Equivalence of total force (and torque) for two formulations of the Lorentz law

TL;DR

This paper demonstrates that two different formulations of the Lorentz law produce identical total force and torque results on objects, whether in free space or immersed in a dielectric medium, confirming their equivalence.

Contribution

It extends the proof of equivalence between two Lorentz force formulations to objects in dielectric media, clarifying their consistent application.

Findings

Total force and torque are identical for both formulations.

Equivalence holds in free space and dielectric media.

The proof is extended to objects immersed in transparent media.

Abstract

Two formulations of the Lorentz law of force in classical electrodynamics yield identical results for the total force (and total torque) of radiation on a solid object. The object may be surrounded by the free space or immersed in a transparent dielectric medium such as a liquid. We discuss the relation between these two formulations and extend the proof of their equivalence to the case of solid objects immersed in a transparent medium.