Geodesic
Exact solutions for equilibrium configurations of the~surface of a~conducting fluid in a~nonuniform magnetic field
Teoretičeskaâ i matematičeskaâ fizika, Tome 188 (2016) no. 3, pp. 497-504

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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.
Mots-clés : equilibrium configuration, exact solution, surface tension
Keywords: free surface, conducting fluid, nonuniform magnetic field, conformal map method. 
@article{TMF_2016_188_3_a9,
     author = {N. M. Zubarev and O. V. Zubareva},
     title = {Exact solutions for equilibrium configurations of the~surface of a~conducting fluid in a~nonuniform magnetic field},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {497--504},
     publisher = {mathdoc},
     volume = {188},
     number = {3},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2016_188_3_a9/}
}
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N. M. Zubarev; O. V. Zubareva. Exact solutions for equilibrium configurations of the~surface of a~conducting fluid in a~nonuniform magnetic field. Teoretičeskaâ i matematičeskaâ fizika, Tome 188 (2016) no. 3, pp. 497-504. http://geodesic.mathdoc.fr/item/TMF_2016_188_3_a9/