Classical Electrodynamics: A Tutorial on its Foundations

Abstract

We will display the fundamental structure of classical electrodynamics. Starting from the axioms of (1) electric charge conservation, (2) the existence of a Lorentz force density, and (3) magnetic flux conservation, we will derive Maxwell's equations. They are expressed in terms of the field strengths $(E,{\cal B})$, the excitations $({\cal D},H)$, and the sources $(ρ,j)$. This fundamental set of four microphysical equations has to be supplemented by somewhat less general constitutive assumptions in order to make it a fully determined system with a well-posed initial value problem. It is only at this stage that a distance concept (metric) is required for space-time. We will discuss one set of possible constitutive assumptions, namely ${\cal D}\sim E$ and $H\sim {\cal B}$. {\em file erik8a.tex, 1999-07-27}