Magnetic Force on a Permeable Wire

1 Problem What is the force per unit length on a wire of radius a and (relative) permeability μ′ when it carries uniform current density J = I ẑ/πa and is placed along the z axis in a magnetic field whose form is Bi = B0 x̂+B1[(x/a) x̂− (y/a) ŷ] before the wire is placed in that field? The medium surrounding the wire is a nonconducting liquid with relative permeability μ = 1. The form of the initial magnetic field has been chosen so that there will be both a J×B force associated with the uniform field B0 = B0 x̂, as well as a force due to the interaction of the induced magnetization with the nonuniform field B1 = B1[(x/a) x̂ − (y/a) ŷ].