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A current-carrying circular loop lies on...

A current-carrying circular loop lies on a smooth horizontal plane. Can a uniform magnetic field be set up in such a manner that the loop turns around it self (i.e. turns about the vertical axis).

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No, because that would require `tau` to tbe in the vertical direction. But `tau=I A xx B`, and since A of the horizontal loop is in the vertical direction, `tau` would be in the plane of the loop for any B.
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