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Calculation of the electrical potentials produced by the current dipole in elliptical conducting cylinder of finite length

N. O. Strelkov, M. N. Kramm
National Research University "Moscow Power Engineering Institute"

Received November 9, 2012


Abstract. The aim of this work is the realization of the analytical method of calculation of electrical potentials, produced by the current dipole in elliptical conducting cylinder of finite length. The need for such a method is associated with the calculation of the potentials on the surface of the chest in the direct problems of cardiology in the quasi-static approximation. The work deals with the analytical method for calculation of electric potential, based on the expansion of potential in double series with respect to the angular and radial variations by using the Mathieu functions. Method of calculation and normalization of Mathieu functions is proposed. The question of choosing the number of the members of the summation of double series is considered. The proposed formulas checked by comparison with the results obtained by numerical methods and other authors. The distributions of surface potentials for a circular cylinder (series with Bessel functions) and for elliptic cylinder with a small eccentricity are compared.

Keywords: distribution of the potential, conducting body, the dipole current source, the direct problem, elliptical cylinder, periodic and modified Mathieu functions.