A low-frequency, plane electromagnetic wave Rayleigh scatters from a sphere with radius a and conductivity . Assume

A low-frequency, plane electromagnetic wave Rayleigh scatters from a sphere with radius a and conductivity σ. Assume that the skin depth δ >> a.
(a) Find the electric dipole moment induced in the sphere by the incident wave.
(b) Calculate the absorption cross section of the sphere.
(c) Show that the optical theorem is satisfied by the absorption cross section (alone) and the electric dipole scattering amplitude.
(d) Rationalize the result of part (c) with the fact that the scattering cross section is not zero.