# Current induced in a superconducting coil

Does the magnitude of current induced in a shorted superconducting coil depend on the external flux's rate of change $$\frac{d\Phi_{EXT}}{dt}$$ ?

Assume that initially the flux through the coil is zero and the initial current circulating in that coil is zero, too, but at some later time, an external flux source attempts to change the flux threading that shorted ideal coil to $$\Phi_{EXT}$$.

Since the total flux through the superconducting loop remains constant at $$0$$ (the reason for this is that any change in flux requires a nonzero emf around the loop, which requires in infinite current, so magnetic flux through the loop cannot change), the flux from the self-inductance $$L$$ of the loop must be equal and opposite to the external flux. We conclude that $$I=\frac{\Phi}{L}$$.
• Note this phenomenon, described by @DanDan0101 is independent on how fast the flux changes; it can be days, it can be nanoseconds. If the changes were on picosecond scale, the corresponding energy ($\hbar/\tau$) could get similar to the pseudogap and some induced energy could be lost in the semiconductor. Oct 14, 2020 at 19:32