We study the influence of surface tension on the shape of the conicalminiscus built up by a magnetic fluid surrounding a current-carrying wire.Minimization of the total energy of the system leads to a singular second orderboundary value problem for the function $\zeta(r)$ describing the axiallysymmetric shape of the free surface. An appropriate transformation regularizesthe problem and allows a straightforward numerical solution. We also study theeffects a superimposed second liquid, a nonlinear magnetization law of themagnetic fluid, and the influence of the diameter of the wire on the freesurface profile.
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