Question

A charge $Q$ is placed at the centre of an uncharged, hollow metallic sphere of radius $a$. If a charge $q$ is put on the sphere, what would be the surface charge densities on the inner and the outer surfaces respectively?

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

Answer 1

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

As charge $Q$ is placed at center, a surface charge on the inner surface will be induced such that total charge on inner surface is $-Q$ . Therefore , charge density on inner surface is $\frac{-Q}{4\pi a^2}$.

As total charge on outer shell is $q$, The charge density on the outer surface will be such that total charge on outer surface is $q+Q$. Therefore, charge density on outer surface is $\frac{Q+q}{4\pi a^2}$