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.

 

 

 
 
 
 
 

Answers (1)

(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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