A metallic spherical shell has an inner radius R₁ and outer radius R₂ . A charge Q is placed at the centre of the spherical cavity. What will be surface charge density on the outer surface? 

The given condition is as shown below

Now, surface charge density on the inner surface of spherical shell is
$\mathrm{\sigma }=\frac{\mathrm{q}}{\mathrm{S}}=\frac{-\mathrm{Q}}{4{\mathrm{\pi R}}_1^2}$
An equal and opposite charge would appear on outer surface,
$\therefore$Surface charge density on the outer surface $=\frac{+\mathrm{Q}}{4{\mathrm{\pi R}}_2^2}$