Maxwell’s equations in material media, momentum balance equations and force densities associated with them

Abstract

It is common to take the Lorentz force density as a postulate independent of Maxwell’s equations. Mansuripur (Phys. Rev. Lett. 108, 193901 (2012)) does so, and applies it using the polarization charge and magnetization current. When he calculates forces and torques arising from a point charge and a magnetic dipole, in relative inertial motion, he arrives at the conclusion that the Lorentz force density is inconsistent with the principle of relativity. Following a line of research already developed (Eur. Phys. J. Plus 126, 50 (2011)) we show that the macroscopic Maxwell equations imply several energy and momentum stress balance equations, which, for point charges in empty space, reduce to the usual Lorentz force density. We show in this work that a force density appearing in one of these balance equations is that proposed by Einstein-Laub, which, according to Mansuripur, does not lead to an inconsistency with the theory of relativity. Thus we prove that there is no inconsistency with the relativity theory. These balance equations are as relativistic as Maxwell’s equations.