On the Foundational Equations of the Classical Theory of Electrodynamics

Abstract

A close examination of the Maxwell-Lorentz theory of electrodynamics reveals that polarization and magnetization of material media need not be treated as local averages over small volumes - volumes that nevertheless contain a large number of electric and/or magnetic dipoles. Indeed, Maxwell's macroscopic equations are exact and self-consistent mathematical relations between electromagnetic fields and their sources, which consist of free charge, free current, polarization, and magnetization. When necessary, the discrete nature of the constituents of matter and the granularity of material media can be handled with the aid of special functions, such as Dirac's delta-function. The energy of the electromagnetic field and the exchange of this energy with material media are treated with a single postulate that establishes the Poynting vector S = ExH as the rate of flow of electromagnetic energy under all circumstances. Similarly, the linear and angular momentum densities of the fields are simple functions of the Poynting vector that can be unambiguously evaluated at all points in space and time, irrespective of the type of material media, if any, that might reside at various locations. Finally, we examine the Einstein-Laub force- and torque-density equations, and point out the consistency of these equations with the preceding postulates, with the conservation laws, and with the special theory of relativity. The set of postulates thus obtained constitutes a foundation for the classical theory of electrodynamics.

16 pages, 4 figures, 18 equations, 74 references

References in corpus (11)

• Trouble with the Lorentz law of force: Incompatibility with special relativity and momentum conservation
• Resolution of the Abraham-Minkowski Controversy
• Spin and Orbital Angular Momenta of Light Reflected from a Cone
• Spin and Orbital Angular Momenta of Electromagnetic Waves in Free Space
• Whence the Minkowski Momentum?
• Nature of Electric and Magnetic Dipoles Gleaned from the Poynting Theorem and the Lorentz Force Law of Classical Electrodynamics
• Deducing radiation pressure on a submerged mirror from the Doppler shift
• Radiation pressure and the distribution of electromagnetic force in dielectric media
• Energy, Momentum, and Force in Classical Electrodynamics: Application to Negative-index Media
• Solar Sails, Optical Tweezers, and Other Light-Driven Machines
• Generalized Lorentz law and the force of radiation on magnetic dielectrics

Cited by in corpus (9)

• Electromagnetic Angular Momentum
• Electromagnetic Force and Momentum
• Force, Torque, Linear Momentum, and Angular Momentum in Classical Electrodynamics
• Thermodynamics of Radiation Pressure and Photon Momentum
• Electromagnetic force and torque in Lorentz and Einstein-Laub formulations
• The Charge-Magnet Paradoxes of Classical Electrodynamics
• Electric and Magnetic Dipoles in the Lorentz and Einstein-Laub Formulations of Classical Electrodynamics
• On the Electrodynamics of Moving Permanent Dipoles in External Electromagnetic Fields
• Nature of the electromagnetic force between classical magnetic dipoles