Four closed surfaces and corresponding charge distributions are shown below.

Let the respective electric fluxes through the surface be `phi_1,phi_2,phi_3` and `phi_4`.Then:

Options

A. `phi_1 lt phi_2 = phi_3 gt phi_4`
B. `phi_1 gt phi_2 gt phi_3 gt phi_4`
C. `phi_1 = phi_2 =phi_3 =phi_4`
D. `phi_1 gt phi_3 , phi_2 lt phi_4`

Answer

C

Explanation

Flux through surface `S_1` in `phi_1` and similar
`phi_1=q_"in"/epsilon_0 =(2q)/epsilon_0`
`phi_2=q_"in"/epsilon_0 =(q+q+q-q)/epsilon_0 =(2q)/epsilon_0`
`phi_3=q_"in"/epsilon_0 =(q+q)/epsilon_0 =(2q)/epsilon_0`
`phi_4=q_"in"/epsilon_0 =(8q-2q-4q)/epsilon_0 =(2q)/epsilon_0`
So, `phi_1=phi_2=phi_3=phi_4`