Question

A metallic spherical shell has an inner radius $R_1$ and outer radius $R_2$. A charge $Q$ is placed at the centre of the spherical cavity. What will be surface charge density on (i) the inner surface, and (ii) the outer surface?

Answer 1

When a charge $+Q$ is placed at the centre of spherical cavity,
The charge induced on the inner surface $=+Q$
The charge induced on the outer surface $=+Q$
$\therefore$ Surface charge density on the inner surface $=\frac{-Q}{4\pi R_1^2}$
Surface charge density on the outer surface $=\frac{+Q}{4\pi R_2^2}$.