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 c², 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.

PACS: 03.30.+p, 03.50.De, 41.20.−q (all) DOI: 10.3367/UFNe.0179.200909e.0995 URL: https://ufn.ru/en/articles/2009/9/e/ 000274047000005 2-s2.0-76149109096 2009PhyU...52..937M Citation: Makarov V P, Rukhadze A A "Force acting on a substance in an electromagnetic field" Phys. Usp. 52 937–943 (2009) BibTexBibNote ® (generic)BibNote ® (RIS) MedlineRefWorks PT Journal Article TI Force acting on a substance in an electromagnetic field AU Makarov V P FAU Makarov VP AU Rukhadze A A FAU Rukhadze AA DP 10 Sep, 2009 TA Phys. Usp. VI 52 IP 9 PG 937-943 RX 10.3367/UFNe.0179.200909e.0995 URL https://ufn.ru/en/articles/2009/9/e/ SO Phys. Usp. 2009 Sep 10;52(9):937-943 Оригинал: Макаров В П, Рухадзе А А «Сила, действующая на вещество в электромагнитном поле» УФН 179 995–1001 (2009); DOI: 10.3367/UFNr.0179.200909e.0995