Torque on a Spinning Hollow Sphere in a Uniform Alternating Magnetic Field

The calculation of torque acting on a spinning spherical shell in a uniform stationary magnetic field first presented by Halverson and Cohen1 is extended to include the alternating magnetic field case. The torque is found under certain conditions to be positive and will increase the sphere's angular velocity up to a stable equilibrium condition at which point the torque changes sign. Differential equations are solved in terms of the magnetic vector potential which is used to calculate the induced eddy currents and resultant magnetic field. A complete solution is given for the solid sphere while approximations are used to obtain a thin shell solution.