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

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5 Author(s)
Epstein, C.L. ; Depts. of Math. & Radiol., Univ. of Pennsylvania, Philadelphia, PA, USA ; Gimbutas, Z. ; Greengard, L. ; Klockner, A.
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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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Magnetics, IEEE Transactions on  (Volume:49 ,  Issue: 3 )