# A spherical conducting shell of inner radius $r_{1}$ and outer radius $r_{2}$ has a charge Q.(a) A charge q is placed at the centre of the shell. Find out the surface charge density on the inner and outer surfaces of the shell. (b) Is the electric field inside a cavity (with no charge) zero; independent of the fact whether the shell is spherical or not? Explain.

(a) -q charge will be induced at the inner surface of the shell

Therefore the surface charge density on the inner shell is given as $\sigma _{1}$ :

So, $\sigma _{1} = -\frac{q}{4\pi r{_{1}}^{2}}$

The surface charge density on the outer shell is,

$\sigma _{2} = \frac{Q+q}{4\pi r{_{2}}^{2}}$

(b) Let us consider a Gaussian surface inside the shell, and net flux is zero since $q_{net}=0$ then,

Therefore according to Gauss's law electric field is zero and it is independent of the fact whether the shell is spherical or not.

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