Abstract
We consider a model system of a permanent magnet above a semi-infinite superconductor, introduce a modified critical-state model, and carry out derivations of the levitation force acting on the magnet. A key feature of the modification allows the current density to be less than the critical value. Theoretical results show an exponential relationship between the force acting on the magnet and the distance between the magnet and the superconductor. Analytical expressions are developed for permanent magnets in the form of a point dipole, a tip of a magnetic force microscope, and a cylindrical magnet. In the latter case, the exponential relationship has been observed in numerous experiments but without previous interpretation.
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