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

(a) Charge placed at the centre is q so induced charge on inner surface of metallic sphere must be equal and opposite so charge -q must appear on inner surface of sphere. Net charge on spherical conductor cannot change: hence charge on outer surface must be `Q+q`.

Surface charge density on inner surface of the spherical shell will be `sigma_(1)= -(q)/(4pi r_(1)^(2))`
Surface charge density on outer surface of the spherical shell will be `sigma_(2)=(Q+q)/(4pi r_(2)^(2))`
(b) Yes, the electric field inside a cavity (with no charge) is zero even if the shell is not spherical, but has any irregular shape because inside the volume of a conductor, the electric field is zero and if we make a cavity inside its volume even then electric field remains zero. This phenomenon is known as electrostatic shielding.