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How multipole electric moments enter into macroscopic Maxwell equations

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Il Nuovo Cimento B (1971-1996)

Summary

This paper is concerned with the correspondence between the macroscopic electric displacementD and the analogous quantityD m of microscopic derivation. Instead of identifying these two fields one with the other, we will equate them, while the identification of the macroscopic polarization with that of microscopic derivation is retained. The result is a new field equation along with the Maxwell equations.

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References

  1. H. A. Lorentz:The Theory of Electrons and its Applications to Phenomena of Light and Radiant Heat (B. G. Teubner, Leipzig, 1909).

    Google Scholar 

  2. L. Rosenfeld:Theory of Electrons (North-Holland, Amsterdam, 1951).

    MATH  Google Scholar 

  3. G. Russakoff:Am. J. Phys.,38, 1188 (1970).

    Article  ADS  MATH  Google Scholar 

  4. J. Van Vleck:The Theory of Electric and Magnetic Susceptibilities, 4th edition (Oxford University Press, London, 1952).

    Google Scholar 

  5. J. Voisin:Physica,52, 195 (1959).

    Article  ADS  Google Scholar 

  6. F. N. H. Robinson:Macroscopic Electromagnetism (Pergamon Press, Oxford, 1973).

    Google Scholar 

  7. S. R. De Groot:Physica,31, 953 (1965).

    Article  MathSciNet  ADS  Google Scholar 

  8. P. Mazur andB. R. A. Nijboer:Physica,19, 971 (1953).

    Article  MathSciNet  ADS  Google Scholar 

  9. F. Sauter:Z. Phys.,126, 207 (1949).

    Article  ADS  MATH  Google Scholar 

  10. C. B. Kafadar andA. C. Eringen:J. Math. Phys.,11, 984 (1970).

    Google Scholar 

  11. R. Becker andF. Sauter:Electromagnetic Fields and Interactions, Vol. 1 (Blackie, London, 1964).

    Google Scholar 

  12. J. D. Jackson:Classical Electrodynamics (Wiley, New York, N.Y., 1975).

    Google Scholar 

  13. C. B. Kafadar:Int. J. Eng. Sci.,9, 831 (1971).

    Article  Google Scholar 

  14. L. Landau andE. M. Lifshitz:Electrodyamics of Continuous Media (Pergamon Press, Oxford, 1960).

    Google Scholar 

  15. C. J. Bötcher:Theory of Electric Polarization: Dielectrics in Static Fields, Vol.1 (Elsevier, Amsterdam, 1973).

    Google Scholar 

  16. L. Onsager:J. Am. Chem. Soc.,58, 1487 (1936).

    Article  Google Scholar 

  17. H. Demiray andA. C. Eringen:Lett. Appl. Eng. Sci.,1, 517 (1973).

    Google Scholar 

  18. I. Müller:Thermodynamics (Pitman, London, 1985).

    MATH  Google Scholar 

  19. C. Kittel:Introduction to Solid State Physics (Wiley, New York, N.Y., 1986).

    Google Scholar 

  20. W. P. Mason:Crystal Physics of Interaction Processes (Academic Press, New York, N.Y., 1966).

    Google Scholar 

  21. O. F. Mossotti:Mem. Mat. Fis. Soc. Ital. Sci. Modena,24, 49 (1850).

    Google Scholar 

  22. R. D. Mindlin:J. Elasticity,2, 217 (1972).

    Article  Google Scholar 

  23. R. A. Toupin:J. Rat. Mech. Anal.,5, 850 (1956).

    MathSciNet  Google Scholar 

  24. G. A. Maugin:Acta Mech.,35, 1 (1980).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  25. A. Prechtl:Int. J. Eng. Sci.,18, 665 (1980).

    Article  MATH  Google Scholar 

  26. A. Askar, P. C. Y. Lee andA. S. Cakmak:Phys. Rev. B,1, 3525 (1970).

    Article  ADS  MATH  Google Scholar 

  27. B. Collet:Elastic Dielectrics with Electric Quadrupoles. Recent Developments in the Theory and Application of Generalized and Oriented Media, Calgary, Canada, 1979, edited byP. G. Glockner, M. Epstein andD. J. Malcom (American Academy of Mechanics, Calgary, 1979), p. 205.

    Google Scholar 

  28. C. Trimarco:Int. J. Eng. Sci.,27, 1569 (1989).

    Article  MathSciNet  MATH  Google Scholar 

  29. C. Trimarco:Int. J. Solids Struct.,29, 1647 (1992).

    Article  MathSciNet  MATH  Google Scholar 

  30. C. A. Truesdell andR. A. Toupin:Encyclopedia of Physics, Vol. III/1 (Springer, Berlin, 1960).

    Google Scholar 

  31. M. Born andK. Huang:Dynamical Theory of Crystal Lattices (Clarendon Press, Oxford, 1988).

    MATH  Google Scholar 

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Work supported by GNFM of CNR and by MURST.

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Trimarco, C. How multipole electric moments enter into macroscopic Maxwell equations. Nuovo Cim B 109, 533–540 (1994). https://doi.org/10.1007/BF02728394

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  • DOI: https://doi.org/10.1007/BF02728394

PACS 03.50.De

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