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According to Meissner effect, there would be no magnetic field outside. But according to Gauss's law, the total magnetic flux must be non zero.

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  • $\begingroup$ Nothing forbids you to try rewriting the London's constitutive equations $\nabla\times j \propto B$ with the extra assumption of $\nabla\cdot B = \rho_{m}$. It seems to me it reads again $\nabla\times\nabla\times B+B/\lambda^{2}=0$ where you can use the identity $\nabla\times\nabla\times B = \nabla\left(\nabla\cdot B\right)-\nabla^{2}B$ and replace the Gauß law for magnetic monopole, so that both effects (Meißner effect and magnetic monopole) are taken into account. $\endgroup$ – FraSchelle Oct 31 '16 at 20:24
  • $\begingroup$ In 2D, it should be the same problem as putting an infinite flux tube in the middle of a superconducting ring, which exhibit the Aharonov-Bohm effect. In 3D it may give interesting results, which I do not know. $\endgroup$ – FraSchelle Oct 31 '16 at 20:25

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