Closed Form Solutions of Maxwell's Equations in the Computer Age

摘要

We will consider four closed form solutions of Maxwell's equations that have been derived or were revisited during the past decade. First we will focus on two problems from electrostatics: the electrostatic image for the dielectric sphere and a generalization of the Thompson and Lampard capacitor. Then we will give two solutions of the full Maxwell equations in 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 rigor in the past we will, in each case, present here a new, shorter and more direct solution.