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Problem 3) Consider a sphere of radius a made of a hard-ferromagnetic material with a uniform magnetization M and moment of inertia I. a) Calculate the magnetic field produced by the sphere inside, ra, and outside, ra, (take M in the --direction). Sketch the magnetic field produced by the sphere. How does the field fall off with radius? b) The sphere is placed in an initially uniform magnetic field Bo. What is the net force acting on the sphere? c) Two identical spheres, each with uniform magnetization, M, are places a distance R apart. There is NO external field in this part of the problem. The spheres are free to rotate but are prevented from having any translational motion. Due to dissipation in the system the spheres eventually become stationary. What is the final relative orientation of the magnetic moments