Microscopic Electromagnetic Theory
In addition to the usual notion of material continuum and the kinematical variables (see Chapter 1), the electrodynamics of continua requires the introduction of new fields. These are the classical electromagnetic fields which exist independently of the fact that space is occupied by a vacuum or is filled by matter. Fields, such as electric charge density, electric polarization, and magnetization reflect the presence of matter. In classical physics, as developed in the nineteenth century, these fields must satisfy a set of partial differential equations known as Maxwell’s equations. Continuum physics is concerned with the gross, macroscopic behavior of bodies. However, the drastic development of physics during the last eighty years has shown that it is logical to start with the existence of particles at the microscopic level, and to show that Maxwell’s equations and electromagnetic theory are but the macroscopic results of the statistical laws that govern them on a finer scale. This line of thought was initiated by H.A. Lorentz in his celebrated theory of electrons. Therefore, in the same way that continuum mechanics is built progressively on the successive notions of mass density, momentum, moment of momentum, and energy, it seems appropriate to introduce those notions (which describe electromagnetic fields in matter) by starting with the initially simple notion of electric point charge (Section 2.2), and then introducing a more realistic but complex picture of assemblies of electric charges and their moments.
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