Abstract

A new electromagnetic force law for real finite-size elastic charged particles is derived by solving simultaneously the fundamental em-pirical laws of classical electrodynamics, i.e. Gauss's laws, Ampere's generalized law, Faraday's law, Lorentz's law, and Lenz's law assuming Galilean invariance and noting that both the superposition principle for electromagnetic fields and the point-particle as-sumption assumed by Maxwell are experimentally false. This derived version of the electromagnetic force law contains extensions to Weber's force law that account for gravity, inertia, relativistic effects including radiation, and also the non-radial terms that explain the experimentally observed curling of plasma currents. The derived force law satisfies Newton's third law, conservation of energy and momentum, and Mach's Principle. Galilean invariance is shown to mathematically require that the electromagnetic force be a contact force based on field extensions of the charge instead of action-at-a-distance and is used to derive the Lorentz force law. From the per-spective of the derived electromagnetic potential between two moving charges, it appears that the 'relativistic' corrections to the Coulomb static potential are just geometrical terms that take into account the effective distance between the charges due to the corkscrew motion of the moving charges and the induced field effects of Lenz's law.