14. Krzysztof Rębilas, Reducing Maxwell's Equations to Gauss's Law

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Volume 19: Pages 434-445, 2006

Reducing Maxwell's Equations to Gauss's Law

Krzysztof Rębilas 1

1Zakład Fizyki, Akademia Rolnicza im. Hugona Kołłątaja, A1. Mickiewicza 21, 31120 Kraków Poland

The general solutions of Maxwell's equations are derived from Gauss's law ruling the electric field E and the assumption that electric effects are transmitted with velocity c. Because the validity of Gauss's law (together with the chargeconservation law) in any frame entails the AmpèreMaxwell law                          × B  − ∂E /c2∂t = j/(c2Ε0), the latter allows us to find the magnetic field. Maxwell's equations then reduce to merely one of them (Gauss's law), provided the retardation of the electric interactions is added.

Keywords: Maxwell's equations, Gauss's law, transformation of force, retardation of interactions

Received: March 14, 2006; Published Online: December 15, 2008