The

magnetic dipole moment is now expressed as follows:

The vector potential associated with the infinitesimal (point-like)

magnetic dipole can be expressed in a simple form in spherical coordinates

The field of

magnetic dipoles is potential, its scalar potential [[phi].sub.m] is analogous to the potential of the electrostatic field [phi].

Therefore, the

magnetic dipole moment dependence on the magnetic field should be also a periodic function.

Thus, in terms of the primary field (13), in view of the unit dyadic, and taking the three projections of the

magnetic dipole in Cartesian coordinates from (2), the condition (59), the gradient operator (36), and the unit normal vector (39) in ellipsoidal coordinates, we apply orthogonality of the surface ellipsoidal harmonics [S.sup.m.sub.l]([mu], v) = [E.sup.m.sub.l]([mu]) [E.sup.m.sub.l](v) for l [greater than or equal to] 0 and m = 1,2, ..., 2l + 1.

With purpose of simulating the borehole electromagnetic method, the vertical

magnetic dipoles were set in the arbitrary point in the model.

The parameters k, s and [mu] are related to the mass quadrupole moment, the current octupole, and the

magnetic dipole, respectively.

The LLG equation describes the movement of a

magnetic dipole in the presence of a time-dependent magnetic field.

For the horizontally polarized omnidirectional radiation pattern, the

magnetic dipole is an alternative solution.

Applied to the already known solar system bodies, the methods developed by Zuluaga and his team are able to predict the so-called

magnetic dipole moment of bodies ranging from Ganymede to Jupiter to the right order of magnitude.

where [S.sub.h] = [pi][a.sup.2] is the area of the loop for the

magnetic dipole. These results lead to an equivalent model that is the combination of electric dipole [I.sub.0]h and

magnetic dipole I0Sh, exactly as assumed in previous work [1,2].

To evaluate the rotation invariance of the descriptor PZMI, we calculate the PZMI vector of the magnetic field radiated by a

magnetic dipole for several orientations.