Open AccessApplication of Sommerfeld-Watson Transformation to an Electrostatics Problem
Author(s) -
Jon Pumplin
Publication year - 1969
Publication title -
american journal of physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.541
H-Index - 99
eISSN - 1943-2909
pISSN - 0002-9505
DOI - 10.1119/1.1975793
Subject(s) - physics , electrostatics , transformation (genetics) , charge (physics) , classical mechanics , point particle , representation (politics) , field (mathematics) , mathematical analysis , mathematical physics , quantum electrodynamics , quantum mechanics , pure mathematics , mathematics , political science , law , biochemistry , chemistry , gene , politics
The electrostatics problem of a point charge between two infinite parallel conducting planes— i.e., the Green function for a parallel plate capacitor—is solved by the method of images. A Sommerfeld-Watson transformation is then used to obtain an integral representation for the potential. An asymptotic expression is derived for the region far from the charge, and the field is found to fall off exponentially.
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