Geomagnetic Perturbations (GMPs) - Ultra and Extremely Low Frequency Electromagnetic Fields - page 272

Fig. 7.2 The current
configuration caused by a
magnetic dipole M .The
closed extrinsic current I e
generates the poloidal
magnetic field B shown with
dotted blue lines

M

I e

B

The quasi-steady electric field of the current element in a homogeneous conduct-
ing medium is given by

1
4 r

d r
r 3 ;

E D (7.2)

where is the medium conductivity and r is the distance from the dipole. The
quasi-steady magnetic field of the current element has only an azimuthal component
given by

0 d sin
4r 2

B ' D ; (7.3)

where is the polar angle shown in Fig. 7.1 .
The electromagnetic field of the closed extrinsic current has another pattern
shown in Fig. 7.2 . Far away from the source the field is described by the vector
of magnetic moment given by (e.g., see Landau and Lifshits 1982 ; Jackson 2001 )

Z

1
2

. r j e /dV 0 ;

M D (7.4)

V

where V denotes the space occupied by the currents. The closed extrinsic current
j e generates the poloidal magnetic field B shown with dotted blue lines. Far away
from the source the quasi-steady magnetic field of the magnetic dipole M in a
homogeneous conducting medium is given by

0
4 r

M r
r 3 :

B D (7.5)

Certainly the presence of the boundary between the conducting earth and the
atmosphere can distort the simple symmetrical pictures given by above equations.
Sometimes a simple solution of the boundary problem can be found by using the
mirror images method. To illustrate this, in Fig. 7.3 we plot the current element d