A justification of Peek's empirical law in electrostatics [Justification de la loi de Peek en électrostatique] - Archive ouverte HAL Access content directly
Journal Articles Comptes Rendus. Mathématique Year : 2006

A justification of Peek's empirical law in electrostatics [Justification de la loi de Peek en électrostatique]

Abstract

We consider the computation of the electrostatic charge density at the tip of a rounded corner. The relation between the curvature radius and the electrostatic field is given by Peek's empirical law which is valid only for thin, cylindrical or spherical, geometries. In this Note, we justify mathematically this law and extend it to other geometries. With the help of multiscaled asymptotic expansions, we derive an expression for the charge density for geometries which coincide at infinity with a cone. A numerical illustration is provided. To cite this article: P. Ciarlet Jr., S. Kaddouri, C. R. Acad. Sci. Paris, Ser. I 343 (2006). © 2006 Académie des sciences.

Dates and versions

hal-00876237 , version 1 (31-10-2013)

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Patrick Ciarlet, Samir Kaddouri. A justification of Peek's empirical law in electrostatics [Justification de la loi de Peek en électrostatique]. Comptes Rendus. Mathématique, 2006, 343 (10), pp.671-674. ⟨10.1016/j.crma.2006.10.009⟩. ⟨hal-00876237⟩
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