How would magnetic fields/electromagnetism interact with a wormhole? e.g. let's say you have something like this:
<--M<-- A|   O   |B

where A| and |B are the two ends of a wormhole, pointed in the direction of the pipes, and the arrows represent the polarity of the magnet (or something.  I may have futzed up the terminology a little).  Take your pick of what kind of wormhole, but it has to be traversable.
How would objects that would be noticeably affected by the magnetic field of M ('O') behave if they were placed between the two mouths A and B?
Additionally, what if there was some sort of tube enclosing the wormhole so that an object could not travel 'outside of the wormhole' (e.g. go around A.)
 A: If the wormhole is field traversable (most wormholes are $field$ traversable, traversable is referred rather about particles and quanta being able to pass through or not) then the problem reduces to solving how magnetic field acts on the object, which depends on the following parameters:


*

*the $area$ of the mouth of the wormhole

*the distance between the field source and the wormhole

*the distance between the wormhole and the affected object

*in case we study a non-static situation we need the retarded positions, and in that case we also need to know the length of the wormhole or rather the length of the $geodesic$ that connects the 2 space-time "sheets"


As for the case you mentioned above it depends on the nature of the object $O$.
If for example the object is a permanent magnet and the distance between the object and each wormhole mouth is small and the area of the mouth is big enough then the north pole of the magnet will be attracted to one side of the wormhole and the south pole to the other side of the wormhole (the force $F$ will depend on $A$ and $l$). The magnet will "levitate" between the 2 mouth of the wormhole (under the above specified constraints).
The greater the distance the smaller the effect; the greater the area the more field can pass through.
One can easily apply classical formulas like in the force between magnets, as long as the wormhole does not distort field lines directions, as long as it can be approximated to an "open door" between space-time sheets.
Otherwise a more complex situation needs to be solved using General Relativity, with the metric $g_{\mu\nu}$ of our wormhole, integrating electromagnetism in the energy tensor of matter $T^{\mu\nu}$ and solving Einstein's field equations.
