Topics in Magnetic Force Theory: Some Avatars of the Helmholtz Formula

  • Alain Bossavit
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 26)


There is a great variety of formulas purporting to describe the force field inside magnetized matter. They don’t always agree, which is puzzling. Starting from the Korteweg–Helmholtz formula, obtained thanks to the highly reliable Virtual Power Principle (VPP), we show how variant expressions can result from algebraic manipulations that assume, without making this explicit, extra physical hypotheses. Those we discuss here, assuming a B = μH magnetic law, are (1) Dependence of μ on density, (2) Incompressibility of the magnetic medium in which the magnetic forces develop.


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© Springer International Publishing AG, part of Springer Nature 2017

Authors and Affiliations

  1. 1.GeePs (ex. LGEP), Centrale-SupelecGif-sur-YvetteFrance

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