A curious and useful theorem in two-dimensional electrostatics

Authors
Citation
Jd. Jackson, A curious and useful theorem in two-dimensional electrostatics, AM J PHYS, 67(2), 1999, pp. 107-115
Citations number
13
Categorie Soggetti
Physics
Journal title
AMERICAN JOURNAL OF PHYSICS
ISSN journal
00029505 → ACNP
Volume
67
Issue
2
Year of publication
1999
Pages
107 - 115
Database
ISI
SICI code
0002-9505(199902)67:2<107:ACAUTI>2.0.ZU;2-L
Abstract
In 1956 metrologists Thompson and Lampard established a new theorem in two- dimensional electrostatics that gives calculable capacitances for practical systems possessing a certain symmetry. The theorem is well known among tho se concerned with electrical standards, but not so well known beyond. This paper brings the theorem to a wider audience with a pedagogical discussion of it, first: by treating a simple example by standard methods of electrost atics, then proving the Riemann mapping theorem on which the theorem is bas ed. The Thompson-Lampard theorem and its generalization are then proved and its use in metrology described. Along the way, some curious results about series and products are exhibited. (C) 1999 American Association of Physics Teachers.