|
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
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.
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
Linking options:
https://www.mathnet.ru/eng/tmf9045https://doi.org/10.4213/tmf9045 https://www.mathnet.ru/eng/tmf/v188/i3/p497
|
Statistics & downloads: |
Abstract page: | 266 | Full-text PDF : | 116 | References: | 47 | First page: | 27 |
|