Discuss the scattering of a plane wave of electromagnetic radiation by a nonper-meable, dielectric sphere of radius α and dielectric constant єr.
(a) By finding the fields inside the sphere and matching to the incident plus scattered wave outside the sphere, determine without any restriction on ka the multipole coefficients in the scattered wave. Define suitable phase shifts for the problem.
(b) Consider the long-wavelength limit (kα << 1) and determine explicitly the differential and total scattering cross sections. Compare your results with those of Section 10.1.B.
(c) In the limit єr → ∞ compare your results to those for the perfectly conducting sphere.