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We study the influence of surface tension on the shape of the conical miniscus built up by a magnetic fluid surrounding a current-carrying wire. Minimization of the total energy of the system leads to a singular second order boundary value problem for the function zeta(r) describing the axially symmetric shape of the free surface. An appropriate transformation regularizes the problem and allows a straightforward numerical solution. We also study the effects a superimposed second liquid, a nonlinear magnetization law of the magnetic fluid, and the influence of the diameter of the wire on the free surface profile.

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