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Toward the Kelvin's Formula Paradox

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US Army Research Laboratory Aberdeen Proving Ground United States

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According to the Kelvins formula paradox, a polarized body will be accelerated by its own electrostatic or magnetostatic field. This paradoxical statement obviously contradicts common sense and everyday experience, and should be eliminated from any rational theory of electromagnetism. We suggested a general approach allowing to get rid of this paradox. However, the approach leads to quite complex formulae. Needless to say, a simpler resolution of the paradox, if possible, would be highly desirable. A potentially simpler resolution of the paradox was recently suggested by our colleagues. According to their suggestion, proper account of the mechanical stresses in the body compensates the resultant polarization force. In this report, we demonstrate, however, that the suggested mechanism of compensation is impossible. Basically, we reinforce the concept that no redistribution of stresses is able to compensate the volume force if the resultant force does not vanish. In other words, with a nonvanishing resulting force, the body is not able to be at rest no matter what its constitutive equation will be.

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Technical Report,01 Jan 2016,01 Jun 2016



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Approved For Public Release;

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