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| Progress In Electromagnetics Research M | ISSN: 1937-8726 |
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AN EXTENSION OF THE KELVIN IMAGE THEORY TO THE CONDUCTING HEAVISIDE ELLIPSOIDBy D. V. Redzic, M. S. A. Eldakli, and M. D. RedzicAbstract: 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.
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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. 4. Searle, G. F. C., "On the steady motion of an electrified ellipsoid," Philos. Mag., Vol. 44, 329-341, 1897. 5. Abraham, M., "Zur Theorie der Strahlung und des Strahlungsdruckes," Ann. Phys., Lpz., Vol. 14, 236-287, 1904. 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. 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.. 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. 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. 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. 12. Redzic, D. V., "Electromagnetostatic charges and fields in a rotating conducting sphere," Progress In Electromagnetics Research, Vol. 110, 383-401, 2010. 13. Thomson, W., "Extrait d'une lettre a M. Liouville," J. de Mathematiques Pures Appliquees, Vol. 10, 364, 1845. 14. Thomson, W., "Extraits de deux lettres adressees a M. Liouville," J. de Mathematiques Pures Appliquees, Vol. 12, 256, 1847. 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. 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. 23. Brown, H. R., "Physical Relativity: Space-time Structure from a Dynamical Perspective," Clarendon, Oxford, 2005. 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. 26. Redzic, D. V., "On the electromagnetic field close to the surface of a moving conductor," Am. J. Phys., Vol. 60, 275-277, 1992. 27. Einstein, A. and J. Laub, "Uber die elektromagnetischen Grundgleichungen fur bewegte Korper," Ann. Phys., Lpz., Vol. 26, 532-540, 1908. 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. 30. Redzic, D. V., "Conductors moving in magnetic fields: Approach to equilibrium," Eur. J. Phys., Vol. 25, 623-632, 2004. 31. Jefimenko, O. D., "Derivation of relativistic force transformation equations from Lorentz force law," Am. J. Phys., Vol. 64, 618-620, 1996. 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. 33. Van Kampen, P., "Lorentz contraction and current-carrying wires," Eur. J. Phys., Vol. 29, 879-883, 2008. 34. Redzic, D. V., "Comment on `Lorentz contraction and current-carrying wires'," Eur. J. Phys., Vol. 31, L25-L27, 2010. 35. Hernandez, A. and M. Rivas, "A relativistic problem: The charge distribution stability on a conductor," Am. J. Phys., Vol. 49, 501-503, 1981. 36. Redzic, D. V., "Various paths to Faraday's law," Eur. J. Phys., Vol. 29, 257-262, 2008. 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. 38. Lindell, I. V., "Image theory for electrostatic and magnetostatic problems involving a material sphere," Am. J. Phys., Vol. 61, 39-44, 1993. 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. 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. 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. |