Displacement vectors electric

Conditions can arise when the material response to the imposition of electric fields is nonlinear. Under such circumstances, more complex constitutive relationships must be employed and it is most common to expand the electric displacement vector, D, as a power series in the electric field according to... 

The total charge density uT is equivalent to the magnitude of the electric displacement vector D, so that... 

Finally, one can define an electric displacement vector D(co), along with three tensors, for the optical dielectric constant s(co), the effective optical susceptibility Xetti03) and the optical index of refraction n(co) ... 

The electric displacement vector D is perpendicular to the unit vector 1, so... 

E and H being the electric and magnetic field strength vectors, D the electric displacement vector, B the magnetic induction vector, J the electric current density, and p, the electric charge density. 

As an alternative formulation we introduce a local current density, J r) that responds to a steady vector potential 4.(r). The associated work element is dW = (1/c) fy d r J dA., where c is the velocity of light. We next introduce Maxwell s relation V x = An/c)J, which applies when the electric displacement vector is independent of time and when J is the free current density. Thus, dW = (47t) /d rdA (V x 7i). On using line (g) of Table 1.3.1, the work increment reads... 

When a thin absorber layer is embedded between the transport layers, the main ingredients of this qualitative description can still be apphed. Since the electric displacement vector across the interfaces is continuous and since the absorber layer is assumed thin and of low conductivity, it is clear that the absorber layer is subject to electric fields similar to the junction field. If the junction curvature is not too small. 

The dielectric properties of a material are properly specified by a symmetric second-rank tensor relating the three components of the electrical displacement vector D to those of the field E. By choosing axes naturally related to the crystal structure the six independent components of this tensor can be reduced to three and, taking account of the hexagonal symmetry of the ice crystal, only two independent components remain. These are the relative permittivities parallel and perpendicular to the unique c-axis direction and we shall denote them by e, and e. We shall discuss the experimental determination of these quantities when we come to consider dielectric relaxation, since some difficulties are involved. For the present we simply note the results which are shown in fig. 9.2. The often-quoted careful measurements of Auty Cole (1952) were made with polycrystalline samples and removed many of the uncertainties in earlier work. They represent, however, a weighted mean of the values of e, and Humbel et al. (1953 [Pg.201]

We begin with the electric displacement vector Dj = ZyEi where i, j = x , y, / are Cartesian coordinates and the summation over repeated indices is inferred. The tensor of dielectric permittivity is symmetric Sy = Ej,and generally (even for biaxial medium) has six independent components. If an insulator is placed in the electric field, the stored electric energy density is given by... 

The same energy may be expressed in terms of the electric displacement vector components ... 

The contribution of the solvent reorganization energy to the total X as considered by Kharkats [8] and later by Marcus [11]. The expressions obtained appeared not entirely consistent, but successive revision established that the key aspect lies in separating the static and optical terms of the integral of the electric displacement vectors over the volume of the two liquids system [37]... 

The electric displacement vector is perpendicular to the propagation direction (the direction of the wavevector), which is true even in anisotropic media. Therefore light is a transverse wave. 

As in previous chapters we work in the continuum limit employing quantities averaged over macroscopically infinitesimal volume elements and disregarding microscopic local variations associated with the molecular structure (see Brown 1956). These considerations will be limited to processes sufficiently slow to restrict the treatment to time independent or quasistatic fields. The validity of Maxwell s equations of electrostatics is presupposed. The basic electric state variables are the electric field strength vector E, the electric flux density (or electric displacement) vector D, and the electric polarization vector P, related by... 

In the absence of free charges the continuity of the electric displacement vector (Maxwell equation) reads ... 

The electric displacement vector Di satisfies the electrostatic equation for an insulator, and shown as ... 

P. Curie and J. Curie discovered the piezoelectric effect in 1880. It was found that, when a compressive or a tensile force was applied on some crystals along some special directions (for example, a quartz) electrical charges could be created on the corresponding surfaces of the crystal and the size of the created charge was proportional to the strength of the apphed force. This phenomenon is called the piezoelectric effect . All ferroelectric crystals show a piezoelectric effect. The piezoelectric effect can be described by piezoelectric equations. On the basis of thermodynamic principles, piezoelectric equations can be derived (e.g., see Xu, 1991). These equations describe linear relationships between the four variables stress tensor [T], strain tensor [S], electrical field vector E and electric displacement vector D. The piezoelectric equations can be expressed as four kinds of equations, depended on the variables. Selecting E and Tas variables, we have ... 

Here we define the material properties of the host medium as the background permittivity and permeability. So the electric displacement vector is defined as... 

However, it is more appropriate to take the electric displacement vector D as the quantity that responds to the imposition of an electric field here, T> = E + 4TctP specifies the response of the medium to the externally applied electric field as well as to the induced polarization. Henceforth, this is the quantity that will be used in the subsequent analysis. Clearly, at constant , the differentials of D and tP are identical. 

D electrical displacement vector (or electrical induction - see Figure 1.3(b)) ... 

---