Torque on a Superconducting Torus in a Uniform Field

The torques of superconducting lead tori immersed in various uniform magnetic fields are calculated as a function of angular position and compared to measured values. The calculations, based on ideal superconducting behavior, are found to agree with experiment for the closed torus if persistent current decrease due to critical surface fields is taken into account. The recognition of trapped flux phenomena is needed to explain measured results for the open torus when it has been cooled in a nonzero field or when a magnetic transition to superconductivity has been made. The analytic model utilizes magnetic moments for a torus in an axial and in a perpendicular field, both having been calculated rigorously elsewhere. In addition, methods of obtaining approximations to these moments are presented because of their possible application to more general toroidal bodies. The total magnetic moment (and thus the torque) for arbitrary angular position is obtained by superposition, a result not heretofore available.