Problem I have with second London equation

[goran d]

Second London Equation, which is supposed to represent the current in a superconductor. (SI units)
∇×j=-(n_s e²/m) B.
Lets have a look at a super-conducting wire. The magnetic field is:
B=μ₀I_r/(2πr)
Where I_r is the current enclosed by the radius r.
We are talking about the current at some depth, not assuming its infinitely thin.
The problem is, the second London equation predicts the curl of the current is opposite the magnetic field, which conflicts with the direction of the current initially specified. It would predict a relationship between the magnetic field and current that seems impossible.

 

[Valerie Park]

The second London equation is actually an expression of the Meissner effect, which is the expulsion of magnetic field from a superconductor. The equation predicts that the curl of the current is opposite to the magnetic field, and this is exactly what happens when a superconductor is cooled below its critical temperature. The current flows in such a way as to oppose the magnetic field, creating an equal and opposite field that cancels out the applied one.