Magnetic functions permeability

The ease of time-varying charge displacement, measured as the time-dependent dielectric or magnetic permittivity (or permeability), is expressed by the dielectric function e and magnetic function /x. Both e and // depend on frequency both measure the susceptibility of a material to react to electric and magnetic fields at each frequency. For succinctness, only the dielectric function and the electrical fluctuations are described in the rest of this introductory section. The full expressions are given in the application and derivation sections of Levels 2 and 3. 

It may be observed that the value of permeability is a function of the flux density being attained to energize the magnetic circuit. It is therefore not a constant parameter and is measured at a particular flux density. 

The primary function of magnetic core materials, that is magnetic flux multiplication, requires both high saturation magnetization and high permeability. Both of these are important for miniaturization. The desire for miniaturization also results in steadily increasing the operation frequencies which, of course, require low eddy-current losses. Similar to amorphous metals, their production-inherent low thickness of about 20 pm and their high residual resistivity of about 100 pQcm minimize eddy currents in nanocrystalline ribbons and make them attractive up to frequencies of 100 kHz or even more. 

Definition of Kerr Constants. In the presence of an external electric field E, the electric pemuttivity e( ) and magnetic permeability n(E) become functions of the field strength. As a consequence the refractive index n also depends on E ... 

The relative magnetic permeability depends on the fiber orientation function, J (see Eq 7.2) ... 

Figure 7.8 shows relationship between the relative magnetic permeability and the fiber orientation function. The results came from an experiment previously discussed (see Figure 7.4). 

Testing procedure. The magnetic permeability measurement is performed on the samples formed to the shape of toroids wrapped uniformly with two sets of wire windings. The primary coil is excited with a sine wave from a function generator. The voltage induced in the secondary coil is measured with a lock amplifier at a frequency range of 0.5 Hz to 120 kHz. ... 

In (2.5) and (2.6), e, /x, a, and a are the constitutive parameters that characterize the electric and magnetic properties of the material. Hence, s is the electric permittivity, /i the magnetic permeability, a the electric conductivity, and a the equivalent magnetic resistivity. The variation of the constitutive parameters as a function of diverse field characteristics (such as intensity, position, direction, and frequency) leads to their classification according to structure and behavior. 

Thus, equations for the field as well as for the elec tromotive force present themselves as the product of two terms. One of them depends on the moment of the dipole, the distance between the dipole and the receiver and in the case of the electromotive force, on the frequency and the magnetic permeability. The second term is a function of only one argument, namely kR, which can be presented as ... 

Inasmuch as we will consider mainly a medium which has a uniform magnetic permeability, jU, it is convenient to present function C in the form ... 

It is appropriate to notice that a sum of these functions is not generally equal to unity, since the magnetic permeabilities of borehole and formation are not equal to each other. As an example, function ... 

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