Question

A solid conducting sphere of radius $a$ has a net positive charge $2Q$. A conducting spherical shell of inner radius $b$ and outer radius $c$ is concentric with the solid sphere as shown in the figure and has a net charge $-Q$. The surface charge density on the inner and outer surfaces of the spherical shell will be

• A. $\frac{-2Q}{4\pi b^2},\frac{Q}{4\pi c^2}$
• B. $\frac{-Q}{4\pi b^2},\frac{-Q}{4\pi c^2}$
• C. $0,\frac{Q}{4\pi c^2}$
• D. $\frac{-2Q}{4\pi b^2},\frac{-Q}{4\pi c^2}$

Answer 1

The correct option is A $\frac{-2Q}{4\pi b^2},\frac{Q}{4\pi c^2}$

After induction the charge distribution at both the surfaces will be as shown in the below figure

As we know that, the surface charge density $\left(\sigma \right)$ is given by
$\sigma =\frac{\text{Charge}}{\text{Surface area}}$
Thus, from the given condition we have
${\sigma }_{outershell}=\frac{Q}{4\pi c^2}$
and, ${\sigma }_{innershell}=\frac{-2Q}{4\pi b^2}$