The paper presents some improvements to the finite element computation of static magnetic fields in three dimensions using a reduced magnetic scalar potential. New methods are described for obtaining an edge element representation of the rotational part of the magnetic field from a given source current distribution. In the case when the current distribution is not known in advance, a boundary value problem is set up in terms of a current vector potential. An edge element representation of the solution can be directly used in the subsequent magnetostatic calculation. The magnetic field in a D.C. arc furnace is calculated by first determining the current distribution in terms of a current vector potential. A three dimensional problem involving a permanent magnet as well as a coil is solved and the magnetic field in some points is compared with measurement results.