(a) The charge `+Q` resides on the outer surface of the shell. The charge q placed of the center of the shell induces charge `-q` on the inner surface and charge `+q` on the outer surface of the shell. Fig.
Therefore, total charge on inner surface of the shell is `-q` and total charge on the outer surface of the shell is (`Q +q)`.
`:. sigma_(1) = (q)/(4pi r_(1)^(2))`
and `sigma_(2) = (Q +q)/(4pi r_(2)^(2))`
(b) Electric field intensity inside a cavity with no charge is zero, even when the shell has any irregular shape. If we were to take a closed loop, part of which is inside the cavity along a field line, and the rest outside it, then net work done by the field in carrying a test charge over the closed loop will not be zero. This is impossible for an electrostaic field. Hence electric field intensity inside a cavity with no charge is always zero.