Consider the scattering of a plane wave by a nonpermeable sphere of radius a and very good, but not perfect, conductivity following the spherical multipole field approach of Section 10.4. Assume that ka < 1=”” and=”” that=”” the=”” skin=”” depth=”” ?=””>< .?=””>
(a) Show from the analysis of Section 8.1 that
Zs/Z0 = kd/2 (1 – i)
(b) In the long-wavelength limit, show that for l = 1 the coefficients a±(l) and ?2±(l) in (10.65) are
(a) Show from the analysis of Section 8.1 that
Zs/Z0 = kd/2 (1 – i)
(b) In the long-wavelength limit, show that for l = 1 the coefficients a±(l) and ?2±(l) in (10.65) are
?2±(1) ?^ 4i/3 (ka)3
(c) Write out explicitly the differential scattering cross section, correct to first order in 81a and lowest order in ka.
(d) Using (10.61), evaluate the absorption cross section. Show that to first order in d it is aabs ?^ 3I?(kd)a2. How different is the value if d =a?
