(a) Show that the energy of a magnetic dipole in a magnetic field B is given by U = â m â B. (6. 34) [Assume that the magnitude of the dipole moment is fixed, and all you have to do is move it into place and rotate it into its final orientation.]

Compare Eq. 4.7.

(c) Express your answer to (b) in terms of the angles Î¸1 and Î¸2 in Fig. 6.30, and use the result to find the stable configuration two dipoles Would adopt if held a fixed distance apart, but left free to rotate.

(d) Suppose you had a large collection of compass needles, mounted on pins at regular interval, along a straight line. How would they point (assuming the earth’s magnetic field can bc neglected)? [A rectangular array of compass needles also aligns itself spontaneously, and thi, is sometimes used as a demonstration oi: “ferromagnetic” behavior on a large scale. It’s a bit of a fraud, however, since the mechanism here is purely classical, and much weaker than the quantum mechanical exchange forces that are actually responsible for ferromagnetis m.]