Equilibrium of a magnet floating above a superconducting disk

A superconducting body will repel a nearby magnet. The repulsion is due to the perfect diamagnetism resulting from the Meissner effect. A small magnet will float above a superconducting disk at an equilibrium position over the disk center, stable against lateral displacements. It is not intuitively obvious why the potential energy of the magnet over a flat disk should have a minimum at the center, rather than a maximum. We have measured the properties of the attractive potential well of a YBa2Cu3O7 disk by two experiments. In the first, we use a low-frequency magnetic field, 0--100 Hz, to excite oscillations of a small, freely levitating bar magnet about its equilibrium position. We find sharp resonances, corresponding to longitudinal, transverse, and torsional modes of oscillation. The frequencies of these resonances define the properties near the bottom of the potential well. In the second experiment, we attach the magnet to a vertical glass fiber of known stiffness. The magnet is suspended horizontally a small known distance, z, above the superconducting disk. By moving the magnet from the center of the disk to the edge and measuring the bending of the support fiber as a function of position we determine the shape of the potential curve for large displacements and the total energy needed to escape from the well