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moving together with instruments. The electric field in the latter reference frame
can be found from Eq. (
7.14
)
E
0
max
k
a
m
ıB
max
V
0
B
0
;
(7.26)
that is, given above parameters, we obtain that E
0
max
0.5-5 V/m.
The electric field magnitude, E
max
, in the earth-fixed reference frame cannot be
estimated from Eq. (
7.11
) because both terms on the right-hand side of Eq. (
7.11
)
are of the same order of magnitude, which means that substitution of Eq. (
7.25
)in
this equation results in the cancellation of these terms. In this notation Eq. (
7.8
)is
best suited for our purpose. It follows from this equation that k
a
E
max
!ıB
max
.
Hence
V
0
C
l
B
0
2f
m
E
max
C
l
ıB
max
:
(7.27)
Comparing the electric fields in both reference frames, we obtain
E
0
max
2f
m
C
l
E
max
1:
(7.28)
The electric field in the moving frame is thus greater than that in the earth-fixed
frame.
Now we shall consider an opposite case and derive alternative estimates of the
electromagnetic perturbations. In the low-frequency limit, i.e., f
0
C
l
=.2/,
the inequality (
7.21
) must be replaced by reverse one.
In such a case the first term on the right-hand side of Eq. (
7.12
) can be omitted
and this equation, in fact, would take the form of Eq. (
7.13
). As has already been
stated, this case corresponds to the “frozen in” magnetic field. For this frequency
band, in a similar manner, one can find the following estimation for the GMP
V
0
C
l
B
0
;
ıB
max
(7.29)
E
max
V
0
B
0
;
(7.30)
2
m
f
C
l
E
0
max
V
0
B
0
E
max
:
(7.31)
Equation (
7.31
) shows that the electric field E
max
in a reference frame fixed to
the earth is greater than that in the moving reference frame, in contrast to the
inequality (
7.28
). Moreover, as is seen from Eqs. (
7.29
)-(
7.31
), the amplitudes
of magnetic and electric perturbations are independent of the frequency. We are
reminded that all the estimations are valid only for the ULF range, i.e., for f
(5-
50) mHz or
a
10
2
-10
3
km. In practice, we encounter such frequencies and
wavelengths extremely seldom.
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