Maxwell's derivation of the Lorentz force from Faraday's law

TL;DR

This paper revisits Maxwell's original derivation of the Lorentz force from Faraday's law, providing a detailed and modernized presentation of his classical approach.

Contribution

It offers a detailed re-derivation of the Lorentz force from Maxwell's original work using contemporary notation, clarifying historical and theoretical perspectives.

Findings

Maxwell's derivation aligns with modern formulations of electromagnetic force.

Historical analysis clarifies the development of electromagnetic theory.

The paper enhances understanding of Maxwell's original methods.

Abstract

In a brief but brilliant derivation that can be found in Maxwell's Treatise and traced back to his 1861 and 1865 papers, he derives the force on a moving electric charge subject to electromagnetic fields from his mathematical expression of Faraday's law for a moving circuit. Maxwell's derivation in his Treatise of this force, which is usually referred to today as the Lorentz force, is given in detail in the present paper using Maxwell's same procedure but with more modern notation.