Image distribution and surface potential of a dipole in a one-shell conducting sphere

Johan Sten (Corresponding Author), George Dassios

Research output: Contribution to journalArticleScientificpeer-review

2 Citations (Scopus)

Abstract

An image solution to account for the static electric field on the surface of a one-shell conducting sphere with an internal source, relevant for example to the electroencephalography problem for a spherical model of the human head, is derived and analysed. The image of a point dipole is found to contain a series of point dipoles and a piecewise continuous distribution of dipoles along the line segment between the source point and the centre of the sphere. These image line sources obey simple power and logarithmic laws of the position. As it turns out that the image dipole distribution is similar for a source dipole of any direction, the expression for the image-based surface potential takes a simple and manageable form.
Original languageEnglish
Pages (from-to)720-731
JournalIMA Journal of Applied Mathematics
Volume75
Issue number5
DOIs
Publication statusPublished - 2010
MoE publication typeA1 Journal article-refereed

Fingerprint

Surface Potential
Surface potential
Dipole
Shell
Electroencephalography
Electric fields
Spherical Model
Piecewise continuous
Continuous Distributions
Point Source
Line segment
Electric Field
Logarithmic
Internal
Series
Line

Keywords

  • image system
  • multilayer sphere
  • conductivity
  • surface potential

Cite this

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Image distribution and surface potential of a dipole in a one-shell conducting sphere. / Sten, Johan (Corresponding Author); Dassios, George.

In: IMA Journal of Applied Mathematics, Vol. 75, No. 5, 2010, p. 720-731.

Research output: Contribution to journalArticleScientificpeer-review

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T1 - Image distribution and surface potential of a dipole in a one-shell conducting sphere

AU - Sten, Johan

AU - Dassios, George

PY - 2010

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AB - An image solution to account for the static electric field on the surface of a one-shell conducting sphere with an internal source, relevant for example to the electroencephalography problem for a spherical model of the human head, is derived and analysed. The image of a point dipole is found to contain a series of point dipoles and a piecewise continuous distribution of dipoles along the line segment between the source point and the centre of the sphere. These image line sources obey simple power and logarithmic laws of the position. As it turns out that the image dipole distribution is similar for a source dipole of any direction, the expression for the image-based surface potential takes a simple and manageable form.

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KW - multilayer sphere

KW - conductivity

KW - surface potential

U2 - 10.1093/imamat/hxq031

DO - 10.1093/imamat/hxq031

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