volume | PIER Journals

Abstract

We consider three different definitions of magnetic dipole moment for electrically neutral compact bunches of charged particles and show that, in general, they are not equivalent to each other with respect to their relativistic transformation. In particular, we prove that the "configurational" definition of magnetic dipole moment m_c = 1/2∫_v(r × j)dV (in the common designations) and its definition through generated electromagnetic field ("source" definition m_s) or experienced force ("force" definition m_f) lead to different relativistic transformations of m_c and m_s (m_f). The results obtained shed light on the available disagreements with respect to relativistic transformation of a magnetic dipole moment, and they can be used in covariant formulation of classical electrodynamics in material media.

1. Panofsky, W. K. H. and M. Phillips, Classical Electricity and Magnetism, 2nd Ed., Wiley, New York, 1962.

2. Barut, A. O., Electrodynamics and Classical Theory of Fields & Particles, Dover, New York, 1980.

3. Jackson, J. D., Classical Electrodynamics, 3rd Ed., Wiley, New York, 1998.

4. Vekstein, G. E., "On the electromagnetic force on a moving dipole," Eur. J. Phys., Vol. 18, 113, 1997.
doi:10.1088/0143-0807/18/2/011 Google Scholar

5. Fischer, G. P., "The electric dipole moment of a moving magnetic dipole," Am. J. Phys., Vol. 39, 1528, 1971.
doi:10.1119/1.1976708 Google Scholar

6. Hnizdo, V., "Magnetic dipole moment of a moving electric dipole," Am. J. Phys., Vol. 80, 645, 2012.
doi:10.1119/1.4712308 Google Scholar

7. Beiser, A., Perspectives of Modern Physics, McGraw-Hill, New York, 1969.

8. Ohanian, H. C., "What is spin?," Am. J. Phys., Vol. 54, 500, 1986.
doi:10.1119/1.14580 Google Scholar

9. Vaidman, L., "Torque and force on a magnetic dipole," Am. J. Phys., Vol. 58, 978, 1990.
doi:10.1119/1.16260 Google Scholar

10. Kholmetskii, A. L., O. V. Missevitch, and T. Yarman, "Electromagnetic force on a moving dipole," Eur. J. Phys., Vol. 32, 873, 2011.
doi:10.1088/0143-0807/32/4/003 Google Scholar

11. Feynman, R. P., R. B. Leighton, and M. Sands, The Feynman Lectures on Physics, 2nd Ed., Addison-Wesley, Reading, MA, 1963.

12. Landau, L. D. and E. M. Lifshitz, The Classical Theory of Fields, 2nd Ed., Pergamon Press, New York, 1962.

13. Aharonov, Y., P. Pearle, and L. Vaidman, "Comment on `proposed Aharonov-Casher effect: Another example of Aharonov-Bohm effect arising from a classical lag' ," Phys. Rev., Vol. A37, 4052, 1988. Google Scholar

14. Kholmetskii, A. L., O. V. Missevitch, and T. Yarman, "Reply to comments on `electromagnetic force on a moving dipole'," Eur. J. Phys., Vol. 33, L7, 2012.
doi:10.1088/0143-0807/33/1/L03 Google Scholar

15. Møller, C., The Theory of Relativity, Clarendon Press, Oxford, 1973.

16. Kholmetskii, A. L., O. V. Missevitch, and T. Yarman, "Different paths to some fundamental physical laws: Relativistic polarization of a moving magnetic dipole," Eur. J. Phys., Vol. 31, 1233, 2010.
doi:10.1088/0143-0807/31/5/022 Google Scholar

Dr. Alexander L. Kholmetskii

Dr. Oleg V. Missevitch

Dr. Tolga Yarman