Geodesic
Examples of the solution of the electrostatic problem about a~conductive ellipse in applied electric fields
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 4 (2011) no. 1, pp. 85-101

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A method of the general problem of electrostatics solution for conductive ellipse in applied electric fields is obtained in complex form in terms of characteristic multipole. Particular examples are considered. The expansion of the applied electric fields potentials in terms of Chebyshev polynomials is proved.
Keywords: characteristic multipole, conductive ellipse, complex potential, induced charge, surface charge density, proper electrostatic energy, interaction electrostatic energy, electrostatic, Chebyshev polynomials. 
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     title = {Examples of the solution of the electrostatic problem about a~conductive ellipse in applied electric fields},
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Vladimir P. Kazantsev; Evgeny N. Shlyahtich. Examples of the solution of the electrostatic problem about a~conductive ellipse in applied electric fields. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 4 (2011) no. 1, pp. 85-101. http://geodesic.mathdoc.fr/item/JSFU_2011_4_1_a9/