Question

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

• A. $\frac{q}{4\pi {ϵ}_0}[\frac{1}{r}-\frac{1}{2R}]$
• B. $\frac{q}{4\pi {ϵ}_{0}r}$
• C. $\frac{q}{4\pi {ϵ}_0}[\frac{1}{r}+\frac{1}{2R}]$
• D. $\frac{q}{8\pi {ϵ}_{0}R}$

Answer 1

The correct option is A $\frac{q}{4\pi {ϵ}_0}[\frac{1}{r}-\frac{1}{2R}]$

A $-q$ charge will be induced on the inner surface of the shell, and a $+q$ charge will be induced on the outer surface.

Potential at centre is $V=\frac{1}{4\pi {ϵ}_0}\left(\frac{q}{r}\right)-\frac{1}{4\pi {ϵ}_o}\frac{q}{R}+\frac{1}{4\pi {ϵ}_o}\frac{q}{2R}$

$V=\frac{1}{4\pi {ϵ}_0}\left(\frac{q}{r}\right)-\frac{1}{4\pi {ϵ}_o}\frac{q}{2R}$