Physics of Magnetism

78 CHAPTER 8. SOME BASIC CONCEPTS AND UNITS

We will now turn to the magnetic susceptibility, defined as with H in

In accordance with the definition of M as expressed in Eq. (8.12), we may define the

M and H

in which

dimension

volume susceptibility which is a dimensionless quantity since are both expressed

Based on Eq. (8.13), we can define the mass susceptibility

has the Division of the mass susceptibility

by the molar mass leads to the molar susceptibility withunit

It follows from the results discussed in the preceding chapters that if a material is

placed in an external magnetic induction, different types of magnetic behavior can be

observed, comprising diamagnetism, paramagnetism, or ferromagnetism. It will be clear

that in diamagnetic materials, the internal magnetic induction, is somewhat smaller

than the external magnetic induction, By contrast, in a paramagnetic material, the

internal magnetic induction is somewhat larger than the external magnetic induction. In a

ferromagnetic material, the internal magnetic induction is much larger than the external

magnetic induction. One may also say that the magnetic induction lines are diluted in

diamagnetic materials, concentrated in paramagnetic materials, and strongly concentrated

in ferromagnetic materials.

In diamagnetic and paramagnetic materials, small applied fields give rise to an internal

magnetic induction that is directly proportional to the applied field strength

In order to find a relation between and

magnetic induction, or an external magnetic field

we consider a material placed in an external

The internal magnetic induction,

can then be written as

provided demagnetization effects are neglected and the internal magnetic field is

approximated by the external magnetic field For diamagnetic or paramagnetic materials,

this approximation is justified and, after combining Eqs. (8.17) and (8.18), one finds

or

where is the (dimensionless) volume susceptibility. For ferromagnetic materials, it is
not justified to approximate by the applied field H in Eq. (8.18). In ferromagnetic
materials, strong demagnetizing fields are present below the Curie temperature with field
strengths that are commonly much larger than the applied fields. Instead of Eq. (8.18), we
therefore write

where is the demagnetizing field, and where we have assumed zero external field. The
existence of a demagnetizing field can best be understood by considering a bar magnet for
which the magnetic induction B and the magnetic field inside and outside the magnet are as

the bar magnet are the same, which is plausible since in free space we have

shown in Fig. 8.1. Inspection of this figure shows that the field lines and flux lines outside