A magnetospheric magnetic field that has a topological structure with one pair of neutral points and one segmental neutral line is studied. Such a magnetic field forms when the interplanetary field is southward. There is a surface current on an open-ended complete flux surface in this magnetospheric magnetic field. This current sheet on which the induced Chapman-Ferraro current flows is the outer separatrix, which separates field lines attached to the Earth and field lines detached from the Earth. In addition, there is an inner separatrix, which separates closed and open field lines. The two neutral points are at the north and south apices of the common wall shared by the two separatrices, on which the surface current is intense. The surface current is weak or even insignificant on other parts of the outer separatrix. The neutral line is on the equatorial plane with two end points at the east and west apices of the common wall shared by the two separatrices. It is a separator at which closed, open, and detached field lines meet. The magnetic topology indicates that field line reconnection, which can take place only at a separator, must occur away from the subsolar part of the dayside magnetopause in order for an open magnetosphere to remain in a quasi-steady state.¿ 1997 American Geophysical Union