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The Maxwell-Lodge effect: Significance of electromagnetic potentials in the classical theory

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Abstract

The Aharonov-Bohm effect has been the starting point of the reconsideration of the reality of the vector potential within quantum physics. We argue that the Maxwell-Lodge effect is its classical equivalent: what is the origin of the electromotive force induced in a coil surrounding a (finite) solenoid fed by an alternative current? We demonstrate theoretically, experimentally and numerically that the effect can be understood using the vector potential while it cannot using only the fields.

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References

  1. M. Redhead, The interpretation of gauge symmetry, edited by M. Kuhlmann H. Lyre and A. Wayne, Proceedings of the International Conference on “Ontological Aspects of Quantum Field Theory”, October 11–13, 1999, Bielefeld, Germany, 2001

  2. R. Feynman, R. Leighton, M. Sands, The Feynman Lectures on Physics, Vol. 2 (Addison Wesley, Reading, Ma., 1964), 15-7/15-14

    Google Scholar 

  3. Y. Aharonov, D. Bohm, Phys. Rev. 115, 485 (1959)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  4. R.C. Jaklevic, J.J. Lambe, A.H. Silver, J.E. Mercereau, Phys. Rev. Lett. 12, 274 (1964)

    Article  ADS  Google Scholar 

  5. D. Goodstein, J. Goodstein, Phys. Perspect. 2, 30 (2000)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  6. A. Tonomura, The quantum world unveiled by electron waves (World Scientific, 1998)

  7. R. Healey, Phil. Sci. 64, 18 (1997)

    Article  MathSciNet  Google Scholar 

  8. G. Belot, Brit. J. Phil. Sci. 49, 531 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  9. P. Teller, Phil. Sci. 67, 466 (2000)

    Article  MathSciNet  Google Scholar 

  10. R. Healey, On the Reality of Gauge Potentials (2001) http://philsci-archive.pitt.edu/archive/00000328

  11. T.O. Eynck, H. Lyre, N. von Rummell, A versus B! Topological nonseparability and the Aharonov-Bohm effect (2001) http://philsci-archive.pitt.edu/archive/00000404

  12. K. Brading, H.R. Brown, Brit. J. Phil. Sci. 55, 645 (2004)

    Article  MathSciNet  Google Scholar 

  13. A. Guay, The arbitrariness of local gauge symmetry (2004) http://philsci-archive.pitt.edu/archive/00002132

  14. A. Guay, Geometrical aspects of local gauge symmetry (2004) http://philsci-archive.pitt.edu/archive/00002133

  15. J.D. Jackson, Classical Electrodynamics (third edition, John Wiley and Sons, 1998)

  16. A. O’Rahilly, Electromagnetic Theory, A critical examination of fundamentals (Dover Publications, 1965)

  17. A. Bork, Isis 58, 210 (1967)

    Article  MATH  Google Scholar 

  18. J. Roche, A critical study of the vector potential, in Physicists Look Back, edited by J. Roche and A. Hilger, Chap. 9 (1990), 144–168

  19. R. Anderson, Stud. Hist. Phil. Sci. 25, 577 (1994)

    Article  Google Scholar 

  20. O. Darrigol, Electrodynamics from Ampère to Einstein (Oxford University Press, 2000)

  21. A.C.T. Wu, C.N. Yang, Int. J. Mod. Phys. A 21, 3235 (2006)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  22. J.C. Maxwell, On Physical Lines of Force (1861–1862), edited by W.D. Niven (The Scientific Papers of James Clerk Maxwell, New York, 1890)

    Google Scholar 

  23. J.C. Maxwell, A Dynamical Theory of the Electromagnetic Field (1865), edited by W.D. Niven (The Scientific Papers of James Clerk Maxwell, New York, 1890)

    Google Scholar 

  24. J.C. Maxwell, Experiment in Magneto-Electric Induction (1868), edited by W.D. Niven (The Scientific Papers of James Clerk Maxwell, New York, 1890)

    Google Scholar 

  25. J.C. Maxwell, A treatise on Electricity and Magnetism, Vol. I & II (Clarendon Press, 1873; Dover Publications, 1954)

  26. G. Rousseaux, Annales de la Fondation Louis de Broglie 28, 261 (2003)

    MathSciNet  Google Scholar 

  27. G. Rousseaux, Europhys. Lett. 71, 15 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  28. M. de Montigny, G. Rousseaux, Eur. J. Phys. 27, 755 (2006)

    Article  MATH  Google Scholar 

  29. M. de Montigny, G. Rousseaux, Am. J. Phys. 75, 984 (2007)

    Article  ADS  Google Scholar 

  30. A.G. Chirkov, A.N. Ageev, Tech. Phys. 46, 147 (2001)

    Article  Google Scholar 

  31. O. Lodge, Phil. Mag. 27, 469 (1889)

    Google Scholar 

  32. E.J. Konopinski, Am. J. Phys. 46, 499 (1978)

    Article  ADS  MathSciNet  Google Scholar 

  33. R.H. Romer, Am. J. Phys. 50, 1089 (1982)

    Article  ADS  Google Scholar 

  34. W. Gough, J.P.G. Richards, Eur. J. Phys. 7, 195 (1986); F. Herrmann, Eur. J. Phys. 8, 217 (1987); W. Gough, J.P.G. Richards, Eur. J. Phys. 8, 218 (1987).

    Article  Google Scholar 

  35. E. Lanzara, R. Zangara, Phys. Educ. 30, 85 (1995)

    Article  ADS  Google Scholar 

  36. M.D. Semon, J.R. Taylor, Am. J. Phys. 64, 1361 (1996)

    Article  ADS  Google Scholar 

  37. D. Iencinella, G. Matteucci, Eur. J. Phys. 25, 1 (2004)

    Article  Google Scholar 

  38. J.H. Poynting, Phil. Trans. 176, 277 (1885)

    Article  Google Scholar 

  39. J. Roche, Phys. Educ. 22, 91 (1987)

    Article  ADS  Google Scholar 

  40. B. Batell, A. Ferstl, Am. J. Phys. 71, 925 (2003)

    Article  ADS  Google Scholar 

  41. K.E. Schmidt, The external magnetic field of a long solenoid, Applet, http://fermi.la.asu.edu/PHY531/solenoid/index.html

  42. M. Babiker, R. Loudon, J. Phys. A 17, 2973 (1984)

    Article  ADS  MathSciNet  Google Scholar 

  43. T. Tominaka, Nucl. Instrum. Meth. A 523, 1 (2004)

    Article  ADS  Google Scholar 

  44. T. Tominaka, Eur. J. Phys. 27, 1399 (2006)

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Laboratoire Jean-Alexandre Dieudonné, Université de Nice-Sophia Antipolis, UMR 6621 CNRS-UNSA, Parc Valrose, 06108, Nice Cedex 02, France

    G. Rousseaux

  2. Laboratoire de Physique de la Matière Condensée, Université de Nice-Sophia Antipolis, UMR 6622 CNRS-UNSA, Parc Valrose, 06108, Nice Cedex 2, France

    R. Kofman & O. Minazzoli

Authors
  1. G. Rousseaux
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  2. R. Kofman
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  3. O. Minazzoli
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Correspondence to G. Rousseaux.

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Rousseaux, G., Kofman, R. & Minazzoli, O. The Maxwell-Lodge effect: Significance of electromagnetic potentials in the classical theory. Eur. Phys. J. D 49, 249–256 (2008). https://doi.org/10.1140/epjd/e2008-00142-y

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