Page 265 - Engineering Electromagnetics, 8th Edition

CHAPTER 8 Magnetic Forces, Materials, and Inductance 247

Table 8.1 Characteristics of magnetic materials
Classification Magnetic Moments B Values Comments
.
Diamagnetic m orb + m spin = 0 B int < B appl B int = B appl
.
Paramagnetic m orb + m spin = small B int > B appl B int = B appl
Ferromagnetic |m spin | |m orb | B int B appl Domains
.
Antiferromagnetic |m spin | |m orb | B int = B appl Adjacent moments oppose
Ferrimagnetic |m spin | |m orb | B int > B appl Unequal adjacent moments
oppose; low σ
Superparamagnetic |m spin | |m orb | B int > B appl Nonmagnetic matrix;
recording tapes

zero, and antiferromagnetic materials are affected only slightly by the presence of
an external magnetic field. This effect was first discovered in manganese oxide, but
several hundred antiferromagnetic materials have been identified since then. Many
oxides, sulfides, and chlorides are included, such as nickel oxide (NiO), ferrous sulfide
(FeS), and cobalt chloride (CoCl 2 ). Antiferromagnetism is only present at relatively
low temperatures, often well below room temperature. The effect is not of engineering
importance at present.
The ferrimagnetic substances also show an antiparallel alignment of adjacent
atomic moments, but the moments are not equal. A large response to an exter-
nal magnetic field therefore occurs, although not as large as that in ferromagnetic
materials. The most important group of ferrimagnetic materials are the ferrites, in
which the conductivity is low, several orders of magnitude less than that of semi-
conductors. The fact that these substances have greater resistance than the ferro-
magnetic materials results in much smaller induced currents in the material when
alternating fields are applied, as for example in transformer cores that operate at
the higher frequencies. The reduced currents (eddy currents) lead to lower ohmic
losses in the transformer core. The iron oxide magnetite (Fe 3 O 4 ), a nickel-zinc fer-
rite (Ni 1/2 Zn 1/2 Fe 2 O 4 ), and a nickel ferrite (NiFe 2 O 4 ) are examples of this class of
materials. Ferrimagnetism also disappears above the Curie temperature.
Superparamagnetic materials are composed of an assembly of ferromagnetic
particles in a nonferromagnetic matrix. Although domains exist within the individual
particles, the domain walls cannot penetrate the intervening matrix material to the
adjacent particle. An important example is the magnetic tape used in audiotape or
videotape recorders.
Table 8.1 summarizes the characteristics of the six types of magnetic materials
we have discussed.

8.6 MAGNETIZATION AND PERMEABILITY
To place our description of magnetic materials on a more quantitative basis, we will
now devote a page or so to showing how the magnetic dipoles act as a distributed
source for the magnetic field. Our result will be an equation that looks very much like
Amp`ere’s circuital law,
H · dL = I. The current, however, will be the movement of