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 is (with no charge) zero, even if the shell is not spherical, but has any irregular shape ? Explain.

Explanation

(a) Surface charge density on the :
(i) Inner surface of the shell , `sigma_("in") = (-q)/(4 pi r_(1)^(2))`
(ii) Outer surface of the shell , `sigma_("out") = (Q + q)/(4 pir_(2)^(2))`
(b) Electric field at a point `x gt r_(2)` from the centre of the shell will be E = `(1)/(4 pi epsi_(0)) ((q + Q)/(x^(2)))`