How to obtain the covariant form of Maxwell's equations from the continuity equation

TL;DR

This paper derives the covariant form of Maxwell's equations starting from the charge continuity equation, highlighting charge conservation as the fundamental principle behind electromagnetic theory.

Contribution

It presents an axiomatic derivation of Maxwell's equations emphasizing charge conservation as the core axiom.

Findings

Maxwell's equations can be derived from charge continuity

Charge conservation underpins the covariant formulation

Provides an axiomatic basis for electromagnetic theory

Abstract

The covariant Maxwell equations are derived from the continuity equation for the electric charge. This result provides an axiomatic approach to Maxwell's equations in which charge conservation is emphasized as the fundamental axiom underlying these equations.