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Magnetic field and current are zero inside ideal conductors
KTH, School of Engineering Sciences (SCI), Mechanics, Theoretical and Applied Mechanics.
KTH, School of Engineering Sciences (SCI), Mechanics, Biomechanics.
2011 (English)In: Progress in Electromagnetics Research B, ISSN 1937-6472, Vol. 27, 187-212 p.Article in journal (Refereed) Published
Abstract [en]

We prove a theorem on the magnetic energy minimum in a system of perfect, or ideal, conductors. It is analogous to Thomson's theorem on the equilibrium electric field and charge distribution in a system of conductors. We first prove Thomson's theorem using a variational principle. Our new theorem is then derived by similar methods. We find that magnetic energy is minimized when the current distribution is a surface current density with zero interior magnetic field; perfect conductors are perfectly diamagnetic. The results agree with currents in superconductors being confined near the surface. The theorem implies a generalized force that expels current and magnetic field from the interior of a conductor that loses its resistivity. Examples of solutions that obey the theorem are presented.

Place, publisher, year, edition, pages
2011. Vol. 27, 187-212 p.
Keyword [en]
Current distribution, Generalized force, Magnetic energies, Surface current density, Thomson's theorem, Variational principles, Electric fields, Variational techniques
National Category
Natural Sciences
URN: urn:nbn:se:kth:diva-48054DOI: 10.2528/PIERB10082701ScopusID: 2-s2.0-78650348153OAI: diva2:456721
Analytical and statistical mechanics for systems of many charged particles
QC 20111116Available from: 2011-11-15 Created: 2011-11-15 Last updated: 2011-11-16Bibliographically approved

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Essén, HannoNordmark, Arne
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