In classical electromagnetistn, the simplest magnetic dipole is a circular current loop, w...

In classical electromagnetistn, the simplest magnetic dipole is a circular current loop, which behaves in a magnetic field just as an electric dipole does in an electric field. Both experience torques and thus have orientation energies, -p E and -μ. B (a) The designation "orientation energy" can be misleading. Of the four cases shown in Figure 8.4, in which would work have to be done to move the dipole horizontally without reorienting it? Briefly explain, (b) In the magnetic case, using B and μ. for the magnitudes of the field and the dipole moment, respectively, how much work would be required to move the dipole a distance dx to the left? (c) Having shown that a rate of change of the "orientation energy" can give a force, now consider equation (8-4). Assuming that B and μ are general, write — μ • B in component form. Then, noting that μ. is not a function of position, take the negative gradient, (d) Now, referring to the specific magnetic field pictured in Figure 8.3, which term of your part (c) result can be discarded immediately? (e) Assuming that μx, and μy vary periodically at a high rate due to precession about the z-axis, what else may be discarded as averaging to 0? (f) Finally, argue that what you have left reduces to equation (8-5).