
+
+51
+00:04:48,320 --> 00:04:55,040
+نص متر if the
+
+52
+00:04:55,040 --> 00:05:00,820
+engine runs at two hundred fifty rpm الاميجا متين
+
+53
+00:05:00,820 --> 00:05:07,880
+و خمسين rpm يعني هتكون متين و خمسين في اتنين باي
+
+54
+00:05:07,880 --> 00:05:14,700
+اكم ستة عشرين radians
+
+55
+00:05:14,700 --> 00:05:16,600
+per second
+
+56
+00:05:24,230 --> 00:05:27,950
+and if the effect of the piston rod diameter
+
+57
+00:05:27,950 --> 00:05:32,570
+المهمل
+
+58
+00:05:32,570 --> 00:05:38,150
+يعني واضح قطر القطر السلندر نص متر معناه ان ال
+
+59
+00:05:38,150 --> 00:05:42,450
+piston rod هكون صغير كتير بالمقارنة مع ال piston
+
+60
+00:05:42,450 --> 00:05:46,270
+rod من هنا calculate
+
+61
+00:05:46,270 --> 00:05:47,890
+the piston effort
+
+62
+00:05:52,690 --> 00:06:01,730
+لفى احنا حاكينا شو يساوي ال F L ال
+
+63
+00:06:01,730 --> 00:06:05,890
+F L minus
+
+64
+00:06:05,890 --> 00:06:09,570
+plus
+
+65
+00:06:09,570 --> 00:06:19,850
+F I minus the frictional resistanceأحنا في اللحظة
+
+66
+00:06:19,850 --> 00:06:21,970
+.. يعني في ال .. يعني احنا مش هنعمل علامة الـ
+
+67
+00:06:21,970 --> 00:06:28,170
+pressure resistance هنعملها هنكلت RF
+
+68
+00:06:28,170 --> 00:06:39,570
+بساوية Zero وما نقلش هنحسب ال load ال load ال FL
+
+69
+00:06:39,570 --> 00:06:47,790
+هيساوية Delta V مساحة المقطع تاع السيلندر صح؟ يعني
+
+70
+00:06:47,790 --> 00:06:59,130
+هيساويةالـ A بي على أربعة دي سكوير في دلتا P يعني
+
+71
+00:06:59,130 --> 00:07:12,270
+عندي ال بي على أربعة الكتر عندي نص متر في
+
+72
+00:07:12,270 --> 00:07:15,350
+في
+
+73
+00:07:15,350 --> 00:07:21,090
+zero point تلاتة fiveفي عشرة و ستة عشان احاول ال
+
+74
+00:07:21,090 --> 00:07:32,770
+نيوتن على البيتيرا 68722
+
+75
+00:07:32,770 --> 00:07:40,570
+نيوتن ال inertia
+
+76
+00:07:40,570 --> 00:07:41,690
+فورتش بالساوية
+
+77
+00:07:53,780 --> 00:07:59,260
+لنيرش فورس FI بساول
+
+78
+00:07:59,260 --> 00:08:06,960
+MR Omega Square MR Omega
+
+79
+00:08:06,960 --> 00:08:10,740
+Square R
+
+80
+00:08:10,740 --> 00:08:28,270
+Cos Theta ذات Cos 2 Theta على Nيعني هكون ال MR 250
+
+81
+00:08:28,270 --> 00:08:43,350
+كيلو أميجا 26 بون 18 تربيع R بون 3 كوساين
+
+82
+00:08:43,350 --> 00:08:47,790
+60 زائد
+
+83
+00:08:47,790 --> 00:08:52,950
+كوساين 120 على 4
+
+84
+00:09:00,150 --> 00:09:10,190
+قصين ستين كم نص و هذه ناقص نص ناقص نص سالف ثمان كم
+
+85
+00:09:10,190 --> 00:09:22,170
+تطلع الجواب تسعة اتاشر الف نيوتن
+
+86
+00:09:28,550 --> 00:09:35,250
+هيكون الأفعل اللي هو تمانية ستين ألف هذا
+
+87
+00:09:35,250 --> 00:09:42,470
+اللي جاء من احتراق الغازات جزء سوف يستنفذ في تسريع
+
+88
+00:09:42,470 --> 00:09:51,150
+ال piston عشان أسرعه محتاج طاقة أضغط عشان أضغط او
+
+89
+00:09:51,150 --> 00:09:53,910
+هو وطيق هو بتباطأ ما هو فيه طاقة و يقعد يخسرها
+
+90
+00:09:53,910 --> 00:09:59,410
+إليه لصالهاهتكون تماما ستين ألف سبعة مية واتنين
+
+91
+00:09:59,410 --> 00:10:09,550
+وعشرين ناقص ال FI تسعتاشر الف ومتين وستة وسبعين
+
+92
+00:10:09,550 --> 00:10:13,890
+تسعة واربعين ألف واربعمية
+
+93
+00:10:18,400 --> 00:10:21,180
+النيوتن هذا ال piston effort يعني حوالي تسعة و
+
+94
+00:10:21,180 --> 00:10:26,980
+أربعين يعني لو قسمنا على عشرة يعني حوالي .. ال
+
+95
+00:10:26,980 --> 00:10:35,220
+piston effort حوالي خمسة طن وزن خمسة طن أه piston
+
+96
+00:10:35,220 --> 00:10:42,650
+ضخم صحيح مواخر أو محطة التوليد أو جزاهيرفي محرك
+
+97
+00:10:42,650 --> 00:10:51,250
+الرشد؟ اه في قطار واحد؟ صحيح في حالة السفن الضخمة
+
+98
+00:10:51,250 --> 00:10:54,970
+او في حالة محطات الكهربا بيكون في الأقطار هذه طيب
+
+99
+00:10:54,970 --> 00:11:00,150
+هذا المطلوب الأول المطلوب التاني
+
+100
+00:11:00,150 --> 00:11:03,530
+thrust in the connecting road ايش يعني thrust in
+
+101
+00:11:03,530 --> 00:11:10,230
+the connecting road؟ الحلق اللي هو جاي ال FQ صح ال
+
+102
+00:11:10,230 --> 00:11:11,290
+FQ ايش الساوية؟
+
+103
+00:11:17,870 --> 00:11:23,070
+الـ Fq بيستوى
+
+104
+00:11:23,070 --> 00:11:35,690
+الـ piston effort على كوسين الفاية طيب
+
+105
+00:11:35,690 --> 00:11:41,870
+الفاية أنا عارف فهي الفاية صح؟
+
+106
+00:11:47,600 --> 00:11:55,700
+يعني هتكون ممكن مباشرة .. مباشرة احكي انا ان ال
+
+107
+00:11:55,700 --> 00:12:10,900
+sin فاي بالساوية .. n بالساوية r sin theta صح؟ و
+
+108
+00:12:10,900 --> 00:12:15,480
+sin فاي بالساوية
+
+109
+00:12:15,480 --> 00:12:23,300
+sin thetaعلى N او مباشرة من المعادلة اعوض طاولة
+
+110
+00:12:23,300 --> 00:12:38,060
+مباشرة يعني هتكون sin 60 على 4 ومنها بحسب ال 5 كم؟
+
+111
+00:12:38,060 --> 00:12:44,520
+ناشر و نص درجة هنا هحكي ال piston effort اللي هو
+
+112
+00:12:44,520 --> 00:12:50,490
+تسعة واربعين الفاربعمية وخمسة واربعين على كساين
+
+113
+00:12:50,490 --> 00:12:57,230
+الاتناش ونص هاي
+
+114
+00:12:57,230 --> 00:13:02,290
+هسأل FQ أكام حاجة اطلع خمسين
+
+115
+00:13:02,290 --> 00:13:07,410
+الف نيوتن
+
+116
+00:13:16,080 --> 00:13:20,160
+بديوا tangential force on the crank pin بديوا F T
+
+117
+00:13:20,160 --> 00:13:30,700
+صح ال F T ال
+
+118
+00:13:30,700 --> 00:13:40,400
+F T ايش بيستخدم؟ بيستخدم
+
+119
+00:13:40,400 --> 00:13:41,060
+F Q
+
+120
+00:13:44,210 --> 00:13:55,250
+Sin ثتا زائد فا يعني ال FQ اللي هي خمسين ألف ستمية
+
+121
+00:13:55,250 --> 00:14:02,910
+و خمسة و أربعين في ال SIN ستين زائد اتناشه نص
+
+122
+00:14:13,160 --> 00:14:21,160
+تبعين واربين ألف و تلت ميت نيوتن معناته العزم على
+
+123
+00:14:21,160 --> 00:14:26,060
+ال .. العزم على ال .. على ال crank ايش بالساوية؟
+
+124
+00:14:26,060 --> 00:14:33,660
+torque R في FT ال R ان دي تلتة من عشرة
+
+125
+00:14:36,280 --> 00:14:43,280
+في التمانية واربعين ألف و تلت مية اربع تانشر الف
+
+126
+00:14:43,280 --> 00:14:48,280
+واربع مية تسعى طيب لو بدي أحسن ال power كيف بدي
+
+127
+00:14:48,280 --> 00:14:52,760
+أحسن ال power في اللحظة هذه power
+
+128
+00:14:52,760 --> 00:15:03,670
+torque في omega صح ال power بيساوي ال torqueفي
+
+129
+00:15:03,670 --> 00:15:06,430
+الومجة في اللحظة هذه يعني ال torque كانت اربع تاشر
+
+130
+00:15:06,430 --> 00:15:15,450
+الف اربع تسنين في الومجة اللي هي ستة و عشرين point
+
+131
+00:15:15,450 --> 00:15:22,010
+تمانتاش تسيبوها
+
+132
+00:15:22,010 --> 00:15:28,130
+تلاتمية
+
+133
+00:15:28,130 --> 00:15:34,300
+تسعة و سبعينتلاتمية و تسعة سبعين الف تلاتمية و ستة
+
+134
+00:15:34,300 --> 00:15:40,200
+و خمسين أكم وات اقسمها على سبعمية و ستة و أربعين
+
+135
+00:15:40,200 --> 00:15:44,220
+اقسمها على سبعمية و ستة و أربعين خمسمية و تسعة
+
+136
+00:15:44,220 --> 00:15:52,060
+خمسمية و تسعة احصان
+
+137
+00:15:52,060 --> 00:15:59,020
+احصان يعني موتور دخل لو
+
+138
+00:15:59,020 --> 00:16:09,060
+بدى اجيب ال FBالـ FBF الساوية بالساوية
+
+139
+00:16:09,060 --> 00:16:14,040
+ال FQ كوساين
+
+140
+00:16:14,040 --> 00:16:17,340
+الثيتا
+
+141
+00:16:17,340 --> 00:16:25,740
+زائد في يعني هتكون ال FQ اللي هي خمسين الف و ستمية
+
+142
+00:16:25,740 --> 00:16:30,640
+و خمسة و أربعين كوساين ثيتا ستة اتنين و سبعين و
+
+143
+00:16:30,640 --> 00:16:30,980
+نصف
+
+144
+00:16:33,940 --> 00:16:38,040
+هذا كم تطلع لف بيه؟
+
+145
+00:16:38,040 --> 00:16:41,700
+لا
+
+146
+00:16:41,700 --> 00:16:47,320
+لأ
+
+147
+00:16:47,320 --> 00:16:54,390
+هذا منطق أكتر لإن ال cosine ال 12.5 كبيرةاحسبك سنة
+
+148
+00:16:54,390 --> 00:16:56,650
+تانية اشتناش هتكون اقل اكتر من تسعة من عشرة
+
+149
+00:16:56,650 --> 00:17:00,690
+سبعمائة
+
+150
+00:17:00,690 --> 00:17:07,090
+ستة واربين كل سبعمائة
+
+151
+00:17:07,090 --> 00:17:14,570
+ستة واربين واط احصان سيبك
+
+152
+00:17:14,570 --> 00:17:17,230
+من القسمية التالية تعني الورشة
+
+153
+00:17:20,400 --> 00:17:24,140
+خلّيك ارجع لل basic دايما .. سبعمائة وستة اربعين
+
+154
+00:17:24,140 --> 00:17:32,840
+واط بحصان .. اه اكتم بتطلع .. اكتش .. FBI اكم
+
+155
+00:17:32,840 --> 00:17:38,220
+بتطلع .. خمسين ألف وستمية وخمس أربعين .. خمستاشر
+
+156
+00:17:38,220 --> 00:17:48,340
+الف متين وستة وتسعين نيوتنيعني حوالي تقريبا بتكون
+
+157
+00:17:48,340 --> 00:17:56,660
+الخبط على ال bearing بتحكي عن طن نص يعني لو ماكانش
+
+158
+00:17:56,660 --> 00:18:02,060
+ال crank موزنه حيكون كإنه ماسك شكوش و وزنه كتلة و
+
+159
+00:18:02,060 --> 00:18:08,480
+طن و نص و بقى يخبط على ال bearing بثوان حيكسرها ال
+
+160
+00:18:08,480 --> 00:18:13,920
+bearing بتوزن
+
+161
+00:18:16,590 --> 00:18:21,870
+بتوزن لأ بتوزن بحيث انه ال cylinder مافيش force
+
+162
+00:18:21,870 --> 00:18:26,490
+متغيرة بالظبط بيوزنها بيحط قطلة معاكسة counter
+
+163
+00:18:26,490 --> 00:18:32,990
+weight طيب
+
+164
+00:18:32,990 --> 00:18:38,210
+في اي سؤال طيب اليوم نكون انهينا المحاضرة المحاضرة
+
+165
+00:18:38,210 --> 00:18:39,070
+الجاية بنكمل
+
diff --git a/PL9fwy3NUQKwa0nXiCdyQcTW4hWDLTGpDb/hsdaCz_t_RE.srt b/PL9fwy3NUQKwa0nXiCdyQcTW4hWDLTGpDb/hsdaCz_t_RE.srt
new file mode 100644
index 0000000000000000000000000000000000000000..66a6442d8372249bb485af2a1cfad94db4cd266a
--- /dev/null
+++ b/PL9fwy3NUQKwa0nXiCdyQcTW4hWDLTGpDb/hsdaCz_t_RE.srt
@@ -0,0 +1,1442 @@
+1
+00:00:05,280 --> 00:00:08,380
+السلام عليكم ورحمة الله وبركاته اليوم هنكمل في 
+
+2
+00:00:08,380 --> 00:00:12,720
+مادة نظرية الآلات هنكمل في chapter 16 term of
+
+3
+00:00:12,720 --> 00:00:19,500
+diagram and flywheels هنكمل
+
+4
+00:00:19,500 --> 00:00:25,780
+هنشوف كيف ايش ال design equations المطلوبة عشان
+
+5
+00:00:25,780 --> 00:00:29,800
+أعمل flywheel طبعا المبينة دي هنا flywheel أو ال
+
+6
+00:00:29,800 --> 00:00:34,820
+rim بتاعة ال flywheel هذه الكتلة الخارجية طبعا في
+
+7
+00:00:34,820 --> 00:00:37,480
+المصدر بيكون في عندي الأضلاع اللي ماسكاها وفي عندي
+
+8
+00:00:37,480 --> 00:00:43,600
+مكان للشافت اللي هو ال hub نتيجة ال flywheel بتكون
+
+9
+00:00:43,600 --> 00:00:50,640
+الدور بي .. لها سرعة بيكون لقوة طرد مركزي بيكون
+
+10
+00:00:50,640 --> 00:00:56,240
+في قوة طرد مركزي لو أخذت element على بعد زاوية
+
+11
+00:00:56,240 --> 00:00:56,560
+theta
+
+12
+00:01:02,060 --> 00:01:08,460
+وأخذت الـ infinitesimal element dθ هاي
+
+13
+00:01:08,460 --> 00:01:13,800
+ال element طبعا
+
+14
+00:01:13,800 --> 00:01:20,940
+اللي بقعد عليه هو في
+
+15
+00:01:20,940 --> 00:01:25,300
+force dF
+
+16
+00:01:29,640 --> 00:01:34,180
+طبعا أعرف ال Geometric Parameters عند ال R هو ال
+
+17
+00:01:34,180 --> 00:01:41,940
+mean radius لل flywheel R كابيتال عند ال A ال
+
+18
+00:01:41,940 --> 00:01:48,540
+cross section عادة بيسموه T والبعد
+
+19
+00:01:48,540 --> 00:01:55,640
+هذا التالت B ال
+
+20
+00:01:55,640 --> 00:02:03,430
+روه الكثافة لمادة ال flywheel الآن سرعة ال flywheel
+
+21
+00:02:03,430 --> 00:02:07,410
+بال RPM ال Omega في سرعة ال flywheel بال radians
+
+22
+00:02:07,410 --> 00:02:11,990
+per second ال V السرعة المنحوطية عند ال radius R
+
+23
+00:02:11,990 --> 00:02:15,810
+اللي هي بيساوي Omega في R و ال Sigma اللي هو ب
+
+24
+00:02:15,810 --> 00:02:18,550
+stress due to centrifugal force لأن في عندي هحسب
+
+25
+00:02:18,550 --> 00:02:23,230
+centrifugal force هيحاول ايش؟ هيحاول .. بده يكبر
+
+26
+00:02:23,230 --> 00:02:29,090
+القطر فبيكون في عندي tangential stress بسميه hoop
+
+27
+00:02:29,090 --> 00:02:29,550
+stress
+
+28
+00:02:32,460 --> 00:02:39,200
+لأ لما ناخد infinitesimal element ال
+
+29
+00:02:39,200 --> 00:02:46,660
+Df لها مركبتين Df
+
+30
+00:02:46,660 --> 00:02:53,740
+cos θ Df
+
+31
+00:02:53,740 --> 00:02:56,780
+sin
+
+32
+00:02:56,780 --> 00:02:58,920
+θ مجموعة ال elements
+
+33
+00:03:02,160 --> 00:03:05,640
+بيطون المركبة الرأسية اللي بتحاول تعمل فصل تعمل
+
+34
+00:03:05,640 --> 00:03:09,560
+حاول stress عند المقطع هذا والمقطع هذا يعني عند
+
+35
+00:03:09,560 --> 00:03:29,300
+المقطع هذا هيكون عنده في sigma و في F sigma ال
+
+36
+00:03:29,300 --> 00:03:38,620
+.. ال .. ال massالـ DM لل element ال
+
+37
+00:03:38,620 --> 00:03:46,600
+raw في ال D volume بيساوي ال raw ال D volume
+
+38
+00:03:46,600 --> 00:03:52,100
+بيساوي
+
+39
+00:03:52,100 --> 00:03:59,520
+اللي هو ال R D theta ال R D theta اللي هو هذا
+
+40
+00:04:12,140 --> 00:04:14,640
+يعني نختصر الموضوع ايه سواء density في اليوم ال
+
+41
+00:04:14,640 --> 00:04:19,380
+raw اللي هي ال density في ال volume و ال volume
+
+42
+00:04:19,380 --> 00:04:29,700
+هيكون مقطع مساحة مقطع رو في ا اللي هي ا ر دي ثيتا
+
+43
+00:04:29,700 --> 00:04:35,480
+في ا ا في ا ر دي ثيتا
+
+44
+00:04:43,450 --> 00:04:50,110
+مساحة المقطع أو الحجم بتاع هذا عبارة عن منشور صح
+
+45
+00:04:50,110 --> 00:04:58,290
+بس هو مساحة المقطع في الارتفاع يعني بيصير عندي يعني
+
+46
+00:04:58,290 --> 00:05:04,530
+مساحة في ارتفاع الطينة volume بالصفة رو اي ار دي
+
+47
+00:05:04,530 --> 00:05:07,470
+ثتا هذا بالنسبة للمس
+
+48
+00:05:17,880 --> 00:05:21,180
+ال centrifugal force ناسج ان الكتلة هذه بتدور
+
+49
+00:05:21,180 --> 00:05:26,480
+فهيكون دي ال centrifugal force هتكون DF اللي هي ال
+
+50
+00:05:26,480 --> 00:05:32,680
+mass في ال a normal صح ال mass في ال a normal و ال
+
+51
+00:05:32,680 --> 00:05:37,540
+a normal عبارة عن ايش omega square في R يعني ال DF
+
+52
+00:05:37,540 --> 00:05:41,300
+بيساوي
+
+53
+00:05:41,300 --> 00:05:50,760
+a normal في DMالـ A نوراللي هي Omega Square R في
+
+54
+00:05:50,760 --> 00:05:57,000
+DM ده أنا بعوض عن DM اللي هي Rho A R D Theta بيصير
+
+55
+00:05:57,000 --> 00:06:00,060
+أن ال DM بيستوي Rho A R Square Omega Square D
+
+56
+00:06:00,060 --> 00:06:06,580
+Theta ال force اللي حللناه هو مركبتين مركبة أفقية
+
+57
+00:06:06,580 --> 00:06:13,620
+و مركبة رأسية المركبة الرأسية هي اللي بتحاول تعمل
+
+58
+00:06:13,620 --> 00:06:19,300
+stress و تنزع هتكون عندي بهذه انا معناته الـ Df
+
+59
+00:06:19,300 --> 00:06:24,900
+sin θ الـ Df sin θ اللي هي Df اللي هي رو اي ار
+
+60
+00:06:24,900 --> 00:06:31,240
+روينقسفير Dθ في sin θ معناته الـ total force الـ
+
+61
+00:06:31,240 --> 00:06:34,940
+total vertical force اللي بتحاول تنزع تنزع ال ..
+
+62
+00:06:34,940 --> 00:06:39,640
+ال .. ال .. ال .. ال .. ال rim بتاعة ال flywheel
+
+63
+00:06:39,640 --> 00:06:45,280
+هتكون تكامل هذه صح يعني أنا هيكون عندي ال raw
+
+64
+00:06:45,280 --> 00:06:50,380
+constant و المقطع constant و ال R constant و ال
+
+65
+00:06:50,380 --> 00:06:54,820
+omega square constant كله بطلع برا بس عندي raw ar²
+
+66
+00:06:54,820 --> 00:07:00,140
+تكامل من صفر ل باى أنا من الصفر ل 180 درجة sin θ d
+
+67
+00:07:00,140 --> 00:07:04,980
+θ تكامل ال sin في ال sin اللي هي minus cosine من
+
+68
+00:07:04,980 --> 00:07:10,390
+صفر ل باى طبعا هتكون مينس مينس واحد هتكون يعني لما
+
+69
+00:07:10,390 --> 00:07:16,010
+نعوض من صفر ل باي هتكون اتنين تمت هذه هتكون ال
+
+70
+00:07:16,010 --> 00:07:22,270
+total vertical force اللي هي اتنين رو اي ار سكوير
+
+71
+00:07:22,270 --> 00:07:30,350
+اوميجا سكوير وهي الرم عندي عندي
+
+72
+00:07:30,350 --> 00:07:31,310
+هنا سيجما
+
+73
+00:07:34,290 --> 00:07:42,830
+أو sigma في a وعند هنا sigma في a معناته ال sigma
+
+74
+00:07:42,830 --> 00:07:46,770
+في a زي ال sigma في a اللي هي اتنين sigma a
+
+75
+00:07:46,770 --> 00:07:50,930
+بالسواء ال total vertical force اللي هي اتنين رو a
+
+76
+00:07:50,930 --> 00:07:54,810
+r square omega square هيروح طبعا عند الاتنين مع
+
+77
+00:07:54,810 --> 00:08:02,170
+الاتنين و ال a مع ال a حصها في ال sigma بيساوي رو
+
+78
+00:08:02,170 --> 00:08:05,630
+R تربيع أمجي تربيع ال R في غمجة تمثل السرعة
+
+79
+00:08:05,630 --> 00:08:11,230
+المحيطية R في غمجة سرعة محيطية معناته R أمجي تربيع
+
+80
+00:08:11,230 --> 00:08:14,850
+رو V تربيع أو السرعة المحيطية بيساوي تربيع
+
+81
+00:08:14,850 --> 00:08:20,410
+لسيجما على رو ال mass بيساوي volume في density
+
+82
+00:08:20,410 --> 00:08:27,200
+ال volume احنا حكينا هذا R capital معناته القطر ايش
+
+83
+00:08:27,200 --> 00:08:36,620
+هيكون D capital المحيط ايش هيكون بيساوي باي في دي باي
+
+84
+00:08:36,620 --> 00:08:42,940
+في دي في ال cross section بيعطيني ايش؟ volume
+
+85
+00:08:42,940 --> 00:08:46,000
+في raw بيعطيني ايش؟ mass
+
+86
+00:08:51,480 --> 00:08:55,440
+يعني هي هتكون ال A بالثورة المادة بتاعة ال rim بتاعة
+
+87
+00:08:55,440 --> 00:09:03,500
+ال flywheel على πاي دي في روب هذه المعادلات
+
+88
+00:09:03,500 --> 00:09:08,400
+اللازمة لتصميم flywheel خلينا نشوف أمثلة
+
+89
+00:09:15,960 --> 00:09:18,960
+turning moment diagram for a multi cylinder engine
+
+90
+00:09:18,960 --> 00:09:21,940
+has been drawn to a scale of one millimeter لأن
+
+91
+00:09:21,940 --> 00:09:26,720
+عندي high turn moment diagram for some engine لأن
+
+92
+00:09:26,720 --> 00:09:33,440
+هذا ال main resisting torque وهذا ال actual torque
+
+93
+00:09:33,440 --> 00:09:40,900
+بتذبذب حوالين ال main هو
+
+94
+00:09:40,900 --> 00:09:44,120
+يعطينا معلومات بيحكي ليه كل واحد millimeter على ال
+
+95
+00:09:44,120 --> 00:09:44,960
+vertical axis
+
+96
+00:09:50,010 --> 00:09:56,350
+يكافئ خمسمية نيوتن متر torque وعلى ال horizontal
+
+97
+00:09:56,350 --> 00:10:06,130
+axis واحد ملي متر يكافئ كم ست درجات معناه
+
+98
+00:10:06,130 --> 00:10:11,250
+واحد ملي متر مربع كم يكافئ بيساوي
+
+99
+00:10:11,250 --> 00:10:18,690
+خمسمية في ستة ال degree ده حول ال radians في باية
+
+100
+00:10:18,690 --> 00:10:28,510
+180 52
+
+101
+00:10:28,510 --> 00:10:33,490
+point
+
+102
+00:10:33,490 --> 00:10:36,690
+نيوتن
+
+103
+00:10:36,690 --> 00:10:44,290
+متر طيب ال engine is running at 800 rpm يعني ال
+
+104
+00:10:44,290 --> 00:10:53,360
+speed الآن بيساوي 800ر بي ام الانجين
+
+105
+00:10:53,360 --> 00:11:02,060
+لديه طرق تعت الانجين تلاتمية ملي ميتر تلاتمية
+
+106
+00:11:02,060 --> 00:11:06,020
+ملي ميتر تلاتمية ملي ميتر تلاتمية
+
+107
+00:11:06,020 --> 00:11:07,620
+ملي ميتر تلاتمية ملي ميتر تلاتمية ملي ميتر تلاتمية
+
+108
+00:11:07,620 --> 00:11:07,880
+ملي ميتر تلاتمية ملي ميتر تلاتمية ملي ميتر تلاتمية
+
+109
+00:11:07,880 --> 00:11:07,900
+ملي ميتر تلاتمية ملي ميتر تلاتمية ملي ميتر تلاتمية
+
+110
+00:11:07,900 --> 00:11:11,260
+ملي ميتر تلاتمية ملي ميتر تلاتمية ملي ميتر تلاتمية
+
+111
+00:11:11,260 --> 00:11:16,180
+ملي ميتر تلاتمية ملي ميتر تلات
+
+112
+00:11:22,420 --> 00:11:25,500
+.Q4 Determine a suitable diameter and cross
+
+113
+00:11:25,500 --> 00:11:32,740
+-section of the flywheel بده ال diameter و ال
+
+114
+00:11:32,740 --> 00:11:40,060
+cross-section ده ال flywheel و flywheel rim for a
+
+115
+00:11:40,060 --> 00:11:44,760
+limiting value of the safe centroidal stress بحيث
+
+116
+00:11:44,760 --> 00:11:51,600
+ال stress ما يتخطاش سبعة ميجا سيجما سبعة
+
+117
+00:11:51,600 --> 00:11:59,680
+ميجا باسكال the material density may be assumed as
+
+118
+00:11:59,680 --> 00:12:03,880
+raw مخ بتاعة ال cast iron
+
+119
+00:12:12,200 --> 00:12:18,700
+the width rim خمس أضعاف ال thickness هاي ال
+
+120
+00:12:18,700 --> 00:12:24,920
+flywheel هذا
+
+121
+00:12:24,920 --> 00:12:32,080
+البعد التالت طبعا هذا
+
+122
+00:12:32,080 --> 00:12:37,140
+ال B هذا
+
+123
+00:12:37,140 --> 00:12:40,400
+ايش ال B وهذا
+
+124
+00:12:42,930 --> 00:12:54,990
+الـ T الـ B بيساوي خمسة T طيب
+
+125
+00:12:54,990 --> 00:13:03,310
+احنا عشان نحسب نبدأ من الآخر عشان نحسب ال ال
+
+126
+00:13:03,310 --> 00:13:10,850
+D هستخدم علاقة نا سيجما بيساوي
+
+127
+00:13:13,620 --> 00:13:21,940
+row R تربيع Omega تربيع لأن ال sigma معروفة عنده و
+
+128
+00:13:21,940 --> 00:13:26,240
+ال row معروفة و ال omega معروفة عنده يعني ال R
+
+129
+00:13:26,240 --> 00:13:29,780
+ستكون
+
+130
+00:13:29,780 --> 00:13:40,560
+بيساوي sigma على row Omega تربيع تحت الجدر صح؟ يعني
+
+131
+00:13:40,560 --> 00:13:46,750
+ال R هتكون بيساوي جزر تربيع ال sigma عندي سبعمية
+
+132
+00:13:46,750 --> 00:13:52,830
+يعني سبعة في عشرة أس ستة باسكال على ال road سبعة
+
+133
+00:13:52,830 --> 00:13:58,890
+الف و متين ال omega احنا لقالنا عندي تمانمية كم
+
+134
+00:13:58,890 --> 00:14:02,250
+تطلع
+
+135
+00:14:02,250 --> 00:14:09,870
+ثمانين و ايش أكتر من ثمانين كم تلت ثمانين تربيع
+
+136
+00:14:15,730 --> 00:14:20,130
+متر تلاتي بوند تلاتي سبعة كم بوند متر تلاتي سبعة
+
+137
+00:14:20,130 --> 00:14:24,990
+كم بوند تلاتي سبعة كم بوند تلاتي سبعة كم بوند
+
+138
+00:14:24,990 --> 00:14:27,550
+تلاتي سبعة كم بوند تلاتي سبعة كم بوند تلاتي سبعة
+
+139
+00:14:27,550 --> 00:14:29,130
+كم بوند تلاتي سبعة كم بوند تلاتي سبعة كم بوند
+
+140
+00:14:29,130 --> 00:14:29,250
+تلاتي سبعة كم بوند تلاتي سبعة كم بوند تلاتي سبعة
+
+141
+00:14:29,250 --> 00:14:31,130
+تلاتي سبعة كم بوند تلاتي سبعة كم بوند تلاتي سبعة
+
+142
+00:14:31,130 --> 00:14:37,230
+كم
+
+143
+00:14:37,230 --> 00:14:40,890
+بوند
+
+144
+00:14:40,890 --> 00:14:53,180
+تلاتي سبعة الـ A بيساوي M على باي دي فرق بدي ال
+
+145
+00:14:53,180 --> 00:15:01,940
+M ال M اللي أنا بجيبها مش
+
+146
+00:15:01,940 --> 00:15:08,320
+عارف أنا اللي .. ماهي نفس المعادلة هو معطيني ال
+
+147
+00:15:08,320 --> 00:15:12,280
+turning point دياجرام ممكن استفيد منه اللي هي
+
+148
+00:15:12,280 --> 00:15:14,460
+Delta E عنده ايش الساعة؟
+
+149
+00:15:17,370 --> 00:15:26,850
+M R Square Omega Square CS CS معروف عندي و ال M
+
+150
+00:15:26,850 --> 00:15:31,130
+معروف عندي و ال R معروف عندي دلتا ايه دلتا ايه
+
+151
+00:15:31,130 --> 00:15:37,050
+اللي أنا بجيبها من ال diagram من ال diagram من ال
+
+152
+00:15:37,050 --> 00:15:43,630
+diagram عندي ال point و
+
+153
+00:15:43,630 --> 00:15:54,670
+ال energy بتاعتها عند A هسميها A عند B E ناقص
+
+154
+00:15:54,670 --> 00:15:59,630
+تلاتين عند C E
+
+155
+00:15:59,630 --> 00:16:13,870
+تلاتمية و تمانين عند D E زائد مية عند E E
+
+156
+00:16:17,090 --> 00:16:24,310
+and F E and
+
+157
+00:16:24,310 --> 00:16:31,470
+G and
+
+158
+00:16:31,470 --> 00:16:35,750
+H and
+
+159
+00:16:35,750 --> 00:16:43,110
+H E ناقص عشرين and
+
+160
+00:16:43,110 --> 00:16:43,450
+K
+
+161
+00:16:51,720 --> 00:16:55,660
+عند L A
+
+162
+00:16:55,660 --> 00:17:00,500
+وين
+
+163
+00:17:00,500 --> 00:17:03,620
+ال maximum؟ المشكلة ده كانت تطلع عند A، هاد
+
+164
+00:17:03,620 --> 00:17:11,260
+المشكلة ده ال minimum
+
+165
+00:17:11,260 --> 00:17:13,240
+عند وين؟ عند B
+
+166
+00:17:23,910 --> 00:17:29,750
+فمشكلة هذه فاهمينها
+
+167
+00:17:29,750 --> 00:17:36,710
+هذه طيب كويس Delta A بيساوي أربعمائة و عشرين
+
+168
+00:17:36,710 --> 00:17:43,010
+زائد تلاتين أربعمائة
+
+169
+00:17:43,010 --> 00:17:46,350
+و خمسين أربعمائة و خمسين مليمتر square
+
+170
+00:17:50,600 --> 00:17:55,340
+يعني هتكون بيساوي أربعمية و خمسين الكل ملي متر square
+
+171
+00:17:55,340 --> 00:18:03,960
+في اخ اتنين و خمسين point تلاتة كم؟ تلاتة و عشان
+
+172
+00:18:03,960 --> 00:18:09,180
+الف و خمسمية طيب
+
+173
+00:18:17,630 --> 00:18:22,690
+الدلتة ايه تلاتة و عشرين ألف خمسمية و خمسة و
+
+174
+00:18:22,690 --> 00:18:32,810
+تلاتين بيساوي M في ال R بونت تلاتة سبعة اتنين
+
+175
+00:18:32,810 --> 00:18:39,570
+تربيع في تلاتة تمانين بونت تمانية تربيع في بونت
+
+176
+00:18:39,570 --> 00:18:45,190
+اربعة و منها بحسب ال M
+
+177
+00:18:55,470 --> 00:19:03,590
+طيب معناته ال A هتكون بيساوي ستمية و خمسة على باي في
+
+178
+00:19:03,590 --> 00:19:15,730
+بوند سبعة أربعة أربعة في سبعة ألف و متين point
+
+179
+00:19:15,730 --> 00:19:18,790
+zero
+
+180
+00:19:20,170 --> 00:19:28,450
+zero تلاتة خمسة متر مربع مظبوط
+
+181
+00:19:28,450 --> 00:19:37,790
+هذه ال area مقطع بيساوي P في T ال P خمسة T يعني خمسة
+
+182
+00:19:37,790 --> 00:19:46,150
+T تربيع بيساوي point O تلاتة خمسة ومنها T
+
+183
+00:19:49,250 --> 00:19:59,230
+تطلع point O تلاتة خمسة على خمسة تحت الجدر point
+
+184
+00:19:59,230 --> 00:20:02,790
+O
+
+185
+00:20:02,790 --> 00:20:08,370
+تمنع الرمية يعني أربعة وتمانين millimeter يعني ال
+
+186
+00:20:08,370 --> 00:20:13,490
+B هتكون خمسة في أربعة بعشرين
+
+187
+00:20:19,420 --> 00:20:29,580
+millimeter صح نعم
+
+188
+00:20:29,580 --> 00:20:36,740
+
+201
+00:22:25,700 --> 00:22:33,860
+the coefficient of fluctuation of energy CE بساوية
+
+202
+00:22:33,860 --> 00:22:39,860
+zero point one and fluctuation of speed is plus or 
+
+203
+00:22:39,860 --> 00:22:41,320
+minus two percent of mean speed
+
+204
+00:22:48,610 --> 00:22:52,950
+if mean diameter of flywheel rim is two meter دي
+
+205
+00:22:52,950 --> 00:22:58,390
+مترين and
+
+206
+00:22:58,390 --> 00:23:12,150
+hub and spoke هاي ال hub
+
+207
+00:23:12,150 --> 00:23:15,850
+في النص في ال spokes
+
+208
+00:23:21,210 --> 00:23:26,610
+هذه ال hub وهذه ال spokes and
+
+209
+00:23:26,610 --> 00:23:29,350
+the hub and spokes provide five percent of the
+
+210
+00:23:29,350 --> 00:23:34,170
+rotation inertia of the flywheel يعني ال I بتاعة ال
+
+211
+00:23:34,170 --> 00:23:40,090
+spokes و ال hub بالساعة point oh five من ال I
+
+212
+00:23:40,090 --> 00:23:43,430
+الكليه ال I الكليه اللي هي بتاعة ال spokes و ال
+
+213
+00:23:43,430 --> 00:23:48,490
+hub و ال rim معناته
+
+214
+00:23:48,490 --> 00:23:54,270
+I الكليه شويه I بتاعة الـ spokes والـ hub زائد I
+
+215
+00:23:54,270 --> 00:23:59,870
+بتاعة الـ rim، صح؟
+
+216
+00:23:59,870 --> 00:24:04,830
+معناته I بتاعة الـ rim يعني هيكون عندي I بتساوي
+
+217
+00:24:04,830 --> 00:24:13,110
+point oh five I الكلية زائد I بتاعة الـ rim معناته
+
+218
+00:24:13,110 --> 00:24:18,570
+I بتاعة الـ rim الـ
+
+219
+00:24:18,570 --> 00:24:25,020
+Find the mass and cross-sectional area of the
+
+220
+00:24:25,020 --> 00:24:31,160
+flywheel rim أوجد ال mass بتاعة ال flywheel rim و
+
+221
+00:24:31,160 --> 00:24:37,540
+ال cross-sectional area Assume
+
+222
+00:24:37,540 --> 00:24:40,800
+density of flywheel material raw
+
+223
+00:24:50,080 --> 00:24:59,440
+متر مكعب طيب
+
+224
+00:24:59,440 --> 00:25:05,780
+انا عارف ال mean speed وعارف
+
+225
+00:25:05,780 --> 00:25:10,700
+ال power ممكن احسب ال mean torque صح ال mean
+
+226
+00:25:10,700 --> 00:25:17,980
+torque يعني ال power سواء ال T mean في omega صح
+
+227
+00:25:19,050 --> 00:25:27,610
+معنى التيمين سواء مية و خمسين ألف على
+
+228
+00:25:27,610 --> 00:25:41,550
+تمانية point تلاتة سبعة اكم تطلع سبعتاشر
+
+229
+00:25:41,550 --> 00:25:48,190
+ألف طيب
+
+230
+00:26:02,720 --> 00:26:09,480
+انا اقول هنا ال work done per cycle لان
+
+231
+00:26:09,480 --> 00:26:13,540
+عندي ال
+
+232
+00:26:13,540 --> 00:26:20,100
+coefficient of fluctuation في ال CE ايش بيساوي ال
+
+233
+00:26:20,100 --> 00:26:29,240
+delta E على ال work done في ال cycle و ال work done
+
+234
+00:26:29,240 --> 00:26:29,900
+في ال cycle
+
+235
+00:26:33,780 --> 00:26:43,900
+و Cycle بيستوى ال power في ستين على N small N
+
+236
+00:26:43,900 --> 00:26:49,760
+small بيستوى N capital in case of steam engine and
+
+237
+00:26:49,760 --> 00:26:51,760
+two stroke internal combustion engine احنا عندنا
+
+238
+00:26:51,760 --> 00:26:56,640
+ايش steam engine يعني هتكون ال P عندى مية و خمسين
+
+239
+00:26:56,640 --> 00:27:01,620
+الف في ستين والصراعي عندى اكم
+
+240
+00:27:05,170 --> 00:27:08,710
+تمنين يعني بيطلع ال work done per cycle أكم
+
+241
+00:27:08,710 --> 00:27:16,610
+بالساوية نوتن
+
+242
+00:27:16,610 --> 00:27:26,410
+متر معناه ال delta A بالساوية CE في W per cycle ال
+
+243
+00:27:26,410 --> 00:27:33,410
+CE point one في مية و اتناشر الف و خمسمية يعني
+
+244
+00:27:33,410 --> 00:27:47,470
+هيكون احداشر الف احداشر
+
+245
+00:27:47,470 --> 00:27:57,330
+الف و متين و خمسين طيب
+
+246
+00:27:57,330 --> 00:28:01,610
+ال delta E ايه في الساوية؟
+
+247
+00:28:06,600 --> 00:28:15,620
+بسوء M في K تربيع Omega تربيع CS هذا لو كانت
+
+248
+00:28:15,620 --> 00:28:23,180
+في ال bus رم فيها بس في عندى رم و spokes و hub ال
+
+249
+00:28:23,180 --> 00:28:31,080
+M في K تربيع إيه؟ يعني Delta E سواء I Omega تربيع
+
+250
+00:28:31,080 --> 00:28:39,940
+في ال CSبحسب ال I دلتا
+
+251
+00:28:39,940 --> 00:28:49,900
+ايه حتكون دلتا ايه حتكون
+
+252
+00:28:49,900 --> 00:28:50,380
+دلتا ايه حتكون دلتا ايه حتكون دلتا ايه حتكون دلتا
+
+253
+00:28:50,380 --> 00:28:50,620
+حتكون دلتا ايه حتكون دلتا ايه حتكون دلتا ايه حتكون
+
+254
+00:28:50,620 --> 00:28:51,060
+دلتا ايه حتكون دلتا ايه حتكون دلتا ايه حتكون دلتا
+
+255
+00:28:51,060 --> 00:28:52,300
+ايه حتكون دلتا ايه حتكون دلتا ايه حتكون دلتا ايه
+
+256
+00:28:52,300 --> 00:28:59,420
+حتكون دلتا ايه حتكون
+
+257
+00:28:59,420 --> 00:29:11,230
+دلتا ايه حتكون دلتا ايه حتكون كيلوجرام متر تربيع ال
+
+258
+00:29:11,230 --> 00:29:18,770
+I تاعة الرم لحالها كم؟
+
+259
+00:29:18,770 --> 00:29:25,290
+point تسعة خمسة في الاربع تلاف واربعتاش point ستة
+
+260
+00:29:25,290 --> 00:29:32,550
+تلت تلاف و تمنمية هذا
+
+261
+00:29:32,550 --> 00:29:33,410
+شو يستوي؟
+
+262
+00:29:38,570 --> 00:29:49,510
+So MR تربيع M للرم و منها بحسب ال M بالساوية تلت
+
+263
+00:29:49,510 --> 00:29:55,510
+تلاف و تانمية و تلتاش على ال R يعني ال D معطيني
+
+264
+00:29:55,510 --> 00:30:03,030
+مترين صح على واحد يعني تطلع تلت تلاف و مية و
+
+265
+00:30:03,030 --> 00:30:04,430
+تلتاشر كيلو جرام
+
+266
+00:30:11,240 --> 00:30:27,240
+هك عسبنا ياش ال mass طيب
+
+267
+00:30:27,240 --> 00:30:36,040
+ال
+
+268
+00:30:36,040 --> 00:30:36,900
+a h الساوية
+
+269
+00:30:39,470 --> 00:30:47,010
+الماس تاعة الرم على باي دي فيرو يعني الماس تاعة
+
+270
+00:30:47,010 --> 00:30:55,250
+الرم هي تلت تلاف و تمان مية و تلتاش على باي في
+
+271
+00:30:55,250 --> 00:31:07,630
+اتنين في سبعة تلاف و متين point o متر
+
+272
+00:31:07,630 --> 00:31:08,130
+مربع
+
+273
+00:31:15,440 --> 00:31:23,620
+هيك جيبنا ال cross section في
+
+274
+00:31:23,620 --> 00:31:27,860
+اي سؤال؟
+
+275
+00:31:27,860 --> 00:31:43,760
+هذه
+
+276
+00:31:43,760 --> 00:31:48,340
+ال rim الخارجيةالريم اللى فى المصدر هدى ال hub
+
+277
+00:31:48,340 --> 00:31:54,140
+وهدى العصاب ال spokes بالظبط
+
+278
+00:31:54,140 --> 00:31:56,900
+لأن ال shaft فيه لثقوب ال shaft بيجي هنا فهدى ال
+
+279
+00:31:56,900 --> 00:32:04,920
+hub هدى ال spokes وهدى ايش ال rim انحل
+
+280
+00:32:04,920 --> 00:32:12,740
+سؤال تانى a multi cylinder engine is to run at a
+
+281
+00:32:12,740 --> 00:32:21,110
+speed of six hundred rpm يعني الان بالسواء
+
+282
+00:32:21,110 --> 00:32:29,010
+ستمائة rpm يعني ال omega كام ال
+
+283
+00:32:29,010 --> 00:32:40,830
+omega اتنين وستين طيب
+
+284
+00:32:43,080 --> 00:32:45,580
+on drawing the trigonometric diagram to a scale
+
+285
+00:32:45,580 --> 00:32:49,860
+لان انا عندى هاي تجارب تجارب تجارب تجارب تجارب
+
+286
+00:32:49,860 --> 00:32:53,180
+تجارب
+
+287
+00:32:53,180 --> 00:32:56,700
+تجارب تجارب تجارب تجارب تجارب تجارب تجارب تجارب
+
+288
+00:32:56,700 --> 00:32:56,720
+تجارب تجارب تجارب تجارب تجارب تجارب تجارب تجارب
+
+289
+00:32:56,720 --> 00:32:57,280
+تجارب تجارب تجارب تجارب تجارب تجارب تجارب تجارب
+
+290
+00:32:57,280 --> 00:32:57,780
+تجارب تجارب تجارب تجارب تجارب تجارب تجارب تجارب
+
+291
+00:32:57,780 --> 00:32:57,800
+تجارب تجارب تجارب تجارب تجارب تجارب تجارب تجارب
+
+292
+00:32:57,800 --> 00:33:10,060
+تجارب تجارب تجارب تجارب تجارب
+
+293
+00:33:10,060 --> 00:33:16,650
+تجواحد ميلي متر يعادل تلت درجات معناه واحد ميلي
+
+294
+00:33:16,650 --> 00:33:24,290
+متر square هيكون اتنين وخمسين في تلاتة في باي عمية
+
+295
+00:33:24,290 --> 00:33:32,510
+و تمانين تلتاش point واحد
+
+296
+00:33:32,510 --> 00:33:34,550
+نيوتن متر
+
+297
+00:33:36,970 --> 00:33:40,010
+the speed is to be kept within plus or minus one
+
+298
+00:33:40,010 --> 00:33:43,670
+percent of the mean speed of the engine يعني ال CS
+
+299
+00:33:43,670 --> 00:33:51,290
+اتنين في المائة calculate necessary moment of
+
+300
+00:33:51,290 --> 00:33:55,410
+inertia of the flywheel بتركز في moment of inertia
+
+301
+00:33:55,410 --> 00:33:56,550
+اللي هي I
+
+302
+00:34:04,460 --> 00:34:07,180
+determine suitable dimensions of a rectangular
+
+303
+00:34:07,180 --> 00:34:13,720
+flywheel rim اذا كان مقطع الريم مستطيل ال breadth
+
+304
+00:34:13,720 --> 00:34:21,820
+بي بتاعها بساوة اتنين ت ال
+
+305
+00:34:21,820 --> 00:34:23,360
+density of cast iron
+
+306
+00:34:36,320 --> 00:34:48,080
+and its hoop stress sigma ستة ميجا اسكال assume
+
+307
+00:34:48,080 --> 00:34:50,860
+that rim contributes ninety two percent of
+
+308
+00:34:50,860 --> 00:34:58,300
+flywheel effect يعني ال rim بتمثل
+
+309
+00:34:58,300 --> 00:35:01,680
+ninety two percent ال flywheel
+
+310
+00:35:08,800 --> 00:35:17,340
+effect طيب هو بده إيش؟ بده ال I و ال cross section
+
+311
+00:35:17,340 --> 00:35:22,700
+أنا
+
+312
+00:35:22,700 --> 00:35:26,900
+عندي اللي بدي أحسب ال delta E في الأول صح؟ المعنى
+
+313
+00:35:26,900 --> 00:35:32,940
+انت بدي أعرف ال max و ال minimum عندي ال pointبس
+
+314
+00:35:32,940 --> 00:35:41,540
+طلع ليش بي و اي هاليد بي point وال اي نقطة اي اللي
+
+315
+00:35:41,540 --> 00:35:56,300
+هي اي بي اي زي المية و ستين وال سي اي ناقص اتناش و
+
+316
+00:35:56,300 --> 00:35:56,760
+دي
+
+317
+00:36:00,940 --> 00:36:05,820
+مية ستة و خمسين ايه؟
+
+318
+00:36:05,820 --> 00:36:09,200
+أو ايه؟
+
+319
+00:36:09,200 --> 00:36:12,640
+أو
+
+320
+00:36:12,640 --> 00:36:21,340
+اف ايه زائد؟
+
+321
+00:36:21,340 --> 00:36:25,880
+أو جيه؟
+
+322
+00:36:30,960 --> 00:36:39,480
+هنا دي ايش ال minimum وال maximum هي عند B أو عند
+
+323
+00:36:39,480 --> 00:36:43,540
+F هنتبهر
+
+324
+00:36:43,540 --> 00:36:50,060
+عند F عشان نغير القاعدة هاي ال max اللي
+
+325
+00:36:50,060 --> 00:36:53,840
+هم بيختلفوا فعلا بيختلفوا بيختلفوا انا طلعت ماشي
+
+326
+00:36:53,840 --> 00:37:04,740
+ال delta E هتكون مية و اتنين و ستينزائد اتناش مية
+
+327
+00:37:04,740 --> 00:37:17,660
+أربعة و سبعين فيه تلتاش point واحد صح؟ اه كم بطلع؟
+
+328
+00:37:17,660 --> 00:37:25,540
+مية و تسعين زائد خمسة و تلاتين مية و سبعة و تسعين
+
+329
+00:37:40,840 --> 00:37:55,320
+الـ Delta A
+
+330
+00:37:55,320 --> 00:38:00,080
+I
+
+331
+00:38:13,360 --> 00:38:24,800
+cs منها بحسب ال I اللي هتكون الفين و خمسمية واحد
+
+332
+00:38:24,800 --> 00:38:29,960
+تمانين على اتنين و ستين
+
+333
+00:38:52,600 --> 00:39:00,000
+انتوا لاحظوا Delta E تتناسب ترضي مع Iمعناته لما هو
+
+334
+00:39:00,000 --> 00:39:05,540
+حكال ان ال rim بتمثل 82% من ال fly و ال effect هي
+
+335
+00:39:05,540 --> 00:39:11,840
+حقيقة برضه تمثل 92% من ال .. من ال ايه؟ من ال I من
+
+336
+00:39:11,840 --> 00:39:17,440
+ال energy معناته هتكون ال I بتاعة ال rim هو point
+
+337
+00:39:17,440 --> 00:39:22,120
+9 2 في 32 point 7
+
+338
+00:39:37,760 --> 00:39:44,540
+تلاتين ال I تاعت رم بسوى
+
+339
+00:39:44,540 --> 00:39:52,420
+MR تربيعي مظبوط
+
+340
+00:39:52,420 --> 00:39:57,180
+و في عندهين سجما
+
+341
+00:40:04,070 --> 00:40:12,210
+بالساوية رو R تربيع أمجا تربيع من هنا بحسب الـ R
+
+342
+00:40:12,210 --> 00:40:19,310
+بالساوية الجذر التربيعي لسجمه
+
+343
+00:40:19,310 --> 00:40:31,010
+على رو أمجا تربيعي هتساوي الجذر التربيعيسجمه ستة
+
+344
+00:40:31,010 --> 00:40:41,570
+ستة في عشر عقل ستة على سبعة تلاف وانتين وخمسين في
+
+345
+00:40:41,570 --> 00:40:51,050
+الامجا Zero
+
+346
+00:40:51,050 --> 00:40:53,950
+point
+
+347
+00:41:00,120 --> 00:41:07,620
+أربعة خمسة تمانية و أربعة
+
+348
+00:41:07,620 --> 00:41:09,320
+خمسة تمانية و أربعة خمسة تمانية و أربعة خمسة
+
+349
+00:41:09,320 --> 00:41:10,400
+تمانية و أربعة خمسة تمانية و أربعة خمسة تمانية و
+
+350
+00:41:10,400 --> 00:41:10,820
+أربعة خمسة تمانية و أربعة خمسة تمانية و أربعة خمسة
+
+351
+00:41:10,820 --> 00:41:15,220
+تمانية و أربعة خمسة تمانية و أربعة خمسة تمانية و
+
+352
+00:41:15,220 --> 00:41:16,420
+أربعة خمسة تمانية و أربعة خمسة تمانية و أربعة خمسة
+
+353
+00:41:16,420 --> 00:41:16,840
+تمانية و أربعة خمسة تمانية و أربعة خمسة تمانية و
+
+354
+00:41:16,840 --> 00:41:23,920
+أربعة خمسة تمانية و أربعة خمسة تمانية و أربعة خمسة
+
+355
+00:41:23,920 --> 00:41:27,040
+تمانية و
+
+356
+00:41:27,040 --> 00:41:28,840
+أربعة خمسة تمانية و أربعة خ
+
+357
+00:41:37,320 --> 00:41:42,560
+منها ال area بتاعة الرم ال area اللي هي بيساوي ايش
+
+358
+00:41:42,560 --> 00:41:53,860
+ال area اللي
+
+359
+00:41:53,860 --> 00:42:04,730
+هي M على B D فرق يعني هتساويمية و تلاتة و اربعين
+
+360
+00:42:04,730 --> 00:42:15,230
+point four على باي اللي هي في اتنين في point اربع
+
+361
+00:42:15,230 --> 00:42:22,830
+خمس تمانية في سبعة تلاف و متين و خمسين اكم
+
+362
+00:42:22,830 --> 00:42:27,490
+بالساوية اكم
+
+363
+00:42:27,490 --> 00:42:31,910
+point
+
+364
+00:42:31,910 --> 00:42:32,530
+o o
+
+365
+00:42:47,790 --> 00:42:51,150
+بتساوي ال B في T و ال B سوا اتنين T يعني سوا اتنين
+
+366
+00:42:51,150 --> 00:43:01,610
+T تربيع و من هنا بحسب ال T اقسمها اتنين و اخد جدر
+
+367
+00:43:06,680 --> 00:43:18,600
+point A 58 ملي و ال B 116 ملي
+
+368
+00:43:18,600 --> 00:43:25,520
+متر طيب
+
+369
+00:43:25,520 --> 00:43:31,240
+المحاضرة الجاي اللي هو chapter بتاع ال balancing
+
+370
+00:43:31,240 --> 00:43:35,890
+of rotating massesو 21 balancing of rotating
+
+371
+00:43:35,890 --> 00:43:40,950
+masses و لبعد balancing of reciprocating masses
+
+372
+00:43:40,950 --> 00:43:45,870
+بعدين اعطيكوا ال gears two chapters بعدين ال
+
+373
+00:43:45,870 --> 00:43:46,190
+counts