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Question
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?
Asked by: John Kells
Answer
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.
Answered by: David Pekker, Physics undergrad., Rice, Houston
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