Comment on "Trouble with the Lorentz Law of Force: Incompatibility with Special Relativity and Momentum Conservation"

Abstract

In a recent Letter [arXiv:1205.0096], Mansuripur considers a magnetic dipole positioned at a fixed location from a point charge. Performing a Lorentz transformation to a laboratory frame where the charge distribution moves he finds that `a net torque acts on the dipole pair'. He then argues that `this torque in the (lab) frame in the absence of a corresponding torque in the (rest) frame is sufficient proof of the inadequacy of the Lorentz (force) law'. In this comment we demonstrate that the presence of a torque is not incompatible with special relativity: it is required by the conservation laws that apply to the total momentum of the system (including the particles). We furthermore stress that classical electrodynamics needs a consistent dynamical description of the particles that involves coupled equations for the electromagnetic fields and the trajectories [M. Brachet and E. Tirapegui, Nuovo Cimento Soc. Ital. Fis. A 47, 210 (1978)] and any conserved quantity will then contain contributions from both the field and the particles.