Positive point charges q +8.25 pC and q, +3.25 pC are moving relative to an obse
ID: 1583686 • Letter: P
Question
Positive point charges q +8.25 pC and q, +3.25 pC are moving relative to an observer at point ' as shown in the following figure. The distance d is 0.125 m, v 4.55 x 106 m/s, and v' 9.40 x 106 m/s. (a) When the two charges are at the locations shown in the figure, what are the magnitude and direction of the net magnetic field they produce at point P? magnitude direclion-Select.. v (b) What are the magnitude and direction of the electric and magnetic forces that cach charge exerts on the other on charge q: electric force magnitude direction magnetic force magnitude direction Select. on charge q elctric force magnitucle magnetic force magnitude directionSelect What is the ratlo of the magnitude of the electric force to the magnitude of the magnetic force? (c) If the direction of ' is reversed, so both charges are moving in the same direction, what are the magnitude and direction of the magnetic forces that the two charges exert on each other? on charge q magnetic force magnitude direction elect on charge q': magnetic force magnitude directionExplanation / Answer
Given,
q = 8.25 uC ; q' = 3.25 uC ; d = 0.125 m
v = 4.55 x 10^6 m/s ; v' = 9.4 x 10^6 m/s
a)We know that the magnetic field of the moving charges is given by:
B = (u0/4 pi) q (v x r)/r^2
B = (4 pi x 10^-7) x 8.25 x 10^-6 (4.55 x 10^6 i x -j)/ 4pi x 0.130^2 = -2.4 x 10^-4 T k
B' = (4 pi x 10^-7) x 3.25 x 10^-6 (9.4 x 10^6 -i x j)/ 4pi x 0.125^2 = -1.96 x 10^-4 T k
B(total) = B + B' = (-2.4 - 1.96) x 10^-4 = -4.36 x 10^-4 T k
Hence, B = 4.36 x 10^-4 T (only magnitude)
Direction : into the page along -z
b)Fe = k q1q2/r^2
Fe = 9 x 10^9 x 8.25 x 10^-6 x 3.25 x 10^-6/(2 x 0.125)^2 = 3.86 N
Hence, Feq = 3.86 N (downwards or -y)
Feq' = 3.86 N (upwards or +y)
Fbq = u0 qq' vv'/4 pi r^2
Fbq = 4 pi x 10^-7 x 8.25 x 10^-6 x 3.25 x 10^-6 x 4.55 x 10^6 x 9.4 x 10^6/4 pi x (2 x 0.125)^2 = 1.8 x 10^-3 N
Fbq = 1.83 x 10^-3 N (upwards)
Fbq' = 1.83 x 10^-3 (downwards)
Ratio = Fe/Fb = 3.86/1.83 c 10^-3 = 2.11 x 10^3
c)Magnitude remains same, direction gets reversed.