QUESTION #378

# If you have a magnet inside a box made of a superconducting material (in its superconducting state), would there be any magnetic field around the exterior?

There should be no magnetic field outside the box assuming that before you turn on the magnet inside the box, there is no field.

1. If you have an isolated superconducting box, then it is possible that it has non-zero current inside of it, and thus a magnetic field. We will assume that box has been prepared to avoid this from happening. This can be achieved by making the transition to the superconducting state with no magnetic fields around.

2. Now we have arranged for a magnet to turn on inside the box. This can be accomplished by having an electromagnet connected to a power source through a timer implanted inside the box before it is made superconducting. When the magnet turns on, the supercurrents in the superconductor will appear so as to exactly cancel the magnetic field inside the box. This will cause magnetic field outside to be zero. (Since outside the box, the box's magnetic field is exactly same as that of the magnet but with opposite polarity causing total field to be zero.) Inside the box, we will see that fields add in such a way that all the field lines are terminated without going inside the superconductor.

An easier way to think about this problem is: what is the magnetic field inside a small cavity in a superconductor that has been immersed in a magnetic field. (This problem is topologically identical to the previous one.) Intuitively we know that field lines can not penetrate inside, so field must be zero.