9.8
Summary

The magnetization density M represents the density of magnetic dipoles. The moment m of a single microscopic magnetic dipole was defined in Sec. 8.2. With _o m p where p is the moment of an electric dipole, the magnetic and electric dipoles play analogous roles, and so do the H and E fields. In Sec. 9.1, it was therefore natural to define the magnetization density so that it played a role analogous to the polarization density, _o M P. As a result, the magnetic charge density _m was considered to be a source of _o H. The relations of these sources to the magnetization density are the first expressions summarized in Table 9.8.1. The second set of relations are different forms of the flux continuity law, including the effect of magnetization. If the magnetization density is given, (9.2.2) and (9.2.3) are most useful. However, if M is induced by H, then it is convenient to introduce the magnetic flux density B as a variable. The correspondence between the fields due to magnetization and those due to polarization is B D.

TABLE 9.8.1 SUMMARY OF MAGNETIZATION RELATIONS AND LAWS

Magnetization Charge Density and Magnetization Density
m -oM	(9.2.4)	sm = -no(Ma - Mb)	(9.2.5)
Magnetic flux Continuity with Magnetization
oH = m	(9.2.2)	n o(Ha - Hb) = sm	(9.2.3)
B = 0	(9.2.9)	n(Ba - Bb) = 0	(9.2.10)
where
B o(H + M)	(9.2.8)
Magnetically Linear Magnetization
Constitutive law
M = mH; m / o - 1	(9.4.3)
B = H	(9.4.4)
Magnetization source distribution
m = -( o/ ) H	(9.5.21)	sm = n oHa (1 - a/ b)	(9.5.22)

The third set of relations pertains to linearly magnetizable materials. There is no magnetic analog to the unpaired electric charge density.

In this chapter, the MQS form of Ampère's law was also required to determine H.

In regions where J=0, H is indeed analogous to E in the polarized EQS systems of Chap. 6. In any case, if J is given, or if it is on perfectly conducting surfaces, its contribution to the magnetic field intensity is determined as in Chap. 8.

In Chap. 10, we introduce the additional laws required to determine J self-consistently in materials of finite conductivity. To do this, it is necessary to give careful attention to the electric field associated with MQS fields. In this chapter, we have generalized Faraday's law, (9.2.11),

so that it can be used to determine E in the presence of magnetizable materials. Chapter 10 brings this law to the fore as it plays a key role in determining the self-consistent J.