  We construct a simple model for stationary, axisymmetric black-hole
magnetospheres, in which the poloidal magnetic field is generated by a toroidal
electric current in a thin disk with the inner edge, by solving the vacuum
Maxwell equations in Schwarzschild background. In this work, to obtain a
concise analytical form of the magnetic stream function, we use the
approximation that the inner edge is far distant from the event horizon. The
global magnetospheric structure with the closed-loop and open field lines
threading the inner and outer parts of the disk is explicitly shown, claiming
that the model is useful as a starting point to study astrophysical problems
involving inward disk-driven winds to a black hole and outward ones to
infinity. The asymptotic shape of the field lines at the event horizon becomes
nearly cylindrical, while at infinity it becomes conical. The magnetic spot in
the disk connected with the black hole through the loop field lines occupies a
very narrow region with the ring area roughly equal to the horizon area. By
taking account of the existence of a uniform (external) magnetic field, we also
obtain the model for collimated open field lines. Then, it is found that the
magnetic connection between the black hole and the disk breaks down if the
uniform field is strong enough. Considering slow rotation of the magnetosphere
and angular momentum transfer by inward winds from the disk, the final
discussion is devoted to gradual disruption of the closed loops due to radial
accretion of disk plasma toward the black hole.
