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. What is 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, even if the shell is not spherical, but has any irregular shape? Explain.

Explanation

(i) Surface charge density om inner surface `sigma=(-q)/(4pir_(1)^(2))`
(ii) Surface charge density on outer surface
`sigma=(Q+q)/(4pir_(2)^(2))`
(b) Electric field at (an outside) point distant x from centre of the shell
`E=(Q+q)/(4piepsilon_(0)x^(2))`