The dynamics of nuclear magnetic resonance (NMR) is primarily due to the interplay of the physical processes of precession and relaxation. The sources of relaxation were discussed in Chapter 8, but precession has been treated more or less as a given physical fact. Precession is at the heart of NMR, and in this appendix the physical origins of precession are developed in more detail for the interested reader. The physical description of NMR presented in the earlier chapters is the classical physics view, but in fact the interaction of a particle possessing spin with a magnetic field is a hallmark example of quantum physics. The reader with NMR experience from chemistry may well be wondering how this classical view of NMR relates to the more fundamental quantum viewpoint. This appendix attempts to bridge that gap by describing how precession arises from both the classical and the quantum physics viewpoints.

THE CLASSICAL PHYSICS VIEW OF NMR

The Field of a Magnetic Dipole

The physics of NMR is essentially the physics of a magnetic dipole interacting with a magnetic field. There are two basic models for a magnetic dipole that we will use: a small circular current loop and a rotating charged sphere. The dipole moment µ has both a magnitude and an associated direction and so is described as a vector. For the current loop, µ is proportional to the product of the current and the area of the loop and points in the direction perpendicular to the plane of the loop. A rotating charged sphere can be thought of as a stack of current loops, produced as the charge on the sphere is carried around by the rotation.