Electric field Subject

This subject has a long history and important early papers include those by Deijaguin and Landau [29] (see Ref. 30) and Langmuir [31]. As noted by Langmuir in 1938, the total force acting on the planes can be regarded as the sum of a contribution from osmotic pressure, since the ion concentrations differ from those in the bulk, and a force due to the electric field. The total force must be constant across the gap and since the field, d /jdx is zero at the midpoint, the total force is given the net osmotic pressure at this point. If the solution is dilute, then... 

An alternative approach is to consider ions of charge z e accelerated by the electric field strengtii, E, being subject to a frictional force, Kj, that increases with velocity, v, and is given, for simple spherical ions of... 

Cathode and insulator walls are less subject to severe electrochemical attack. In the case of the cathode wall, this is because of the reducing conditions which prevail, and in the case of the insulator wall, because the wall nominally carries no current. However, certain surfaces of cathode and insulator walls are anodic with respect to other surfaces, because of the axial electric field present in the generator, and these surfaces do require protection against electrochemical attack. 

Figure 6.1. (a) Atom not subject to external electric field. Centre of electron cloud and nucleus coincident, (b) Electron cloud displacement through application of external electric field, (c) Charged condenser plates separated by vacuum, (d) Condenser plates separated by dielectric... 

Nonlinear properties of normal dielectrics can be studied in the elastic regime by the method of shock compression in much the same way nonlinear piezoelectric properties have been studied. In the earlier analysis it was shown that the shape of the current pulse delivered to a short circuit by a shock-compressed piezoelectric disk was influenced by strain-induced changes in permittivity. When a normal dielectric disk is biased by an electric field and is subjected to shock compression, a current pulse is also delivered into an external circuit. In the short-circuit approximation, the amplitude of this current pulse provides a direct measure of the shock-induced change in permittivity of the dielectric. 

A normal dielectric may be characterized by Eq. (4.1) with the piezoelectric terms deleted. For an isotropic dielectric subject to uniaxial strain and a collinear electric field this equation takes the form... 

Certainly the most prominent feature of the breakdown process is its dependence on the polarity of the electric field relative to the shock-velocity vector. This effect is manifest in current pulse anomalies from minus-x orientation samples or positively oriented samples subjected to short-pulse loading (see Fig. 4.8). The individual effects of stress and electric field may be delineated with short-pulse loadings in which fields can be varied by utilizing stress pulses of various durations [72G03]. 

The behavior of a polar dielectric in an electric field is of the same kind. If the dielectric, is exposed to an external electric field of intensity X, and this field is reduced in intensify by an amount SX, the temperature of the dielectric will not remain constant, unless a certain amount of heat enters the substance from outside, to compensate for the cooling which would otherwise occur. Alternatively, when the field is increased in intensity by an amount SX, we have the converse effect. In ionic solutions these effects are vciy important in any process which involves a change in the intensity of the ionic fields to which the solvent is exposed—that is to say, in almost all ionic processes. When, for example, ions are removed from a dilute solution, the portion of the solvent which was adjacent to each ion becomes free and no longer subject to the intense electric field of the ion. In the solution there is, therefore, for each ion removed, a cooling effect of the kind mentioned above. If the tempera-... 

Dielectric loss The dielectric loss factor represents energy that is lost to the insulator as a result of its being subjected to alternating current (AC) fields. The effect is caused by the rotation of dipoles in the plastic structure and by the displacement effects in the plastic chain caused by the electrical fields. The frictional effects cause energy absorption and the effect is analogous to the mechanical hysteresis effects except that the motion of the material is field induced instead of mechanically induced. 

When using molded plastics parts such as the connectors and the circuit supports, it is important to make sure that the moldings, in addition to being made to close tolerances, be made under molding conditions that make for stable products. Electrical products are subjected to strong electrical fields in addition to the usual environmental abuse. Distortion of the product can lead to serious electrical malfunction by changing spacings that will alter electrical characteristics and if... 

Important ferroelectric materials are those with piezoelectric characteristics. They are crystalline ceramics that exhibit expansion along one crystal axis and contraction along another when subjected to an electrical field. Conversely, compression generates an electrical voltage across the material. These materials have a large number of industrial applications. 

Crystal-field theory (CFT) was constructed as the first theoretical model to account for these spectral differences. Its central idea is simple in the extreme. In free atoms and ions, all electrons, but for our interests particularly the outer or non-core electrons, are subject to three main energetic constraints a) they possess kinetic energy, b) they are attracted to the nucleus and c) they repel one another. (We shall put that a little more exactly, and symbolically, later). Within the environment of other ions, as for example within the lattice of a crystal, those electrons are expected to be subject also to one further constraint. Namely, they will be affected by the non-spherical electric field established by the surrounding ions. That electric field was called the crystalline field , but we now simply call it the crystal field . Since we are almost exclusively concerned with the spectral and other properties of positively charged transition-metal ions surrounded by anions of the lattice, the effect of the crystal field is to repel the electrons. 

For a one-dimensional model system of 2Ne independent particles moving in a harmonic effective potential v(jc) = and simultaneously subjected to an electric field E, the... 

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