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

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5 Author(s)
Charles L. Epstein$^{1}$Departments of Mathematics and Radiology,, University of Pennsylvania,, Philadelphia,, PA, USA ; Zydrunas Gimbutas ; Leslie Greengard ; Andreas Klockner
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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.

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IEEE Transactions on Magnetics  (Volume:49 ,  Issue: 3 )