Migration of a solid conducting sphere immersed in a liquid metal near a plane conducting solid wall under the action of uniform ambient electric and magnetic fields

This work examines the migration of a solid conducting sphere freely immersed in a liquid metal near a plane and perfectly conducting solid wall under the action of a uniform electric field E normal to the wall and of an arbitrary magnetic field B. The wall-sphere interactions are investigated by resorting to bipolar coordinates and both the net magnetohydrodynamic force and the torque, acting on a motionless sphere, and the rigid-body motion of a freely-suspended sphere are determined. Those interactions are found to be significant only when the sphere lies close to the wall and to dramatically depend on the orientation of the magnetic field.