Introduction

Abstract

Consider Maxwell’s equations for a medium at rest with scalar constants for the permeability µ permittivity ϵ and conductivity σ. Furthermore, we have the electric and magnetic field strengths E and H, electric charge and current density ρ_e and g_e as well as electric and magnetic flux densities D and B. Using the International System of units we get:

$$curlH = \in \frac{{\partial E}}{{\partial t}} + {{g}_{e}}$$

((1))

$$- curlE = \mu \frac{{\partial E}}{{\partial t}}$$

((2))

$$\epsilon divE = {{\rho }_{e}}$$

((3))

$$\mu divH = 0$$

((4))

$$\epsilon E = D$$

((5))

$$\mu E = B$$

((6))

$${{g}_{e}} = \sigma E$$

((7))

Maxwell’s equations have made an enormous contribution both to the understanding and the practical use of electromagnetic phenomena. The number of published solutions is not enumerable. But the careful reader soon recognizes that almost all these solutions are steady state solutions that have a periodic sinusoidal time variation in the whole interval −∞ < t < +∞. An infinitely extended sinusoidal wave has necessarily infinite energy and is thus outside the conservation law of energy. Furthermore, a claim that a wave that started an infinite time ago was due to a cause that occured a finite time earlier is meaningless, which puts such waves outside the causality law¹. It is usual to write Maxwell’s equations in more compact and elegant forms than used here.