Abstract
In 1967 Shockley and James addressed the situation of a magnet in an electric field. The magnet is at rest and contains electromagnetic momentum, but there was no obvious mechanical momentum to balance this for momentum conservation. They concluded that some sort of mechanical momentum, which they called “hidden momentum”, was contained in the magnet and ascribed this momentum to relativistic effects, a contention that was apparently confirmed by Coleman and Van Vleck. Since then, a magnetic dipole in an electric field has been considered to have this new form of momentum, but this view ignores the electromagnetic forces that arise when an electric field is applied to a magnet or a magnet is formed in an electric field. The electromagnetic forces result in the magnet-charge system gaining electromagnetic momentum and an equal and opposite amount of mechanical momentum so that it is moving in its original rest frame. This moving reference frame is erroneously taken to be the rest frame in studies that purport to show hidden momentum. Here I examine the analysis of Shockley and James and of Coleman and Van Vleck and consider a model of a magnetic dipole formed in a uniform electric field. These calculations show no hidden momentum.
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References
J.J. Thomson, Phil. Mag. 31, 149 (1891)
J.J. Thomson, Phil. Mag. 8, 331 (1904)
K.T. McDonald, http://www.hep.princeton.edu/˜mcdonald/examples/thomson.pdf (2015)
W. Shockley, R.P. James, Phys. Rev. Lett. 18, 876 (1967)
S. Coleman, J.H.V. Vleck, Phys. Rev. 171, 1370 (1968)
C.G. Darwin, Phil. Mag. 39, 537 (1920)
D.J. Griffiths, Am. J. Phys. 80, 7 (2012)
D. Babson et al., Am. J. Phys. 77, 826 (2009)
J.D. Jackson, Classical Electrodynamics, 3rd edn. (John Wiley & Sons, New York, 1999)
T.H. Boyer, Phys. Rev. E 91, 013201 (2015)
W.H. Furry, Am. J. Phys. 37, 621 (1969)
V. Hnizdo, Am. J. Phys. 65, 515 (1997)
M. Planck, Phys. Z.S. 9, 828 (1909)
F.T. Trouton, H.R. Noble, Proc. R. Soc. 74, 132 (1903)
M. von Laue, Verhandlungen der Deutschen Physikalischen Gesellschaft 13, 513i (1911)
F.R. Redfern, http://prism-redfern.org/physicsjournal/trouton-noble.pdf (2016), last accessed in January, 2017
T.H. Boyer, Am. J. Phys. 83, 433 (2015)
J.R. Reitz, F.J. Milford, Foundations of Electromagnetic Theory (Addison-Wesley, Reading, Massachusetts, 1960)
T.H. Boyer, Phys. Rev. A 36, 5083 (1987)
Y. Aharonov, P. Pearle, L. Vaidman, Phys. Rev. A 37, 4052 (1988)
Y. Aharonov, A. Casher, Phys. Rev. Lett. 53, 319 (1984)
L. Vaidman, Am. J. Phys. 58, 978 (1990)
M. Mansuripur, Phys. Rev. Lett. 108, 193901 (2012)
V. Namias, Am. J. Phys. 57, 171 (1989)
D. Bedford, P. Krumm, Am. J. Phys. 54, 1036 (1986)
F.R. Redfern, Phys. Scr. 91, 045501 (2016)
Added in proof: It turns out that the effect of the vector potential is canceled by that of the scalar potential, but the conclusion concerning hidden momentum still holds
A. Einstein, J. Laub, Ann. Phys. 331, 541 (1908)
D.A.T. Vanzella, Phys. Rev. Lett. 110, 089401 (2013)
S.M. Barnett, Phys. Rev. Lett. 110, 089402 (2013)
P.L. Saldanha, Phys. Rev. Lett. 110, 089403 (2013)
M. Khorrami, Phys. Rev. Lett. 110, 089404 (2013)
D.J. Griffiths, V. Hnizdo, Am. J. Phys. 81, 570 (2013)
P.L. Saldanha, J.S.O. Filho, last accessed in January, 2017 (2016)
J.S.O. Filho, P.L. Saldanha, Phys. Rev. A 92, 052017 (2015)
G. Spavieri, Eur. Phys. J. D 70, 263 (2016)
W. Rindler, Relativity: Special, General, and Cosmological, 2nd edn. (Oxford University Press, Oxford, 2006)
F.R. Redfern, http://prism-redfern.org/physicsjournal/relofsimul.pdf (2016), last accessed in February, 2017
M. Mansuripur, Proc. SPIE 9548, 95480K,1 (2015)
F.R. Redfern, http://prism-redfern.org/nohidden.pdf (2015), last accessed in January, 2017
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Redfern, F. Magnets in an electric field: hidden forces and momentum conservation. Eur. Phys. J. D 71, 163 (2017). https://doi.org/10.1140/epjd/e2017-70263-3
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DOI: https://doi.org/10.1140/epjd/e2017-70263-3