Exact solutions for equilibrium configurations of the surface of a conducting fluid in a nonuniform magnetic field

N. M. Zubarev^ab, O. V. Zubareva<sup>b

a</sup> Lebedev Physical Institute, Russian Academy of Sciences, Moscow, Russia
^b Institute of Electrophysics, Ural Branch, Russian Academy of Sciences, Ekaterinburg, Russia

Abstract: We study the two-dimensional magnetic shaping problem for the situation where the free surface of a perfectly conducting fluid is deformed by the magnetic field of a system of linear current-carrying conductors. Equilibrium is achieved due to the balance of capillary and magnetic pressures. We obtain exact solutions of the problem using conformal map techniques. These solutions describe a system of two-dimensional dimples that appear on the initially flat surface of a liquid conductor under the action of a nonuniform magnetic field. We consider the case of two symmetrically located dimples in detail.

Keywords: equilibrium configuration, exact solution, free surface, conducting fluid, surface tension, nonuniform magnetic field, conformal map method.

DOI: 10.4213/tmf9045

 English version: Theoretical and Mathematical Physics, 2016, 188:3, 1394–1400

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