Revisiting the far-field model of the force and torque induced on a conductive nonmagnetic sphere by a rotating magnetic dipole

Time-varying magnetic fields generate eddy currents in an electrically conductive object, which then interact with the applied magnetic field, inducing force and torque on the object. This phenomenon has been used to perform dexterous noncontact manipulation of conductive nonmagnetic objects using multiple rotating magnetic dipole fields, utilizing an empirical model of the force-torque wrench induced by a rotating magnetic dipole field on a solid conductive sphere (which serves as an approximation for other geometries). In this study, we make two new contributions to the model. First, we gather data of the induced force-torque at a previously unconsidered configuration, which enables a complete characterization of the induced force-torque. Second, we identify a simplified model, valid at low rotation frequencies of the rotating magnetic dipole, that is substantially more intuitive, enabling new insight into how different independent parameters affect the induced force-torque. As with the prior model, our improved models are still far-field models, valid when two conditions are met: the magnetic dipole (which is assumed to be at the center of any physical field source) is at a distance from the surface of the conductive sphere that is at least as large as the sphere's diameter; and when the conductive sphere is outside of the minimum bounding sphere of the physical field source.