REVIEW
Magnetic polarization effects are similar to electric polarization effects. Just as electric dipole moments control the behavior of dielectric materials, magnetic dipole moments control the behavior of magnetic materials: An applied field causes the dipole moments to (partially) align, and the material is said to be polarized. This polarization produces a new field that adds to the applied field. However, there are important differences. We will emphasize two of them:
1) While dielectric materials reduce an applied electric field, typical magnetic materials enhance an applied magnetic field. These materials are said to be paramagnetic. Aluminum and sodium are paramagnetic at room temperatures, as is iron oxide. Iron oxide will be our representative paramagnet.
In addition, materials like iron, cobalt and nickel can retain their polarization after the applied magnetic field is turned off. These materials are said to be ferromagnetic. Ferromagnetic materials generally enhance an applied magnetic field, but their ability to hold a "permanent" polarization complicates the story. It is useful to think of ferromagnetism as a limiting case of paramagnetism, in which the substance is "polarized by its own field." In this picture, all paramagnets must become ferromagnets at low enough temperatures; a conjecture which remains to be demonstrated.
2) No magnetic charge has ever been isolated. Thus, while electric dipole moments are caused by a pair of electric charges with opposite sign, this does not seem to be the mechanism for creating magnetic dipole moments. For all cases in which the origin of a magnetic dipole moment is understood classically, the moment is caused by a circulating current. (This omits intrinsic magnetic moments such as that possessed by the electron, which is apparently a point object.)
The most important similarity between dielectric and paramagnetic phenomena is the relation between the applied field and the resulting polarization (measured by the dipole moment per unit volume). For isotropic dielectric materials , we described this relation with the equation:
where
is the polarizability and 
is the net electric field which results from the vector sum of the applied electric field and the electric field due to polarization. It is the field that exists after the dielectric material has been introduced into the field region.
For paramagnetic materials, we will represent the dipole moment per unit volume by
We will describe the relation of polarization to applied magnetic field in a slightly different way. For isotropic magnetic materials,
where
is the magnetic polarizability
Magnetic Field and Magnetic Moment
The magnetic field,
is a fundamental physical quantity. 
is the field which produces forces and torques on magnetic objects. Thus, is as basic to our understanding as the electric field, . We will be interested in two effects caused by :
1)
can force a moving charge to change the direction of its velocity. This acceleration is attributed to a magnetic force. The force vector on a moving charge of magnitude q is
where
is the particle velocity.
This force is called the Lorentz force. Because charge, velocity and force can all be measured, we can use the Lorentz force on a known charge to measure magnetic field. When measured this way, the unit of magnetic field is given the name Tesla. From the Lorentz force equation we surmise that the Tesla must be
2)
can cause a piece of magnetic material to rotate. An object which possesses a magnetic dipole moment (such as a compass needle) rotates in response to a magnetic field. We ascribe this effect to a magnetic torque. For a given field, the strength of the magnetic torque on an object is taken as a measure of the magnetic moment of the object, which is given the symbol
.
The torque vector is given by
.
(Compare this to the expression for torque on an electric dipole moment,
Thus defined, the magnetic dipole tends to align parallel to the applied magnetic field (just as the electric dipole field aligns with an applied electric field). From this result, we surmise that the units of magnetic moment must be
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