Question

A spherical shell with an inner radius 'a' and an outer radius 'b' is made of conducting material. A point charge +Q is placed at the center of the spherical shell and a total charge -q is placed on the shell.
(a) Charge $-q$ is distributed on the surfaces as
(A) $-Q$ on the inner surface, $-Q$ on outer surface
(B) $-Q$ on the inner surface, $-q+Q$ on outer surface
(C) $+Q$ on the inner surface, $-q-Q$ on outer surface
(D) The charge $-q$ is spread uniformly between the inner and outer surface.
(b) Assume that the electrostatic potential is zero at an infinite distance from the spherical shell. The electrostatic potential at a distance $R(a<R<b)$ from the centre of the shell is $[whereK=\frac{1}{4\pi {\epsilon }_0}]$

• A. $0$
• B. $\frac{KQ}{a}$
• C. $K\frac{Q-q}{R}$
• D. $K\frac{Q-q}{b}$

Answer 1

The correct option is D $K\frac{Q-q}{b}$

The presence of charge $Q$ at the center of the spherical shell induces a equal and opposite charge on the inner surface of the shell, i.e., $-Q$ at the inner surface.
This $-Q$ charge will induce a equal and opposite charge on the outer surface of the shell, i.e., $Q$. Also charge $-q$ is placed on the shell.
Therefore total charge on the outer surface is $-q+Q$ electrostatic potential at a distance R(a from the center of the shell.
$Electricpotential=\frac{K\times (Q-q)}{b}$