Conducting Axisymmetric Body
in a Coaxial Varying Magnetic Field

A. O. Savchenko^a* and O. Ya. Savchenko^b

^a Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch, Russian Academy of Sciences,
pr. Akademika Lavrent’eva 6, Novosibirsk, 630090 Russia
^b Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090 Russia
*e-mail: savch@ommfao1.sscc.ru

Received July 20, 2012; in final form, March 14, 2013

Abstract—We calculate the vector potential and magnetic field strength in an axisymmetric conductor introduced
into a preset coaxial external magnetic field varying harmonically with time. The proposed method involves the
representation of the vector potential as the sum of a converging series each term of which is a solution to the
Helmholtz equation with constant coefficient at infinity. The next terms of each series are determined from the pre-
ceding terms using the known Green function. The adequacy of the numerical results is confirmed by their com-
parison with the exact values for a sphere in a uniform magnetic field and by comparison of the numerical results
obtained using two different series for an ellipsoid in a nonuniform magnetic field.

10.1134/S1063784214010150

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