A simple derivation of the electromagnetic field of an arbitrarily moving charge

TL;DR

This paper presents a straightforward, Lorentz-invariant derivation of the electromagnetic field for an arbitrarily moving charge, avoiding complex calculations typically used in such derivations.

Contribution

It introduces a simple, elegant method for deriving the electromagnetic field of a moving charge without differentiating Lienard-Wiechert potentials, based on Lorentz invariance and Thomson's impulsive acceleration field.

Findings

Derivation is direct, elegant, and Lorentz invariant.

Avoids differentiation of Lienard-Wiechert potentials.

Provides a transparent physical interpretation.

Abstract

The expression for the electromagnetic field of a charge moving along an arbitrary trajectory is obtained in a direct, elegant, and Lorentz invariant manner without resorting to more complicated procedures such as differentiation of the Lienard-Wiechert potentials. The derivation uses arguments based on Lorentz invariance and a physically transparent expression originally due to J.J.Thomson for the field of a charge that experiences an impulsive acceleration.