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A WoPhO problem from here reads as follows:

A rectangular superconducting plate of mass $m$ has four identical circular holes, one near each corner, see figure. Each hole carries a certain magnetic flux (all the four fluxes are equal and of the same polarity). The plate is put on a horizontal surface which is also in a superconducting state. The magnetic push between the plate and the surface compensates the weight of the plate when the width of the air gap beneath the plate is $d$, which is much smaller than the distance between the plate's and holes' edges (denoted by $\Delta$ in figure); $d$ is also much smaller than the radii of the holes. When the plate levitates in such a way above the support, the frequency of its small vertical oscillations is $v_o$. Next, a load of mass $M$ is put on the plate, so that the load lays on the plate, and the plate levitates above the support. What is the new frequency $v$ of small vertical oscillations (when the load and plate together oscillate up and down)?

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Maybe my question is stupid, but... how can a hole in superconductor carry a magnetic flux? Can it be explained this way: the superconductor was cooled to its critical temperature in the presence of appropriate magnetic field and it somehow remembers that magnetic field?

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Yep, that's it exactly. If you have a large enough magnetic field present when the superconductor is cooled through it's critical temperature $T_c$, then the flux can be trapped instead of expelled.

Interestingly, once the flux is trapped, it remains even if you turn off the source field. Note that for that to be true, it must be the case that there is supercurrent flowing around the edges of the holes.

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  • $\begingroup$ If you want more details I can look up the formula for how much field you need in order to trap flux. $\endgroup$ – DanielSank Apr 16 '17 at 16:52

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