Current density field lines

In tissue, an implant may be conductive (metallic) or insulating (Dacron ). Tissues of different electrical properties may result in the bending of current density field lines (Figure 4.33). At a sharp interface the following rules apply ... 

A bending of current density field lines occurs at the interface between two homogeneous materials of different conductivity, as shown on Figure 4.34. Let 6 be the angle between a... 

Figure 4.34 Bending of current density field lines.

Singularities, Stagnation Lines and Stagnation Graph of a Current Density Field... 

Fig. 7.44 Current density field induced via the Fermi contact interaction by two magnetic dipoles at the vicinal protons of eclipsed ethane. The coupling pattern, for anti-parallel (parallel) dipoles, is represented on the left (right). The streamlines are shown in (a) and (d) b and e are contour levels for the intensity, in au the values of the solid (dashed) lines increase (decrease) in steps of 5 X 10 from the 0-contour, up to 0.5 au c and f are the corresponding 3-dimensional perspective views. The position of the nuclei is marked by a cross a corresponding symbol can be seen in the contour maps...

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... 

An example for the field cones and equipotential surface is shown in Fig. 3.9 for d = 1.2 mm and rt= 420 A. The vertical line represents a position of 5rt away from the tip. The field lines are drawn so that their density is proportional to the field strength. Field distributions and equipotential surfaces of other tip shapes have also been investigated, particularly as regards the field emission current density distribution,24,31 but will not be discussed here. 

On study of the equation related to the magnetic field, and taking into account all the previous remarks, both current density lines and magnetic field lines appear to be orthogonal with one another. 

Fig. 7.185. In a self-driving cell, the plot of cell overpotential vs. log cell current density should be a straight line if the charge transfers at both electrodes are both rate controlling and valid under the high-field approximation. An apparent /0 for the cell as a whole can be deduced.

In contrast, the quasi-straight-line log. /-log U plots for the Al/Alq3/Ca system from Fig. 69a, replotted in the Schottky-type coordinates in Fig. 79b, deviate apparently from the straight lines, and the current decreases with the sample thickness. Moreover, the thickness dependence of the current density obeys the d-1 law for d > 125 nm (Fig. 80) suggesting the free-carrier SCLC (168a) to underlie the current flow in this system. The fitting of the experimental data with the power law Fn (n > 3) seen in Fig. 69a has been explained by the field-dependent mobility [355]. (see also Sec. 4.6). 

Figure 105 Electron injection current density vs. average electric field (F U/d) for a Mg/Alq3/Mg sandwich device with a 300 nm— thick Alq film (circles). The dash-dotted line corresponds to a j U2 dependence the dashed line represents a linear plot j U. After Ref. 470. Copyright 2002 American Institute of Physics.

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