Force acting on a substance in an electromagnetic field

Abstract

This article, in essence, is a continuation of the work by V L Ginzburg and V A Ugarov (Usp. Fiz. Nauk 118 175 (1976) [Sov. Phys. Usp. 19 94 (1976)]). It is shown that the results given in 75 of the book Electrodynamics of Continuous Media by L D Landau and E M Lifshitz (Moscow: Nauka, 1982, in Russian) and in 105 of the book Fundamentals of the Theory of Electricity by I E Tamm (Moscow: Nauka, 1989, in Russian) unambiguously follow only from the Maxwell equations of macroscopic electrodynamics, the corresponding constitutive equations, and the equations of motion of a substance (the hydrodynamic equations). These results are as follows: (1) the force acting on a unit volume of a motionless substance is given by the sum of the Helmholtz force and the Abraham force; (2) the momentum density of an electromagnetic field is the Umov-Poynting vector divided by c(2), and (3) the stress tensor related to the field coincides in its form with the sum of the stress tensor of the electrostatic field and the stress tensor of the magnetostatic field. Thus, it is proved that the symmetric form of the Abraham tensor stands for the energy-momentum tensor of an electromagnetic field in a motionless medium.