Hi, I am new to superconductivity and have been doing a lot of reading to try and become familiar with it. I have come across a few questions that I would be grateful is someone could answer. I am confused about the mechanism that describes the expulsion of magnetic fields from inside a superconductor. The source of my confusion came from this YouTube clip from an MIT professor where he talks about superconductivity at 30mins 30seconds in. He argues that a superconductor expels magnetic fields because if one did penetrate it then an emf would be generated across it and if the resistance is zero, the current would go to infinity according to Ohm's Law. If this is true then what about if you take a superconducting material above the critical temperature and expose it to a magnetic field. This would cause a magnetic field to go through the superconducting material. If you then cool it until it becomes superconducting then all the sources I have read say that the magnetic field is expelled. Would this not be considered a change in magnetic field and therefore generate an infinite current using this logic from the lecturer? What is the reason magnetic fields are expelled from superconductors? Is it to satisfy the infinite current caused by a changing flux? Thanks.