Question

A charge Q is distribute uniformly on a ring radius r. A sphere of equal radius r is constructed with its center at the periphery of the ring. Find the flux of the electric field through the surface of the sphere.

Answer 1

Here $OB{O}_1$ and $OA{O}_1$ will make two equilateral triangle because the sides are equal length of radius r. Thus $<BOA={60}^o+{60}^o={120}^o$

This is the one-third angle of circular ring (360). So charge enclosed by sphere will be $Q/3$.

By Gauss's law, the flux $\varphi =\frac{Q_{en}}{{ϵ}_0}=\frac{Q}{3{ϵ}_0}$