Question

A concentric spherical cavity is cut out from a solid conducting sphere and a charge $+Q$ is placed at the centre of the cavity. The magnitude of net electric field $E$ and net potential $V$ at point $A$ is

• A. $E=0,V=0$
• B. $E=0,V=\frac{3kQ}{2R}$
• C. $E=\frac{kQ}{R^2},V=\frac{kQ}{2R}$
• D. $E=0,V=\frac{kQ}{2R}$

Answer 1

The correct option is D $E=0,V=\frac{kQ}{2R}$

Based on the concept of Gauss's Law, since the electric field inside a conductor is zero, the charge distribution is as shown in figure.



We know electric field inside a conductor is zero, thus the magnitude of net electric field, $E_A=0$ at point $A$ as it is inside the material of the conducting shell.

Also, net potential, $V_A=V_{s_1}+V_{s_2}+V_Q$
$V_{s_1}\to$ potential due to outer shell
$V_{s_2}\to$ potential due to inner shell
$V_Q\to$ potential due to point charge

$\Rightarrow V_A=\frac{k(-Q)}{3R/2}+\frac{k\left(Q\right)}{2R}+\frac{k\left(Q\right)}{3R/2}$
$\Rightarrow V_A=\frac{kQ}{2R}$