A Consistency Condition for the Vector Potential in Multiply-Connected Domains

Author

Epstein, C.L. ; Gimbutas, Z. ; Greengard, L. ; Klockner, Andreas ; O´Neil, M.

Author_Institution

Depts. of Math. & Radiol., Univ. of Pennsylvania, Philadelphia, PA, USA

Volume

49

Issue

3

fYear

2013

fDate

Mar-13

Firstpage

1072

Lastpage

1076

Abstract

A classical problem in electromagnetics concerns the representation of the electric and magnetic fields in the low-frequency or static regime, where topology plays a fundamental role. For multiply-connected conductors, at zero frequency, the standard boundary conditions on the tangential components of the magnetic field do not uniquely determine the vector potential. We describe a (gauge-invariant) consistency condition that overcomes this nonuniqueness and resolves a long-standing difficulty in inverting the magnetic field integral equation.

Keywords

electromagnetic field theory; magnetic field integral equations; magnetostatics; topology; classical problem; consistency condition; electric field representation; electromagnetic concerns; gauge-invariant consistency condition; low-frequency regime; magnetic field integral equation; magnetic field representation; multiply-connected conductors; multiply-connected domains; standard boundary conditions; static regime; tangential components; topology; vector potential; zero frequency; Conductors; Educational institutions; Electric potential; Electromagnetics; Magnetostatics; Vectors; Electromagnetic theory; Maxwell equations; electromagnetic (EM) scattering; magnetic field integral equation (MFIE); multiply-connected domains;

fLanguage

English

Journal_Title

Magnetics, IEEE Transactions on

Publisher

ieee

ISSN

0018-9464

Type

jour

DOI

10.1109/TMAG.2012.2223480

Filename

6327672