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A current loop generates a magnetic field all around itself as shown in picture.

enter image description here

My question is: does this magnetic field produce mechanical effects (force or torque) on the loop itself? If so, what effects are involved?

If we take two opposites elements of the loop and evaluate the force on each element due to this magnetic field the resultant is not zero, as shown in the figure below.

enter image description here

The its seems like there is a force downwards! But how can that happen? Will the loop start moving just because of its own magnetic field?

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    $\begingroup$ How did you come to the conclusion that the force on the "elements" is non-zero? $\endgroup$ – ACuriousMind Jan 10 '17 at 14:40
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The answer lies in the figure itself. The field lines points in opposite directions at diametrically opposite points on the loop. Hence the forces will be equal and opposite at diametrically opposite points on the loop, by symmetry along the axis of the loop. So, in effect the loop stays put since there is no net force acting on the loop as a whole. However there are forces at each and every points on the loop if you consider every single point on the loop individually. But as a whole, the loop feels no force at all.

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