Deduction of the law of motion of the charges from Maxwell equations

TL;DR

This paper demonstrates that the law of motion for electric charges can be derived directly from Maxwell's equations using a fundamental theorem by Hilbert, highlighting a theoretical connection between charge dynamics and electromagnetic field equations.

Contribution

It introduces a novel derivation of charge motion laws from Maxwell equations leveraging Hilbert's theorem, providing a deeper theoretical understanding.

Findings

Charge motion laws follow from Maxwell equations

Hilbert's theorem is key to the derivation

The approach unifies charge dynamics with electromagnetic theory

Abstract

By exploiting suitably a fundamental theorem by Hilbert, we show that the equation of motion of the electric charges is a consequence of Maxwell field equations.