On Magnetic Forces and Work

TL;DR

This paper demonstrates that classical magnetic forces can do work by analyzing a particle with spin and dipole moments, deriving a generalized force law, and confirming energy-momentum conservation.

Contribution

It provides a detailed derivation showing magnetic fields can perform work on particles with intrinsic dipole moments, resolving a longstanding debate.

Findings

Magnetic forces can do work on particles with dipole moments.

The generalized Lorentz force law accounts for magnetic work.

Energy-momentum conservation confirms the validity of the force law.

Abstract

We address a long-standing debate over whether classical magnetic forces can do work, ultimately answering the question in the affirmative. In detail, we couple a classical particle with intrinsic spin and elementary dipole moments to the electromagnetic field, derive the appropriate generalization of the Lorentz force law, show that the particle's dipole moments must be collinear with its spin axis, and argue that the magnetic field does mechanical work on the particle's elementary magnetic dipole moment. As consistency checks, we calculate the overall system's energy-momentum and angular momentum, and show that their local conservation equations lead to the same force law and therefore the same conclusions about magnetic forces and work. We also compute the system's Belinfante-Rosenfeld energy-momentum tensor.