Geoscience Reference
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Fig. 1.7
A sketch of dipole
magnetic field of the Earth
shifted with respect to the Earth center and the dipole vector makes an angle about
11:5
ı
with respect to the Earth spin. In addition, the south magnetic pole is situated
in the northern hemisphere. The Earth's dipole magnetic field,
B
0
, is given by
3.
M
e
r
/
r
r
2
M
e
;
0
4r
3
B
0
D
(1.32)
where r is the distance from the dipole/Earth center. The reference frame used in
this study assumes that the
z
axis is positive parallel to the Earth's magnetic moment
M
and the origin of the coordinate system is in the Earth center. Using the spherical
coordinates r, , and , the geomagnetic field components in Eq. (
1.32
) can be
written as
2
0
M
e
cos
4r
3
0
M
e
sin
4r
3
B
r
D
;B
D
:
(1.33)
The component B
'
D
0 because the vector
B
0
lies in a meridional plane.
As illustrated in Fig.
1.7
, the field lines in the dipole approximation would extend
in loops of ever increasing dimension while the magnitude of the magnetic field
decreases with distance as r
3
. The mean value of the magnetic induction on the
ground surface is about 5
10
5
T, while at the aclinic line .
D
=2/ the Earth
field is 3
10
5
T.
If the polar angle is expressed through the magnetic latitude (northern
hemisphere) via
D
=2, then one should substitute cos
D
sin and
sin
D
cos in Eq. (
1.33
). Applying the modified spherical coordinate system, the
equation for the magnetic field lines can be written as
r ./
D
R
e
L cos
2
;
(1.34)
where R
e
6;371 km is the mean Earth radius, L is the so-called McIllwain
parameter defined as the radius of the equatorial crossing point of the field line.
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