Electromagnetic field of the magnetic dipole in a uniform conducting medium

ELECTROMAGNETIC FIELD OF THE MAGNETIC DIPOLE IN A UNIFORM CONDUCTING MEDIUM 

Simplicity of this model allows us to investigate not only frequency responses of the magnetic field, measured by a receiver, but also a distribution of currents in a conducting medium. Such will help us to understand deeper physical principles of the induction logging as well as some approximate methods of calculation of fields which are widely used for interpretation. 

In most cases dimensions of the transmitter coil are significantly smaller than a diameter of a borehole and distances to interfaces between layers. For this reason one can replace a coil with an alternating current by the magnetic dipole with the moment  

As was shown in the previous chapter the quasistationary electromagnetic field is described by equations  

Substituting expressions 2.6 and 2.7 into the first Maxwell equation, 2.2, we obtain  

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