Average Lorentz Self-Force From Electric Field Lines

TL;DR

This paper derives the average Lorentz self-force for a charged particle undergoing arbitrary non-relativistic motion by extending classical electromagnetic field derivations to variable acceleration scenarios.

Contribution

It introduces a method to compute the average Lorentz self-force for particles with non-constant acceleration using Coulomb's law and relativistic field transformations.

Findings

Derived the average Lorentz self-force for variable acceleration.

Extended classical field derivations to non-uniform acceleration.

Provided a framework for analyzing self-force in non-relativistic regimes.

Abstract

We generalize the derivation of electromagnetic fields of a charged particle moving with a constant acceleration [1] to a variable acceleration (piecewise constants) over a small finite time interval using Coulomb's law, relativistic transformations of electromagnetic fields and Thomson's construction [2]. We derive the average Lorentz self-force for a charged particle in arbitrary non-relativistic motion via averaging the fields at retarded time.