  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.
