volume | PIER Journals

Abstract

This article contains a digest of the theory of electromagnetism and a review of the transformation between inertial frames, especially under low speed limits. The covariant nature of the Maxwell's equations is explained using the conventional language. We show that even under low speed limits, the relativistic effects should not be neglected to get a self-consistent theory of the electromagnetic fields, unless the intrinsic dynamics of these fields has been omitted completely. The quasi-static limits, where the relativistic effects can be partly neglected are also reviewed, to clarify some common misunderstandings and imprecise use of the theory in presence of moving media and other related situations. The discussions presented in this paper provide a clear view of why classical electromagnetic theory is relativistic in its essence.

1. Hehl, F. W. and Y. N. Obukhov, Foundations of Classical Electrodynamics: Charge, Flux, and Metric, Springer International Publishing, 2003.

2. Zhou, X., "On independence, completeness of Maxwell's equations and uniqueness theorems in electromagnetics," Progress In Electromagnetics Research, Vol. 64, 117, 2006. Google Scholar

3. Kong, J. A., "Interaction of acoustic waves with moving media," The Journal of the Acoustical Society of America, Vol. 48, 236, 1970. Google Scholar

4. Tai, C., "A study of electrodynamics of moving media," Proceedings of the IEEE, Vol. 52, 685, 1964. Google Scholar

5. Schwinger, J., Classical Electrodynamics, Perseus Books, Reading, Mass, 1998.

6. Jackson, J. D., Classical Electrodynamics, 3rd Ed., Wiley, 1999.

7. Pollack, G. L. and D. R. Stump, Electromagnetism, Addison Wesley, 2002.

8. Jefimenko, O. D., "On the relativistic invariance of Maxwell's equation," Zeitschrift für Naturforschung A, Vol. 54, 637, 1999. Google Scholar

9. Einstein, A., "Zur elektrodynamik bewegter Körper [AdP 17, 891 (1905)]," Annalen der Physik, Vol. 14, 194, 2005. Google Scholar

10. Ferraro, R., Einstein's Space-time: An Introduction to Special and General Relativity, Springer, 2007.

11. Pines, D. and D. Bohm, "A collective description of electron interactions: II. Collective vs individual particle aspects of the interactions," Physical Review, Vol. 85, 338, 1952. Google Scholar

12. Landau, L., "On the theory of superconductivity," Collected Papers of L.D. Landau, 546-568, Elsevier, 1965. Google Scholar

13. Jiang, K., X. Dai, and Z. Wang, "Quantum anomalous vortex and majorana zero mode in iron-based superconductor Fe(Te,Se)," Physical Review X, Vol. 9, 011033, 2019. Google Scholar

14. Feynman, R. P., R. B. Leighton, M. Sands, M. A. Gottlieb, and R. Leighton, The Feynman Lectures on Physics, Addison-Wesley, 2006.

15. Purcell, E. M., Electricity and Magnetism, 3rd Ed., Cambridge University Press, 2013.

16. König, J., "How to get from static to dynamic electromagnetism," European Journal of Physics, Vol. 42, 045204, 2021. Google Scholar

17. Sheng, X.-L., Y. Li, S. Pu, and Q. Wang, "Lorentz transformation in Maxwell equations for slowly moving media,", arXiv:2202.03122 [cond-mat, physics:hep-ph, physics:nucl-th, physics:physics], 2022, arXiv: 2202.03122. Google Scholar

18. Wang, Z. L., "On the expanded Maxwell's equations for moving charged media system - General theory, mathematical solutions and applications in TENG," Materials Today, S136970212100359X, 2021. Google Scholar

19. Rousseaux, G., "Forty years of Galilean electromagnetism (1973-2013)," The European Physical Journal Plus, Vol. 128, 81, 2013. Google Scholar

20. Montigny, M. D. and G. Rousseaux, "On the electrodynamics of moving bodies at low velocities," European Journal of Physics, Vol. 27, 755, 2006. Google Scholar

21. De Montigny, M. and G. Rousseaux, "On some applications of Galilean electrodynamics of moving bodies," American Journal of Physics, Vol. 75, 984, 2007. Google Scholar

22. Le Bellac, M. and J. M. Lévy-Leblond, "Galilean electromagnetism," Il Nuovo Cimento, Vol. 14, 217, 1973. Google Scholar

23. Landau, L. D., E. M. Lifšic, and L. P. Pitaevskij, "Electrodynamics of Continuous Media,", Course of theoretical physics, 2nd Edition, Vol. 8, Elsevier Butterworth-Heinemann, Amsterdam; Heidelberg, 2009. Google Scholar

24. Pauli, W. and C. P. Enz, Electrodynamics, MIT Press, 1973.

25. Lax, M. and D. F. Nelson, "Maxwell equations in material form," Physical Review B, Vol. 13, 1777, 1976. Google Scholar

26. Fano, R. M., L. J. Chu, and R. B. Adler, Electromagnetic Fields, Energy, and Forces, MIT Press, 1960.

Dr. Hao Chen

Dr. Wei E. I. Sha

Professor Xi Dai

Dr. Yue Yu