Electric field in a dielectric

The third group is the continuum, models, and these are based on simple concepts from classical electromagnetism. It is convenient to divide materials into two classes, electrical conductors and dielectrics. In a conductor such as metallic copper, the conduction electrons are free to move under the influence of an applied electric field. In a dielectric material such as glass, paraffin wax or paper, all the electrons are bound to the molecules as shown schematically in Figure 15.2. The black circles represent nuclei, and the electron clouds are represented as open circles. 

The tension due to the electric field in a dielectric medium follows this relation [31] ... 

One important stracture in molecules are polar bonds and, as a result, polar molecules. The polarity of molecules had been first formulated by the Dutch physicist Peter Debye (1884-1966) in 1912, as he tried to build a microphysical model to explain dielectricity (the behaviour of an electric field in a substance). Later, he related the polarity of molecules to the interaction between molecules and ions. Together with Erich Hiickel he succeeded in formulating a complete theory about the behaviour of electrolytes (Hofimann, 2006). The discovery of the dipole moment caused high efforts in the research on physical chemistry. On the one hand, methods for determining the dipole momerrt were developed. On the other hand, the correlation between the shape of the molectrle and its dipole moment was investigated (Estermanrr, 1929 Errera Sherrill, 1929). 

To illustrate the use of the vector operators described in the previous section, consider the equations of Maxwell. In a vacuum they provide the basic description of an electromagnetic field in terms of the vector quantifies the electric field and 9C the magnetic field The definition of the field in a dielectric medium requires the introduction of two additional quantities, the electric displacement SH and the magnetic induction. The macroscopic electromagnetic properties of the medium are then determined by Maxwell s equations, viz. 

Figure 6.44 Dielectric loss factor as a function of cure time and frequency of the oscillating electric field in a fiber-reinforced polymer. Reprinted, by permission, from P. K. Mallick, Fiber-Reinforced Composites, p. 365. Copyright 1988 by Marcel Dekker, Inc.

FIG. 11.3 The electric field in a parallel plate capacitor (a) the dielectric is a vacuum and (b) a material of dielectric constant er is present. 

For a pure dielectric response of the matter the polarization is proportional to the electric field in a linear approximation by... 

The mechanism of breakdown originating from discharges in a pore is by no means self-evident, but the starting point is that the electric field in a pore is greater than that in the surrounding dielectric. For a disc-shaped cavity with its plane normal to the applied field E, the field Ec within the cavity is given by... 

Polarization density (of a dielectric medium) — The polarization density P is the difference between the electric displacement in a - dielectric medium Dc and the electric displacement in a vacuum Do- (Note The electric displacement is defined as the product of the electric field strength E and the - permittivity e.) The polarization density of a dielectric medium may also be... 

V. The curves in Figure 1 were calculated by using the static value of the dielectric constant for each liquid. However, the dielectric constant of a medium is time dependent, because it requires a certain amount of time for the medium to attain its new polarization equilibrium after the sudden application of an electric field. In a polar liquid the permanent molecular dipoles require a certain time to rotate to line up with the electric field. When the value of tgn is in the vicinity of or smaller than that of the dielectric relaxation time t of the liquid—i.e., when tgn S 10t,— then a time-averaged complex dielectric constant should be used in Equations II, IV, and V. At a time t after the instantaneous application of a d.c. electric field, the dielectric constant of the medium in the field is given approximately by... 

Fig. 3.5.18. Umbilics induced by an electric field in a nematic film of negative dielectric anisotropy crossed polarizers. (Saupe. )...

The mechanism of electrical conductivity in insulators, particularly polymers, is still under consideration, but it is established that the current resulting upon application of an electrical field across a dielectric (depending on its nature) is due to the following ... 

Electrostriction, which is a change in sample dimensions in response to the application of an electric field to a dielectric, is a universal characteristic and provides another example of an electromechanical effect. Some materials get thinner while others get thicker in the direction of the electric field. This effect is not reversible and a deformation does not produce any polarisation. The effect is found in all materials, not just those that lack a centre of symmetry, including glasses and hquids. However, the electrostrictive effect is generally very small except for ferroelectric perovskites, especially relaxor ferroelectrics described in the following (Section 6.7). 

In the EDL, the electric potential and net charge density are described by the Poisson-Boltzmann equation [1-4]. The Poisson equation describes the electric field within a dielectric medium ... 

The electric power P passing from a homogeneous electric field to a dielectric (which uniformly fills the field), is in the general case... 

Here Pe is the electric dipole induced by the electric field in a molecule having mean molecular polarizability y. Then we used the Lorentz approximation for the local field acting on a molecule and found corresponding field induced polarization. From that we have obtained the electric susceptibility of the dielectric (Eq. 7.18) ... 

Finally, discharge breakdown may occur when gas discharges occur in the pores of a dielectric material. The electric strength of the ceramics depends upon the specimen and pore sizes in other words, larger pores will increase the probabUily of failure as the electric field in a pore, Ep, is greater than that in the surrounding... 

Dielectric Constant The ratio of electric displacement in a dielectric medium to the applied electric-field strength, defined by e in the following equation ... 

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