Field, Force, Energy and Momentum in Classical Electrodynamics

The classical theory of electrodynamics is based on Maxwell's equations and the Lorentz law of force. This book begins with a detailed analysis of these equations, and proceeds to examine their far-reaching consequences. The traditional approach to electrodynamics treats the "microscopic" equations of Maxwell as fundamental, with electric charge and electric current as the sole sources of the electric and magnetic fields. Subsequently, polarization and magnetization are introduced into Maxwell's equations to account for the observed behavior of material media. The augmented equations, known as Maxwell's "macroscopic" equations, are considered useful for practical applications, but ultimately reducible to the more fundamental "microscopic" equations. In contrast, the present book takes Maxwell's "macroscopic" equations as the foundation of classical electrodynamics, and treats electrical charge, electrical current, polarization, and magnetization as the basic constituents of material media. These constituents not only produce the electromagnetic fields, but also interact with these fields and exchange energy and momentum with them. The laws that govern the distribution of energy and momentum in space-time are introduced and discussed in great detail. Interactions of electromagnetic fields with matter involve exchanges of energy with electrical currents, with polarization, and with magnetization, and also exchanges of linear and angular momenta via electromagnetic force and torque exerted on the aforementioned constituents of matter. Throughout the book, a large number of examples demonstrate the solution of Maxwell's equations in diverse situations, and examine the flow of energy and momentum as well as the distribution of force and torque throughout the matter-field systems under consideration.