# How can a hole in superconductor contain magnetic flux?

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)?

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?

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.