Question

A point charge $q$ is placed at a distance of $R$ from the centre of a conducting shell of inner radius $2R$ and outer radius $3R$ . The electric potential at the centre of the shell will be

• A. $\frac{1}{4\pi {\epsilon }_0}\left(\frac{\mathrm{q}}{2\mathrm{R}}\right)$
• B. $\frac{1}{4\pi {\epsilon }_0}\left(\frac{4\mathrm{q}}{3\mathrm{R}}\right)$
• C. $\frac{1}{4\pi {\epsilon }_0}\left(\frac{5\mathrm{q}}{6\mathrm{R}}\right)$
• D. $\frac{1}{4\pi {\epsilon }_0}\left(\frac{5\mathrm{q}}{3\mathrm{R}}\right)$

Answer 1

Answer: (C)

The induced charges will be $-q$ and $+q$ as shown in the figure.
The potential at the centre $O$ will be
${\mathrm{V}}_0=\frac{1}{4\pi {\epsilon }_0}\left[\frac{\mathrm{q}}{\mathrm{R}}-\frac{\mathrm{q}}{2\mathrm{R}}+\frac{\mathrm{q}}{3\mathrm{R}}\right]=\frac{1}{4\pi {\epsilon }_0}\left(\frac{5\mathrm{q}}{6\mathrm{R}}\right)$