Old Inconsistency In Electromagnetism And A Way To Eliminate It
Classical electromagnetic theory uses axial pseudo-vectors to describe magnetic interactions. It is impossible to explain adequately magnetic interaction at the micro level (elements of conductors and the magnetic interactions of charges) by axial vectors. As a result, the correct form of interactions in classical electrodynamics is only an integral one. The differential formulas for magnetic interactions violate the third Newton’s law.
In the paper, we use polar vectors (real physical vectors) to describe magnetic interactions. On this way, we show that the real physical magnetic field, in contrast to the solenoidal field of the axial vector magnetic induction B, has two components: a potential field with nonvanishing divergence and a solenoidal field with vanishing divergence. These two fields act separately and independently and have different models of interactions.
Doing so, we can write differential form for the Ampere’s law obtaining correct formula for the magnetic interactions and adequate interpretation of the Biot-Savart law.
 Ampère A 1826 (in German), Théorie des phénomènes électro-dynamiques, uniquement déduite de l’expérience, Méquignon-Marvis. Retrieved 2010-9-26
 Tamm I 1979 Fundamentals of the theory of electricity - Mir publisher, Moscow
 Ørsted H C 1820 (in latin) Experimenta circa effectum conflictus electrici in acum magneticam, Typis Schultzinis
 Faraday M 1846 Experimental researches of electricity Phil. Trans. R. Soc. Lond. 1846 136, 1-20
 Maxwell J S 1873 A Treatise on Electricity and Magnetism vol. 2 Oxford Clarendon press
 Sigalov R G et al.1965 (in Russian) New investigations of magnetomotive forces. (Science Publishing, Tashkent, Uzbekistan)
 Pappas P T 1983 The Original Ampere Force and Biot-Savart and Lorentz Forces . Il Nuovo Cimento. 11 Agosto, 1983,V.76 B, №2, P 189-196
 Grassman H 1845 Neue Theorie der Elektrodynamik. Annalen der Physik und Chemie - Bd. 64, №1– S. 1–18
 Whittaker E 1910 A history of the theories of aether and electricity. The classical theories. Thomas Nelson and Sons Ltd, London
 ] Nikolaev G V 1997 (in Russian) Consistent electrodynamics. Theory, experiments, paradoxes. STL Publishing, Tomsk, Russia.
 Korobeynikov 2005(in Russian) A new kind of electromagnetic radiation. http://n-t.ru/tp/ts/nv.htm
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