(a) Charge at the outer surface of the spherical shell is Q
Since, charge q is placed at center, thus the charge induced at the inner surface is -q and outer surface is +q.
Therefore, total charge on inner surface will be -q and on outer surface will be Q+q.
Surface charge density on inner surface = Total charge/Inner surface area = -q/4πr12
Surface charge density on the outer surface = Total charge/Outer surface area = Q+q/4πr22
(b) The electric field at a distance x from the center, using Gauss law is:
E(x) = 1/4πε0(Q+q/x2)