Magnetic permeability response

In this chapter we will derive an expression for the vertical component of the magnetic field on the axis of a borehole when the source of the primary field is a vertical magnetic dipole and the formation has an infinite thickness. Special attention will be paid to the analysis of frequency responses of quadrature and inphase components of the field, including their asymptotic behavior. The influence of various parameters of a geoelectric section will also be investigated. Such questions as the influence of finite dimensions of coils, displacement of the induction probe wdth respect to the borehole axis, the role of magnetic permeability and dielectric constant will be studied. 

It is appropriate to notice that eq. 7.15 can be used for calculation of radial responses of differential probes in a medium which is not uniform with respect to magnetic permeability. 

The total angular momentum is conserved as in Equation 12.41 therefore, locally, the particle currents should be deflected in a finite system. This is numerically demonstrated as the complex eigenvalue of the electronic dielectric constant l(r). The complex eigenvalues of e(r), magnetic permeability p(r), effective charge Z(r), and electric conductance o(r) mean rotational deflected response of electron toward applied electromagnetic field. ... 

Further discussion of magnetic behavior requires definition of some terms. The flux density or induction, B, in a material in a magnetic field is its response to the intensity of the magnetic field, H. The ratio of B to H is the permeability, fi ... 

P is the dielectric polarization vector (dipole moment per volume, C m m = C m ) induced by the electric field and M the magnetization vector (magnetic dipole moment per volume, A m ) induced by the magnetic field. The constants in (5) and (6) are the vacuum permittivity o = 8.85419 x 10 C m and the vacuum permeability ixq = AttX 10 V s m It is implied by (5) and (6) that the response of the medium is purely local (dipole approximation). 

The basic magnetic properties expected in soft magnets are high initial and maximum permeabilities, p-, and r,., and low coercivity, (lower than 10 A/m). In many applications, soft magnets are subjected to ac fields their frequency response and, particularly, their ac losses are therefore important. 

Susceptibilities are generally used when the response to an applied magnetic field is weak (of interest only to physicists ). Permeabilities are used when the response is large—of great interest to engineers ... 

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