question

a spherical conducting shell of inner radius  and outer radius  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 :

so, 

the surface charge density on the outer shell is,

(b) let us consider a gaussian surface inside the shell, and net flux is zero since 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.