Solution of potential problems near the corner of a conductor

Autor:	J. R. Reitz, L. C. Davis
Rok vydání:	1975
Předmět:	Surface (mathematics) Mathematical analysis Statistical and Nonlinear Physics Function (mathematics) Directional derivative Riemannian geometry Space (mathematics) symbols.namesake symbols Elementary function Elliptic integral Cylindrical coordinate system Mathematical Physics Mathematics
Zdroj:	Journal of Mathematical Physics. 16:1219-1226
ISSN:	1089-7658 0022-2488
DOI:	10.1063/1.522671
Popis:	The Green’s function for a space defined (in cylindrical coordinates) by the intersection of two half‐planes S1 (φ=0) and S2 (φ=ϑ where 0 < ϑ ⩽ 2π) is found by a technique due to Sommerfeld. The Green’s function (or its normal derivative) is required to vanish on the surface S1 + S2 as well as at infinity. When ϑ = mπ/k where k and m are integers, the solution can be written in terms of the Green’s function um for a Riemann space of m windings (in φ). For m = 1 and 2, um can be expressed in terms of elementary functions. For m = 3, we find um to be given in terms of complete elliptic integrals. Application to some simple electrostatic and magnetostatic problems is made, particularly for ϑ = 3π/2.
Databáze:	OpenAIRE
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