How Does the Meissner Effect Cause a Superconductor to Levitate?

[wasia]

I have been considering a situation, where a piece of superconducting (SC) material is put onto a magnet and then cooled through SC transition. As I understand, repulsion occurs and the SC piece gets away from the magnet (is it correct?).

Assuming this happens, the SC piece may shoot upwards resisting gravity. In this case work is done (against gravity) and energy should be conserved. Where does this energy come from?

Yes, I have done a search on this and did not find an answer. Thank you.

 

[marcusl]

The energy to consider is the Helmholtz free energy of the SC. When the transition temperature is crossed, electrons in the metal form Cooper pairs and condense into a lower energy state. This released energy does the mechanical work you observe. The free energy was first examined by the London brothers ("London equations"), and developed fully by Ginzburg and Landau ("Ginzburg-Landau Theory"). Tinkham's book "Introduction to Superconductivity" has a full discussion.

 

[charng]

I can confirm that the scenario you have described is a result of the Meissner effect, which is a phenomenon that occurs when a superconducting material is placed in a magnetic field and cooled below its critical temperature. This effect causes the magnetic field to be expelled from the interior of the superconductor, resulting in a repulsive force between the superconductor and the magnet.

You are correct in your understanding that in this situation, the superconductor will experience a repulsive force and may move away from the magnet. This is due to the fact that the magnetic field lines are not able to penetrate the superconductor and are instead forced to travel around it, creating a repulsive force.

In regards to the question of where the energy comes from in this scenario, it is important to note that the superconductor does not actually shoot upwards. In reality, the repulsive force is balanced by the force of gravity, resulting in the superconductor levitating in a stable position. The energy required to overcome gravity is provided by the magnetic field itself, as the magnetic field lines are rearranged to accommodate the presence of the superconductor.

It is also important to keep in mind that the superconductor will only levitate if it is kept at a temperature below its critical temperature. If the temperature were to rise above this point, the superconductor would lose its superconducting properties and the magnetic field lines would be able to penetrate it, causing it to lose its levitating ability.

I hope this explanation helps to clarify the concept of the Meissner effect and the energy involved in this scenario. As with many phenomena in science, it is important to carefully consider all factors and variables in order to fully understand the mechanisms at play.