Question

A charge $Q$ is placed at the centre of an uncharged, hollow metallic sphere of radius $a$. Find the surface charge density on the inner surface and on the outer surface.

• A. $\frac{Q}{4\pi a^2},\frac{-Q}{4\pi a^2}$
• B. $\frac{-Q}{4\pi a^2},\frac{Q}{4\pi a^2}$
• C. $\frac{Q}{4\pi a^2},\frac{Q}{4\pi a^2}$
• D. $\frac{-Q}{4\pi a^2},\frac{-Q}{4\pi a^2}$

Answer 1

The correct option is B $\frac{-Q}{4\pi a^2},\frac{Q}{4\pi a^2}$

Charge at center = $Q$

Due to the charge at center a charge density of $-Q/4\pi a^2$ will be induced on the inner surface such that total charge on the inner surface is $-Q$.

As the shell is neutral, to balance the inner surface charge , a surface charge density of $Q/4\pi a^2$ wll be induced on the outer surface such that total charge on outer surface is $Q$.