Macroscopic electromagnetics

Abstract

In the classical Maxwell–Lorentz theory, matter is regarded as being composed of point charges (e.g., point electrons and point protons and nuclei) that produce microscopic electric and magnetic fields. The microscopic equations of electromagnetics given in Eqs. (2.33)–(2.36) together with the Lorentz force relation given in Eq. (2.21) describe the detailed classical behavior of the charged particles and fields, as presented in Chaps. 2 and 3. The macroscopic equations of electromagnetics, in turn, describe the average behavior of the charged particles and fields. It is then expected that, through a suitable averaging procedure, the macroscopic electromagnetic field equations may be derived from the microscopic equations, a viewpoint that was initially developed by H. A. Lorentz in 1906 and has since been extended by J. H. van Vleck, R. Russakoff, and F. N. H. Robinson.