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Variational estimates in electrostatics. Gauss's principle and the method of equivalent charges

  • Optics And Spectroscopy
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Abstract

A variational modification of the method of equivalent charges is developed using the variational Gauss's principle. It is shown how one can use it to obtain simple analytic formulas for upper estimates of the matrices of the potential coefficients of systems of conductors. Estimates are given for systems of any number of nonintersecting spheres, parallel conductors of circular cross section above a grounded infinite plane, coaxial thin conducting circular discs, a sphere and an oblate ellipsoid of rotation. The effectiveness of the variational estimates obtained is illustrated with specific examples.

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Authors
  1. V. P. Kazantsev
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  2. E. A. Lysenko
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Additional information

Krasnoyarsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 30–36, February, 1995.

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Kazantsev, V.P., Lysenko, E.A. Variational estimates in electrostatics. Gauss's principle and the method of equivalent charges. Russ Phys J 38, 127–133 (1995). https://doi.org/10.1007/BF00560234

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  • DOI: https://doi.org/10.1007/BF00560234

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