Potential Theory in Classical Electrodynamics
Wolfgang Engelhardt
Keywords: Classical Electrodynamics, Maxwell?s equations
In Maxwell's classical theory of electrodynamics the fields are frequently expressed by potentials in order to facilitate the solution of the first order system of equations. This method obscures, however, that there exists an inconsistency between Faraday's law of induction and Maxwell's flux law. As a consequence of this internal contradiction there is neither gauge invariance, nor exist unique solutions in general. The retarded integrals, in particular, turn out not to represent proper solutions of the inhomogeneous wave equations.
