Heaviside who lent D the present significance it now has. Consider an infinite parallel plate capacitor where the space between the plates is empty or contains In physics, the electric displacement field (denoted by D), also called electric flux density, is a vector field that appears in Maxwell's equations. It accounts for the electromagnetic effects of polarization and that of an electric field, combining the two in an auxiliary field. It plays a major role in the physics of phenomena such as the capacitance of a material, the response of dielectrics Consider an infinite parallel plate capacitor where the space between the plates is empty or contains a neutral, insulating medium. In both cases, the free charges are only on the metal capacitor plates. Since the flux lines D end on free charges, and there are the same number of uniformly distributed charges of opposite sign on both plates, then the flux lines must all simply traverse the capacitor from one side to the other. In SI units, the charge density on the plates is proportional to the value of the D field between the plates. This follows directly from Gauss's law, by integrating over a small rectangular box straddling one plate of the capacitor: where d is their separation. Introducing the dielectric increases ε by a factor ε r {\displaystyle \varepsilon _{r}} and either the voltage difference between the plates will be smaller by this factor, or the charge must be higher. The partial cancellation of fields in the dielectric allows a larger amount of free charge to dwell on the two plates of the capacitor per unit of potential drop than would be possible if the plates were separated by vacuum. If the distance d between the…

The uniform electric field approximation of parallel plates with guard rings is well recognized. However, near corners a high electric field exists in some circumstances, and it can give rise to electron or ion emission. A theoretical study of this field intensity, for example, shows that for a 10-mm electrode separation, 2-mm gap between an electrode and a guard ring, and a 0.005-mm corner radius, the electric field is as high as 5.4 times the uniform field found between infinite plane electrodes.

The Schwinger mechanism of particle production in a strong and uniform electric field for an infinite system is generalized to the case where the strong field is confined between two condenser plates separated by a finite distance. The production rates, for both bosons and fermions, are obtained by solving the Klein-Gordon equation and the Dirac equation in a linear vector potential. They are expressed in terms of parabolic cylinder functions for bosons, and in terms of the confluent hypergeometric functions for fermions. Numerical evaluation of these results shows large deviations of the production rate from what one deduces with the Schwinger formula, indicating a large finite-size effect in particle production.