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. Charge is distributed on the surface as :

• A. $-Q$ on the inner surface, $-q$ on outer surface
• B. $-Q$ on the inner surface, $-q+Q$ on the outer surface
• C. $+Q$ o the inner surface, $-q-Q$ on the outer surface
• D. The charge $-q$ is spread uniformly between the inner and outer surface.

Answer 1

Answer: (B)

$-Q$ on the inner surface, $-q+Q$ on the outer surface

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 $-q+Q$