On the Laws of Electromagnetic Induction

TL;DR

This paper reformulates electromagnetic induction laws using differential forms and Lie derivatives, demonstrating Galilei invariance and clarifying the role of the Lorentz force as part of the electric field rather than a separate law.

Contribution

It introduces a covariant formulation of Faraday-Ampere laws with differential forms, emphasizing Galilei invariance and reinterpreting the Lorentz force within classical electromagnetism.

Findings

Galilei invariance of induction laws established

Lorentz force is a correction to electric field, not a separate law

Electromagnetic fields are observer-dependent in four-dimensional space-time

Abstract

The Faraday-Ampere laws of electro-magnetic induction are formulated in terms of plain and twisted differential forms, taking in due account the body motion in terms of Lie time-derivatives. Covariance of Lie derivatives with respect to arbitrary relative motions, and Galilei invariance of the electro-magnetic fields, imply Galilei invariance of the induction laws, contrary to most claims in literature. A noteworthy outcome of the theory is the conclusion that the so called Lorentz force on a charged particle is not an additional law of electromagnetism, but rather, when corrected by a factor one-half, a contribution to the electric field evaluated, according to Faraday law, by an observer testing a translating charged body crossing a region of uniform magnetic field. The formulation of the laws of electromagnetism in the four dimensional classical space-time, by stating the observer-dependent splitting for bodies in motions, provides a proof of Galilei invariance of all the electric and magnetic fields involved in the analysis.