2011-06-15
An Extension of the Kelvin Image Theory to the Conducting Heaviside Ellipsoid
By
Progress In Electromagnetics Research M, Vol. 18, 233-246, 2011
Abstract
The Kelvin image theory for a conducting sphere is extended to the case of a conducting oblate spheroid in uniform motion along its axis of revolution (a Heaviside ellipsoid) using the well-known method provided by Special Relativity. The results derived are checked in various ways.
Citation
Dragan Redžić, Mohsan S. A. Eldakli, and Milan D. Redzic, "An Extension of the Kelvin Image Theory to the Conducting Heaviside Ellipsoid," Progress In Electromagnetics Research M, Vol. 18, 233-246, 2011.
doi:10.2528/PIERM11051504
References

1. Redzic, D. V., "Image of a moving spheroidal conductor," Am. J. Phys., Vol. 60, 506-508, 1992.
doi:10.1119/1.16863        Google Scholar

2. Maxwell, J. C., A Treatise on Electricity and Magnetism, 3rd edition, Vol. 1, 93-96, 244-252, Clarendon, Oxford, 1891. Reprinted by Dover, New York, 1954.

3. Einstein, A., "Zur Elektrodynamik bewegter Korper," Ann. Phys. Lpz., Vol. 17, 891-921, 1905.
doi:10.1002/andp.19053221004        Google Scholar

4. Searle, G. F. C., "On the steady motion of an electrified ellipsoid," Philos. Mag., Vol. 44, 329-341, 1897.        Google Scholar

5. Abraham, M., "Zur Theorie der Strahlung und des Strahlungsdruckes," Ann. Phys., Lpz., Vol. 14, 236-287, 1904.
doi:10.1002/andp.19043190703        Google Scholar

6. Miller, A. I., Albert Einstein's Special Theory of Relativity: Emer-gence (1905) and Early Interpretation (1905-1911), Addison-Wesley, Reading, MA, 1981.

7. Poincare, H., "Sur la dynamique de l'electron," Rend. Circ. Mat. Palermo, Vol. 21, 129-175, 1906. Reprinted in H. Poincare, LaMecanique Nouvelle, Editions Jacques Gabay, Sceaux, 1989.        Google Scholar

8. Schwartz, H. M., "Poincare's Rendiconti paper on relativity. Part II," Am. J. Phys., Vol. 40, 862-872, 1972 Reprinted in J.-P. Hsu and Y.-Z. Zhang, Lorentz and Poincare invariance: 100 years of relativity, World Scientific, Singapore, 2001..
doi:10.1119/1.1986684        Google Scholar

9. Ciarkowski, A., "Scattering of an electromagnetic pulse by a moving wedge," IEEE Transactions on Antennas and Propagation, Vol. 57, No. 3, 688-693, 2009.
doi:10.1109/TAP.2009.2013418        Google Scholar

10. Ho, M., "Simulation of scattered EM fields from rotating cylinder using passing center swing back grids technique in two dimensions," Progress In Electromagnetics Research, Vol. 92, 79-90, 2009.
doi:10.2528/PIER09030302        Google Scholar

11. Cheng, X. X., H. S. Chen, B.-I. Wu, and J. A. Kong, "Cloak for bianisotropic and moving media," Progress In Electromagnetics Research, Vol. 89, 199-212, 2009.
doi:10.2528/PIER08120803        Google Scholar

12. Redzic, D. V., "Electromagnetostatic charges and fields in a rotating conducting sphere," Progress In Electromagnetics Research, Vol. 110, 383-401, 2010.
doi:10.2528/PIER10100504        Google Scholar

13. Thomson, W., "Extrait d'une lettre a M. Liouville," J. de Mathematiques Pures Appliquees, Vol. 10, 364, 1845.        Google Scholar

14. Thomson, W., "Extraits de deux lettres adressees a M. Liouville," J. de Mathematiques Pures Appliquees, Vol. 12, 256, 1847.        Google Scholar

15. Thomson, W., (Lord Kelvin), Reprint of Papers on Electrostatics and Magnetism, 2nd edition, Paragraphs 75-127, 208-20, Macmillan, London, 1884.

16. Stratton, J. A., Electromagnetic Theory, 201-205, McGraw-Hill, New York, 1941.

17. Jackson, J. D., Classical Electrodynamics, 3rd edition, Wiley, New York, 1999.

18. Purcell, E. M., Electricity and Magnetism, 2nd edition, McGraw-Hill, New York, 1985.

19. Rosser, W. G. V., An Introduction to the Theory of Relativity, 303-310, Butterworth, London, 1964.

20. Martinez, A. A., "Kinematic subtleties in Einstein's first derivation of the Lorentz transformations," Am. J. Phys., Vol. 72, 790-798, 2004.
doi:10.1119/1.1639011        Google Scholar

21. Jammer, M., Concepts of Mass in Classical and Modern Physics, Chapter 11, Harvard U. P., Cambridge, MA, 1961.

22. Redzic, D. V., "Image of a moving sphere and the FitzGerald-Lorentz contraction," Eur. J. Phys., Vol. 25, 123-126, 2004.        Google Scholar

23. Brown, H. R., "Physical Relativity: Space-time Structure from a Dynamical Perspective," Clarendon, Oxford, 2005.        Google Scholar

24. Redzic, D. V., Recurrent Topics in Special Relativity: Seven Essays on the Electrodynamics of Moving Bodies, authorial edition, Belgrade, 2006.

25. Torres, M., J. M. Gonzalez, A. Martin, G. Pastor, and A. Ferreiro, "On the surface charge density of a moving sphere," Am. J. Phys., Vol. 58, 73-75, 1990.
doi:10.1119/1.16323        Google Scholar

26. Redzic, D. V., "On the electromagnetic field close to the surface of a moving conductor," Am. J. Phys., Vol. 60, 275-277, 1992.
doi:10.1119/1.16910        Google Scholar

27. Einstein, A. and J. Laub, "Uber die elektromagnetischen Grundgleichungen fur bewegte Korper," Ann. Phys., Lpz., Vol. 26, 532-540, 1908.
doi:10.1002/andp.19083310806        Google Scholar

28. Einstein, A. and J. Laub, Ann. Phys., Lpz., Vol. 27, 232, 1908 (erratum)..

29. Einstein, A. and J. Laub, "Bemerkungen zu unserer Arbeit `Uber die elektromagnetischen Grundgleichungen fur bewegte Korper'," Ann. Phys., Lpz., Vol. 28, 445-447, 1909.
doi:10.1002/andp.19093330212        Google Scholar

30. Redzic, D. V., "Conductors moving in magnetic fields: Approach to equilibrium," Eur. J. Phys., Vol. 25, 623-632, 2004.        Google Scholar

31. Jefimenko, O. D., "Derivation of relativistic force transformation equations from Lorentz force law," Am. J. Phys., Vol. 64, 618-620, 1996.
doi:10.1119/1.18165        Google Scholar

32. Redzic, D. V., D. M. Davidovic and M. D. Redzic, "Derivations of relativistic force transformation equations," Journal of Electromagnetic Waves and Applications, Vol. 25, No. 8-9, 1146-1155, 2011.
doi:10.1163/156939311795762178        Google Scholar

33. Van Kampen, P., "Lorentz contraction and current-carrying wires," Eur. J. Phys., Vol. 29, 879-883, 2008.
doi:10.1088/0143-0807/29/5/002        Google Scholar

34. Redzic, D. V., "Comment on `Lorentz contraction and current-carrying wires'," Eur. J. Phys., Vol. 31, L25-L27, 2010.
doi:10.1088/0143-0807/31/1/N04        Google Scholar

35. Hernandez, A. and M. Rivas, "A relativistic problem: The charge distribution stability on a conductor," Am. J. Phys., Vol. 49, 501-503, 1981.
doi:10.1119/1.12496        Google Scholar

36. Redzic, D. V., "Various paths to Faraday's law," Eur. J. Phys., Vol. 29, 257-262, 2008.
doi:10.1088/0143-0807/29/2/008        Google Scholar

37. Lindell, I. V., G. Dassios, and K. I. Nikoskinen, "Electrostatic image theory for the conducting prolate spheroid," J. Phys. D, Vol. 34, 2302-2307, 2001.
doi:10.1088/0022-3727/34/15/309        Google Scholar

38. Lindell, I. V., "Image theory for electrostatic and magnetostatic problems involving a material sphere," Am. J. Phys., Vol. 61, 39-44, 1993.
doi:10.1119/1.17407        Google Scholar

39. Lindell, I. V. and K. I. Nikoskinen, "Electrostatic image theory for the dielectric prolate spheroid," Journal of Electromagnetic Waves and Applications, Vol. 15, No. 8, 1075-1096, 2001.
doi:10.1163/156939301X00436        Google Scholar

40. Redzic, D. V., "Comment on `Electrostatic image theory for the dielectric prolate spheroid' by I. V. Lindell and K. I. Nikoskinen," Journal of Electromagnetic Waves and Applications, Vol. 17, No. 11, 1625-1627, 2003.
doi:10.1163/156939303772681488        Google Scholar

41. Lindell, I. V. and K. I. Nikoskinen, "Electrostatic image theory for the dielectric prolate spheroid, reply to comments by D. Redzic," Journal of Electromagnetic Waves and Applications, Vol. 17, No. 11, 1629-1630, 2003.
doi:10.1163/156939303772681497        Google Scholar