Open AccessAveraging of harmonic physical fields over an annular region enclosing field sources
Author(s) -
Lin Z. Li
Publication year - 2002
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 - 10.1119/1.1491264
Subject(s) - physics , laplace's equation , harmonic , harmonic function , boundary value problem , laplace transform , electromagnetic field , field (mathematics) , property (philosophy) , classical mechanics , mathematical analysis , quantum electrodynamics , quantum mechanics , mathematics , philosophy , epistemology , pure mathematics
Fields such as temperature, current density, and static electromagnetic fields in regions with no field sources are harmonic functions that satisfy the Laplace equation. Such functions on a sphere have a well-known mean value property. A new mean value property is derived for fields that are harmonic on an annular region, with the field sources enclosed by the inner boundary. Some examples are discussed.