A consistency condition for the vector potential in multiply-connected domains

Charles L. Epstein, Zydrunas Gimbutas, Leslie Greengard, Andreas Klockner, Michael O'Neil

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Article number6327672
Pages (from-to)1072-1076
Number of pages5
JournalIEEE Transactions on Magnetics
Issue number3
StatePublished - 2013


  • Electromagnetic theory
  • Maxwell equations
  • electromagnetic (EM) scattering
  • magnetic field integral equation (MFIE)
  • multiply-connected domains

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Electrical and Electronic Engineering


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