I'm studying the behaviour of superconductors in different cases, and I can't understand this.
We have a superconducting cylinder with a coaxial hole inside (vacuum). When the cylinder is cooled below it's critical temperature, and later a magnetic field is applied (case a), the superconductor will exclude the field even from the hole (B=0 inside the hole). However, if we first apply the magnetic field and then we cool down the cylinder (case b), the magnetic field will be excluded from the superconductor but not from the empty hole (as seen in the image below). Thus, depending on the procedure, we have two possible final states.
My question is, why is there this difference? Why doesn't the superconductor allow a magnetic field inside the hole in case a? It would still be excluding it from all the superconducting volume.
(Sorry, I don't know the source of the image, I took it from my professor's notes)