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When a magnet is instantly placed on a conductive plate, the field**************************************************************************
remains expelled from the plate by the induced current. Resistance
gradually removes energy, the flowing charges slow, and the field
"sinks into" the plate in tens of milliseconds. Standard stuff. If the
plate was a perfect conductor, it would take infinite time for the
current to decay, and the field would never sink in at all. There is
repulsion force between plate and magnet which decays as the current
decays.
If the magnet has been on the plate long enough that the current has
decayed and the fields have penetrated, and if the plate is suddenly
removed, the plate takes the fields along with it. Or alternately, the
changing flux induces a current loop which maintains the fields even
when the magnet is not there. If the plate was a perfect conductor, the
currents would persist forever, and the penetrated flux would forever
remained trapped in the plate even with no magnet around. Similar to
superconductive flux-pinning phenomena.
Half way between the above two situations we have "field dragging"
effects. If a copper plate is swept past a bar magnet, the field "sinks
into" the plate partially, current loops are induced, and the moving
plate can drag/stretch the field lines as it departs.
Now the following I'm not so sure about. If a bar magnet was in the
center of some sort of liquid metal fountain, and the metal was expanding
outwards asymmetrically (perhaps in a disk shape), then I would expect
that flows of charge would be induced in the metal so that the outward
moving metal would drag the loops of b-field along with it. The field
around the bar magnet would be distorted into a flat disk rather than
typical dipole, with loops of flux directed outward along one face of the
disk, diving through the disk at great distance, then returning inwards
along the other face of the disk.
If the sun essentially spews conductive plasma from it's equator, and if
the sun's magnetic dipole is through the poles, then I would expect that
the moving plasma would drag field lines along with it and distort the
sun's field radially outwards from the equator. The extended loops of
b-field might even neck down, pinch off, and fly away from the sun as
closed loops which penetrate a gob of moving plasma (with loops of
charge-flow in the plasma of course, like a 1-turn electromagnet.)
Electrical resistance would eventually slow the charge flow and collapse
the field loops, but until it did, the fields might form magnetic bottle
effects, and maintain "clots" of plasma by magnetic pressure.