Generalized Reciprocity

Abstract

The remarkable theorem of reciprocity as described by D. I. Hoult and R. E. Richards (J. Magn. Reson.24, 71 (1976)) may be generalized to account for the near, intermediate, and radiation zone fields of a magnetic dipole. This form of reciprocity may be important when the wavelength of the NMR signal is not large compared to the distance scale of the system. In these situations the effects of interference may be significant. In addition, both the frequency dependence and distance dependence of the NMR signal amplitude are altered. In general, the distance dependence of the signal follows a weighted sum of 1/r3, 1/r2, and 1/rdependence. The frequency dependence of the signal amplitude is a function of ω, ω2, and ω3. Finally, the signal reflects the full vector field nature of the magnetic dipole. The mathematical expression of generalized reciprocity is completely equivalent to that of Hoult and Richards if the appropriate retarded potential form of the magnetic field is utilized.