Alternative separation of Laplace's equation in toroidal coordinates and its application to electrostatics

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dc.contributor.authorAndrews, Mark
dc.date.accessioned2015-12-07T22:21:38Z
dc.date.issued2006
dc.date.updated2015-12-07T09:00:06Z
dc.description.abstractThe usual method of separation of variables to find a basis of solutions of Laplace's equation in toroidal coordinates is particularly appropriate for axially symmetric applications; for example, to find the potential outside a charged conducting torus. An alternative procedure is presented here that is more appropriate where the boundary conditions are independent of the spherical coordinate θ (rather than the toroidal coordinate η or the azimuthal coordinate ψ). Applying these solutions to electrostatics leads to solutions, given as infinite sums over Legendre functions of the second kind, for (i) an arbitrary charge distribution on a circle, (ii) a point charge between two intersecting conducting planes, (iii) a point charge outside a conducting half plane. In the latter case, a closed expression is obtained for the potential. Also the potentials for some configurations involving charges inside a conducting torus are found in terms of Legendre functions. For each solution in the basis found by this separation, reconstructing the potential from the charge distribution (corresponding to singularities in the solutions) gives rise to integral relations involving Legendre functions.
dc.identifier.issn0304-3886
dc.identifier.urihttp://hdl.handle.net/1885/20136
dc.publisherElsevier
dc.sourceJournal of Electrostatics
dc.subjectKeywords: Electric charge; Functions; Laplace transforms; Mathematical models; Polynomials; Laplace equation; Legendre polynomials; Separation of variables; Toroidal coordinates; Electrostatics; Electric charge; Electrostatics; Functions; Laplace transforms; Mathem Laplace equation; Legendre polynomials; Separation of variables; Toroidal coordinates
dc.titleAlternative separation of Laplace's equation in toroidal coordinates and its application to electrostatics
dc.typeJournal article
local.bibliographicCitation.lastpage672
local.bibliographicCitation.startpage664
local.contributor.affiliationAndrews, Mark, College of Physical and Mathematical Sciences, ANU
local.contributor.authoremailrepository.admin@anu.edu.au
local.contributor.authoruidAndrews, Mark, u921077
local.description.embargo2037-12-31
local.description.notesImported from ARIES
local.identifier.absfor020204 - Plasma Physics; Fusion Plasmas; Electrical Discharges
local.identifier.ariespublicationu4103646xPUB11
local.identifier.citationvolume64
local.identifier.doi10.1016/j.elstat.2005.11.005
local.identifier.scopusID2-s2.0-33745826990
local.identifier.uidSubmittedByu4103646
local.type.statusPublished Version

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