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 outer surface of the shell is:

$\frac{Q+q}{4πr_2^2}$

The correct answer is Option (1) → $\frac{Q+q}{4πr_2^2}$

Given,

The spherical shell has an inner radius $r_1$ and $r_2$

→ Charge Q placed on the shell

→ Charge q placed on the centre

$∴Q_{outer}=Q+q$

Surface charge density, $σ=\frac{Q_{outer}}{Area\,of\,outer\,surface}$

$=\frac{Q+q}{4πr_2^2}$