Magnetic drag in the quasi-static limit: A computational method

Abstract

The method of successive approximations is applied to Maxwell’s equations to calculate the magnetic drag on a conducting disk rotating under the influence of a localized nonuniform magnetic field. An expression for the damping torque produced by the magnetic field is obtained in the low-velocity (quasi-static) limit of the disk’s motion: The damping force, in the case of rectilinear motion, is also calculated. When the theoretical expression for the damping torque is specialized to the case of a uniform magnetic field, the result is found to be identical with that of an existing textbook treatment. In the Appendix, a simplified treatment of the magnetic drag problem suitable for an introductory-level laboratory class is given. This treatment yields a final expression for the damping torque which is identical in form to the rigorous result except for a scaling factor.