Ponderomotive forces in electrodynamics of moving media: The Minkowski and Abraham approaches

TL;DR

This paper derives explicit formulas for ponderomotive forces in moving media using Minkowski and Abraham approaches, highlighting differences and providing a covariant framework for electromagnetic forces in media.

Contribution

It presents compact, explicit formulas for ponderomotive forces in moving media within both Minkowski and Abraham frameworks, including the Abraham force and a covariant formulation.

Findings

Derived compact formulas for ponderomotive forces in moving media.

Identified the difference between Minkowski and Abraham forces as the Abraham force.

Established a covariant approach to electromagnetic forces in media.

Abstract

In the general setting of the problem, the explicit compact formulae are derived for the ponderomotive forces in the macroscopic electrodynamics of moving media in the Minkowski and Abraham approaches. Taking account of the Minkowski constitutive equations and making use of a special representation for the Abraham energy-momentum tensor enable one to obtain a compact expression for the Abraham force in the case of arbitrary dependence of the medium velocity on spatial coordinates and the time and for nonstationary external electromagnetic field. We term the difference between the ponderomotive forces in the Abraham and Minkowski approaches as the Abraham force not only under consideration of media at rest but also in the case of moving media. The Lorentz force is found which is exerted by external electromagnetic field on the conduction current in a medium, the covariant Ohm law and the constitutive Minkowski relations being taken into account. The physical argumentation is traced for definition of the 4-vector of the ponderomotive force as the 4-divergence of the energy-momentum tensor of electromagnetic field in a medium.