The levitron works by having opposing like poles facing each other
to float the rotating one. The gyroscopic forces of rotation stabilize
the floating one from flipping over. Even then it is really tricky to
get it going and stable.
The levitron has the magnetic field oriented north to south as up and down.
So you won't see any changing field lines because the rotation is on-axis
and there is no variation in field strength as it rotates. You would get
nothing
out even if you did have a coil wrapped around it.
It is necessary to have a field at least varying in field strength or
changing from north to south to create current flow.
If you did have the field changing it would not be the copper coils
that would cause the drag and stop rotation.
It is the back emf generated if you tried to draw current out of the
coil. This opposes the changing field and couples to the rotating
magnet and would stop it dead pretty fast. The rotating magnet
supplies the energy to push electrons through the coil. If any
are allowed to move by completing a circuit then presto you
have energy pulled from the rotational energy of the magnet
and it looks just like air friction or even worse. So the rotation
would stop. But this is a moot point since the field orientation
is not right to start with.
Dave Squires