When the solenoid was energized, it produces a magnetic field. The ring thus experienced an increase in magnetic flux linkage. This results in an induced emf around the ring. (Faraday’s Law: emf=dΦ/dt)

The magnetic flux captured by all three rings are exactly the same. (It’s is the same solenoid, so B is the same. The rings have the same circular area, so A is the same. And Φ=BA) Clearly, all three rings experienced the same change in magnetic flux linkage. This leads to the conclusion that the induced emf in all three rings are exactly the same!

So why do they jump to different heights?

Firstly, they jump because the induced current (caused by the induced emf) produces its own magnetic field. The interaction of the magnetic field of the ring and the magnetic field of the solenoid leads to a mutually repulsive force. (This outcome is predicted by Lenz’s Law). Note that the effect of the induced emf is felt only when it results in an induced current.

The solid ring presents the largest cross sectional area, and thus smallest resistance to the induced emf. (R=ρL/A) The induced current is the largest, hence it jumped the highest. The holes in the second ring confines the current to the edges of the ring. With a larger resistance, the induced current is less (despite the same induced emf), hence it jumped less high. As for the broken ring, there was practically zero induced current (despite the same induced emf) thanks to the infinite resistance presented by the air gaps.

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