Abstract

Experimental evidence questions the widely recognized concept of the Lorentz force. Specifically it fails to account for (1) the repulsive force within Amp?re?s bridge; (2) Amp?re?s early copper boat experiment, in which the boat moves away from the contact point where an electric current is applied to a basin filled with mercury; (3) the phase shift between the currents of a primary and secondary circuit in a typical transformer. The fundamental source of the fault is the ?Induction Law?, extensively explored elsewhere by this author. This author has even begun to specify alternative conceptual methods to explain the above mentioned phenomena. The effort has succeeded by using Coulomb?s Law, carefully taking into account the effects due firstly to the delay of action, and secondly the effects due to Special Relativity Theory (SRT). The Induction Law can successfully be replaced by using Coulomb?s Law, as other papers by this author describe. In this paper it is rigorously explored how the attractive force between two electric currents can be explained using Coulomb?s Law, thereby applying the effects due to delayed action and SRT. It is also indicated how the hypothetic-deductive practice by Amp?re that lead to the definition of ?Amp?re?s Law? can be given a strict mathematical formulation. The two terms of Amp?re?s Law appear as the derivative of a serial expansion of the expressions attained using Coulomb?s Law, delayed action and SRT altogether. A look into the efforts done by Amp?re has been shown elsewhere to be the outcome of a ?guessing procedure? in the best hypothetical-deductive way, though not offering any idea of why his two terms appear. On the contrary, this paper offers a comprehensive understanding, based on a logical chain from a ?first cause?, until the final result, where every step can be motivated.