Question

Find out the outward flux to a point charge +q placed at the centre of a cube of side ‘a’. Why is it found to be independent of the size and shape of the surface enclosing it? Explain.

Answer 1

Let a cube of side a enclose charge +q at its centre.

Because the electric flux through the square surface is `phi=q/(6in_0)`the square surfaces of cube are six. Hence, according to Gauss’s theorem in electrostatics, the total outward flux due to a charge +q of a cube is

`phi=6xx(q/(6in_0))=q/in_0`

The result shows that the electric flux passing through a closed surface is proportional to the charge enclosed. In addition, the result reinforces that the flux is independent of the shape and size of the closed surface.