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  4. 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

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Q. 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

NTA AbhyasNTA Abhyas 2020Electrostatic Potential and Capacitance

Solution:

The induced charges will be $-q$ and $+q$ as shown in the figure.
The potential at the centre $O$ will be
$\mathrm{V}_0=\frac{1}{4 \pi \varepsilon_0}\left[\frac{\mathrm{q}}{\mathrm{R}}-\frac{\mathrm{q}}{2 \mathrm{R}}+\frac{\mathrm{q}}{3 \mathrm{R}}\right]=\frac{1}{4 \pi \varepsilon_0}\left(\frac{5 \mathrm{q}}{6 \mathrm{R}}\right)$
Solution