Fun magnetics question with the Meissner Effect

[mike232]

I was hoping I could get some help deriving a formula that shows how much current is needed to generate enough of a magnetic field to lift an X Newton mass L meters above a superconductor. ( Probably in centimeters but meters here for the sake of SI easiness )

I was helping one of my professors with a display using the Meissner Effect to float a magnet above a superconductor. The superconductor was made as a Sr. Research project and we soaked it in liquid nitrogen and could float a magnet above it as long as the conductor was cold enough. It was a Yttrium Barium Copper Oxide superconductor.

I just finished an intermediate E&M class with Griffith's book yesterday so I'm hoping my new found knowledge on magnetic fields and magnetic flux is enough to understand this!

Any help or direction on where to start or more would be very much appreciated!

 

[Vailanor]

Unfortunately, it is impossible to predict the current needed to generate a magnetic field capable of lifting an object of a certain mass L meters above a superconductor without knowing more information about the system. This is because there are many other factors that affect the strength of the magnetic field, such as the size and shape of the magnet, the distance between the magnet and the superconductor, and the type of superconductor used. However, one way to estimate the current needed to generate a magnetic field strong enough to lift an object is to use the Biot-Savart law. This law states that the magnitude of the magnetic field at any point in space due to a current loop is proportional to the current in the loop and inversely proportional to the square of the distance from the loop. The Biot-Savart law can be used to calculate the magnetic field strength at any given point in space. From this, you can then calculate the force that the magnetic field will exert on the object, which can then be used to determine the amount of current needed to generate a magnetic field of a sufficient strength to lift the object. For example, if you know the mass of the object, the distance between the object and the superconductor, and the type of superconductor used, you can calculate the required force to lift the object by using Newton's second law of motion (F = ma). You can then use the Biot-Savart law to calculate the magnetic field strength at that point in space, and then calculate the amount of current needed to generate a magnetic field of that strength. I hope this helps!