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

(N/A) Since the charge in the spherical cavity is $+Q$,the charge induced on the inner surface of the metallic spherical shell will be $-Q$ to ensure the electric field inside the conductor is zero.
Because the shell is metallic and neutral,the total charge on the shell must remain zero. Therefore,a charge of $+Q$ is induced on the outer surface to compensate for the $-Q$ charge on the inner surface.
The surface charge density $\sigma$ is defined as charge per unit area,$\sigma = \frac{q}{A}$.
$(i)$ For the inner surface with radius $R_1$,the surface charge density is $\sigma_1 = \frac{-Q}{4 \pi R_1^2}$.
$(ii)$ For the outer surface with radius $R_2$,the surface charge density is $\sigma_2 = \frac{+Q}{4 \pi R_2^2}$.