Question

A charge $q$ is uniformly distributed on a ring of radius $r$. A sphere of an equal radius is constructed with its centre lying on the periphery of the ring. The flux of electric field through the surface of the sphere will be

• A. $\frac{q}{{\epsilon }_0}$
• B. $\frac{q}{2{\epsilon }_0}$
• C. $\frac{q}{3{\epsilon }_0}$
• D. $\frac{q}{4{\epsilon }_0}$

Answer 1

Answer: (C)

Charge on ring $q$, centre of ring $=O$
Centre of sphere $=O^{\prime }$
Linear charge density of ring, $\lambda =\frac{q}{2\pi a}$ Charge on arc $AB$ of ring,
$q_{AB}=\lambda (\mathrm{arc}AB)=\frac{1}{2\pi a}\cdot a\cdot \frac{2\pi }{3}$
$q_{AB}=q/3$
i.e.., charged enclosed by sphere $=q/3$
$\therefore$ Flux coming out of sphere $=q/3{\epsilon }_0$