Analytic solutions for the longitudinal and the transverse components of the vector potential in the Lorenz gauge

TL;DR

This paper derives exact analytic solutions for both the longitudinal and transverse components of the vector potential in the Lorenz gauge, applicable to any time-dependent charge-current distribution.

Contribution

It provides a general analytic framework for solving vector potential components in the Lorenz gauge for arbitrary time-dependent sources.

Findings

Derived explicit formulas for vector potential components.

Applicable to arbitrary time-dependent charge-current distributions.

Enhances understanding of electromagnetic potentials in Lorenz gauge.

Abstract

We derive analytic solutions for the longitudinal and the transverse components of the vector potential in the Lorenz gauge for an arbitrary time-dependent charge-current distribution.