Potential-Well Description of Electromagnetic Levitation

Abstract

Levitational forces exerted by spatially nonuniform ac magnetic fields on nonmagnetic conducting spheres are derived as the negative gradient of a potential function. Surfaces representing this potential for a small rigid diamagnetic sphere are used to visualize the levitational properties of several typical fields established by circular coils. Topological characteristics of these surfaces indicate that dipole fields have very shallow potential wells only for vertical and near‐vertical positions of the coil axis, and are only marginally levitational. Helmholtz and mirror fields have similar shallow potential wells. Quadrupole fields, however, have deeper potential wells in the vicinity of the central nodal point for all positions of the coil axis, and are strongly levitational. Higher‐order multipole fields can have potential wells similar to those in quadrupole fields. The description is also applicable to the levitation of nonmagnetic superconducting bodies in nonuniform ac magnetic fields.