Electrodynamics for Nonrelativistic Point Charges in Electrical Engineering: A framework based on Maxwell’s equations and Ampère’s original force law

In electrical engineering, electric charges usually move at speeds substantially slower than the speed of light. Therefore, relativistic mechanics and the Lorentz transformation are rarely applied; instead, the much simpler Newtonian mechanics and the Galilean transformation are used. This approximation is hoped to yield useful results. In this article, the exact solution of Maxwell’s equations for arbitrarily moving point charges is used to demonstrate that this approximation is not suitable for point charges, even if they move extremely slowly. Nevertheless, in electrical engineering, great practical demand exists for a functioning and consistent electrodynamic model for nonrelativistic point charges. This article presents such a model and demonstrates that it ensures the universal constancy of the speed of light for all receiving antennas while satisfying the Galilean principle of relativity regarding the point charges. The framework can describe electromagnetic waves as well as all static and quasi-static effects with excellent quality if they are generated by nonrelativistic point charges. The framework is based on the exact solution of Maxwell’s equations for arbitrarily moving point charges and a simplified Lorentz force law, which has been calibrated so that the force for slow velocities matches Ampère’s original force law and thus fulfills the predictions of magnetostatics and quasi statics.