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Carl described alternative methods of solving this problem:
A circular loop of flexible wire is placed in a uniform
magnetic field perpendicular to its plane. The radius of
the loop is R and its current is I. What is the tension?
This was very useful to me. Thanks. I like this little
problem because at first it is nearly a paradox. Not a single
radial force has a tangential component but the tangential
force, I*B*R, is not zero in the loop.