  Exactly soluble models in the theory of electromagnetic propagation and
scattering are essentially restricted to horizontally stratified or spherically
symmetric geometries, with results also available for certain waveguide
geometries. However, there are a number of new problems in remote sensing and
classification of buried compact metallic targets that require a wider class of
solutions that, if not exact, at least support rapid numerical evaluation.
Here, the exact Chandrasekhar theory of the electrostatics of heterogeneously
charged \emph{ellipsoids} is used to develop a "mean field" perturbation theory
of low frequency electrodynamics of highly conducting ellipsoidal targets, in
insulating or weakly conducting backgrounds. The theory is based formally on an
expansion in the parameter $\eta_s = L_s/\delta_s(\omega)$, where $L_s$ is the
characteristic linear size of the scatterer and $\delta_s(\omega)$ is the
electromagnetic skin depth. The theory is then extended to a numerically
efficient description of the intermediate-to-late-time dynamics following an
excitation pulse. As verified via comparisons with experimental data taken
using artificial spheroidal targets, when combined with a previously developed
theory of the high frequency, early-time regime, these results serve to cover
the entire dynamic range encountered in typical measurements.
