a. A solid cylinder is cut from iron magnetized to saturation so that its axis coincides with the direction of magnetization. Prove that the magnetic field of this cylinder is equivalent to the field of a transverse current flowing over its surface, the linear density of which is equal to the magnetic moment of a unit volume of iron.
b. A cube was cut from a long rod magnetized to saturation along the axis so that one of the edges of the cube was directed along the direction of magnetization. How many times will the induction of the magnetic field in the center of the cube be less than the induction in the rod?
c. Determine the magnetic field induction in the center of a cylinder of length 4l and radius r. The magnetic moment of a unit volume of iron is equal to M. What is this induction equal to for r ≪ l ? for r ≫ l?
d. Solve the previous problem if a small-radius hole is drilled along the axis of the cylinder.