Galilean invariant retarded electric interaction of moving charges

TL;DR

This paper develops a Galilean invariant framework for retarded electric interactions, deriving a velocity-dependent potential that reproduces Weber's force law and suggests magnetic effects emerge from retarded electric forces.

Contribution

It introduces a new retarded Coulomb potential consistent with Galilean invariance, linking electric and magnetic phenomena through retarded electric interactions.

Findings

Derivation of a Galilean invariant Weber's force law

Retarded Coulomb potential depends on charges' velocities

Magnetic forces emerge from retarded electric interactions

Abstract

A Galilean invariant description of the retarded electric interaction of two moving charges is carried out, considering the EM action to propagate at the speed of light. Through the altering of the Li\'enard-Wiechert potential (LWP) a new retarded, electric potential called retarded Coulomb potential (RCP) is ordered to the moving charges. RCP depends on the velocities both of the interacting charges. The force law of the electric interaction of moving charges is determined by means of the second order approximation of RCP. The force law obtained is the Galilean invariant Webers force law, surprisingly. The rediscovery of the Webers force law from a retarded electric potential confirms its significance and proves it to be an approximated law, based on retardation. From the fact that the purely electric RCP provides not only the electric, but even the magnetic forces, a substantial ascertainment follows: In Galilean invariant description, magnetic phenomena are the manifestation of the retarded electric interaction exclusively.