(680) |

where the integral is over the volume of the atom. If there are such atoms or molecules per unit volume then the magnetization, , (i.e., the magnetic dipole moment per unit volume) is given by . More generally,

(681) |

where is the average magnetic dipole moment of the th type of molecule in the vicinity of point , and is the average number of such molecules per unit volume at .

Consider a general medium that is made up of molecules that are polarizable, and possess a net magnetic moment. It is easily demonstrated that any circulation in the magnetization field gives rise to an effective current density in the medium. In fact,

(682) |

This current density is called the

(683) |

Thus, the total current density, , in the medium is given by

(684) |

It must be emphasized that all three terms on the right-hand side of the previous equation represent real physical currents, although only the first term is due to the motion of charges over more than atomic dimensions.

The fourth Maxwell equation, (4), takes the form

(685) |

which can also be written

(686) |

where use has been made of the definition . The previous expression can be rearranged to give

where

is termed the

(689) |

In other words, the line integral of around some closed loop is equal to the flux of true current through any surface attached to that loop. Unlike the magnetic field (which specifies the force acting on a charge moving with velocity ), or the magnetization (which specifies the magnetic dipole moment per unit volume), the magnetic intensity has no clear physical meaning. The only reason for introducing it is that it enables us to calculate magnetic fields in the presence of magnetic materials without first having to know the distribution of magnetization currents. However, this is only possible if we possess a constitutive relation connecting and .