This one was a cheat. The deception lies in the picture, in psychology, and
in the way we described it:
Clearly the N end of the horseshoe magnet will be repelled by being in such close proximity to the outer magnet's North end. Likewise, the S end of the horseshoe magnet will be attracted to the outer magnet's North end. We supply helpful arrows to show the directions of these two forces.So the horseshoe magnet will experience a counterclockwise torque, which will be the same for any position, and therefore sustain its motion.
Well, not so clearly. Those arrows were anything but "helpful".
The horseshoe magnet is a common visual icon, and
many people think that somehow such a magnet attracts objects preferentially
straight in front of its ends. Road Runner cartoons illustrate that concept.
We have shown the force arrows in the diagram to
reinforce that (wrong) interpretation. To a first approximation magnets
with two poles behave as if the poles were nearly localized, and what lies
between the poles doesn't much affect their attraction to other objects.
This could as well have been a short, straight magnet, offset from the axle.
We show it here with only the poles. Now we see that since the outer N
pole is symmetric and of uniform strength all around the circle, the
vector sum of all forces it exerts on the horseshoe magnet's N pole is
(by symmetry argument) aimed toward the axle. It exerts no torque on the
horseshoe magnet. The same argument holds for the horeshoe magnet's S pole.
Nothing will move.
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