Classical Electrodynamics · Problem 10.2

Radiating Systems, Multipole Fields and Radiation — John David Jackson

Physics — E&M · scattering-conducting-sphere-elliptic-polarization

Problem

Electromagnetic radiation with elliptic polarization, described (in the notation of Section 7.2) by the polarization vector,

\boldsymbol{\epsilon} = \frac{1}{\sqrt{1+r^2}}(\boldsymbol{\epsilon}_+ + r e^{i\alpha} \boldsymbol{\epsilon}_-)

is scattered by a perfectly conducting sphere of radius

a

. Generalize the amplitude in the scattering cross section (10.71), which applies for

r = 0

r = \infty

, and calculate the cross section for scattering in the long-wavelength limit. Show that

\frac{d\sigma}{d\Omega} = k^4 a^6 \left[\frac{5}{8}(1+\cos^2\theta) - \cos\theta - \frac{3}{4}\left(\frac{r}{1+r^2}\right)\sin^2\theta\cos(2\phi - \alpha)\right]

Compare with Problem 10.1.