Magnetic dipole orientation energetics

We analyze the energies involved in quasistatically changing the orientatio n of a magnetic dipole with unperturbed magnetic moment mu in the magnetic field B of a stationary source. We define an effective potential energy V-e ff for the dipole in a stationary orientational state as that part of the H amiltonian plus the field energy that changes from one such state to anothe r. The detailed energy contributions are quite different for solenoids than for permanent magnets. For a small current-carrying coil (the dipole) in t he field of a large one, V-eff = +mu.B, the interaction field energy; for a permanent magnet dipole in the field of a coil, V-eff=0; for a permanent m agnet dipole in the field of another magnet, V-eff=-mu.B, equal to the usua l interaction Hamiltonian. The external work required to change the orienta tion quasistatically from one stationary state to another is of course inde pendent of system structure, and is equal to the change in V-eff, plus the incremental changes in battery potential energy and resistive dissipation, if any, caused by the turning process, so all energy is indeed accounted fo r in all cases. (C) 1999 American Association of Physics Teachers.