The Ampere-Neumann Electrodynamics of Metallic Conductors

This is a review of the old electrodynamics which prevailed during the first half of the 165-year history of electromagnetism. Amperes principal achievement was the deduction of his empirical force law from experiments with several current balances. Faraday then discovered electro-magnetic induction. This prompted F. E. Neumann to work out a quantitative explanation of induction based on Amperes force law. It involved the concept of the electrodynamic potential which, as we know now, is the same entity as magnetic energy. With the newtonian principle of virtual work, Neumann found his potential yielded the correct mechanical forces on metallic current circuits. Neumanns theory contains a physical quantity which today is called the magnetic vector potential and treated as a mathematical contrivance.

Neumanns mutual inductance formula has become a powerful tool of inductance calculations. Maxwell made a major contribution to the Ampere-Neumann electrodynamics by developing the mean-geometric-distance method for calculating the inductance of conductors of finite cross-sections. This became particularly useful after Sommerfeld solved Neumanns double integral for parallel, straight wires. Maxwell built all of Neumanns mathematical theory into his field equations but the lingo changed. Electrodynamic potential became kinetic energy of the field; conductor element interactions became flux linkage; and so on. Maxwells equations do not contain a magnetic force law. He believed both Amperes law and the law currently in use, which was first suggested by Grassmann in 1845, were compatible with field theory. Lorentz later found that the motion of charges in vacuum obeyed only Grassmanns law and not Amperes. From then onward the old electrodynamics fell into disuse and field theory has reigned supremely ever since.

Recent developments have shown the conflict between Amperes and Grassmanns law to be related to the nature, of the electric current. Conduction currents in metals obey Amperes law and convection currents in vacuum obey Grassmanns law. Both laws agree on the reaction forces between closed metallic circuits, because the relativistic contribution from the Grassmann law then integrates to zero. This fact appears to have mislead Lorentz in believing that the drifting electron in vacuum is magnetically equivalent to the current element of metals.

An examination of the long debate concerning the validity of Newtons third law of motion in electromagnetism proves the Ampere-Neumann electro-dynamics to be valid for metallic circuits while the theory of special relativity and field momentum conservation are required for convecting charges in vacuum. This conclusion is strongly supported by experimental evidence. It demands a change in the concept of the metallic current element.