Question

A metallic spherical shell has an inner radius $R_1$ and outer radius $R_2$. A charge is placed at the centre of the spherical cavity. The surface charge density on the inner surface is

• A. $\frac{q}{4\pi R_1^2}$
• B. $\frac{-q}{4\pi R_1^2}$
• C. $\frac{q^2}{4\pi R_2^2}$
• D. $\frac{q}{4\pi R_2^2}$

Answer 1

Answer: (B)

When a charge $+q$ is placed at the centre of spherical cavity as shown in figure.

Charge induced on the inner surface of shell
$=-q.....(i)$
Charge induced on the outer surface of shell
$=+q......(ii)$
$\therefore$ Surface charge density on the inner surface $=\frac{-q}{4\pi R_1^2}$