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. $\frac{q}{\varepsilon_{0}}$
• B. $\frac{q}{2\varepsilon_{0}}$
• C. $\frac{q}{3\varepsilon_{0}}$
• D. $\frac{q}{4\varepsilon_{0}}$

Answer 1

Answer: (C)

$\frac{q}{3\varepsilon_{0}}$

Answer 2

Charge on ring $q$, centre of ring $=O$ Centre of sphere $=O'$ Linear charge density of ring, $\lambda=\frac{q}{2 \pi a}$ Charge on arc $A B$ of ring, $q_{A B}=\lambda(\operatorname{arc} A B)=\frac{1}{2 \pi a} \cdot a \cdot \frac{2 \pi}{3}$ $q_{A B}=q / 3$ i.e.., charged enclosed by sphere $=q / 3$ $\therefore$ Flux coming out of sphere $=q / 3 \varepsilon_{0}$