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 region is `(q)/(in_(0))`
D. The net electric flux crossing the plane `z = + a//2` is equal to the net electric flux crossing the plane `z = -a//2`

Answer

B

Explanation

In the fig
We have shown a cubical region of side `a`.
It encloses three fixed point charges :
`q` at `A (0, -a//4), +3 q` at `O (0,0,0)` and `-q` at `B(0, a//4,0)`
As `+3q` is the origin `O`, and charges `-q, -q` are placed summetrically about planes `x = +a//2` and ` x = -a//2` and `x = -a//2`, therefore, electric flux through them is same. Choice (a) is correct.
The net electric flux crossing tht given region, accroding to Gauss's theroem is
`phi = (Sigma q)/(in_(0)) = (-q +3q -q)/(in_(0))`
Choice (c ) is correct.
Again as `+3q` is the orgin `O`, and charges `-q, -q` are placed symmetrically about the planes `z = +a//2` and `x = a//2` so net electric flux crossing these planes is equal . Choice (d) is correct.
The only wrong option is (b).