Closed form solutions of Maxwell's equations in the computer age

摘要

We consider four closed form solutions of Maxwell's equations that have been derived or were revisited during the past decade. First we focus on two problems from electrostatics: the electrostatic image for the dielectric sphere and a generalisation of the Thompson and Lampard capacitor. Then we give two solutions of the full Maxwell equations in the time-harmonic regime: the Green dyadics for a homogeneous bianisotropic medium with similar medium dyadics and the scattering of a plane wave at a diaphanous wedge. Although we have studied these problems with some rigour in the past we present, in each case, a new, shorter and more direct solution.