Particles, charged charge-current density

Equation (5.93) is a statement of a physical principle as it can be restated in terms of the flux in the infinitesimal change in vector current density through the surface bounding the atom. In analogy with the definition of the charge density, the single-particle vector current density, j(r), of a many-particle... 

An electric current is a consequence of the movement of charged particles, ions in our case. Since we have an expression for the flux of each charged particle, the current density is easily obtained by adding each flux multiplied by the corresponding charge per mole. 

We now have to construct the interaction term between the dynamical variables, i.e., the gauge field and the sources of the electrodynamical field, i.e., charged particles giving rise to a charge-current density cf. Eq. (3.161). Again, the contribution of this interaction term to the action S has to be Lorentz and gauge invariant, and the simplest choice is therefore given by... 

If we were to forget that the flow of current is due to a random motion which was already present before the field was applied—if we were to disregard the random motion entirely and assume that each and every electron, in the uniform field X, moves with the same steady velocity, the distance traveled by each electron in unit time would be the distance v used in the construction of Fig. 16 this is the value which would lead to a current density j under these assumptions, since all electrons initially within a distance v of the plane AB on one side would cross AB in unit time, and no others would cross. Further, in a field of unit intensity, the uniform velocity ascribed to every electron would be the u of (34) this quantity is known as the mobility of the charged particle. (If the mobility is given in centimeters per second, the value will depend on whether electrostatic units or volts per centimeter are used for expressing the field strength.)... 

This section began with the realization that the supply of the material requirements of the interface may sometimes not be sufficient to meet the demands of charge transfer and therefore one has to be able to analyze such supply problems. The transport of particles through the solution is one of the essential steps thatjoin with the step (or steps) of the charge-transfer reaction to constitute the overall reaction. Hence, the rate of the transport may at relatively high current densities determine the overall rate. Thus, one began to think of current densities that may be transport controlled. It turned out that diffusion control, in particular one type of transport process, is easy to describe in a very simple physical way. 

The electrical conductivity a is defined as the electrical current density or the amount of charges passing through a unit cross-sectional area per second in an electrical field with strength E of 1 V/m. The electrical conductivity can be determined from the particle number concentration n, the charge on a particle q, and the mobility of a particle p by... 

Consider the charge transfer between two spherical particles of diameters dpi and dp2. A direct analogy between the charge transfer by collisions and the heat transfer by convection appears to be in order. Thus, the current density through the contact area of these two... 

By means of Eq (9-8) we can calculate the relation between the charge and the diameter of a particle for any instant of time, or for any current density and field intensity. The data computed by Eq (9-8) have been verified experimentally by Fuchs et al (1936) for particles 0.5 to 3 m in size. 

The particle flux density multiplied by the elementary charge yields the electric current density... 

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