Zero electrostatic potential gradient

Equation (14.23) can also be deduced from Eq. (14.14) by assuming a zero electrostatic potential gradient (i.e., v

[Pg.320]

However, in this case the EMF measured will be distorted by another effect [i.e., the variation of electrostatic potential within a given conductor, which is caused by a temperature gradient in the conductor (the Thomson effect, 1856)]. Potential gradients will arise even at zero current, in both the electrolyte (between points and Aj)... 

The thermopower or thermoelectric power is the electrostatic potential difference between the high and low temperature regions of a material with an impressed thermal gradient and zero electric current flow. The sign gives an indication of the sign of the charge carriers - positive for hole carriers. 

The gradient of the electric field is the second derivative of the electrostatic potential, and as such, it obeys certain symmetries The EFG is a symmetric tensor with zero trace. This mean that it can be represented as a physical object An ellipsoid where off-diagonal elements represents reorientation of the principal axes system (See Figure 10). 

If the electrolyte has large ionic disorder and since the blocked ionic current i,o is zero. Equations (9.5) and (9.6) indicate that no gradient can exist in the electrostatic potential within the sample. Then the steady-state transport of electrons and holes occurs only due to diffusion nnder the influence of gradients in their concentrations. These gradients must be uniform if the diffusion coefficient does not depend markedly on the concentration. From Equations (9.2) and (9.3) and the ionization equilibrium, the cell voltage determines the ratio of the activities of the electronic species at both sides of the electrolyte ... 

A gradient path of V has a simple physical interpretation. It is a line of force—the path traversed by a test charge moving under the influence of the potential F(r X). At a critical point other than a (3, — 3) critical point, the force vanishes. Thus a critical point in the field V(r X) denotes a point of electrostatic balance between the attractors of the system. Since trajectories defining the surface which separates neighbouring basins satisfy the zero-flux condition... 

Let us consider again the electrostatic example of a two dimensional electrostatic field E(x,7), with potential V(x,y,) in a medium of dielectric constant e and zero charge density. The analogue of this situation is the soap film with zero excess pressure and small gradients. One might conjecture that the minimum area property of the soap film, or minimum energy of the soap film, may correspond in the electrostatic problem to the minimization of the electrostatic energy of the field. 

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