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Dipole moments and near field potentials

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Abstract

Expressions are derived for the moments of electric and magnetic dipoles whose far field is equivalent to the Rayleigh term in the far field of a given radiating electromagnetic field. The equivalent dipole moments are expressed as integrals over an arbitrary closed surface of the near electromagnetic fields and simplification is achieved by rewriting these expressions in terms of the static potentials from which the near fields are derived. The results are valid regardless of the complexity of the field and the medium within the integration surface as long as the exterior is homogeneous, isotropic and source-free.

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Abbreviations

B :

smooth closed bounded surface in 3-space

E, H :

radiating electric and magnetic field vectors

E 0, H 0 :

static near field limits of E and H

E i :

incident electric field vector

E t0 , H t0 :

total static field (incident plus scattered)

F, f :

arbitrary vector and scalar functions of position

k :

wave number

\(\hat n\) :

unit normal from B to exterior

p, m :

normalized electric and magnetic dipole moments

r :

position vector of field point with respect to origin in B

\(\hat r\) :

unit vector in direction of r

r :

magnitude of r

r B :

position vector of point on B

V :

volume enclosed by B

φ, ψ :

scalar potentials for E 0 and H 0 respectively

π (e), π (m) :

electric and magnetic Hertz vectors

References

  1. Van Bladel, J., Electromagnetic Fields, New York, McGraw-Hill, 1964.

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  2. Kleinman, R. E., Appl. Sci. Res. 18 (1967) 1–8.

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  3. Jones, D. S., The Theory of Electromagnetism, London, Pergamon Press, 1964.

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Authors and Affiliations

  1. Dept. of Math., University of Delaware, 19711, Newark, Del., USA

    R. E. Kleinman

Authors
  1. R. E. Kleinman
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Additional information

Research sponsored by the U.S. Air Force Office of Scientific Research under Grant No. AFOSR 69-1794.

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Kleinman, R.E. Dipole moments and near field potentials. Appl. Sci. Res. 27, 335–340 (1973). https://doi.org/10.1007/BF00382496

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  • DOI: https://doi.org/10.1007/BF00382496

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