Summary
An explicit formula is derived expressing the low frequency expansion of the far field coefficient for any radiating electromagnetic field in terms of the low frequency expansion of the near field. It is shown that a knowledge of a given number of near field terms suffices to determine the same number of far field terms, thus disproving the previously held contention that p+1 near field terms were needed to determine p far field terms.
Similar content being viewed by others
References
Lord Rayleigh, Philos. Mag. XLIV (1897) 28.
Kleinman, R. E., Proc. IEEE 53 (1965) 848.
Stevenson, A. F., J. Appl. Phys. 24 (1953) 1134.
Kleinman, R. E., Proceedings of the Symposium on Electromagnetic Wave Theory at Delft, Sept. 1965, Pergamon Press, 97–111 (to be published).
Kleinman, R. E., Low Frequency Solution of Three-Dimensional Scattering Problems, The University of Michigan Radiation Laboratory, Report 7133-4-T (1965).
Werner, P., J. Math. Anal. Appl. 7 (1963) 348.
Stratton, J. A., Electromagnetic Theory, p. 464–467, McGraw-Hill, New York, 1941.
Jones, D. S., The Theory of Electromagnetism, p. 55, MacMillan (Pergamon Press), New York, 1964.
Author information
Authors and Affiliations
Additional information
On leave from The Radiation Laboratory, The University of Michigan, U.S.A.
Rights and permissions
About this article
Cite this article
Kleinman, R.E. Far field scattering at low frequencies. Appl. Sci. Res. 18, 1–8 (1968). https://doi.org/10.1007/BF00382328
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00382328