Generalized Lorentz law and the force of radiation on magnetic dielectrics

TL;DR

This paper presents a comprehensive, relativistically consistent framework combining Maxwell's equations with a generalized Lorentz law to accurately describe electromagnetic forces in magnetic dielectric media, emphasizing momentum conservation and force calculations.

Contribution

It introduces a complete set of equations that unify electromagnetic theory with force calculations in magnetic dielectrics, ensuring compatibility with relativity and conservation laws.

Findings

Electromagnetic momentum in media is given by p_EM = E x H / c^2.

The generalized Lorentz law yields force results consistent with electromagnetic momentum transfer.

Proper accounting for dispersion, absorption, and boundary effects is crucial in force calculations.

Abstract

The macroscopic equations of Maxwell combined with a generalized form of the Lorentz law are a complete and consistent set; not only are these five equations fully compatible with the special theory of relativity, they also conform with the conservation laws of energy, momentum, and angular momentum. The linear momentum density associated with the electromagnetic field is p_EM(r,t)=E(r,t)\timesH(r,t)/c^2, whether the field is in vacuum or in a ponderable medium. [Homogeneous, linear, isotropic media are typically specified by their electric and magnetic permeabilities epsilon_0*epsilon(w) and mu_0*mu(w).] The electromagnetic momentum residing in a ponderable medium is often referred to as Abraham momentum. When an electromagnetic wave enters a medium, say, from the free space, it brings in Abraham momentum at a rate determined by the density distribution p_EM(r,t), which spreads within the medium with the light's group velocity. The balance of the incident, reflected, and transmitted (electromagnetic) momenta is subsequently transferred to the medium as mechanical force in accordance with Newton's second law. The mechanical force of the radiation field on the medium may also be calculated by a straightforward application of the generalized form of the Lorentz law. The fact that these two methods of force calculation yield identical results is the basis of our claim that the equations of electrodynamics (Maxwell + Lorentz) comply with the momentum conservation law. When applying the Lorentz law, one must take care to properly account for the effects of material dispersion and absorption, discontinuities at material boundaries, and finite beam dimensions. This paper demonstrates some of the issues involved in such calculations of the electromagnetic force in magnetic dielectric media.