Electromagnetic force and torque in Lorentz and Einstein-Laub formulations

TL;DR

This paper compares the Lorentz and Einstein-Laub formulations of electromagnetic force and torque, highlighting differences in force distribution predictions without hidden entities, and clarifying their implications in classical electrodynamics.

Contribution

It provides a detailed comparison of the Lorentz and Einstein-Laub formulations, emphasizing their differences in force distribution predictions in media.

Findings

Lorentz law requires hidden energy and momentum in certain cases

Total force and torque are consistent across both formulations

Differences lie in force and torque distributions within materials

Abstract

The Lorentz force law of classical electrodynamics requires the introduction of hidden energy and hidden momentum in situations where an electric field acts on a magnetic material. In contrast, the Einstein-Laub formulation does not invoke hidden entities. The total force and torque exerted by electromagnetic fields on a given object are independent of whether the force and torque densities are evaluated using the law of Lorentz or that of Einstein and Laub. Hidden entities aside, the two formulations differ only in their predicted force and torque distributions throughout material media.