Focal image charge singularities for the dieletric elliptic cylinder

Johan Sten

Research output: Contribution to journalArticleScientificpeer-review

3 Citations (Scopus)

Abstract

The electrostatic potential problem involving a dielectric elliptic cylinder and an external parallel line charge is solved in terms of continuous image charge and dipole layer distributions on the focal strip of the cylinder. As a starting point, two integral identities are derived from the relation between the true charge distributions on a flat conducting strip induced by a parallel line charge and the corresponding series expansion of the potential. It turns out that two different solutions must be applied, depending on the distance of the source and shape of the cylinder. By letting the cross-section of the cylinder approach a circle, the image is seen to coincide with the line image solution available for the circular cylinder. A simple expression is given for the equivalent polarisation distribution on the focal strip due to a homogeneous field.
Original languageEnglish
Pages (from-to)9-15
Number of pages7
JournalElectrical Engineering
Volume79
Issue number1
DOIs
Publication statusPublished - 1996
MoE publication typeA1 Journal article-refereed

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Charge
Singularity
Strip
Charge distribution
Circular cylinders
Line
Electrostatics
Polarization
Continuous Image
Potential Problems
Circular Cylinder
Series Expansion
Dipole
Circle
Cross section

Cite this

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abstract = "The electrostatic potential problem involving a dielectric elliptic cylinder and an external parallel line charge is solved in terms of continuous image charge and dipole layer distributions on the focal strip of the cylinder. As a starting point, two integral identities are derived from the relation between the true charge distributions on a flat conducting strip induced by a parallel line charge and the corresponding series expansion of the potential. It turns out that two different solutions must be applied, depending on the distance of the source and shape of the cylinder. By letting the cross-section of the cylinder approach a circle, the image is seen to coincide with the line image solution available for the circular cylinder. A simple expression is given for the equivalent polarisation distribution on the focal strip due to a homogeneous field.",
author = "Johan Sten",
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language = "English",
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Focal image charge singularities for the dieletric elliptic cylinder. / Sten, Johan.

In: Electrical Engineering, Vol. 79, No. 1, 1996, p. 9-15.

Research output: Contribution to journalArticleScientificpeer-review

TY - JOUR

T1 - Focal image charge singularities for the dieletric elliptic cylinder

AU - Sten, Johan

PY - 1996

Y1 - 1996

N2 - The electrostatic potential problem involving a dielectric elliptic cylinder and an external parallel line charge is solved in terms of continuous image charge and dipole layer distributions on the focal strip of the cylinder. As a starting point, two integral identities are derived from the relation between the true charge distributions on a flat conducting strip induced by a parallel line charge and the corresponding series expansion of the potential. It turns out that two different solutions must be applied, depending on the distance of the source and shape of the cylinder. By letting the cross-section of the cylinder approach a circle, the image is seen to coincide with the line image solution available for the circular cylinder. A simple expression is given for the equivalent polarisation distribution on the focal strip due to a homogeneous field.

AB - The electrostatic potential problem involving a dielectric elliptic cylinder and an external parallel line charge is solved in terms of continuous image charge and dipole layer distributions on the focal strip of the cylinder. As a starting point, two integral identities are derived from the relation between the true charge distributions on a flat conducting strip induced by a parallel line charge and the corresponding series expansion of the potential. It turns out that two different solutions must be applied, depending on the distance of the source and shape of the cylinder. By letting the cross-section of the cylinder approach a circle, the image is seen to coincide with the line image solution available for the circular cylinder. A simple expression is given for the equivalent polarisation distribution on the focal strip due to a homogeneous field.

U2 - 10.1007/BF01840702

DO - 10.1007/BF01840702

M3 - Article

VL - 79

SP - 9

EP - 15

JO - Electrical Engineering

JF - Electrical Engineering

SN - 0948-7921

IS - 1

ER -