# 2.15  A spherical conducting shell of inner radius r1 and outer radius r2 has a charge Q.(a) A charge q is placed at the centre of the shell. What is the surface charge density on the inner and outer surfaces of the shell?

The charge placed on the centre is q, so -q will be the charge induced in the inner shell and + q will be induced in the outer shell

So,

Charge density on the inner shell

$\sigma_{inner}=\frac{-q}{4\pi r_1^2}$

Charge Density on the outer shell

$\sigma_{outer}=\frac{Q+q}{4\pi r_2^2}$

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