# UCL Discovery

## Classical Electrodynamics: A Tutorial on its Foundations

Hehl, FW; Obukhov, YN; Rubilar, GF; (1999) Classical Electrodynamics: A Tutorial on its Foundations.

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## 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 $(\rho,j)$. 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}

Type: Article Classical Electrodynamics: A Tutorial on its Foundations 21 pages Latex-script, 6 figures, Festschrift for Grafarend UCL > School of BEAMS > Faculty of Maths and Physical Sciences > Mathematics

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