Question

A metal sphere of radius $R$ carrying charge $q$ is surrounded by a thick concentric metal shell of inner and outer radii $a$ and $b$ respectively. The net charge on the shell is zero. The potential at the centre of the sphere, when the outer surface of the shell is grounded will be

• A. $\frac{q}{4\pi {ϵ}_0}\left(\frac{1}{a}-\frac{1}{b}\right)$
• B. $\frac{q}{4\pi {ϵ}_0}\frac{1}{a}$
• C. $\frac{q}{4\pi {\in }_0}\left(\frac{1}{R}-\frac{1}{a}\right)$
• D. $\frac{q}{4\pi {ϵ}_0}\frac{1}{R}$

Answer 1

Answer: (C)

$V_{\text{centre }}=\frac{Kq}{R}-\frac{Kq}{a}$
$=\frac{q}{4\pi {\in }_0}\left(\frac{1}{R}-\frac{1}{a}\right)$