Foundations of the Classical Maxwell-Lorentz Theory of Electrodynamics

The sources of electromagnetic fields are electric charge, electric current, polarization and magnetization. The relationships among the fields and their sources, all of which represented by functions of space and time, are described by Maxwell’s macroscopic equations. The fields carry energy, whose rate-of-flow at each point in space at any instant of time is given by the Poynting vector. At any location where one or more fields and one or more sources reside simultaneously, there could occur an exchange of energy between the fields and the sources. The time-rates of such exchanges are uniquely specified by the Poynting theorem, which is a direct consequence of Maxwell’s macroscopic equations in conjunction with the definition of the Poynting vector. Electromagnetic fields also carry momentum and angular momentum, whose densities at all points in space-time are simple functions of the local Poynting vector. A generalized version of the Lorentz law of force dictates the time-rate of exchange of momentum between the fields and the sources in regions of space-time where they overlap. There also exists a simple expression for the torque exerted by the fields on the sources, which defines the time-rate of exchange of angular momentum between them. This chapter is devoted to a precise and detailed description of the relations among the fields and their sources, as well as their interactions involving electromagnetic force, torque, energy, momentum, and angular momentum.