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 center of the shell. What is the surface charge density on the inner and outer surfaces of the shell ?
(b) Is the electric field intensity inside a cavity (with no charge) zero, even if the shell is not spherical, but has any irregular shape ? Explain.

Explanation

(a) Surface charge density on the inner surface of shell is
`sigma_("in") = (-q)/(4pi r_(1)^(2))`
and on the outer surface of shell is
`sigma_("out") = (Q+q)/(4pi r_(2)^(2))`
(b) The electric flux linked with any closed surface S inside the conductor is zero as electric field inside conductor is zero.
So, by Gauss.s theorem net charge enclosed by closed surface S is also zero i.e.,
`q_("net") = 0`

So, if there is no charge inside the caicity, then there cannot be any charge on the inner surface of the shell and hence electric field inside the cavity will be zero, even though the shell may not be spherical.