question
5.10. a magnetic needle free to rotate in a vertical plane parallel to the magnetic meridian has its north tip pointing down at with the horizontal. the horizontal component of the earth’s magnetic field at the place is known to be . determine the magnitude of the earth’s magnetic field at the place.
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(a) clockwise would be the direction of magnetic field in wire a.(b) the direction of the magnetic field in the wire b is anticlockwise.maxwell’s right hand thumb rule. that depends on a lot of things. in particular, you would need to find the electric susceptibility of the paper. the field produced by static charge is inverse-square. the polarization of the paper varies directly with the external field, with a proportionality constant equal to the electric susceptibility. the dipole field created by the polarized paper is inverse-cube. overall, the force between the ruler and the paper will vary with the inverse fifth power of distance. to get any more detailed, you would need to know the geometry of the situation, and the charge distribution. we first define our axisupward is along + y direction of axiseastward is along + x direction of axisvelocity of a aeroplane = velocity of a bullet = a person on the earth will see the bullet having a resultant velocity and angle θ with the vertical (y axis)θ = angle with the vertical (y axis) the force on the wire due to the interaction of magnetic fields of the bar magnet and current carrying wire can act only in upwards or downwards direction. a. dimensions of h = [l]dimensions of s = [mt-2]dimensions of ρ = [ml-3]dimensions of r = [l]dimensions of g = [lt-2]checking the r.h.sdimensionally= = [m0l1t0]a. is dimensionally correctb. dimensions of v = [lt-1]dimensions of p = [ml-1t-2]dimensions of ρ = [ml-3]checking the r.h.sdimensionally= b. is dimensionally correctc. dimensions of v = [l3]dimensions of p = [ml-1t-2]dimensions of r4 = [l4]dimensions of t = [t]dimensions of l = [l]dimensions of η = [ml-1t-1]checking the r.h.sdimensionally= =[l3]c. is dimensionally correctd. dimensions of v = [t-1]dimensions of m = [m]dimensions of g = [lt-2]dimensions of l = [l]dimensions of i = [ml2]checking the r.h.sdimensionally= d. is dimensionally correct physics 101 notes: 8/25 (week 2 continued)  force o defined as a push or a pull, and is a vector quantity, meaning that it has direction depending on which way it is being pushed or pulled o it has amount and direction (how much force is being applied and in which direction it is moving)  newton’s first law o first draft: “an object that is free of forces move in a straight line and covers equal distances in equal time” o final: “an object that is free of external forces moves at a constant velocity”  how does a skater start, stop, or turn? o acceleration: “the rate at which an object’s velocity is changing with time o acceleration, s vertical and horizontal you don't say that the area must be a rectangle. the true largest area would be a circle, with the circumference equal to 400m and the area would be 12,732.4 m^2. however, evidently, the area is restricted to a rectangle, in which case the maximum area is a square, and the side of the square will be 
400/4 = 100 m. the area is 100x100 = 10,000 m^2.
algebraically,
let x = one pair of opposite sides
(400-2x)/2 = 200-x = the other pair of opposite sides

area = a(x) = x(200 - x) = -x^2 + 200x
x-coordinate of vertex = -b/2a = 200/2 = 100
a(100) = 10,000

that's it! ;) without calculus, the  horizontal coordinate of a quadratic of  f(x) =ax^2 + bx + c  is equal to - b/ 2a
   which in this case of
       f( x) =  - 5 x^2 + 3x + 2  
 
       equals :    - 3/[2(-5)] = -3/ -10 = 3/10 net work done in carrying charge along closed loop by electric field is zero. hence, the tangential component of the electric field is continuous from one side of a charged surface to the other.