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

@article{Epstein2013ACC, title={A Consistency Condition for the Vector Potential in Multiply-Connected Domains}, author={C. Epstein and Z. Gimbutas and L. Greengard and A. Klockner and M. O'Neil}, journal={IEEE Transactions on Magnetics}, year={2013}, volume={49}, pages={1072-1076} }

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… CONTINUE READING

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