
Proceedings Paper
The force law of classical electrodynamics: Lorentz versus Einstein and LaubFormat | Member Price | Non-Member Price |
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Paper Abstract
The classical theory of electrodynamics is built upon Maxwell’s equations and the
concepts of electromagnetic field, force, energy, and momentum, which are intimately tied
together by Poynting’s theorem and the Lorentz force law. Whereas Maxwell’s macroscopic
equations relate the electric and magnetic fields to their material sources (i.e., charge, current,
polarization and magnetization), Poynting’s theorem governs the flow of electromagnetic energy
and its exchange between fields and material media, while the Lorentz law regulates the backand-
forth transfer of momentum between the media and the fields. As it turns out, an alternative
force law, first proposed in 1908 by Einstein and Laub, exists that is consistent with Maxwell’s
macroscopic equations and complies with the conservation laws as well as with the requirements
of special relativity. While the Lorentz law requires the introduction of hidden energy and hidden
momentum in situations where an electric field acts on a magnetic material, the Einstein-Laub
formulation of electromagnetic force and torque does not invoke hidden entities under such
circumstances. Moreover, the total force and the total torque exerted by electromagnetic fields
on any given object turn out to be independent of whether force and torque densities are
evaluated using the Lorentz law or in accordance with the Einstein-Laub formulas. Hidden
entities aside, the two formulations differ only in their predicted force and torque distributions
throughout material media. Such differences in distribution are occasionally measurable, and
could serve as a guide in deciding which formulation, if either, corresponds to physical reality.
Paper Details
Date Published: 12 September 2013
PDF: 18 pages
Proc. SPIE 8810, Optical Trapping and Optical Micromanipulation X, 88100K (12 September 2013); doi: 10.1117/12.2024808
Published in SPIE Proceedings Vol. 8810:
Optical Trapping and Optical Micromanipulation X
Kishan Dholakia; Gabriel C. Spalding, Editor(s)
PDF: 18 pages
Proc. SPIE 8810, Optical Trapping and Optical Micromanipulation X, 88100K (12 September 2013); doi: 10.1117/12.2024808
Show Author Affiliations
Masud Mansuripur, College of Optical Sciences, Univ. of Arizona (United States)
Published in SPIE Proceedings Vol. 8810:
Optical Trapping and Optical Micromanipulation X
Kishan Dholakia; Gabriel C. Spalding, Editor(s)
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