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I was attempting a homework question which went like this:

enter image description here

Where the crosses indicate a magnetic field in that rectangular region pointed into the screen, and we're asked which of the rings would fall first.

The increase in magnetic flux (as the loop enters the magnetic field) creates a counter-clockwise current in the loop, by Lenz's law. This motion in the magnetic field creates an upward magnetic force on the electrons near the bottom of the loop and a downward force on those at the top of the loop, but has no effect on the motion of the loop itself. The magnetic force on the loop itself will be in the horizontal direction.

However, the answer key tells me that the second loop will be slowed down by the magnetic field.

Is this true? Why?

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    $\begingroup$ An application of this phenomenon: en.wikipedia.org/wiki/Eddy_current_brake $\endgroup$ – rob Aug 14 '17 at 16:54
  • $\begingroup$ Just remember that Lenz's law says that a closed conducting loop will always experience a force that attempts to preserve its current magnetic-flux condition. For the loop on the right, there is no magnetic flux through the loop until it falls into the magnetic field. The force on the loop will be such that it tries to keep zero magnetic flux in the loop; the force has to be in the upwards direction to do this. $\endgroup$ – David White Oct 2 at 19:38
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The thing is that you need to consider each step of the loop's descent. In the beginning only the bottom part of the loop is inside the magnetic field so this part only experiences an upward force. This implies that there is a net force slowing down the descent.

This fact continues to be true as long as the whole loop isn't inside the magnetic field. Once it is completely inside there would be no net force (if there still were current in the loop) but it doesn't matter because there would be no more current.

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enter image description here we aim to use very basic laws of physics while answering the question . You can observe that the flux of the magnetic field changes as the loop starts entering the region . As $ \phi = B.A $ and as A increases so does the flux . The changing flux induces am emf in the loop which in turn produces an anti - clockwise current whose magnitude is given by $ \frac{d \phi }{dt}( \frac{1}{R}) $ . Now see in the diagram posted above for the part inside the magnetic field we can calculate the force exerted on the loop using $ |F| = \int_{- \theta`}^{ \theta '} BiRcos(\theta) d \theta $ and by using noticing it's direction you can conclude that the loop is slowing down . You can also understand this using Lenz law. The link is :- https://en.m.wikipedia.org/wiki/Lenz's_law

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  • $\begingroup$ One must also notice that the current is also a function of time in this problem $\endgroup$ – Aditya Garg Apr 20 at 20:49

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