When a group of spins is placed in a magnetic field, each spin aligns in one of the two possible orientations. The relative numbers of spins with different alignments will be given by the Boltzmann distribution.
Definition: if a system of particles, which are able to exchange energy in collisions is in thermal equilibrium, then the relative number (population) of particles, N1 and N2, in two particular energy levels with corresponding energies, E1 and E2, is given by N1/N2 = exp [-(E1 - E2)/kT ] where k is the Boltzmann constant and T is the absolute temperature. For example, in NMR of protons at room temperature in a magnetic field of 0.25 tesla, the difference in relative numbers of spins aligned with the magnetic field and against the field is about one part in a million; the small excess of nuclei in the lower energy state is the basis of the net magnetization and the resonance phenomenon.

(H) The region surrounding a magnet (or current carrying conductor) is equipped with certain properties like that a small magnet in such a region experiences a torque that tends to align it in a given direction. Magnetic field is a vector quantity; the direction of the field is defined as the direction that the north pole of the small magnet points when in equilibrium.

The numbers of nuclei or electrons in different energy levels. At thermal equilibrium, the relative populations of the energy levels will be given by the Boltzmann distribution.

See also Boltzmann Distribution.