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Three distribution identities and Maxwell's atomic field equations including the Röntgen current

Published online by Cambridge University Press:  26 February 2010

E. A. Power
Affiliation:
University College London.
T. Thirunamachandran
Affiliation:
University College London.
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Extract

Maxwell's equations within a dielectric and/or a magnetic medium were first developed macroscopically and must be complemented by constitutive relations to obtain solutions. These relations connect D with E (and with B in optically active material) and H with B (and again with E in optically active material). The atomic and molecular theories of quantum mechanics allow a microscopic approach to derive these constitutive relations where the macroscopic electric and magnetic fields are averages of the microscopic fields e and b. In classical electromagnetic theory Lorentz [1] originally showed how to derive the Maxwell's macroscopic equations from electron theory using microscopic fields obeying the Maxwell's equations in vacuo but coupled to electronic and ionic sources. There are two distinct steps in this procedure. The first introduces microscopic polarization fields, both electric amd magnetic, p and m from which microscopic electric displacement vector field d and auxiliary magnetic field h are simply constructed. The resulting equations for the microscopic fields e, b, d, and h are called the atomic field equations. The second step is the statistical one where the macroscopic fields E, B, D, and H are defined as averages of the microscopic fields and these macroscopic fields are then shown to obey the phenomenological macroscopic Maxwell's equations. A historical appraisal may be found in the recent book by de Groot [2].

MSC classification

Type
Research Article
Copyright
Copyright © University College London 1971

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References

1Lorentz, H. A., “The fundamental equations for electromagnetic phenomena in ponderable bodies, deduced from theory of electrons ”, Proc. Roy. Acad. Amsterdam, 5 (1902), 254266.Google Scholar
2de Groot, S. R., The Maxwell Equations (North Holland, Amsterdam, 1969).Google Scholar
3Fokker, A. D., “On the contributions to the electric current from the polarization and magnetization electrons,” Phil. Mag., 39 (1920), 404415.CrossRefGoogle Scholar
4Frenkel, J., Lehrbuch der Elektrodynamik, Vol. II (Berlin 1928).Google Scholar
5Fiutak, J., “The multipole expansion in quantum theory ”, Canad. J. Phys., 41 (1963), 1220.CrossRefGoogle Scholar
6Woolley, R. G., “Molecular quantum electrodynamics ”, Proc. Roy. Soc., A321 (1971), 557572.Google Scholar
1 For a discussion of longitudinal and transverse dyadics see: Power, E. A., Introductory Quantum Electrodynamics (Longmans, London, 1964), pp. 7375.Google Scholar