A monochromatic plane wave scatters from a perfectly conducting wire where a h. Assume that both the

Question:

A monochromatic plane wave scatters from a perfectly conducting wire where a h. Assume that both the propagation vector and the electric field of the incident wave lie in the y-z plane as shown below.

(a) In the Rayleigh limit when k₀h 0α(ẑ · E₀)ẑ. Assume an induced surface current density,

and determine the parameter I0 by imposing the perfect-conductor condition, [E_scatt+ E₀] · ẑ = 0, at a single point: the origin of coordinates at the center of the wire. Specifically, calculate Escatt from a near-zone expansion of the retarded potentials and show that

(b) Drop the terms of order (k₀h)²and (k₀h)³from the expression for I_0, compute the induced electric dipole moment, and use this to find the total scattering cross section.
(c) Show that the terms dropped in part (b) must be retained in the radiation zone forward scattering amplitude to satisfy the optical theorem with the cross section computed in part (b).