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In his educational series "Demonstrations in Physics" the late Prof. Julius Sumner Miller posed the following riddle:

Given two identical bars of iron, one magnetized and one not, how can you determine which is magnetized just from the interactions between them (without using anything else, such as iron filings or a compass for example)

Here is a link the video, the question in it's original form is at the 8 minute mark:

https://www.youtube.com/watch?v=C4EWxTTGW0s&t=7m58s

I have been puzzling over this and no matter how I spin it in my head I can't figure it out. Perhaps I misunderstood his phrasing, for example if you break both in half, turn one of the halves around, the permanent magnet's two halves will repel, but that seems like cheating.

Since the two bars are identical in every way, and the forces between the induced and permanent magnet are symmetrical as per Newton, I really don't see any way around this. What am I missing?

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The poles of the magnetized bar (I assume it is magnetized along its main axis for simplicity), will attract the other bar independently of the contact point (with only minor difference in strength), just as a paper clip is attracted to the poles of a permanent magnet regardless of the paper clip's orientation.

But the ends of the unmagnetized bar will barely attract the middle section of the magnetized bar (but rather they will be pulled to the poles, where the field is strongest, again think of a paper clip and a permanent magnet).

So while the force is symmetrical in all cases, the forces are different depending on the relative alignment of the bars.

Apart from this, your scheme of breaking the bars in half is just fine in my opinion.

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