A spherical shell of radius `R = 1.5 cm` has a charge `q = 20muC` uniformly distributed over it. The force exerted by one half over the other half is

Options

A. zero
B. `10^(-2)N`
C. 500 N
D. 2000 N

Answer

D

Explanation

d. `E = sigma/(2epsilon_0)`
`F = E dr = (sigma d A sigma)/(2epsilon_0)`
`P = F/(dA) = sigma^2/(2epsilon_0)`
`Force = PpiR^2 = sigma^2/(2epsilon_0)piR^2`
`=Q^2/(16pi^2R^4) (piR^2)/(2epsilon_0) = Q^2/(32piepsilon_0R^2)`
`= ((20 xx 10^(-6)) xx 9 xx 10^(9))/(8(1.5 xx 10^(-2))^2) = 2000N`.