Within the atoms of any piece of material, all the electrons are forever in motion, both orbital motion and spin motion. These circulating charges constitute currents, which give the atom a magnetic moment generating a magnetic field surrounding the atom. When we place the material in an external magnetic field, the atomic magnetic moments suffer readjustments, and the magnetic fields of these moments then modify the original external magnetic field. The magnitude of this modification depends on the kind of magnetic material. In paramagnetic and ferromagnetic materials, the main readjustment within the magnetic material is an alignment of the atomic magnetic moments with the external field. This enhances the magnetic field in a ferromagnetic material, this enhancement can amount to a factor of several thousand. In diamagnetic materials, the main readjustment arises from currents and magnetic moments induced in the atoms by the external magnetic field. As we will see, this reduces the magnetic field.

11.1 Magnetic Dipole in an External Field

According to the results of Section 9.6, the torque that an external magnetic field B exerts on a closed loop carrying a steady current I is

where

is the magnetic moment of the loop (see Fig. 11.1).

Equation (1) is exact for a constant magnetic field, but it also is a good approximation for a small loop in an arbitrary magnetic field. In the latter case, the magnetic field in Eq. (1) must be evaluated in the vicinity of the loop. If the loop is at or...