Continuity equation electric charge

The equation of continuity for electric charge (11.75) has the stmcture of a four-dimensional divergence... 

It is noticed that taking the divergence of this last equation leads to conflict with the continuity equation (eqn. 1.7) for electric charge,... 

Like the performance of chemical reactors, in which the transport and reactions of chemical species govern the outcome, the performance of electronic devices is determined by the transport, generation, and recombination of carriers. The main difference is that electronic devices involve charged species and electric fields, which are present only in specialized chemical reactors such as plasma reactors and electrochemical systems. Furthermore, electronic devices involve only two species, electrons and holes, whereas 10-100 species are encountered commonly in chemical reactors. In the same manner that species continuity balances are used to predict the performance of chemical reactors, continuity balances for electrons and holes may be used to simulate electronic devices. The basic continuity equation for electrons has the form... 

Equation (73) is a generalization of the continuity equation for electric charge. Indeed, the left-hand side is the standard Eq. (13), which obtains when... 

The electric currents and charges are interrelated by the continuity equation... 

Suppose that a semiconductor of thickness L is contacted with an electrode that, hy virtue of a low-energy barrier at the interface, is able to supply an unlimited number of one type of carrier. The current is then limited by its own space charge which, in die extreme case, reduces the electric field at the injecting contact to zero. This is realized when the number of carriers per unit area inside the sample approaches the capacitor charge, i.e. sso/e. It is this number of carriers dial can be transported per transit time ttr=d/fji. Hence, the maximum current is iscL = s,E,QfiF ld. A more rigorous treatment has to take into account the non-uni-form distribution of space charge and, concomitantly, electric field [34]. Starting with Poisson s equation and the continuity equation. 

Then what is the source of /iM in electromagnetic theory Are there restrictions on A that should also apply to /iM The answer is yes —it is the restriction of gauge invariance in order to yield a unique representation for the electric and magnetic field variables. Additionally, gauge invariance is the necessary and sufficient condition for the existence of conservation laws in the formalism—in this case the requirement of the conservation of electrical charge [13]. The latter follows from the continuity equation,... 

He also assumed that the surface charge density undergoes a tangential as well as a vertical variation when an electric field is applied. By solving the continuity equation with appropriate boundary conditions, he obtained an equation for an ellipsoid which has the same form as Fricke s Equation 17 except for the magnitude of the excess conductivity. 

The divergence of the current density at a point x, y, z represents the net outward flux of electric charge from that point. Since electric charge is conserved, the flow of charge from every point must be balanced by a reduction of the charge density p(r, t) in the vicinity of that point. This leads to the equation of continuity... 

When there is an electric field parallel to the double layer, the external electric field will drive the ions to move. Because of the viscosity of the liquid, the bulk liquid will move with the diffuse layer and the resulted motion of the bulk liquid is termed as electroosmotic flow (EOF), which is also referred to as the classic electroosmotic flow comparing with the induced-charge electroosmotic flow. In a microchannel (Fig. 2), the value of the electroosmotic velocity can be solved by continuity equation and Navier-Stokes equation ... 

The applied electric field interacts with the net charges of the EDL on the walls of the microchannel and microchamber. This interaction generates EOF in the channel. Meanwhile, the fully conducting particle reacts to the applied electric field, surface charges are induced on the conducting surface, and the particle moves. The net velocity of the particle will be determined by the electrophoretic motion of the particle, the bulk liquid EOF, and the complex flow field (vortices) around the particle. Consider a Newtonian incompressible fluid continuously flows in the microchannels. The continuity equation... 

The basic governing equations for the stable jet region are the equation of continuity, conservation of electric charges, linear momentum balance, and electric field equation. As main source for these flow equations we refer to Refs. [1, 62, 69]. 

The electric conduction efficiency (%), obtained by direct simulation of the charge continuity equation in 500x (%,5oo) and 5000x (rik,50oo) resolutions, can be generalized by its product in a single micrometric efficiency parameter rimUro- ilk>soo >5,ooo)- In this way, the electric conduction efficiency of the nano-metric structure can be estimated by ... 

The drift-difiusion model captures the drift of charge carrier concentrations in an electric field and their diffusion due to gradients in the concentrations. In organic solar cells, it is necessary to solve the continuity equations for electron (n), hole [p], and exciton (x) concentrations. " These are updated along with the Poisson s equation for the electrostatic potential ((/>). These four equations can be written as... 

Both of the above approaches rely in most cases on classical ideas that picture the atoms and molecules in the system interacting via ordinary electrical and steric forces. These interactions between the species are expressed in terms of force fields, i.e., sets of mathematical equations that describe the attractions and repulsions between the atomic charges, the forces needed to stretch or compress the chemical bonds, repulsions between the atoms due to then-excluded volumes, etc. A variety of different force fields have been developed by different workers to represent the forces present in chemical systems, and although these differ in their details, they generally tend to include the same aspects of the molecular interactions. Some are directed more specifically at the forces important for, say, protein structure, while others focus more on features important in liquids. With time more and more sophisticated force fields are continually being introduced to include additional aspects of the interatomic interactions, e.g., polarizations of the atomic charge clouds and more subtle effects associated with quantum chemical effects. Naturally, inclusion of these additional features requires greater computational effort, so that a compromise between sophistication and practicality is required. 

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