(a) Show that the energy of a magnetic dipole in a magnetic field B is given by U = ?? m ?? 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 θ1 and θ2 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.]

Transcribed Image Text:

U но I 4 r r m₂, 0₂ [m₁ m₂-3(m F) (m₂. f)].