A long, straight wire with a radius of 1.0 mm is coated with an insulating ferromagnetic material that has a thickness of 3.0 mm and a relative magnetic permeability of Km = 400. The coated wire is in air and the wire itself is nonmagnetic. The wire carries a current of 40 A.

(a) Find the magnetic field inside the wire as a function of radius r.

(b) Find the magnetic field inside the ferromagnetic material as a function of radius r.

(c) Find the magnetic field outside the ferromagnetic material as a function of r.

(d) What must the magnitudes and directions of the amperian currents be on the surfaces of the ferromagnetic material to account for the magnetic fields observed?