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No. Because there is a potential difference

Yes, it is possible.

'Cryogenic' electromagnets, such as those in MRI machines, are supercooled

loops of superconducting material, with no ends, in which an electric current is

started by a temporary potential difference. But then the ends are joined, and

the current continues, in principle for as long as the loop remains supercooled.

I have seen an MRI loop current sustained for 4 months, and stopped only when

a lab assistant allowed a liquid helium cooling tank to run dry.

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