Eight point charges (can be assumed as small spheres uniformly charged and their centres at the corner of the cube) having values q each are fixed at vertices of a cube. The electric flux through square surface ABCD of the cube is

Options

A. `q/(24 in_(0))`
B. `q/(12 in_(0))`
C. `q/(6 in_(0))`
D. `q/(8 in_(0))`

Answer

C

Explanation

The electric flux through ABCD due to charges at A,B,C,D is zero

The flux through ABCD due to any of the charges at E,F,G nad H are `q/(24 in_(0))` each.
Hence the net electric flux through ABCD is `phi=4xx0+4xxq/(24in_(0))=q/(6 in_(0))`
Alternate solution.
Net charge enclosed inside the cube `=8(q/8) =q`
net electric flux through cube `q/(in_(0))`
`:'` charges are symmetrically placed so the flux through each face =`q/(6in_(0))`