A Distributional Investigation of Hertz-Heaviside Field Equations

Abstract

Hertz-Heaviside field equations (HHFEs) that formulate electrodynamics of bodies in arbitrary motion are studied in the sense of Schwartz-Sobolev distributions. HHFE can be interpreted as a generalization of Maxwell's equations (ME) of stationary media by introducing convective electric/magnetic conduction and displacement current sources. The investigation starts with a short review of the required distributional tools for volumetric and nonvolumetric (surface, space curve, and point type) singularities in arbitrary motion. The boundary relations on the enclosure of a volumetric body with arbitrary constitutive parameters and velocity field are obtained as observed in the stationary reference frame. Degenerate HHFEs (DHHFE) that appear in the presence of nonvolumetric moving media are introduced. This is followed by systematic distributional investigations of DHHFE, which reveals boundary, edge, and tip conditions on point, surface, and space curve type sources in arbitrary motion as observed in the stationary reference frame.