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The author presents a contribution to the open boundary axisymmetric electromagnetic field problem. A hybrid method is developed that combines the finite element method (FEM) inside an inner region with a special boundary element method (BEM) that is able to treat the field in the open homogeneous outer region. Both regions are separated by a spherical fictitious surface. The FEM, applied for the field description in the inner region, is able to take into account complex shaped devices in the presence of heterogeneous, anisotropic or even nonlinear media. The new BEM is based on an analytical treatment in spherical coordinates, consisting in a series development, which contains the pertinent Legendre functions. The static magnetic field is treated, in terms of a current flowing through a main coil in the air. Results are compared with those obtained either from experiments or by using other numerical methods. The magnetic field lines, for equal increments of the magnetic flux, are presented for both the inner and outer regions.