A solid uniform sphere of radius R and conductivity σ acts as a scatterer of a plane-wave beam of unpolarized radiation of frequency ω, with ωR/c≪1. The conductivity is large enough that the skin depth δ is small compared to R.
(a) Justify and use a magnetostatic scalar potential to determine the magnetic field around the sphere, assuming the conductivity is infinite. (Remember that ω=0.)
(b) Use the technique of Section 8.1 to determine the absorption cross section of the sphere. Show that it varies as (ω)1/2 provided σ is independent of frequency.