文章基本信息

标题：Stored Coulomb Self-Energy of a Uniformly Charged Rectangular Plate
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作者：Orion Ciftja
期刊名称：Advances in Mathematical Physics
印刷版ISSN：1687-9120
电子版ISSN：1687-9139
出版年度：2016
卷号：2016
DOI：10.1155/2016/7207536
出版社：Hindawi Publishing Corporation
摘要：A large number of electronic devices contain charged, flat plates (electrodes) as their components. The approximation of considering such components as infinitely large plates is not satisfactory for the current status of consumer electronics where size is now extremely small. In particular, the nanotechnology revolution has made the fabrication of truly finite systems with arbitrary shape and characteristic lengths that measure in nanometers possible. As a result the only accurate approach for such situations is to consider the system realistically as one with a finite size extent. In this work we calculate the amount of electrostatic energy that is stored in a charged finite size electrode that is modelled as a uniformly charged rectangular plate with arbitrary length and width. Nontrivial mathematical transformations allow us to derive a closed form exact expression for the Coulomb self-energy of such a system as a function of its length and width (therefore, shape, too). The exact result derived can be useful to understand the storage process of electrostatic energy as a function of size/shape in uniformly charged plate systems. The result also applies to calculations that deal with the properties of a finite two-dimensional electron gas within the jellium model where the finite jellium domain can have an arbitrary rectangular shape.