Can Maxwell's equations be obtained from the continuity equation?

Details Can Maxwell's equations be obtained from the continuity equation? Can Maxwell's equations be obtained from the continuity equation?

2008-12-28

arxiv.org/abs/0812.4785v1

Am. J. Phys. 75, 652-657 (2007)

Physics

Classical Physics

14 pages. See the comment: "O. D. Jefimenko, Causal equations for electric and magnetic fields and Maxwell's equations: commen

Scientific paper

10.1119/1.2739570

We formulate an existence theorem that states that given localized scalar and vector time-dependent sources satisfying the continuity equation, there exist two retarded fields that satisfy a set of four field equations. If the theorem is applied to the usual electromagnetic charge and current densities, the retarded fields are identified with the electric and magnetic fields and the associated field equations with Maxwell's equations. This application of the theorem suggests that charge conservation can be considered to be the fundamental assumption underlying Maxwell's equations.

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