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The Electromagnetic Force between Two Parallel Electric Currents of "Infinite" Length Attained Using Respectively Amp?re's Law and Coulomb‟s Law Including a Relativistic Analysis

Jan Olof Jonson
Year: 2010 Pages: 19
Keywords: Electromagnetism, Amp?re's law, Amp?re's Bridge, Coulomb's law, Special Relativity, retardation
In this paper an analysis is being made of a physical electric circuit that might correspond to the famous case of two parallel electric conductors of "infinite length". The case, invented by Amp?re, is not physically possible, of course. All electric currents must namely be guided back to their origin. Therefore one ought to present a physical circuit that contains as a part two conductors infinitesimally close to each other. It appeared that Amp?re‟s bridge would be a suitable choice as a starting model, provided a pair of conductors is inserted inside Practically, it resembles an "eight", with two closed circuits coming close to each other along one branch. This is explained more rigorously in the text. A benefit is that a set of detailed computations on Amp?re‟s bridge by this author may be used as a mathematical basis. A comparison between the results attained by using Amp?re‟s law and Coulombs law respectively is being made. Further, the Lorentz Transformation of the Special Relativity Theory is being applied on the Coulomb result. The result is that also the latter method succeeds in predicting the force between two conductors. This result must further be chosen, since it has been shown elsewhere that the very definition of Amp?re‟s law is devoid of logically consistent argument, whereas Coulomb's law constitutes a 'simplest possible assumption. The usage of Coulomb‟s law is completed with a relativistic analysis, relevant to the properties of the actual circuit, i.e. geometry, velocities.