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A sustained current circulates in a ring-shaped superconductor. Assuming the superconductor to be a gigantic Bohr orbit show that the current and the magnetic flux are quantized. Take into account the pairing of electrons in a superconductor.

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Solution :Let the concentration of PAIRS in the superconductor be `N.=n//2`. Then the current will be `i=qn.Sv=2en/2Sp/(2m_(e))`, where p is the momentum of the pair. According to Bohr.s rule, the angular momentum is quantized: pr = Nh, where N = 1, 2, 3, (the principal quantum number). We have for the currect
`i=N(nS)/r*(eh)/(2m_(e))`
where S is the conductor.s cross section, and r is the radius of the ring. Clearly the current is quantized: `i=N_(i_(0))`, where `i_(0)` is the MINIMUM current, `i_(0)=(nS)/r*(eh)/(2m_(2))`
Since the magnetic flux is proportional to the current, it too turns out to be quantized:
`Phi=Li=NLi_(0)=NPhi_(0)`
where L is the INDUCTANCE of the ring, and `Phi_(0)` is the minimum magnetic flux. Rigorous theory yields `Phi_(0)=h//2e=2.07xx10^(-15)` Wb.


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