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

Options

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. The net electric flux crossing the plane `y = +a//2` is more than the net electric flux crossing the plane ` y = -a//2`.
C. The net electric flux crossing the entire origin is `q//epsilon_0`.
D. The net electric flux crossing the plane `z = +a//2` is equal to the net electric flux crossing the plane `x = +a//2` .

Explanation

Position of all the charges are symmetric about the planes `x = + a//2` and `x = - a//2`. So net electric flux then will be same. Similarly, flux through `y = + a//2`is equal to flux through `y = - a//2`/
`phi = (q_("in))/(epsilon_(0)) = (3q - q - q)/(epsilon_(0)) = (q)/(espilon_(0))`
By symmetry flux through `z = + q//2` is equal to flux through `x = + q//2`