I have a collection of bar magnets on a frictionless plane, immobilized at their centers, but able to rotate freely. I flick each magnet to randomize its rotational orientation.
Is there a magnetic potential I can apply to the field s.t. half of the magnets will rotate to be antiparallel to the other half? In other words, can I engineer two attractive states where half the magnets will want to point in a direction rotated 90 degrees from the other half based on their random initial orientation?