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

Patrick Ciarlet 1 Samir Kaddouri 1
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
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.
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Submitted on : Thursday, October 31, 2013 - 4:58:20 PM
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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, Elsevier Masson, 2006, 343 (10), pp.671-674. ⟨10.1016/j.crma.2006.10.009⟩. ⟨hal-00876237⟩

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