volume | PIER Journals

Abstract

We investigate the thermal and relativistic effects produced when an electrically conductive object is moving in tandem with a source of a variable electromagnetic field. First, we derive an energy–frequency relation to quantify the temperature rise induced by such a field. This relation is then combined with the Lorentz-Fitzgerald contraction and time dilation from special relativity to identify a force, F_c, required to reconcile energy conservation between stationary and moving observers. We further relate F_c to the relativistic energy of a moving mass, extending the analysis to objects without electrical conductivity. This connection leads to the prediction of an inertial force F_cf generated by the frequency sweep of an electromagnetic wave (whether caused by relative motion or by internal modulation) that interacts with mass regardless of its electrical properties.

1. Peregoudov, D. V., "Relativistic length contraction and time dilation as dynamical phenomena," European Journal of Physics, Vol. 41, No. 1, 015602, Dec. 2019.
doi:10.1088/1361-6404/ab454a Google Scholar

2. Redžić, Dragan V., "Image of a moving sphere and the FitzGerald-Lorentz contraction," European Journal of Physics, Vol. 25, No. 1, 123, 2004.
doi:10.1088/0143-0807/25/1/015 Google Scholar

3. Heaviside, Oliver, "XXXIX. On the electromagnetic effects due to the motion of electrification through a dielectric," The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, Vol. 27, No. 167, 324-339, 1889.
doi:10.1080/14786448908628362 Google Scholar

4. Searle, G. F. C., "On the steady motion of an electrified ellipsoid," Proceedings of the Physical Society of London, Vol. 15, No. 1, 264, 1896.
doi:10.1088/1478-7814/15/1/323 Google Scholar

5. Le Bellac, M. and J. M. Lévy-Leblond, "Galilean electromagnetism," Il Nuovo Cimento B (1971-1996), Vol. 14, No. 2, 217-234, Apr. 1973.
doi:10.1007/bf02895715 Google Scholar

6. De Montigny, M. and G. Rousseaux, "On the electrodynamics of moving bodies at low velocities," European Journal of Physics, Vol. 27, No. 4, 755, 2006.
doi:10.1088/0143-0807/27/4/007 Google Scholar

7. Harsha, N. R. Sree, Anupama Prakash, and D. P. Kothari, The Foundations of Electric Circuit Theory, IOP Publishing, 2016.
doi:10.1088/978-0-7503-1266-0

8. Koivurova, Matias, Charles W. Robson, and Marco Ornigotti, "Time-varying media, relativity, and the arrow of time," Optica, Vol. 10, No. 10, 1398-1406, 2023.
doi:10.1364/optica.494630 Google Scholar

9. Incropera, Frank P. and David P. DeWitt, Fundamentos de Transferencia de Calor, 4th Ed., Prentice Hall, 1999.

10. John, Davies and Peter Simpson, Induction Heating Handbook, McGraw-Hill, London, 1979.

11. Jackson, John David, Classical Electrodynamics, 3rd Ed., Wiley, 2021.

12. Ulaby, Fawwaz Tayssir and Umberto Ravaioli, Fundamentals of Applied Electromagnetics, Vol. 7, Pearson Education UK, 2015.

13. Ovando-Martinez, R. B. B., C. Hernandez, and M. A. Arjona, "An adaptive time-stepping algorithm in weakly coupled electromagnetics-thermal-circuit modeling," Applied Computational Electromagnetics Society Journal (ACES), Vol. 28, No. 9, 871-878, Sep. 2021. Google Scholar

14. Ovando-Martinez, R. B. B., M. A. Arjona Lopez, and C. Hernandez Flores, "A finite-element variable time-stepping algorithm for solving the electromagnetic diffusion equation," IEEE Transactions on Magnetics, Vol. 48, No. 2, 647-650, Feb. 2012.
doi:10.1109/tmag.2011.2177448 Google Scholar

15. Hernandez, C., R. B. B. Ovando-Martinez, and M. A. Arjona, "Application of tensor analysis to the finite element method," Applied Mathematics and Computation, Vol. 219, No. 9, 4625-4636, Jan. 2013.
doi:10.1016/j.amc.2012.10.074 Google Scholar

16. Ovando, Roberto B. B., Apparatus and method for leakage electromagnetic field sensing in electrical inductive equipment, US Patent 11,047,895, 2021.

17. Misner, C. W., K. S. Thorne, and J. A. Archibald, Gravitation, W. H. Freeman and Company, New York, 1973.

18. Thim, H. W., "Absence of the relativistic transverse Doppler shift at microwave frequencies," IEEE Transactions on Instrumentation and Measurement, Vol. 52, No. 5, 1660-1664, Oct. 2003.
doi:10.1109/tim.2003.817916 Google Scholar

19. Johnson, Montgomery H. and Edward Teller, "Intensity changes in the Doppler effect," Proceedings of the National Academy of Sciences, Vol. 79, No. 4, 1340, Feb. 1982.
doi:10.1073/pnas.79.4.1340 Google Scholar

20. Rindler, W., Introduction to Special Relativity, 2nd Ed., Oxford University Press, United States , 1991.

21. Valagiannopoulos, Constantinos A. and Andrea Alú, "The role of reactive energy in the radiation by a dipole antenna," IEEE Transactions on Antennas and Propagation, Vol. 63, No. 8, 3736-3741, Aug. 2015.
doi:10.1109/tap.2015.2436410 Google Scholar

22. Lee, Hyoung-In, "Near-field behaviors of internal energy flows of free-space electromagnetic waves induced by electric point dipoles," Optics, Vol. 3, No. 3, 313-337, Sep. 2022.
doi:10.3390/opt3030029 Google Scholar

23. Braver, I. M., P. Sh. Fridberg, Kh. L. Garb, and I. M. Yakover, "Electromagnetic field near the common edge of a perfectly conducting wedge and a resistive half-plane," ArXiv Preprint ArXiv:2408.13916, 2024.
doi:10.48550/arXiv.2408.13916 Google Scholar

24. Valagiannopoulos, Constantine A., "On smoothening the singular field developed in the vicinity of metallic edges," International Journal of Applied Electromagnetics and Mechanics, Vol. 31, No. 2, 67-77, Oct. 2009.
doi:10.3233/jae-2009-1048 Google Scholar

25. Einstein, Albert, "Does the inertia of a body depend upon its energy-content," Annalen Der Physik, Vol. 18, No. 13, 639-641, 1905. Google Scholar

26. Tolman, R. C., The Theory of the Relativity of Motion, University of California Press, Berkelye, CA, 1917.

27. Rindler, Wolfgang, Relativity: Special, General, and Cosmological, Oxford University Press, 2006.

28. Stoev, Iliya D., Benjamin Seelbinder, Elena Erben, Nicola Maghelli, and Moritz Kreysing, "Highly sensitive force measurements in an optically generated, harmonic hydrodynamic trap," eLight, Vol. 1, No. 1, 7, Dec. 2021.
doi:10.1186/s43593-021-00007-7 Google Scholar

Dr. Roberto Bernardo Benedicto Ovando