Meissner effect

In superconductivity, the exclusion of magnetic fields from the body of the superconducting material; discovered by German physicist Walther Meissner in 1933. If a block of metal is placed in a magnetic field, the field will exist throughout the material. When the temperature is lowered to below a certain substance-dependent critical temperature, the field vanishes from inside the material, being forced to flow round it.

The Meissner effect (or Meissner-Ochsenfeld effect) is the effect by which a weak magnetic field decays rapidly to zero in the interior of a superconductor. This active exclusion of magnetic fields is distinct from perfect diamagnetism. It is seen that the magnetic field will be zero inside the material in the superconducting state regardless of what it was before the material became superconducting.

is the London equation, where Jd is the current density, B is the magnetic field and λ is the penetration depth. Since the magnetic field is solenoidal, we have the relation

Using the above relations, it is shown that

Since the Laplacian of B is zero, it follows that the field inside a superconductor, beyond the penetration depth decays to zero.

This effect will levitate a magnet as long as the magnetic field does not exceed the critical magnetic field. The ability for the magnet to stay perfectly still is due to flux pinning, in which the magnetic field lines become trapped within the superconductor at sites of impurity in the crystal structure.