# Magnetic Flux and Induced Current

#### Nivlac2425

1. Homework Statement
The drawing shows a bar magnet falling through a metal ring. In part a the ring is solid all the way around, but in part b it has been cut through. (a) Explain why the motion of the magnet in part a is retarded when the magnet is above the ring and below the ring as well. (b) Explain why the motion of the magnet is unaffected by the ring in part b.

2. Homework Equations
Lenz's Law
Right hand rule

3. The Attempt at a Solution
I know that since the magnet is falling, the ring will feel a magnetic flux when the magnet is above and below the ring because the magnetic field is either increasing or decreasing. Since there is magnetic flux, an induced emf, and therefore an induced current flows through the ring whose direction is predicted by Lenz's Law and the right hand rule.
Knowing this, I can answer (b) because since the ring is cut, there is no current flowing through it so it doesn't affect the magnet's motion.

But my question is how does the induced current alter the motion of the magnet in part a? I can't seem to figure out how the induced current will cause the change in motion.

Thanks everyone who can help me out!

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#### Delphi51

Homework Helper
The induced current in the ring acts like an electromagnet and causes a magnetic field that opposes the motion of the magnet. You can figure out the direction of the magnetic field using the hand rules, or just realize that it can't be increasing the speed of the magnet because that would be creating energy.

It is easy to see this experimentally. Tape the middle of a long thread onto a short piece of copper pipe (or a copper joint fitting from a hardware store). Use the threads to hang the copper in a doorway or something so that it is free to swing in one dimension along the axis of the pipe. Then you need a magnet thin enough to fit into the tube. As you push it in and pull it out, you will see that it has an attraction to the copper ring.

#### Nivlac2425

So the only opposition to the motion is the attraction to the ring? Or is there something else that the ring does?
I'm still not toooo clear on this.

Thanks.

#### Delphi51

Homework Helper
Repulsion. The ring is an electromagnet with polarity in reverse of the permanent magnet.

#### Nivlac2425

So as the magnet approaches the ring, it will feel repulsion from the electromagnet because of the induced current, and as it continues to fall below the ring, it will feel an attraction to the electromagnet?
Does that obey energy conservation?

#### Delphi51

Homework Helper
That attraction sounds a bit tricky until you remember that nothing happens unless the magnet is moving so its flux lines cut through the conductor. So this effect always converts kinetic energy into heat. They use it in exercise bikes.

#### Nivlac2425

I see, so the magnet's motion is dampened because its kinetic energy was converted into other forms.

Thank you for helping me out!

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