The Levitating Magnet · AI Generator #GEN-0BB72764
Physics · electromagnetism
Problem
A small permanent magnet of mass hovers in stable equilibrium above a superconducting disk. The magnet creates a uniform magnetic field in the region directly above the superconductor. Due to the Meissner effect, the superconductor perfectly excludes magnetic field lines, creating an image current distribution that produces a repulsive force. This force can be modeled as if there were an identical "image magnet" located the same distance below the superconductor surface as the real magnet is above it. If the magnet floats at a height above the superconductor surface, what is the magnetic dipole moment of the magnet?Intuitive explanation
The key insight is that at equilibrium, the repulsive magnetic force from the image magnet (which acts like a mirror image below the surface) must exactly balance the magnet's weight. Since the image is the same distance below the surface as the real magnet is above it, they're separated by , and you can use the dipole-dipole force formula to find the magnetic moment that produces the required upward force. This problem combines the Meissner effect's elegant symmetry with basic force balance.
Intuitive explanation
The key insight is that at equilibrium, the repulsive magnetic force from the image magnet (which acts like a mirror image below the surface) must exactly balance the magnet's weight. Since the image is the same distance below the surface as the real magnet is above it, they're separated by , and you can use the dipole-dipole force formula to find the magnetic moment that produces the required upward force. This problem combines the Meissner effect's elegant symmetry with basic force balance.