
avesh ghanatva

vidyut chumbakatva mein, avesh ghanatva prati ikai lambai, satah kshetra yaa aayatan mein vidyut avesh kii matra haye. aayatan avesh ghanatva (yunani akshar ρ dwara prateekrit) prati ikai aayatan avesh kii matra haye, jise ack aayatan mein kissy bhee bindu parr coolomb prati ghana meater (c              m − 3) mein maapane key liye aiss. aaee. pranali mein maapa jaataa haye. satah avesh ghanatva (σ) prati ikai kshetra mein avesh kii matra haye, jise dou ayami satah parr satah avesh vitaran parr kissy bhee bindu parr prati varg meater (c raikhik avesh ghanatva (λ) prati ikai lambai mein avesh kii matra haye, jise ack rekha avesh vitaran parr kissy bhee bindu parr kulamb prati meater (c avesh ghanatva yaa tou sakaratmak yaa nakaratmak hoe sakata haye, kyonki vidyut avesh yaa tou sakaratmak yaa nakaratmak hoe sakata haye.
dravyamaan ghanatva kii tarah, avesh ghanatva sthiti key saath bhinn hoe sakata haye. shaastriya vidyut chumbakiya siddhant mein avesh ghanatva koo sthiti sootra key "nirantar" scalar function key roop mein aadarsh banaaya jaataa haye, jaise kii ack drav, aur sootra _ 2, sootra _ 3, aur sootra _ 4 koo aamtaur parr nirantar avesh vitaran key roop mein maanaa jaataa haye, bhale hii sabhi vaastavik avesh vitaran asatat aaveshit kanon seey baney houn. vidyut avesh key sanrakshan key kaaran, kissy bhee aayatan mein avesh ghanatva kewal tabhi badal sakata haye jaba avesh kaa vidyut pravaah aayatan mein yaa usase baahar bahata haye. yeh ack nirantarta sameekaran dwara vyakt kiya jaataa haye joe avesh ghanatva sootra _ 2 key parivartan kii darr aur vartamaan ghanatva sootra _ 6 koo jodata haye.
choonki sabhi avesh upaparmaanvik kanon dwara wahan kiye jaate hain, jinhen binduon key roop mein aadarsh banaaya jaa sakata haye, isaliye "nirantar" avesh vitaran kii avadharana ack anuman haye, joe chhoti lambai key taraju parr galat hoe jaataa haye. ack avesh vitaran antatah alag-alag aaveshit kanon seey banaa hotaa haye joe binaa avesh vaale kshetron dwara alag kiye jaate hain. udaaharan key liye, ack vidyut aaveshit dhaatu vastu mein avesh dhaatu key chrystal jaali mein yaadrichhik roop seey chalane vaale chaalan electrons seey banaa hotaa haye. sthir bijli vastuon kii satah parr ayanon seey yukt satah aaveshon key kaaran hoti haye, aur ack nirvaat nully mein antariksh avesh antariksh mein yaadrichhik roop seey chalane vaale mukt electrons key baadal seey banaa hotaa haye. ack chaalak mein avesh vaahak ghanatva gatishil avesh vaahakon (electron, aayan, aadi) kii sankhya key barabar hotaa haye.) prati ikai matra. kissy bhee bindu parr avesh ghanatva avesh vaahak ghanatva key barabar hotaa haye jise kanon parr praathamik avesh seey gunaa kiya jaataa haye. haalaanki, kyonki ack electron parr praathamik avesh itna chhota hotaa haye (1.6 ≤10−19 c) aur unamen seey kaee macroscopic aayatan mein hotey hain (tambe key ack ghana centimeter mein lagbhag 1022 chaalan electron hotey hain) nirantar sanniktan bahut sateek hotaa haye jaba macroscopic maatraon parr lagu kiya jaataa haye, aur yahaan taka kii nanometer star seey oopar sookshm matra bhee.
parmaanuon aur anuon key chhote paimaane parr, quantum yantriki key anishchitata siddhant key kaaran, ack aaveshit kann kii "sateek sthiti" naheen hoti haye, lekin ack sambhaavyata vitaran dwara darshaaya jaataa haye, isaliye ack vyaktigat kann kaa avesh ack bindu parr kendrit naheen hotaa haye, balki antariksh mein 'smear out' hotaa haye aur ack vaastavik nirantar avesh vitaran kii tarah kaary kartaa haye. yeh rasayan vigyaan aur rasayanik bandhan mein upayog kiye jaane vaale 'avesh vitaran' aur 'avesh ghanatva' kaa arth haye. ack electron koo ack "tarang falan" sootra _ 7 dwara darshaaya jaataa haye jiska varg antariksh mein kissy bhee bindu sootra _ 1 parr electron koo khojane kii sambhavana key samanupati hotaa haye, isaliye sootra _ 9 kissy bhee bindu parr electron key avesh ghanatva key samanupati hotaa haye. parmaanuon aur anuon mein electrons kaa avesh baadlon mein vitarit hotaa haye jinhen kakshiya kahaa jaataa haye joe paramanu yaa anu koo gherate hain, aur rasayanik bandhanon key liye jimmedaar hotey hain.
paribhaashaaen.
nirantar shulk.
nirantar avesh vitaran key liye nimnalikhit paribhaashaaen hain.
raikhik avesh ghanatva ack aseem vidyut avesh "dq" (si ikaaih c) aur ack aseem rekha tatva kaa anupaat haye, 
sootra _ 10
isi tarah satah avesh ghanatva ack satah kshetra tatva "ds" kaa upayog kartaa haye." 
sootra _ 11
aur aayatan avesh ghanatva aayatan tatva "dee. vee". kaa upayog kartaa haye."
sootra _ 12
paribhashaon koo ekikrit karane seey ack rekha parr raikhik avesh ghanatva "λ" "q" (r) key rekha samakalan key anusaar ack kshetra kaa kull avesh "q" milata haye yaa 1d vakr "c", 
sootra _ 13
isi tarah satah key avesh ghanatva kaa ack satah abhinn σ "q" (r) ack satah "s" parr,
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aur aayatan avesh ghanatva kaa ack aayatan abhinn "ρ" q "(r) aayatan" v "parr, 
sootra _ 15
jahan abhilikhit "q" yeh spasht karane key liye haye kii ghanatva vidyut avesh key liye haye, dravyamaan ghanatva, sankhya ghanatva, sambhaavyata ghanatva jaisi anya ghanatvon key liye naheen, aur tarang dairdhya, vidyut pratirodhakta aur chaalakta key liye vidyut chumbakatva mein "λ", "σ", "ρ" key kaee anya upayogon key saath sangharsh koo rokta haye.
vidyut chumbakatva key sandarbh mein, sadasyata koo aamtaur parr saralata key liye chhod diyaa jaataa haih "λ", "σ", "ρ". anya sanketanon mein shamil hoe sakate hainh "ρl", "ρs", "ρv", "ρl", "ρs", "ρv" aadi.
kull avesh koo lambai, satah kshetra yaa aayatan seey vibhajit karke ausat avesh ghanatva hogaah
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nihshulk, baadhya aur kull shulk.
paraavartak samagri mein, kissy vastu key kull avesh koo "mukt" aur "baadhya" aaveshon mein vibhajit kiya jaa sakata haye.
baadhya avesh ack lagu vidyut kshetra ee key jawab mein vidyut dwidhruv sthaapit karate hain, aur unhein oopar karane kii or badhane vaale anya aas-paas key dwidhruvon kaa dhruvikaran karate hain, dwidhruvon key abhivinyas seey avesh kaa shuddh sanchay baadhya avesh haye. unhein baadhya kahaa jaataa haye kyonki unhein hataaya naheen jaa sakata haih paraavartak samagri mein avesh naabhik seey bandhe electron hotey hain.
mukt avesh way atirikt avesh hain joe sthir vidyut santulan mein jaa sakate hain.ee. jaba avesh naheen chala rahey hotey hain aur parinami vidyut kshetra samay seey swatantra hotaa haye, yaa vidyut dhaaraon kaa gathan kartaa haye.
kull charge ghanatva.
aayatan avesh ghanatva key sandarbh mein, kull avesh ghanatva haih
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satah avesh ghanatva key liyeh
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jahan abhilikhit "f" aur "b" kramshah "mukt" aur "baadhya" koo darshaate hain.
baadhya prabhaar.
baadhya satah avesh paraavartak kii satah parr dher kiya gayaa avesh haye, joe satah key lambavat dvidhruviya kshan dwara diyaa jaataa haih
sootra _ 19
jahan s dwidhruv kaa gathan karane vaale bindu aaveshon key beach kaa vibhajan haye, sootra _ 20 vidyut dwidhruv kshan haye, sootra _ 21 satah key liye ikai samanya sadish haye.
anantata lenaah
sootra _ 22
aur vibhedak satah tatva "ds" seey vibhajit karane seey baadhya satah avesh ghanatva milata haih
sootra _ 23
joe satah avesh (satah samakalan) kii kshamata aur aayatan avesh (aayatan samakalan) key kaaran kshamata mein alag hotaa haih
vaha haye
sootra _ 24
mukt prabhaar ghanatva.
mukt avesh ghanatva bijli key liye goss key niyam mein ack upayogi saralikaran key roop mein kaary kartaa haye; iska aayatan abhinn ack aaveshit vastu mein sanlagn mukt avesh haye-vastu seey ubharate vidyut visthaapan kshetra key shuddh pravaah key baraabarh
adhik vivaran key liye maxwell key sameekaran aur samvaidhaanik sambandh dekhein.
sajaatiya avesh ghanatva.
ack sajaatiya avesh ghanatva "ρ" 0 key vishesh mamle key liye, sthiti i seey swatantra.ee. samagri key poore kshetra mein sthir, sameekaran saral hoe jaataa haih
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pramaan.
nirantar aayatan avesh ghanatva kii paribhasha key saath shuru karenh
sootra _ 26
phir, sajaatiyataa kii paribhasha key anusaar, "ρ" "q" (r) ack sthiraank haye jise "ρ" "q", 0 (sthir aur gair-sthir ghanatvon key beach antar karane key liye) dwara darshaaya jaataa haye, aur isaliye ack samakalan key gunon dwara samakalan key baahar kheencha jaa sakata haye jisake parinaamswaroopah
sootra _ 27
tou,
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raikhik avesh ghanatva aur satah avesh ghanatva key liye samatulya pramaan oopar diye gaye samaan tarkon kaa paalan karate hain.
asatat shulk.
ack ekal bindu avesh "q" key liye 3d sthaan "r" key kshetra key ander r0 kii sthiti mein, ack electron kii tarah, aayatan avesh ghanatva koo diarock delta function dwara vyakt kiya jaa sakata haih
sootra _ 29
jahan r avesh kii ganana karane kii sthiti haye.
hamesha kii tarah, sthaan key ack kshetra parr avesh ghanatva kaa abhinn anga usa kshetra mein nihit avesh haye. delta falan mein kissy bhee falan "f" key liye "sifting property" haih
sootra _ 30
isaliye delta falan yeh sunishchit kartaa haye kii jaba avesh ghanatva "r" parr ekikrit hotaa haye, tou "r" mein kull avesh "q" hotaa haih
sootra _ 31
ise "aine" asatat bindu jaise avesh vaahak taka badhaaya jaa sakata haye. ack bindu r parr pranali kaa avesh ghanatva pratyek avesh "qi" key liye avesh ghanatva kaa yog haye, jahaan r "i" sthiti mein haih
sootra _ 32
pratyek avesh "qi" key liye delta falan, yog mein, "δ" (r − r "i"), yeh sunishchit kartaa haye kii "r" parr avesh ghanatva kaa abhinn hissa "r" mein kull avesh detaa haih
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yadi sabhi avesh vaahakon kaa avesh "q" samaan haye (electrons key liye "q" = − "e", electron avesh) tou avesh ghanatva koo prati ikai aayatan, "n" (r), dwara avesh vaahakon kii sankhya key madhyam seey vyakt kiya jaa sakata haye.
sootra _ 34
raikhik aur satah avesh ghanatva key liye samaan samikaranon kaa upayog kiya jaataa haye.
vishesh saapekshata mein avesh ghanatva.
vishesh saapekshata mein, taar key ack khand kii lambai lambai key sankuchan key kaaran paryavekshak key wegg parr nirbhar karati haye, isaliye avesh ghanatva bhee wegg parr nirbhar karega. anthany french
iss saapeksh avesh ghanatva seey vidyut dhaara dhaaran karane vaale taar kaa chumbakiya kshetra bull kaise utpann hotaa haye, iska varnan kiya gayaa haye. unhone ack minkovsky aarekh kaa upayog kiya (pee 260) yeh dikhaane key liye kii kaise ack tatasth dhaara-vaahak taar ack shuddh avesh ghanatva koo leey jaane key liye dikhaai detaa haye jaisa kii ack chalati frame mein dekhaa gayaa haye."jaba ack avesh ghanatva koo sandarbh key ack gatishil frame mein maapa jaataa haye tou ise uchit avesh ghanatva kahaa jaataa haye.
yeh charge ghanatva "ρ" aur vartamaan ghanatva jey koo lorentz parivartanon key tahat chaar-vartamaan sadish key roop mein ack saath parivartit kartaa haye.
quantum yantriki mein avesh ghanatva.
quantum yantriki mein, avesh ghanatva "ρ" "q" sameekaran dwara tarang falan "si" (r) seey sambandhit haye.
sootra _ 35
jahan "q" kann kaa avesh haye aur sambhaavyata ghanatva falan i haye.ee. r parr sthit kann kii prati ikai aayatan kii sambhavana.
jaba tarang falan samanya hoe jaataa haye-tou kshetra mein ausat avesh r ± "r" hotaa haye
sootra _ 36
jahan "d" 3r 3d sthiti sthaan parr ekikaran maap haye.
aavedan.
vidyut pravaah key liye nirantarta sameekaran mein avesh ghanatva dikhaai detaa haye, aur maxwell key samikaranon mein bhee. yeh vidyut chumbakiya kshetra kaa pramukh srot shabd haye; jaba avesh vitaran chalata haye, tou yeh ack vartamaan ghanatva key anuroop hotaa haye. anuon kaa avesh ghanatva rasayanik aur prithakkaran prakriyaon koo prabhaavit kartaa haye. udaaharan key liye, avesh ghanatva dhaatu-dhaatu bandhan aur hydrogen bandhan koo prabhaavit kartaa haye. nanofiltration jaisi prithakkaran prakriyaon key liye, ayanon kaa avesh ghanatva jhilli dwara unaki asweekriti koo prabhaavit kartaa haye.

