- #1
krysith
- 23
- 0
Hello.
Recently I have been inspired by the classic "drop a NdFeB magnet down a copper tube" demonstration, and I have been thinking about a superconductor falling in an ambient magnetic field. I want to determine the terminal velocity, if one exists.
Now, I'm interested only in the effect of the superconductivity. I realize that if I perform this experiment, that air drag and evaporation of refrigerant would have an effect, but pretend that the superconductor is insulated quite well and falling in a vacuum. It becomes clear quite quickly that using an "ideal" superconductor is not appropriate for modeling this, simply because a perfect superconductor (one without a critical current density) would always have a terminal velocity of zero. Since we don't observe superconductors floating around on the Earth's weak magnetic field, this is a non-physical solution.
If I were to use, say, a superconductor of mass M with a critical magnetic field of Hc, in a weak magnetic field of strength B orthogonal to the direction of the fall, then when the superconducting sample begins to fall (Vo=0), then the only screening currents will be those required to exclude the B-field from the sample. As the velocity increases, the B-field will induce a current in the superconductor. In a perfect superconductor, even a small velocity and weak field would cause a large current which moves any energy associated with the velocity quickly into the magnetic field associated with the screening current. However, for a real-world type I or II superconductor, what happens? If the Hc is large enough relative to B and M is there a terminal velocity? If not, what happens?
I have tried searching for an answer to this, and I found this interesting paper: arxiv.org/pdf/physics/0609141. I'm uncertain if this paper is implying that once the screening currents associated with moment through a particular field are established that no more energy can then be absorbed by the field (and thus there is no terminal velocity) or if that implication is just associated with the particular geometry (a superconducting tube around a magnet) that they are using.
Any help, thoughts, ideas, etc. would be greatly appreciated.
Recently I have been inspired by the classic "drop a NdFeB magnet down a copper tube" demonstration, and I have been thinking about a superconductor falling in an ambient magnetic field. I want to determine the terminal velocity, if one exists.
Now, I'm interested only in the effect of the superconductivity. I realize that if I perform this experiment, that air drag and evaporation of refrigerant would have an effect, but pretend that the superconductor is insulated quite well and falling in a vacuum. It becomes clear quite quickly that using an "ideal" superconductor is not appropriate for modeling this, simply because a perfect superconductor (one without a critical current density) would always have a terminal velocity of zero. Since we don't observe superconductors floating around on the Earth's weak magnetic field, this is a non-physical solution.
If I were to use, say, a superconductor of mass M with a critical magnetic field of Hc, in a weak magnetic field of strength B orthogonal to the direction of the fall, then when the superconducting sample begins to fall (Vo=0), then the only screening currents will be those required to exclude the B-field from the sample. As the velocity increases, the B-field will induce a current in the superconductor. In a perfect superconductor, even a small velocity and weak field would cause a large current which moves any energy associated with the velocity quickly into the magnetic field associated with the screening current. However, for a real-world type I or II superconductor, what happens? If the Hc is large enough relative to B and M is there a terminal velocity? If not, what happens?
I have tried searching for an answer to this, and I found this interesting paper: arxiv.org/pdf/physics/0609141. I'm uncertain if this paper is implying that once the screening currents associated with moment through a particular field are established that no more energy can then be absorbed by the field (and thus there is no terminal velocity) or if that implication is just associated with the particular geometry (a superconducting tube around a magnet) that they are using.
Any help, thoughts, ideas, etc. would be greatly appreciated.