  The interaction between a straight vortex line in a superconducting film and
a soft magnetic nanodisk in the magnetic vortex state in the presence of a
magnetic field applied parallel to the film surfaces is studied theoretically.
The superconductor is described by London theory and the nanodisk by the
Landau-Lifshitz continuum theory of magnetism, using the approximation known as
the rigid vortex model. Pinning of the vortex line by the nanodisk is found to
result, predominantly, from the interaction between the vortex line and the
changes in the nanodisk magnetization induced by the magnetic field of the
vortex line and applied field. In the context of the rigid vortex model, these
changes result from the displacement of the magnetic vortex. This displacement
is calculated analytically by minimizing the energy, and the pinning potential
is obtained. The applied field can tune the pinning potential by controlling
the displacement of the magnetic vortex. The nanodisk magnetization curve is
predicted to change in the presence of the vortex line
