Forces on permeable conductors in magnetic fields

Abstract

It is often implied that the force density formula dF/dV=J×B is all that is required to calculate the force that would be experienced by any stationary current-carrying medium in a region of space containing a magnetic field. However, representations of this formula are not all compatible, and the methods of applying such formulas when the conductor or surrounding medium have permeabilities different from vacuum are not widely known. The simplest case that one might consider is that of a current-carrying wire in an otherwise uniform field. It appears that the experimental measurements corresponding to such a situation have not been carried out for permeable media, and these results are reported here. The permeability and current can cause substantial changes in the field distribution from its background form, but the total force per unit length on the wire remains compatible with the formula I×B0, with I being the conduction current and B0 being the flux density that was present before the permeable current-carrying wire was introduced.