Question

A hollow 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 sphere. The surface charge densities on the inner and outer surfaces of the sphere will be respectively :-

• A. $\frac{q}{4 \pi r_{1}^{2}}$ and $\frac{q}{4 \pi r_{2}^{2}}$
• B. $\frac{- q }{4 \pi r_{1}^{2}}$ 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: (B)

$\sigma_{\text {in }}=\frac{-q}{4 \pi r_{1}^{2}}$
$\sigma_{\text {out }}=\frac{Q+q}{4 \pi r_{2}^{2}}
$