Assuming we have the following circuit consisting of a superconducting loop having the same superconductor material everywhere, and interrupted by the short Josephson junction J1 with a phase difference π/2 when no external magnetic field bias is applied to it. Is is the current through the superconductor, Ib is the current through an external circuit providing a bias magnetic field perpendicular to the junction J1. Assume Is is smaller or equal than the critical current Ic of the junction J1.
According to this presentation on Josephson junctions, when a magnetic field is applied perpendicular to the short Josephson junction, the phase difference of the junction will change accordingly.
According to Josephson's equations, if the phase difference is π/2, the current through the junction J1 should be equal to the critical current Ic, and if the phase difference is π, the current through the junction should be 0.
What I don't really understand is, if we increase the current Ib such that the magnetic field causes the junction J1 phase difference to be π, there should be no current flowing through the junction. Does this mean that the current through the entire superconducting loop Is becomes 0 when J1 is in this state? Charge cannot disappear, so it would be simply stationary all over the loop? If there is no moving charge, would the magnetic field produced by the superconducting current Is also be 0 in this case?
In other words: can varying an external magnetic applied perpendicular to a short Josephson junction interrupting a superconducting loop change the magnetic flux density around the entire superconductor?
