Magnetic permittivity

Various data sources (44) on plasma parameters can be used to calculate conditions for plasma excitation and resulting properties for microwave coupling. Interactions ia a d-c magnetic field are more compHcated and offer a rich array of means for microwave power transfer (45). The Hterature offers many data sources for dielectric or magnetic permittivities or permeabiHty of materials (30,31,46). Because these properties vary considerably with frequency and temperature, available experimental data are iasufficient to satisfy all proposed appHcations. In these cases, available theories can be appHed or the dielectric parameters can be determined experimentally (47). 

Magnetic permittivity of free space, (1.1). impermeability tensor, (2.64). 

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. 

Relative isotropic dielectric, magnetic permittivity or permeability at zero frequency s(0) is the dielectric constant. 

Dielectric constant (e ) and dielectric loss factor (e") are the two most important properties, which have a pronounced effect on the effectiveness of microwave processing of a material. The dielectric constant (s ) is a ratio of the permittivity of a substance to the permittivity of free space. The dielectric constant of a material gives the extent the material could concentrate the electric flux. It is an electrical equivalent of the relative magnetic permittivity (Regier and Schubert, 2001 Venkatesh and Raghavan, 2004). 

The above consideration of nanoparticles has been carried out in a supposition that they have more or less the same size. To be more precise, we assumed that the width of the nanoparticles sizes distribution function is smaller then its mean value. The mean value R is usually extracted from, e.g., X-Ray diffraction measurements [91] and it is supposed, that the size of all the particles corresponds to R. In this part we will show, that the neglection of sizes distribution can lead to incorrect results, when measurements are performed on the samples with essential scattering of sizes. Besides that, actually the size distribution defines the spectral lines inhomogeneous broadening. Moreover, it essentially influences the observed anomalies of many physical properties (like specific heat and dielectric or magnetic permittivity) of nanomaterials. Note that in real nanomaterials, like nanoparticles powders and/or nanogranular ceramics there is unavoidable size distribution which in general case should be taken into account. However, we will show below, that in perfect samples, where the width of size distribution is small, it is possible to suppose safely that all particles have the same size. In this part we primarily follow the approaches from the paper [92]. 

Table 15.1 lists the magnetic permittivity values of some Ni-Zn ferrites in room temperature. It is worth mentioning that variations in these values due to differences in morphological parameters, processing and structure are expected. 

Here E and H are vectors of electric and magnetic field strength, (o)) and p(co) are frequency dependent dielectric and magnetic permittivities, ct is permanent conductivity. In the second equation, the two terms describe the displacement and Ohmic current, respectively. 

Here, yr is the superconductor gap order parameter. It corresponds to the wave function of the superconducting pair in BCS theory and has the X Y symmetry of the smectic order parameter. The magnetic vector potential A comes analogous to the director n (m and e are the mass and charge of a single electron, fi Planck s constant, c the velocity of light and jU the magnetic permittivity). 

The dielectric permittivity as a function of frequency may show resonance behavior in the case of gas molecules as studied in microwave spectroscopy (25) or more likely relaxation phenomena in soUds associated with the dissipative processes of polarization of molecules, be they nonpolar, dipolar, etc. There are exceptional circumstances of ferromagnetic resonance, electron magnetic resonance, or nmr. In most microwave treatments, the power dissipation or absorption process is described phenomenologically by equation 5, whatever the detailed molecular processes. 

The apphcation of microwave power to gaseous plasmas is also of interest (see Plasma technology). The basic microwave engineering procedure is first to calculate the microwave fields internal to the plasma and then calculate the internal power absorption given the externally appHed fields. The constitutive dielectric parameters are useful in such calculations. In the absence of d-c magnetic fields, the dielectric permittivity, S, of a plasma is given by equation 10 ... 

To eliminate the ambiguities in the subject of electricity and magnetism, it is convenient to add charge q to the traditional I, m and t dimensions of mechanics to form the reference dimensions. In many situations permittivity S or permeabiUty ]1 is used in Heu of charge. For thermal problems temperature Tis considered as a reference dimension. Tables 2 and 3 Hst the exponents of dimensions of some common variables in the fields of electromagnetism and heat. 

As far as the inductive mode is concerned this technique is less sensitive because the low permittivity of the solution keeps the magnetic flux low. 

In isotropic media 0 and S are related by = < , where the scalar parameter a is now referred to as the permittivity. In the international (SI) system it is given by s = erso. where o is the permittivity of vacuum (see Appendix fl) and e, is a dimensionless permittivity that characterizes the medium. Furthermore, according to Ohm s law the current is given by 7 = cr< , where a is the electrical conductivity. The relation V S3 = 0 is a mathematical statement of the observation that isolated magnetic poles do not exist. 

Consequences of the thermal changes of the dielectric permittivity 1 Conduction losses 13 Magnetic losses 13... 

Vacuum magnetic permeability 245 Vacuum permittivity 31 Variable field NMR relaxometry 406 Volclay 306, 308-9... 

Dependence of certain physical properties, like the electric permittivity, refractive index and magnetic susceptibility on direction. It is created by long-range orientational order in a mesophase, provided the corresponding molecular property is anisotropic. 

Similarly, the velocity of light in a medium is related to the electric permittivity and magnetic permeabilities in the medium, e and fi, respectively ... 

Thus, we see the initial connection between optical properties and the electrical and magnetic properties from the two previous sections. Substimtion of Eqs. (6.78) and (6.79) into (6.77) shows that the refractive index can be expressed in terms of the relative electric permittivity (dielectric constant), (cf. Table 6.5), and relative magnetic permeability of the medium, (1 - - x) [cf. Eq. (6.63)], where x is the magnetic susceptibility ... 

As its name suggests, a liquid crystal is a fluid (liquid) with some long-range order (crystal) and therefore has properties of both states mobility as a liquid, self-assembly, anisotropism (refractive index, electric permittivity, magnetic susceptibility, mechanical properties, depend on the direction in which they are measured) as a solid crystal. Therefore, the liquid crystalline phase is an intermediate phase between solid and liquid. In other words, macroscopically the liquid crystalline phase behaves as a liquid, but, microscopically, it resembles the solid phase. Sometimes it may be helpful to see it as an ordered liquid or a disordered solid. The liquid crystal behavior depends on the intermolecular forces, that is, if the latter are too strong or too weak the mesophase is lost. Driving forces for the formation of a mesophase are dipole-dipole, van der Waals interactions, 71—71 stacking and so on. 

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