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Teoreticheskaya i Matematicheskaya Fizika, 2016, Volume 188, Number 3, Pages 497–504
DOI: https://doi.org/10.4213/tmf9045 (Mi tmf9045) 		 
Exact solutions for equilibrium configurations of the surface of a conducting fluid in a nonuniform magnetic field

N. M. Zubarevab, O. V. Zubarevab

a Lebedev Physical Institute, Russian Academy of Sciences, Moscow, Russia
b Institute of Electrophysics, Ural Branch, Russian Academy of Sciences, Ekaterinburg, Russia
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DOI: https://doi.org/10.4213/tmf9045
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.
Funding agency Grant number
Russian Foundation for Basic Research 14-08-00235
16-08-00228
Ural Branch of the Russian Academy of Sciences 15-8-2-8
This research was performed in the framework of a Government Program (Project No. 0389-2014-0006) and supported by the Russian Foundation for Basic Research (Grant Nos. 14-08-00235 and 16-08-00228) and the Presidium of the Ural Branch of the Russian Academy of Sciences (Project No. 15-8-2-8).
English version:
Theoretical and Mathematical Physics, 2016, Volume 188, Issue 3, Pages 1394–1400
DOI: https://doi.org/10.1134/S0040577916090105
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: N. M. Zubarev, O. V. Zubareva, “Exact solutions for equilibrium configurations of the surface of a conducting fluid in a nonuniform magnetic field”, TMF, 188:3 (2016), 497–504; Theoret. and Math. Phys., 188:3 (2016), 1394–1400
Citation in format AMSBIB
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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