Editing Meissner effect (section)

==Explanation==

The Meissner effect was given a phenomenological explanation by the brothers [[Fritz London|Fritz]] and [[Heinz London]], who showed that the electromagnetic [[Thermodynamic free energy|free energy]] in a superconductor is minimized provided

:<math> \nabla^2\mathbf{H} = \lambda^{-2} \mathbf{H}\, </math>

where '''H''' is the magnetic field and λ is the [[London penetration depth]].

This equation, known as the [[London equation]], predicts that the magnetic field in a superconductor [[exponential decay|decays exponentially]] from whatever value it possesses at the surface. This exclusion of magnetic field is a manifestation of the [[superdiamagnetism]] emerged during the phase transition from conductor to superconductor, for example by reducing the temperature below critical temperature.

In a weak applied field (less than the critical field that breaks down the superconducting phase), a superconductor expels nearly all [[magnetic flux]] by setting up electric currents near its surface, as the magnetic field '''H''' induces [[magnetization]] '''M''' within the London penetration depth from the surface. These surface currents [[Electromagnetic shielding#Magnetic shielding|shield]] the internal bulk of the superconductor from the external applied field. As the field expulsion, or cancellation, does not change with time, the currents producing this effect (called [[persistent current]]s or screening currents) do not decay with time.

Near the surface, within the [[London penetration depth]], the magnetic field is not completely canceled. Each superconducting material has its own characteristic penetration depth.

Any perfect conductor will prevent any change to magnetic flux passing through its surface due to ordinary [[electromagnetic induction]] at zero resistance. However, the Meissner effect is distinct from this: when an ordinary conductor is cooled so that it makes the transition to a superconducting state in the presence of a constant applied magnetic field, the magnetic flux is expelled during the transition. This effect cannot be explained by infinite conductivity, but only by the London equation. The placement and subsequent levitation of a magnet above an already superconducting material does not demonstrate the Meissner effect, while an initially stationary magnet later being repelled by a superconductor as it is cooled below its critical [[temperature]] does.

The persisting currents that exist in the superconductor to expel the magnetic field is commonly misconceived as a result of [[Lenz's Law]] or [[Faraday's law of induction|Faraday's Law]]. A reason this is not the case is that no change in flux was made to induce the current. Another explanation is that since the superconductor experiences zero resistance, there cannot be an induced emf in the superconductor. The persisting current therefore is not a result of Faraday's Law.