Effect of size on levitation force in a magnet/superconductor system

We consider a model system consisting of an infinitely long magnetic dipole line placed symmetrically above an infinitely long superconducting strip. Using the Meissner effect of superconductors, we derive analytical expressions of the levitation forces acting on the dipole line. At lowest-order approximation, we discuss the possible application of our model system to estimate the upper limit of the levitation forces in some magnetic bearing systems. In one example, the model correctly calculated the vertical vibration frequency of an experimental superconducting bearing.