Electromagnetic Constitutive Relations in Eccentric Rotating Frames

Document Type : Original Article

Author

Assistant Professor, Gonabad University, Gonabad, Iran

Abstract

In this article, while analytically reviewing the Landau formalism for electrodynamic equations in the presence of a gravitational field, we show that the three-dimensional electromagnetic constitutive relations in this formalism can be expressed by two equivalent methods. Then we obtain the constitutive relations for the Galilean rotating observer with both methods and show its compatibility with the previous results. We also present the electromagnetic constitutive relations for an eccentric rotating observer. To solve some ambiguities, especially in the articles related to this topic in the field of electrical engineering, different representations of the three-dimensional form of constitutive relations in the Galilean rotating observer’s frame are expressed in full detail. Also, the connection between different representations of three-dimensional constitutive relations will be explained. In the end, considering the practical and experimental importance of the eccentric rotating observer, we will obtain the electromagnetic constitutive relations for this particular observer.

Keywords


Smiley face

  1. . D. Landau and E. M. Lifshitz, “The classical theory of fields,” Pergamon Press, Oxford, Ch 10, 1975.
  2. Plebanski, “Electromagnetic waves in gravitational fields,” Phys. Rev. Vol. 118, pp. 1396-1407, 1960
  3. de. Felice, “On the gravitational field acting as an optical medium,” General Relativity and Gravitation, Vol. 2, pp. 347-357, 1971
  4. Mashhoon, “Scattering of Electromagnetic Radiation from a Black hole,” Physical Review D, Vol. 7, pp. 2087-2814, 1973.
  5. Mashhoon, “Can Einstein's theory of gravitation be tested beyond the geometrical optics limit?,” Nature Vol. 250, pp. 316-317, 1974.
  6. M. Volkov, A. A. Izmest'ev and G. V. Skrotskii, “The propagation of electromagnetic wavesin a Riemannian space,” Sov. Phys. JETP, Vol. 32, pp. 686-689, 1971.
  7. Besharat, M. Miri and M. Nouri-Zonoz, “Optical Aharonov–Bohm effect due to toroidal moment inspired by general relativity,” J. Phys. Commun, Vol. 3, pp. 115019-115028, 2019.
  8. Chin. Mo, “Theory of Electrodynamics in Media in Noninertial Frames and Applications,” J. Math. Phys. Vol. 11, pp. 2589-2610, 1970.
  9. C. Scorgie, “Theory of Electrodynamics in Media in Noninertial Frames and Applications,” J. Phys. A: Math. Gen. Vol. 23, pp. 5169-5184, 1990.
  10. H. Tyler and L. A. Mysak, “Theory of Electrodynamics in Media in Noninertial Frames and Applications,” Can. J. Phys, Vol. 73, pp. 393-402, 1995.
  11. F. T. del Castillo, and J. Mercado-Perez, “Three-dimensional formulation of the Maxwell equations for stationary space–times,” J. Math. Phys, Vol. 40, pp. 2882-2890, 1999.
  12. Shiozawa, “Phenomenological and electron-theoretical study of the electrodynamics of rotating systems,” Proc. IEEE, Vol.61, pp.1694-1702, 1973.
  13. Georgiou, “The electromagnetic field in rotating coordinates,” Proc. IEEE, Vol. 76, pp. 1051-1052, 1988.
  14. Hillion, “Relativistic electromagnetism in rotating media,” Turk. J. Elec. Eng, Vol. 18, pp. 281, 2010.
  15. Van. Bladel, “Electromagnetic fields in the presence of rotating bodies,” Proc. IEEE, Vol. 64, pp.301-318, 1976.
  16. Van. Bladel, “Rotating dielectric sphere in a low-frequency field,” Proc. IEEE, Vol. 67, pp.1654-1655, 1979.
  17. Van. Bladel, “Relativity and Engineering,” Berlin: Springer, Ch 9, 1984.
  18. Van. Bladel, “Electromagnetic Fields,” John Wiley and Sons, Second Edition, Ch 17, 2007.
  19. C. Hauck, and B. Mashhoon, “Electromagnetic waves in a rotating frame of reference,” Ann. Phys. Vol. 12, pp. 275-288, 2003.
  20. V. Skrotskii, Dokl. Akad. Nauk. SSSR, Vol. 114, pp. 73-76, 1957.
  21. F. R. Ellis, R. Maartens and M. A. H. Maccallum, “Relativistic Cosmology,” Cambridge University Press, 2012.
  22. Ramezani-Aval, “The relation between different definitions of electromagnetic field tensor and Maxwell’s equations in stationary spacetimes,” Indian. J. Phys, Vol. 39, 2022.
  23. Nouri-Zonoz, H. Ramezani-Aval and R. Gharechahi, “On Franklin’s relativistic rotational transformation and its modification,” Eur. Phys. J. C Vol. 74, 3098, 2014.
  24. Nouri-Zonoz and H. Ramezani-Aval, “Fermi coordinates and modified Franklin transformation: a comparative study on rotational phenomena ,” Eur. Phys. J. C, Vol. 74, 3128, 2014.
Volume 11, Issue 2 - Serial Number 27
September 2023
Pages 69-77
  • Receive Date: 31 May 2023
  • Revise Date: 29 August 2023
  • Accept Date: 22 September 2023
  • Publish Date: 07 November 2023