The simple proof of the Maxwell's vacuum equation (original) (raw)

This manuscript presents a streamlined proof of Maxwell's vacuum equation, asserting the source-free nature of Maxwell's equations. By utilizing a simple cased scenario with a point charge and applying concepts such as electric displacement and solid angles, the author demonstrates the vacuum equation's validity through mathematical derivations and the application of Stoke's theorem. The discussion concludes by highlighting the equivalence of both sides of Maxwell's vacuum equation, elucidating the relationship between electric displacement and magnetic fields.