Dipole in a magnetic field, work, and quantum spin
Abstract
The behavior of an atom in a nonuniform magnetic field is analyzed, as well as the motion of a classical magnetic dipole (a spinning charged ball) and a rotating charged ring. For the atom it is shown that, while the magnetic field does no work on the electronorbital contribution to the magnetic moment (the source of translational kinetic energy being the internal energy of the atom), whether or not it does work on the electronspin contribution to the magnetic moment depends on whether the electron has an intrinsic rotational kinetic energy associated with its spin. A rotational kinetic energy for the electron is shown to be consistent with the Dirac equation. If the electron does have a rotational kinetic energy, the acceleration of a silver atom in a SternGerlach experiment or the emission of a photon from an electron spin flip can be explained without requiring the magnetic field to do work. For a constant magnetic field gradient along the z axis, it is found that the classical objects oscillate in simple harmonic motion along the z axis, the total kinetic energy—translational plus rotational—being a constant of the motion. For the charged ball, the change in rotational kinetic energy is associated only with a change in the precession frequency, the rotation rate about the figure axis remaining constant.
 Publication:

Physical Review E
 Pub Date:
 March 2008
 DOI:
 10.1103/PhysRevE.77.036609
 Bibcode:
 2008PhRvE..77c6609D
 Keywords:

 45.20.dg;
 45.40.f;
 03.50.De;
 03.65.w;
 Mechanical energy work and power;
 Dynamics and kinematics of rigid bodies;
 Classical electromagnetism Maxwell equations;
 Quantum mechanics