If a point charge q is placed at the centre of a cube.
What is the flux linked (a) with the cube? (b) with each face of the cube?

Explanation

(a) According to Gauss's law flux linked with a closed body is `(1//epsilon_(0))` times the charge enclosed and here the closed body cube is enclosing a charge q so, `phi_(T)=1/epsilon_(0)(q)`
(b) Now as cube is a symmetrical body with 6- faces and the point charge is at centre, so electric flux linked with each face will be `phi_(F)=1/6(phi_(T))=q/(6epsilon_(0))`
Note: (i) Here flux linked with cube or one of its faces is independent of the side of cube.
(ii) If charge is not at the centre of cube (but anywhere inside it), total flux will not change, but the flux linked with different faces will be different.