A Consistency Condition for the Vector Potential in MultiplyConnected Domains
Abstract
A classical problem in electromagnetics concerns the representation of the electric and magnetic fields in the lowfrequency 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 (gaugeinvariant) consistency condition that overcomes this nonuniqueness and resolves a longstanding difficulty in inverting the magnetic field integral equation.
 Publication:

IEEE Transactions on Magnetics
 Pub Date:
 March 2013
 DOI:
 10.1109/TMAG.2012.2223480
 arXiv:
 arXiv:1203.3993
 Bibcode:
 2013ITM....49.1072E
 Keywords:

 Physics  Classical Physics;
 Mathematics  Numerical Analysis
 EPrint:
 doi:10.1109/TMAG.2012.2223480