Question

What is the surface charge density on the
(i) inner surface
(ii) outer surface of the shell

Answer 1

Charge $Q$ resides on outer surface of spherical conducting shell. Due to charge $q$ placed at centre, charge induced on inner surface is $–q$ and on outer surface it is $+q$. So, total charge on inner surface $-q$ and on outer surface it is $Q+q$.

Surface charge density on inner surface $=\frac{-q}{4\pi r_1^2}$

Surface charge density on outer surface $=\frac{(Q+q)}{4\pi r_2^2}$