Introduction

Abstract

In recent times treatments of electromagnetism develop the field equations for material continua from Maxwell’s equations for free-space by defining the macroscopic field variables as statistical averages over the microscopic particle model of the matter. This averaging procedure is not appropriate because in the microscopic particle description only the field equations for free-space are required because the point particles¹ are external to the field. In fact, along these lines Einstein once remarked² that the electron is a foreigner to the field. It is important to recognize that in the microscopic particle description the fields need not be defined in regions occupied by continuous distributions of sources, while in the macroscopic description in material continua the fields must be defined in such regions. In the latter case care must be taken to assure that the defined fields in these regions are consistent with the fundamental laws, i.e., Coulomb’s and Ampere’s, and the rules of mathematics. In the treatments mentioned above such an examination is not ever made and the field equations in material continua are simply averages written. Indeed, although the resulting field equations are perfectly correct for regions containing macroscopic charge and current densities and, in fact, for regions containing macroscopic polarization and magnetization, the reason for their being correct is not established mathematically.