Electric field definition

Electric Field Definition and Prefactors of Third-Order Effects. . . 128... 

Figure 10,5 Definition of the variables used to describe the electric field produced by the oscillation of the charge q under the influence of vertically polarized light. (Reprinted from Ref. 2, p. 164.)...

Now the effective conductivity ia the direction of the electric field is <7/(1 + /5 ), ie, the scalar conductivity reduced by a factor of (1 + /5 ) by the magnetic field. Also, the electric current no longer flows in the direction of the electric field a component j exists which is perpendicular to both the electric and magnetic fields. This is the Hall current. The conductivity in the direction of the Hall current is greater by a factor of P than the conductivity in the direction of the electric field. The calculation of the scalar conductivity starts from its definition ... 

The term electrochromism was apparently coined to describe absorption line shifts induced in dyes by strong electric fields (1). This definition of electrocbromism does not, however, fit within the modem sense of the word. Electrochromism is a reversible and visible change in transmittance and/or reflectance that is associated with an electrochemicaHy induced oxidation—reduction reaction. This optical change is effected by a small electric current at low d-c potential. The potential is usually on the order of 1 V, and the electrochromic material sometimes exhibits good open-circuit memory. Unlike the well-known electrolytic coloration in alkaU haUde crystals, the electrochromic optical density change is often appreciable at ordinary temperatures. 

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 ... 

Electro-osmosis has been defined in the literature in many indirect ways, but the simplest definition comes from the Oxford English Dictionary, which defines it as the effect of an external electric held on a system undergoing osmosis or reverse osmosis. Electro-osmosis is not a well-understood phenomenon, and this especially apphes to polar non-ionic solutions. Recent hterature and many standard text and reference books present a rather confused picture, and some imply directly or indirectly that it cannot take place in uniform electric fields [31-35]. This assumption is perhaps based on the fact that the interaction of an external electric held on a polar molecule can produce only a net torque, but no net force. This therefore appears to be an ideal problem for molecular simulation to address, and we will describe here how molecular simulation has helped to understand this phenomenon [26]. Electro-osmosis has many important applications in both the hfe and physical sciences, including processes as diverse as water desahnation, soil purification, and drug delivery. 

For each EA spectrum, the transmission T was measured with the mechanical chopper in place and the electric field off. The differential transmission AT was subsequently measured without the chopper, with the electric field on, and with the lock-in amplifier set to detect signals at twice the electric-field modulation frequency. The 2/ dependency of the EA signal is due to the quadratic nature of EA in materials with definite parity. AT was then normalized to AT/T, which was free of the spectral response function. To a good approximation [18], the EA signal is related to the imaginary part of the optical third-order susceptibility ... 

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. 

Definitions.Expressions. The electric field E of an optical beam induces in a material a polarization AP which can be written (12) ... 

Formally the unperturbed Hamiltonian is equivalent to the Hamiltonian of the hydrogen atom in constant homogenious electric field. Chaotic dynamics of hydrogen atom in constant electric field under the influence of time-periodic field was treated earlier (Berman et. al, 1985 Stevens and Sundaraml987). To treat nonlinear dynamics of this system under the influence of periodic perturbations we need to rewrite (1) in action-angle variables. Action can be found using its standard definition ... 

The highly complex and unusual textures observed for B7 materials is complemented by unusual X-ray diffraction behavior. While the beautiful mystery of the B7 texture is not understood in detail, MHOBOW shows EO behavior, which allows some definitive statements regarding its nature. Thus, while some B7 materials are reported to be EO-inactive (no EO switching),54 and some are reported to exhibit antiferroelectric EO behavior,59 MHOBOW exhibits a unique texture change upon application of electric fields. 

General properties and definitions of polarizabilities can be introduced without invoking the complete DFT formalism by considering first an elementary model the dipole of an isolated, spherical atom induced by a uniform electric field. The variation of the electronic density is represented by a simple scalar the induced atomic dipole moment. This coarse-grained (CG) model of the electronic density permits to derive a useful explicit energy functional where the functional derivatives are formulated in terms of polarizabilities and dipole hardnesses. 

This chapter is intended to provide basic understanding and application of the effect of electric field on the reactivity descriptors. Section 25.2 will focus on the definitions of reactivity descriptors used to understand the chemical reactivity, along with the local hard-soft acid-base (HSAB) semiquantitative model for calculating interaction energy. In Section 25.3, we will discuss specifically the theory behind the effects of external electric field on reactivity descriptors. Some numerical results will be presented in Section 25.4. Along with that in Section 25.5, we would like to discuss the work describing the effect of other perturbation parameters. In Section 25.6, we would present our conclusions and prospects. 

I consider there to be a sharp distinction between the most polar form of a molecule and its ionically dissociated form. The reason for this is empirical An ion is defined as a species carrying a charge equal to an integral multiple of the electronic charge, and this definition implies that it will have a characteristic predictable electronic spectrum and, under suitable conditions, mobility in an electric field. There is so far no evidence which would compel one to abandon this definition, and I think it is important to distinguish clearly in this context between reaction intermediates (chain carriers, active species) of finite life-time, and transition states. 

The possible formation of a dipole is a feature of covalent bonding but it is obvious that an ionic bond results in a definite unequal distribution of electrons within a molecule and such molecules (or ions) are extremely polar. However, the fact that they carry a definite charge enables additional separation techniques to be applied. The rate of migration in an electric field (electrophoresis) and the affinity for ions of opposite charge (ion-exchange chromatography) are extremely valuable techniques in the separation of ionic species. 

An important consequence of the presence of the metal surface is the so-called infrared selection rule. If the metal is a good conductor the electric field parallel to the surface is screened out and hence it is only the p-component (normal to the surface) of the external field that is able to excite vibrational modes. In other words, it is only possible to excite a vibrational mode that has a nonvanishing component of its dynamical dipole moment normal to the surface. This has the important implication that one can obtain information by infrared spectroscopy about the orientation of a molecule and definitely decide if a mode has its dynamical dipole moment parallel with the surface (and hence is undetectable in the infrared spectra) or not. This strong polarization dependence must also be considered if one wishes to use Eq. (1) as an independent way of determining ft. It is necessary to put a polarizer in the incident beam and use optically passive components (which means polycrystalline windows and mirror optics) to avoid serious errors. With these precautions we have obtained pretty good agreement for the value of n determined from Eq. (1) and by independent means as will be discussed in section 3.2. 

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