Electric field, expression

The potentials V(5 ) and [ V(L) — V(L )] have already been evaluated [eqns. (200) and (205)], so it is now only necessary to evaluate the potential [V(L ) V(5 )] across zone 2. Substituting the electric field expression given by eqn. (182) into the general expression given by eqn. (18) for the electrostatic potential gives... 

As an example, consider the original PML absorber in a 2-D computational space. Regarding the propagation of the TE case, the fourth-order electric field expression for Ex in the interior of the layer, becomes... 

A is the emitting area, the work function (in ev), and F the electric field expressed in volts/A the dimensionless quantities / and g are very slowly varying functions of x — 3.79 Fli2l (which is just the fractional change in the work function induced by the applied field). The field is related to the applied voltage V and the radius r of the emitter... 

The regions around an electrically small radiator contain three types of field terms, that is, electrostatic field terms (fields that decrease as 1/r where r is the distance from the center of the radiator), induction field terms (fields that decrease as 1/r ), and the radiation field or Fraunhofer region term (fields that decrease as 1/r). The electrostatic and induction field terms do not contribute to the radiated power and are responsible for the reactive component to the input impedance of the radiator. The complete electric field expression of a very short ideal dipole is given by... 

Again, remember that C, expresses the concentration of species i in terms of moles of charges produced (i.e., 1 mole CaCl2 generates 2 moles of charge). The ionic velocity U is the product of ionic mobility and the electrical field ( ) expressed in V/m [Eq. (D.20)] ... 

By using the method of the dyadic Green s function [4] and the adequate boundary conditions [5], the expressions of the electric field in the zone where the transducer is placed can be written as [2]... 

Derive the expression for the electric field around a point dipole, Eq. VI-5, by treating the dipole as two charges separated by a distance d, then moving to distances X d. 

Consider the interaction of a neutral, dipolar molecule A with a neutral, S-state atom B. There are no electrostatic interactions because all the miiltipole moments of the atom are zero. However, the electric field of A distorts the charge distribution of B and induces miiltipole moments in B. The leading induction tenn is the interaction between the pennanent dipole moment of A and the dipole moment induced in B. The latter can be expressed in tenns of the polarizability of B, see equation (Al.S.g). and the dipole-mduced-dipole interaction is given by... 

This expression may be interpreted in a very similar spirit to tliat given above for one-photon processes. Now there is a second interaction with the electric field and the subsequent evolution is taken to be on a third surface, with Hamiltonian H. In general, there is also a second-order interaction with the electric field through which returns a portion of the excited-state amplitude to surface a, with subsequent evolution on surface a. The Feymnan diagram for this second-order interaction is shown in figure Al.6.9. 

In order to evaluate equation B1.2.6, we will consider the electric field to be in the z-direction, and express the interaction Hamiltonian as... 

When light is incident on a material, the optical electric field E results in a polarization P of the material. The polarization can be expressed as the sum of the linear polarization and a nonlinear polarization P ... 

This result, called the Clausius-Mosotti equation, gives the relationship between the relative dielectric constant of a substance and its polarizability, and thus enables us to express the latter in terms of measurable quantities. The following additional comments will connect these ideas with the electric field associated with electromagnetic radiation ... 

The direction of the alignment of magnetic moments within a magnetic domain is related to the axes of the crystal lattice by crystalline electric fields and spin-orbit interaction of transition-metal t5 -ions (24). The dependency is given by the magnetocrystalline anisotropy energy expression for a cubic lattice (33) ... 

Piezoelectrics. AH ceramics display a slight change ia dimension, or strain, under the appHcation of an electric field. When the iaduced strain is proportional to the square of the field iatensity, it is known as the electrostrictive effect, and is expressed by ... 

For electrolytic solutions, migration of charged species in an electric field constitutes an additional mechanism of mass transfer. Thus the flux of an ionic species Nj in (g mol)/(cm s) in dilute solutions can be expressed as... 

Piezoelectric solids are characterized by constitutive relations among the stress t, strain rj, entropy s, electric field E, and electric displacement D. When uncoupled solutions are sought, it is convenient to express t and D as functions of t], E, and s. The formulation of nonlinear piezoelectric constitutive relations has been considered by numerous authors (see the list cited in [77G06]), but there is no generally accepted form or notation. With some modification in notation, we adopt the definitions of thermodynamic potentials developed by Thurston [74T01]. This leads to the following constitutive relations ... 

Let us consider small metallic particles with complex dielectric function e /jfco) embedded in an insulating host with complex dielectric function e/fco) as shown in Fig. 6. The ensemble, particles and host, have an effective dielectric function = e j i(co) -I- We can express the electric field E at any point... 

H now differentiate these expressions with respect to some parameter a that (jould be a Cartesian coordinate, the component of an applied electric field, or whatever. We then have... 

This is the general expression for film growth under an electric field. The same basic relationship can be derived if the forward and reverse rate constants, k, are regarded as different, and the forward and reverse activation energies, AG are correspondingly different these parameters are equilibrium parameters, and are both incorporated into the constant A. The parameters A and B are constants for a particular oxide A has units of current density (Am" ) and B has units of reciprocal electric field (mV ). Equation 1.114 has two limiting approximations. 

Consider now the observed values of the equivalent conductivity for the various species of ions given in Table 2 [disregarding the ions (OH)-and H+, which need special consideration]. If we ask, from this point of view, why such a wide variety of values is found, this must be ascribed to the wide variety in the character of the random motion executed by different species of ions in the absence of an electric field. We shall not go into the details of Einstein s theory of the Brownian motion but the liveliness of the motion for any species of particle may be expressed by assigning a value to a certain parameter for a charged particle in an... 

In discussing the loss of entropy in an electric field, we may consider a charged sphere immersed either in an alcohol or in a dioxane-water mixture. In (19) in Sec. 8 we obtained an expression for the total amount... 

Studies of double carrier injection and transport in insulators and semiconductors (the so called bipolar current problem) date all the way back to the 1950s. A solution that relates to the operation of OLEDs was provided recently by Scott et al. [142], who extended the work of Parmenter and Ruppel [143] to include Lange-vin recombination. In order to obtain an analytic solution, diffusion was ignored and the electron and hole mobilities were taken to be electric field-independent. The current-voltage relation was derived and expressed in terms of two independent boundary conditions, the relative electron contributions to the current at the anode, jJfVj, and at the cathode, JKplJ. 

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