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second current in that same expression, but of course, it is arbitrary, which one is treated as sending or receiving current. This treatment makes it possible to see a product between two currents in an application of Coulomb's law, and, hence, there will be no need for the Lorentz force. When that analysis has been done, it remains to take into account to the effects of the Special relativity theory, especially the Lorentz transformation of lengths. Since this effect is related only to the relative movements of the two coordinate axes, and has nothing to do with the propagation delay an observer faces, it may be multiplied straightforwardly to the effect of propagation delay. The expression for the force between the two currents are compared to the expression that Ampère arrive at and to Lorentz' force law. Thereafter follows a discussion of the pro et contra of respective model. The result in this article is based on two wellcorroborated natural laws: Coulomb's law [23] and the Special relativity theory. Ampére in turn, derives his law in a strictly empirical sense [32], searching for similarities with Coulomb's law. However, since in his time, the individual electron had not yet been discovered and, secondly, the Special relativity theory had not been defined. Hence, Ampère had no other choice than to establish a fairly good empirical law. Lorentz (or first: Grassmann) faced the same problem, but his formula was derived through evident mathematical faults [15]. Nb. This term 'Ampère's force law´ is not the same law as that Jackson denotes Ampère's law. Please cf. the original paper by Ampère [13] and Jackson [24]. This would make it possible to create a continuous, logical chain, from the findings by Ampère to the established Maxwell electro‐ dynamics. Assis has made an effort to prove that both Ampère's law and Grassmann's law produce the same result, when the forces within Ampère's bridge are being derived [15]. Admittedly, he concedes that they are not equal at every point, but in the integral sense, when a complete, closed electric circuit is taken into account. From a strictly mathematical pint of view, however, if two functions are not equal at every point, they don't express equal functions. This is taught in the most basic undergraduate courses. Anyhow, stating that all electric circuits are necessarily closed, he arrives at the conclusion that both laws are equally applicable on

To conclude, all three of them: Coulomb's law, Lorentz' force law and Ampère's force law can account for the attractive force exerted between two parallel electric conductors, carrying a current in the same direction. On the mere basis of the shape of the functions, it is not possible to decide, which one is best expressing physical reality, since the very measurements of currents involves a theory for the force between currents in the context of traditional meas‐ urement instruments. Hence, for every choice of model, there will necessarily appear a coupling constant that makes the measurements fit with the theory. Therefore, it remains to make a qualitative analysis of the three models. Above it has already been explored that Coulomb's has been used in a very strict manner, applying only the effects of propagation delay and the Special Relativity theory, whereas Ampère's force law is only expressing an empirical estimation of the force and the Lorentz force has been fallaciously derived, using

Hence, the conclusion to be drawn is that Coulomb's law gives the most comprehensive

electric circuits.

88 Advanced Electromagnetic Waves

Ampère's force law.

explanation to the force.

Jan Olof Jonson1,2,3

Address all correspondence to: jajo8088@bahnhof.se


3 European Physical Society and the John Chappell Natural Philosophy Society, USA
