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 shell. What will be the surface charge density on the (i) inner surface, and (ii) outer surface of the shell?

(i) Surface charge density on the inner surface will be

$\therefore \sigma =\frac{-Q}{4\pi (R_{1})^{2}}$ where, $R_{1}$ is the radius of the inner surface.

(ii) Surface charge density on the outer surface will be

$\therefore \sigma =\frac{+Q}{4\pi (R_{2})^{2}}$ where, $R_{2}$ is the radius of the outer surface.

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