# Why will a magnetic field cause a ring to hover?

I was attempting a homework question which went like this:

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?

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