Electric field lines

In the simplest case of one-dimensional steady flow in the x direction, there is a parallel between Eourier s law for heat flowrate and Ohm s law for charge flowrate (i.e., electrical current). Eor three-dimensional steady-state, potential and temperature distributions are both governed by Laplace s equation. The right-hand terms in Poisson s equation are (.Qy/e) = (volumetric charge density/permittivity) and (Qp // ) = (volumetric heat generation rate/thermal conductivity). The respective units of these terms are (V m ) and (K m ). Representations of isopotential and isothermal surfaces are known respectively as potential or temperature fields. Lines of constant potential gradient ( electric field lines ) normal to isopotential surfaces are similar to lines of constant temperature gradient ( lines of flow ) normal to... 

Microscopic analysis of the photobehaviour demonstrated that phobic responses are inhibited only in those organisms which move more or less parallel to the electric field lines. In those leaving the light trap perpendicular to the field lines, the phobic responses were not impaired. But since the light trap was not completely closed, no accumulations were formed. 

Ionized donors - Electrons (majority carriers) + Holes (minority carriers) -Electric field lines... 

Fig. 1. Electrical dipole development around a conductor crossing redox equipotential lines. Positive current in the country rock (not shown) travels perpendicular to electrical field lines from the anode to the cathode (modified after Govett 1976 and Hamilton 1998).

In this case the surfaces fi = constant correspond to the equipotentials and the surfaces a = constant correspond to the surfaces on which the electric field lines are fixed. The distance from the origin to the focus, a, is related to the distance between the apex and the origin, d, and the radius of curvature of the tip, rt, by a = [d(d + rt) m. 

Figure 2. Schematic diagram of the imaging apparatus with ion lens. The detector is a dual microchannel plate/phosphor screen assembly (40 mm active diameter) coupled with a CCD camera. Electric field lines are shown to illustrate the ion lens. Equipotential surfaces in the repeller/extractor region are also included.

Fig. 13 Effect of an electric field on the lamellar distance of a block copolymer solution, (a) 2D scattering pattern of a 50 wt% solution of SI51 dissolved in THF for different electric field strengths, (b) Dependence of the lamellar distance d of parallel (filled circles) and perpendicular (open circles) aligned lamellae, with respect to the electric field lines, on the electric field strength for the same solution, (c) Proposed chain stretching effect for lamellae aligned parallel to the field lines. Adapted with permission from Nature Materials [57]. Copyright (2008) Nature Publishing Group...

Though not strictly functioning as resistors/conductors, carbon nanotubes have just been reported in an extraordinarily vapor-sensitive capacitive device [19]. The electric field lines emanating from the nanotubes are responsible for a localized dielectric response that can be modulated by minute quantities of adsorbate on the nanotube surface. A layer of hydrogen-bonding polymer, or even a mono-layer terminated in mildly acidic groups, increased sensitivity to parts per billion levels. Response strength was correlated with the dipole moment of the analytes. 

Figure 5 presents the variation of the electrophoretic velocities of the cylinder with X. It is shown that the translational velocity normal to the plane decreases with increasing X, whereas the parallel mobility increases with X. In addition to the translation, the cylinder rotates when the external electric field is applied parallel to the wall. The enhancement of the parallel migration results from the squeezed electric field lines in the small gap between the particle and wall surfaces. This velocity enhancement also occurs for the electrophoresis of a sphere parallel to a plane boundary when the gap width is sufficiently small [40]. The boundary effects on electrophoresis are stronger for a cylinder than for a sphere. 

Figure 10. Electric field lines in the vicinity of an elevated grounded wire...

The disadvantage of this simple relationship is that it does not show how coefficient K depends on the frequency of dielectric dispersion (expression for the frequency dependence see p. 48). Nevertheless, Eq. (26) implies that a dry plastic foam may be considered as a laminated two-phase system of the type dielectric — gas with layers ariat ed parallel to the electric field lines. This conclusion is based on the well-known observation that a linear dependence (Eq. (26)) indicates a precise solution to the problem of dielectric permeability of a laminated dielectric with layers parallel to the field. 

Fig. 1 also shows that the electric field lines concentrate on the sharp edges of the part. Some of the electric field lines actually wrap around the back of the target. In addition to the electric field lines, aerodynamics will also contribute to this wrap effect. Increased film thickness at the edge is usually referred... 

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