Question

If a charge q is located at the corner of a cube what is the flux through it ?

Answer 1

Imagine there were 8 cubes and the charge was placed at the common corner.

By Gauss’ law flux would be

q/ϵ_0 .

Since all 8 cubes are identical flux through each cube is

1/8 q/ϵ_0 .

Now in the cube the 3 faces which share the corner at which cube is kept would have no flux through it. In the remaining 3 faces, the flux is distributed evenly hence total flux is

1/3 1/8 q/ϵ_0 =1/24 q/ϵ_0 .