Intensity electric field

Heuristic Fxplanation As we can see from Fig. 22-31, the DEP response of real (as opposed to perfect insulator) particles with frequency can be rather complicated. We use a simple illustration to account for such a response. The force is proportional to the difference between the dielectric permittivities of the particle and the surrounding medium. Since a part of the polarization in real systems is thermally activated, there is a delayed response which shows as a phase lag between D, the dielectric displacement, and E, the electric-field intensity. To take this into account we may replace the simple (absolute) dielectric constant by the complex (absolute) dielectric... 

Relative dielectric constant, dimensionless kV/m Electric field intensity, Idlovolts/meter... 

Static charge generation causes an ignition hazard only if the accumulated charges create an electric field sufficient to produce an electrical discharge in a flammable atmosphere. In most processes, this means that the electric field intensity at some location must reach the breakdown strength of air (nominally 3 X lO " V/m). The objective of static-control measures is to ensure that electric field intensities cannot reach this value. 

Figure 3. Vertical cross-section showing equipotential contours inside a conductive cylindrical silo containing a symmetric conical heap of uniformly charged solids. The electrostatic potential maximum exists on the center line somewhat below the powder surface, while the maximum electric field intensity occurs near the wall just above the powder.

Figure 2.79 For 0 = 0. (a) The angular dependence of the reflectivity R and relative phase V of the reflected plane wave, (b) The angular dependence of the electric field intensity at =0 and 2 = 2DC for Ej = I. After Bedzyk et at. (1990) and M. J. Bedzyk, Synchrotron Radiation News. 3 (1990) 25, Copyright 1990 Gordon and Breach Science Publishers, S.A.

A spark is generated between two conductors when the distance between the conductors is small compared to the diameter of the conductors and when the electric field intensity between the conductors is approximately 3 MV/m. A brush discharge is generated if the distance between the conductors is large compared to the radius of curvature of the conductor. 

Fig. 8.30 (a) Radial electric field intensity distribution of E, and (b) the resonance shift as a function of liquid index change for resonant mode E u. Reprinted from Ref. 68 with permission. 2008 Optical Society of America... 

Fig. 8.36 Radial electric field intensity distribution for the resonant mode E m...

Electric discharge ozone generator, 77 798 Electric-field-induced second harmonic generation (EFISH), 20 515 Electric field intensity, exponents of dimensions, 8 585t Electric field perturbations, 74 616 Electric fields... 

In order to achieve breakdown, electrons (either from the air or from the body) must be accelerated to a sufficient velocity to ionize the air and breed more electrons by any one of several processes. In an actual gas, however, some of the kinetic energy of the electrons is lost in collisions with air molecules without resulting in ionization. This combined effect has been expressed in terms of the Townsend ionization coefficient. As a body becomes smaller, its curvature increases and the electric field intensity drops off more rapidly with distance from the surface consequently, to accelerate electrons a given amount, the body surface field intensity must be higher than for a flat surface. Actually, because of increased attenuation resulting from the increased distance that an electron must travel through air to achieve a given acceleration, the required surface intensity must increase even faster. 

When a material is subjected to an electric field intensity greater than 107 V/cm (1000 V/micron), electrons may be emitted. At intensities greater than 108 V/cm (104 V/micron), ions may be emitted as the result of electron bombardment while at 5 x 108 V/cm direct field desorption may occur. 

Applied Voltage Theoretically, the best resolution is obtained at high voltages. In practice, variation of the electric field intensity under typical analysis conditions for CIEF (300 to 1000 V/cm) is a parameter of relatively minor... 

The problem of influence of the electric field intensity on the permittivity of solvents has been discussed in many papers. The high permittivity of water results from the intermolecular forces and is a cumulative property. The electric field intensity is the lowest at the potential of zero charge (pzc), thus allowing water molecules to adsorb in clusters. When the electrode is polarized, the associated molecules, linked with hydrogen bonds, can dissociate due to a change in the energy of their interaction with the electrode. Moreover, the orientation of water molecules may also change when the potential is switched from one side of the pzc to the otha. 

For weakly guiding structures, the second term can be neglected, and we obtain the standard Helmholtz equation in which individual components of the electric field intensity vector E remain uncoupled. For high contrast waveguides this is clearly not the case. The second term in Eq. (2) in which the transversal electric field components are mutually coupled must be retained. 

The definitions of the parameters for describing piezoelectric effect are shown in Fig. 9.3. A voltage V is applied on a rectangular piece of piezoelectric material. Inside it, the electrical field intensity is... 

Fig. 9.3. Definition of piezoelectric coefficients. A rectangular piece of piezoelectric material, with a voltage V applied across its thickness, causes a strain in the x as well as the z directions. A piezoelectric coefficient is defined as the ratio of a component of the strain with respect to a component of the electrical field intensity.

The piezoelectric coejficients are defined as the ratios of the strain components over a component of the applied electrical field intensity, for example,... 

Here d is the dielectric constant of the medium which we simply assume constant throughout (that is, concentration and electric field intensity independent). Furthermore, p in (1.4a) is the density of the space charge... 

Some typical stationary voltage-current VC curves along with the ionic concentration, space charge density, and the electric field intensity profiles for an intermediate voltage range are presented in Fig. 5.3.1. The appropriate profiles are constructed using a numerical solution of the system (5.3.1), (5.3.5). The essence of the numerical procedure employed for this and similar problems discussed in due course is as follows. 

Equation (6.1.4) asserts that the volumetric flow rate is a superposition of two components. They are the electro-osmotic component proportional to the electric field intensity (voltage) with the proportionality factor u> and the filtrational Darcy s component proportional to —P with the hydraulic permeability factor i>. Teorell assumed both w and t> constant. Finally another equation, crucial for Teorell s model, was postulated for the dynamics of instantaneous electric resistance of the filter R(t). Teorell assumed a relaxation law of the type... 

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