Current and field penetration in a superconductor in the field of a permanent magnet

We calculate the current and field profiles in a finite cylindrical type-II superconducting sample which result from displacing it within the magnetic field created by a coaxial permanent magnet. The method of calculation is based on minimizing the magnetic energy in the superconductor, by introducing currents with a maximum density, following the critical-state model. The effects of the superconductor finite size are fully incorporated in the calculations. The levitation force of such a system is calculated from the previous results.