A cubical region of side a has its centre at the origin. It encloses three point charges , `-q` at `(0, -a//4 , 0),+3q at (0,0,0)` and `-q` at `(0,+a//4 ,0)`.
Choose the correct option (s)

(i) The net electric flux crossing the plane `x = +(q)/(2)` is equal to the net electric flux crossing the plane `x = -(a)/(2)`
(ii) The net electric flux crossing the plane `y = +(a)/(2)` is more than the net electric flux crossing the plane `y = -(a)/(2)`
(iii) The net electric flux crossing the entire region is `(q)/(epsilon_(0))`
(iv) The net electric flux crossing the plane `z = +(a)/(2)` is equal to the net electric flux crossing the plane `x = +(a)/(2)`

Options

A. (a) The net electric flux crossing the plane `x=+a//2` is equal to the net electric flux crossing the plane `x=-a//2`
B. (b) The net electric flux crossing the plane `y=+a//2` is more than the net electric flux crossing the plane `y=-a//2`.
C. (c) The net electric flux crossing the entire region is `q/epsilon_0`
D. (d) The net electric flux crossing the plane `z=+a//2` is equal to the net electric flux crossing the plane `x=+a//2`.

Answer

A, C, D

Explanation

The electric flux passing through `x=+a/2`,
`x=-a/2`, `z=+a/2` is same due to symmetry.
The net electric flux through the cubical region is `(-q+3q-q)/(epsilon_0)=1/epsilon_0`.