Thickness dependence of magnetic force acting on a magnetic dipole over a type-II superconducting thin film

The thickness dependence of the magnetic force acting on a point magnetic dipole over a superconducting thin film in the mixed state with a single vortex line is calculated by London theory. The magnetic force is decomposed into two parts, vertical and lateral components. Both vertical and lateral force components approach to the saturated value with increasing thickness when the thickness is much larger than the London penetration depth. A single vortex created in the thin film by the field of the magnetic dipole is also considered. The thickness dependence of the critical position of the point dipole for creating the first vortex line in the thin film is exploited and derived.