Abstract
The idea that charges are the sources of electric fields is expressed in a local, differential equation, Gauss' law. The generality and utility of local, differential equations is stressed as the precise language to express the principles of relativity. The charge–current four-vector is introduced, and charge conservation is expressed as the relativistic “continuity” equation. Maxwell's equations are obtained by boosting Gauss' law for electric and magnetic fields. The Ampere–Maxwell law is obtained with the displacement current. Faraday's law is derived similarly the integral expressions of electrodynamics are derived. The wave equation of electrodynamics is derived, and the fact that light travels at the speed limit of relativity is obtained.
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