Electric vector potential and the Biot-Savart like law in electrostatics

Abstract

A vector potential formulation is shown in this article to compute the electric field of planar surface electrodes. The electric field is derived from from the solution of the Laplace’s equation in the free-charge space. Neumann-boundary conditions must be set on the region between planar metallic sheets as the separation goes to zero. It is shown that the electric field can be written via a Biot Savart- like integral. The strategy enables to generalize the analytical result for its application in the gaped surface electrodes description.

Comparative analysis of molecular dynamics and method of moments in two-dimensional concentric circular layers

“…The angular integral in the previous expression can be written in terms of special functions, by following an analogous procedure than the one in equation (1). The angular integral is…”

“…The system can be also modeled as two-dimensional plasma where within Ω in , reside N 1 particles with charge q 1 ∈ R, while Ω out holds N 2 particles with charge q 2 ∈ R (see figure 1). The foregoing study draws inspiration from [1], where the gapped SE was characterized by two-conductor flat regions with differing potentials and a distinct gap. Electric field and surface charge density analysis in that system involved resolving Laplace's equation with specified conditions.…”

“…In that study, interactions followed an inverse power law potential 1/r, where the coupling parameter Γ has been found inversely proportional to the system's temperature and proportional to q 2 . Furthermore, authors of [1] explored the electric vector potential and the Biot-Savart law analogy in electrostatics. These efforts set the zero stage for the present study, aiming to further analyze the system in question with the statistical mechanics approach.…”

“…Furthermore, authors of Ref. [1] explored the electric vector potential and the Biot-Savart law analogy in electrostatics. These efforts set the zero stage for the present study, aiming to further analyze the system in question with the statistical mechanics approach.…”