A simple 'derivation' of Maxwell's equations relying on the new extended Helmholtz theorem

Originally Maxwell's equations were obtained by the creation of mathematical expressions that modeled measurements and by Maxwell's hypotheses that filled in some of the missing relationships. Maxwell's equations were not actually derived until 1929 when Weyl (1950) using the methods of gauge theory obtained the electromagnetic field strength tensor in terms of potentials. In the 1980s Kobe (1980, 1981), in a set of papers, showed that they can be found by both classical mechanical and quantum mechanical gauge transformations. In 1985 Kapuscik proposed an extended Helmholtz theorem by which any two coupled time dependent vector fields can be related. He suggested, and Heras (see Am J. Phys., vol.62, p.949-950, 1994) formalized, a derivation of Maxwell's equations directly in terms of the fields, thereby avoiding gauges, potentials, and the methods of classical and quantum mechanics. The author also uses the extended Helmholtz theorem, but based on a set of hypotheses that diverge from those of Heras.