Question

A spherical conducting shell of inner radius $r_{1}$ and outer radius $r_{2}$ has a charge $Q$. A charge $-q$ is placed at the centre of the shell. The surface charge density on the inner and outer surfaces of the shell will be

• A. $\frac{q}{4 \pi r_{2}^{1}}$ and $\frac{Q}{4 \pi r_{2}^{2}}$
• B. $\frac{-q}{4 \pi r_{2}^{1}}$ and $\frac{Q+q}{4 \pi r_{2}^{2}}$
• C. $\frac{q}{4 \pi r_{1}^{2}}$ and $\frac{Q-q}{4 \pi r_{2}^{2}}$
• D. $0$ and $\frac{Q-q}{4 \pi r_{2}^{2}}$

Answer 1

Answer: (C)

$\frac{q}{4 \pi r_{1}^{2}}$ and $\frac{Q-q}{4 \pi r_{2}^{2}}$

Answer 2

Surface charge density
$(\sigma)=\frac{\text{Charge}}{\text { Surface area }}$
$\therefore \sigma_{\text {inner }}=\frac{-q}{4 \pi r_{1}^{2}}$
and $\sigma_{\text {outer }}=\frac{Q-q}{4 \pi r_{2}^{2}}$