Environmental Engineering Reference
In-Depth Information
Fig. 3.7 a Demagnetization
eld and the material-air boundary, b a ferromagnetic sphere in a
uniform external magnetic
eld
material. Therefore, the demagnetization
eld is associated with the shape anisot-
ropy of the magnetic material.
For the case in Fig.
3.7
-left, which shows a material-air boundary, the external
magnetic
ʼ
0
H
out
) will equal the internal magnetic
fl
ux density in the air gap (B
out
=
fl
ux density:
B
out
¼ l
0
H
out
¼
B
in
¼ l
0
H
in
þ
M
ð
3
:
40
Þ
In the case of Fig.
3.7
-right, the ferromagnetic sphere is placed in a uniform
external magnetic
eld. This, because of the sphere
'
s shape, induces a uniform
magnetic
eld inside the sphere. However, in this case we will consider the entire
volume. In contrast to the case above, with Eq. (
3.39
) the magnetic
fl
ux density in
the sphere will be higher than the external magnetic
fl
ux density:
\
B
in
B
out
ð
3
:
41
Þ
Therefore:
H
out
\
H
in
þ
M
ð
3
:
42
Þ
The relationship in Eq. (
3.42
) can now be described by using of the de
nition of
the demagnetization
eld:
H
out
H
in
þ
N
dem
M
ð
3
:
43
Þ
eld and con-
sequently the magnetization are not usually uniform (although they would be in the
case of an ellipsoid). For the case of spontaneous magnetization with no external
magnetic
Equation (
3.43
) is actually an approximation, since the internal
eld, Eqs. (
3.36
) and (
3.43
) will lead to the following de
nition of the
internal magnetic
fl
ux density:
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