1. Jul 28, 2014

### carrz

There is a homopolar generator on a train moving at 215 km/h. The magnet of the generator is attached to the disk so they would rotate together, but they are stationary now, except that they are moving along with the train. Is there any current generated by the generator?

I expect the answer will be "no", so next I ask what is the difference between the disk and the magnet rotating together, and them moving together along in a train?

2. Jul 28, 2014

### voko

Consider the motion of electrons relatively to the magnetic field in both cases.

3. Jul 28, 2014

### carrz

When the magnet is attached to the disk and they are rotated together there is actually current induced, that's the paradox. And if that works, then I don't see why wouldn't stationary generator on a train work, but I don't think it actually does, hence the questions. What's your answer?

4. Jul 28, 2014

### voko

Are you familiar with the Lorentz force?

5. Jul 28, 2014

### carrz

Yes.

6. Jul 28, 2014

### vanhees71

Of course, there is no paradox. The only paradox is that people use the Faraday Law in integral form in a wrong or incomplete way in forgetting the "magnetic partic" of the electromotive force. It's pretty well explained on the Wikipedia

Of course, there is no difference whether you do the experiment in a moving train or at rest (as long as you can consider both reference frames as inertial frames). You only have to use the Lorentz transformation and the covariance of Maxwell's equations under Lorentz transformations to argue about that. There's not even a need to do an explicit calculation to prove it by this argument.

7. Jul 28, 2014

### carrz

Can you explain what is the difference between the disk and the magnet rotating together, and them moving together along in a train? In other words, in both cases they are moving without any relative velocity, so why would rotating them together induce current, and why transporting them together on a train would not induce current?

8. Jul 28, 2014

### atyy

I'm not sure, but why not just make the rule that the disk must be rotating? The disk is not rotating on the train so why would there be a current?

If you move the magnet and disk with constant speed in a straight line on the ground, there won't be a current. The disk has to rotate.

9. Jul 28, 2014

### Staff: Mentor

I am missing something here. In a homopolar generator the disk and the magnet do not rotate together; the disk rotates in the static magnetic field produced by fixed magnet, right?

10. Jul 28, 2014

### atyy

Yes, I was puzzled too. I thought maybe he means if the disk and magnet rotate together, there is still a current. If this is true, then I think it is because at a slow speed, the magnet can just be treated as producing a rotating magnetic field, but because of the rotational symmetry, the magnetic field seen by the disk is the same as if the magnet were not rotating. So all that matters if that the disk rotates relative to an inertial frame (about the axis of symmetry of the magnet)

11. Jul 28, 2014

### carrz

Because the point is to compare their rotational and translational movement, and why would one induce current and not the other when in both cases their relative velocity is zero.

I agree with that question but I also ask, why not?

Now we're talking. But why? In both cases there is no any relative velocity between them, and in both cases they are moving, let's say relative to Earth. So why not? What is different when they are rotating and when they are moving in a straight line?

12. Jul 28, 2014

### carrz

There are three combinations and two paradoxes:

1.) disk rotates, magnet stationary -> induced current
2.) magnet rotates, disk stationary -> no current (paradox 1)
3.) disk and magnet rotate together -> induced current (paradox 2)

13. Jul 28, 2014

### voko

It is not important that the magnet and disk have no relative velocity. It is important that charges in the disk and the magnetic field have a relative velocity that is not completely aligned with the magnetic field.

EDIT: The correct statement is: what is important is that the velocity of charges and direction of the magnetic field are not completely aligned, then there is non-zero Lorentz force acting on the charges.

Last edited: Jul 28, 2014
14. Jul 28, 2014

### Staff: Mentor

I'm still confused. Have we established that there is a difference?

There will be a current if the conductor is moving relative to the magnet, whether rotating or straight line. If the magnet and the conductor are at rest relative to one another, there will be no current if they are moving inertially. Is it established that there will be a current if the magnet and the conductor are both undergoing uniform circular motion together?

15. Jul 28, 2014

### carrz

I gather everyone so far thinks there is a difference, so that non rotating generator on a moving train will not induce current, and stationary rotating generator will induce current even if the disk and the magnet are rotating together without any relative velocity.

16. Jul 28, 2014

### carrz

How is it that charges in the disk and the magnetic field have a relative velocity if they are rotating together?

17. Jul 28, 2014

### voko

I actually mi-stated the condition: what is important is that the velocity of charges and direction of the magnetic field are not completely aligned, then there is non-zero Lorentz force acting on the charges.

18. Jul 28, 2014

### carrz

How/why are they not aligned when rotating together? And why are they aligned when moving together in a straight line?

19. Jul 28, 2014

### atyy

Wikipedia's explanation http://en.wikipedia.org/wiki/Faraday_paradox seems reasonable to me. This is the explanation that voko has been giving in the thread.

"This mechanism agrees with the observations: an EMF is generated whenever the disc moves relative to the magnetic field, regardless of how that field is generated.

The use of the Lorentz equation to explain the Faraday Paradox has led to a debate in the literature as to whether or not a magnetic field rotates with a magnet. Since the force on charges expressed by the Lorentz equation depends upon the relative motion of the magnetic field to the conductor where the EMF is located it was speculated that in the case when the magnet rotates with the disk but a voltage still develops, that the magnetic field must therefore not rotate with the magnetic material as it turns with no relative motion with respect to the conductive disk."

Bolding above is mine. It looks like the only tricky part is whether the magnetic field moves with the magnet. Classically, a magnetic field would be produced by a current loop, and if the current loop executes circular motion, its motion is non-inertial, and the charges in the loop will accelerate producing radiation, ie. the magnetic field will move. However, at very slow speeds, this should be a small effect and the magnetic will not move.

20. Jul 28, 2014

### carrz

I'd say it's lacking and it leaves many questions open.

Also this:
- "Several experiments have been proposed using electrostatic measurements or electron beams to resolve the issue, but apparently none have been successfully performed to date."

That part doesn't make sense. How can possibly magnetic field not rotate with the magnetic material?

I don't see what radiation has to do with any of this. It's just Lorentz force that is supposed to explain it all.