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Electrostatic image theory for layered dielectric sphere

Electrostatic image theory for layered dielectric sphere

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Static image theory for a homogeneous dielectric sphere, recently formulated by one of the authors, is generalised to the problem of a multilayer dielectric sphere in terms of a line-image charge. The imageline source is seen in this case to be in relation to the so-called static reflection coefficient that could be labelled as a finite Mellin transformation. This transformation is discussed and a Table of corresponding transforming functions is given. The result can be applied in a more complete quasistatic analysis of interactions of layered dielectric spherical particles in an artificial dielectric media. More closely, a two-layer sphere is considered with special cases of a thin layer, and that of a low contrast between the layers. Numerical results are calculated for the radiowave propagation problem of attenuation due to melting hail particles, assumed to be composed of a spherical ice core with a spherical water shell.

References

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      • I.V. Lindell . Electrostatic image theory for the dielectric sphere. Radio Sci.
    2. 2)
      • Lindell, I.V., Lehtola, E.A.: `Magnetostatic image theory for the permeable sphere', 82, Helsinki University of Technology Electromagnetics Laboratory Report, January 1991.
    3. 3)
      • A.H. Sihvola , I.V. Lindell . Transmission line analogy for calculating the effective permittivity of mixtures with spherical multilayer scatterers. J. Electromagn. Waves Appl , 8 , 741 - 756
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      • J.A. Stratton . (1941) , Electromagnetic theory.
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      • R.N. Bracewell . (1986) , The Fourier transform and its applications.
    6. 6)
      • S.M. Selby . (1969) Standard Mathematical Tables, The Chemical Rubber Company.
    7. 7)
      • Sten, J.C.-E., Lindell, I.V.: `Electrostatic image theory for the dielectric sphere with an internal source', 88, Helsinki University of Technology Electromagnetics Laboratory Report, March 1991.
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