Faraday's and Ampere's Laws
Keywords: Faraday's and Ampere's Laws, electromagnetic theory, moving charge
Two potentials associated with a moving charge are derived by assuming that the mutual energy between it and a stationary test charge are generated in their fields and that the generation involves as random propagation at the velocity of light relative to a stationary point. Expressed in terms of B, the velocity of the charge divided by the velocity of light, the potentials are: (1) the static potential of the moving charge divided by 1 - B2 if the velocity is along the radial to the test charge; and (2) the static potential divided by  if the velocity if transverse to the radial. The low velocity approximations of these potentials lead to very direct derivations of the differential relations for the induced fields associated with changing currents and for the magnetic forces associated with stationary currents. They thereby provide a basis for the development of electromagnetic theory.