Geology Reference
In-Depth Information
Fig. 3.10
The Langevin
function
and a magnitude approximately proportional to
the magnitude of this field. However, the mag-
netization current
j
m
generates itself a magnetic
field,
0
M
, which contributes with
B
ext
to form
the
total field
B
. Therefore, Maxwell's Eq. (
3.27
)
can be rewritten to show explicitly the contri-
bution of both the macroscopic and microscopic
currents:
M
D
¦H
(3.61)
Therefore, the total magnetic field
B
assumes
the following simple expression:
B
D
B
ext
C
0
M
D
0
.H
C
M/
D
0
.1
C
¦
/ H
H
(3.62)
The quantity is called
absolute magnetic
permeability
. For some substances the law (
3.62
),
which establishes a simple relation of proportion-
ality between magnetic field intensity and total
field, is not valid. In this case, a more complex
tensor expression describes the relation between
the two fields and we say that the material has
magnetic anisotropy
. For this class of substances,
B
and
H
are
not
parallel, and a field applied in
the
x
-direction determines an induced magneti-
zation also in the
y
and
z
directions. Therefore,
in general the magnetic permeability (and the
susceptibility) is described by a 3
3tensor.The
magnetic susceptibility of paramagnetic materi-
als is on average from 50 to 150 times greater,
in absolute value, than the susceptibility of dia-
magnetic materials. However, for both classes of
substances the removal of the external field deter-
mines the disappearance of the induced magne-
tization. In the next section, we shall consider a
third class of materials, the ferromagnetic solids,
which retain some magnetization even in absence
of external magnetic fields.
r
B
D
0
.j
Cr
M/
(3.57)
where
j
represents the macroscopic currents. This
equation implies that:
r
.B
0
M/
D
0
j
(3.58)
Let us introduce now a new vector field, which
is the
magnetic field intensity
:
1
0
.B
0
M/
D
B
0
M
H
(3.59)
Note that
H
has the same units of
M
, namely
A/m.Usingthisfieldinthe(
3.58
) we obtain
the
following
simple
form
for
the
Maxwell
Eq. (
3.27
):
r
H
D
j
(3.60)
Now, considering that the field
H
is a way to
represent the
external
field, and the correspond-
ing macroscopic currents, we can write:
