The problem of the static shape of the surface of a magnetic fluid drop in the vicinity of a line conductor located on the axis of an axisymmetric surface with a variable cross section is solved. It is shown that the hysteresis of the shape of the magnetic fluid is absent. The surface shape of a magnetized fluid in the field of a horizontal conductor is also investigated, taking into account the gravity force and the surface tension of the medium. It is shown that, for a fixed value of the current, there exist several simply connected solutions satisfying the wetting conditions on the walls of the vessel.
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