Energy transfer in electromagnetic induction


by entropy15
Tags: electromagnetic, energy, induction, transfer
davenn
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Dec28-12, 07:58 PM
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Quote Quote by Jano L. View Post
Davenn, the magnetic field is not supposed to be rigidly connected to the magnet. If we move the magnet suddenly, the magnetic and electric lines will get deformed in the vicinity of the magnet, but the lines in greater distance will not change instantaneously. The deformation of those lines will propagate at the speed of light in all directions from the magnet.
uh huh, I didnt say they were fixed, but yeah i can see how it could be taken that way
I like your answer better :)

BUT ... do they prop at the speed of light or just at the speed of the motion of the magnet ?
cant you qualify/clarify that

thanks Jano
am always willing to learn ;)

Dave
entropy15
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Dec28-12, 08:54 PM
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Quote Quote by Andrew Mason View Post
Yes. It appears that it does. But it is complicated.
AM
Quote Quote by entropy15 View Post
But consider the case when the coil is not present. Surely the moving magnet should not experience resistance then.

According to the Wheeler-Feynman absorber theory radiation resistance is experienced instantaneously because of the advanced waves travelling back from the absorber. This radiation resistance does not depend on the density of absorbers in the vicinity of the emitting particle.

Radiation resistance being the same in every direction, a radiating particle cannot detect the presence of absorbers instantaneously by measuring this resistance.

But in the case of electromagnetic induction the moving magnet will feel resistance only if
the coil is present. The moving magnet will be able to instantaneously detect the presence of any coil nearby.
Hi Andrew,
So will this not amount to a violation of causality. It appears that the moving magnet has knowledge about the events of the future.

We can also assume that there is a switch in the coil which will allow us to turn on/off the current flow.
Now consider the magnet and stationary coil separated by a distance x. Initially the switch is turned off so that no current can be induced in it.

Now the magnet starts accelerating at instant t=t1. Now it will take a time for the effect of this changing magnetic field to reach the coil.
It would reach the coil at instant t1+(x/c). But if we turn on the switch before this effect reaches the coil, there should be a current induced in it and according to the Wheeler-Feynman absorber theory the moving magnet should have experienced resistance at t=t1.

Hence the magnet appears to know at t=t1 whether the switch would be on or off at t= (t1+x/c)
Andrew Mason
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Dec29-12, 10:11 AM
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Quote Quote by entropy15 View Post
Hi Andrew,
So will this not amount to a violation of causality. It appears that the moving magnet has knowledge about the events of the future.
Not quite. It is explained in QED - Quantum Electrodynamics. As I said, it is complicated. I am not the person to explain QED to you, however. Try Richard Feynman's book: http://press.princeton.edu/titles/8169.html There is also a good lecture series by Feynman on Youtube. The first lecture in the series is here: http://www.youtube.com/watch?v=LPDP_8X5Hug

AM
BruceW
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Dec29-12, 10:37 AM
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I'm pretty sure this problem can be completely explained by just classical electrodynamics. Since we are talking about a classical magnet and coil. But I guess the explanation in QED is more 'deep' and more general, since it also applies to the quantum world
BruceW
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Dec29-12, 11:12 AM
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entropy15 raises a pretty good point. Will the 'reaction force' have a time delay or not? We don't want information to travel at faster than light. And knowledge of the existence of a coil definitely seems like information. Here's a little thought experiment. Imagine that the 'reaction force' happens instantaneously, and there is 'person B' at the coil, and 'person A' at the magnet.

Now, if person B smashes up the coil before person A nudges the magnet, person A will not feel the (instantaneous) 'reaction force', and so he can immediately deduce that person B smashed up the coil. Then person A might be angry, because that was a very nice coil.

But if we think of another frame of reference, moving fast enough relative to this first frame, then according to this reference frame, it is possible that "person A is angry" happened before "person B smashes the coil" . So in this frame, things do not make sense.

So from this thought experiment, it seems to me that the 'reaction force' must have a time delay.
entropy15
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Dec29-12, 02:34 PM
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Quote Quote by BruceW View Post
it seems to me that the 'reaction force' must have a time delay.
But if there is a time delay, what happens to the total energy of the system at time x/c after the magnet starts moving.
(x=distance between the magnet and the coil.)

At this point of time we have the magnet which has not experienced resistance and hence has not lost energy and also a current induced in the coil which constitutes extra energy.

Also has such an experiment been conducted in reality? It should not be that difficult to test this with modern advances in practical physics.
jtbell
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Dec29-12, 02:53 PM
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Quote Quote by davenn View Post
the field is already around the coil, the moment the field moves a current is induced
But the field does not "move" (change) instantaneously everywhere in space when the magnet starts to move.

This page has a Java applet that shows the effect on the electric field produced by a point charge, when the charge's velocity changes suddenly. (I couldn't find something similar for a magnetic dipole after a quick search)

http://webphysics.davidson.edu/apple...etard_FEL.html

Choose "Inertial" from the menu at the top, drag the velocity slider over to zero, let the field lines settle down into a stationary radial configuration, and then drag the velocity slider quickly to set the charge in motion.
BruceW
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Dec29-12, 04:45 PM
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Quote Quote by entropy15 View Post
But if there is a time delay, what happens to the total energy of the system at time x/c after the magnet starts moving.
(x=distance between the magnet and the coil.)

At this point of time we have the magnet which has not experienced resistance and hence has not lost energy and also a current induced in the coil which constitutes extra energy.

Also has such an experiment been conducted in reality? It should not be that difficult to test this with modern advances in practical physics.
I see no problem with energy. The 'resistance force' can happen at the same time as the current is induced in the coil. Also, the electromagnetic field between the magnet and coil can contain energy. So it need not be as simple as energy being either in the current or in the KE of the magnet.
davenn
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Dec29-12, 08:17 PM
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Quote Quote by jtbell View Post
This page has a Java applet that shows the effect on the electric field produced by a point charge, when the charge's velocity changes suddenly. (I couldn't find something similar for a magnetic dipole after a quick search)

http://webphysics.davidson.edu/apple...etard_FEL.html

Choose "Inertial" from the menu at the top, drag the velocity slider over to zero, let the field lines settle down into a stationary radial configuration, and then drag the velocity slider quickly to set the charge in motion.
that's neat,
Thanks :)

Dave
entropy15
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Dec29-12, 09:32 PM
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Quote Quote by BruceW View Post
I see no problem with energy. The 'resistance force' can happen at the same time as the current is induced in the coil. Also, the electromagnetic field between the magnet and coil can contain energy. So it need not be as simple as energy being either in the current or in the KE of the magnet.
So what is the actual delay? 0 or (x/c) or (2x/c) ?
If it is x/c there will be no problem with energy.
But the point here is how can the delay be x/c since the resistance is caused by the induced current in the coil and there should be a time gap between the cause and effect since they are physically separated by a distance x.

The energy stored in the magnetic field is fixed. But we can transfer an arbitrarily large amount of energy from the magnet to the coil simply by increasing the velocity of the moving magnet.
So how can a decrease in this fixed energy explain the energy transfer unless we pull it from the Kinetic energy of the moving magnet?
Drakkith
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Dec30-12, 01:18 AM
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What do you mean the energy stored in the field is fixed? If we quickly accelerate to a high speed it will have more energy stored in the field than simply pushing the magnet slowly into the coil. (From what it looks like to me)

In the first case, if we quickly decelerate the magnet after the initial acceleration the induced current should, for a small amount of time, try to become very high because the change in the magnetic field will be very high.

If we did the same thing in the 2nd example, where we slowly pushed the magnet towards the coil, the induced current would be very low, as the magnetic field is changing very slowly. So more energy should be stored in the field in the 1st case compared to the 2nd case.

Well, that's what it appears to be to me at least. Someone correct me if I'm mistaken.
entropy15
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Dec30-12, 11:43 AM
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If we consider the coil to be moving and the magnet stationary, then it is pretty straightforward that the coil will experience resistance instantaneously.This is because the magnetic field is present where the coil is.

Should not this be symmetrical ie it should not matter who is moving towards what, all that matters should be that there be a relative velocity between them.

Both the coil and the magnet should experience resistance instantaneously as soon as they detect relative velocity between them.
entropy15
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Dec30-12, 12:12 PM
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Quote Quote by Drakkith View Post
What do you mean the energy stored in the field is fixed? If we quickly accelerate to a high speed it will have more energy stored in the field than simply pushing the magnet slowly into the coil. (From what it looks like to me)
If the magnet is stationary then the magnetic field around it is constant and so should the energy stored in it.
On accelerating if the energy stored is increasing it is due to the fact that the kinetic energy of the magnet being converted to the energy of the magnetic field.
BruceW
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Dec30-12, 06:39 PM
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Quote Quote by entropy15 View Post
So what is the actual delay? 0 or (x/c) or (2x/c) ?
If it is x/c there will be no problem with energy.
But the point here is how can the delay be x/c since the resistance is caused by the induced current in the coil and there should be a time gap between the cause and effect since they are physically separated by a distance x.
I would think the delay is 2x/c since nudging the magnet would cause a wave, which travels to the coil, then the acceleration of charges in the coil causes a wave which travels back. And as Drakkith says, I don't see a problem with energy since the energy can get stored in the EM field. Also, I think you are right that it needs to be at least 2x/c because of the causality argument.
BruceW
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Dec30-12, 07:00 PM
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Quote Quote by entropy15 View Post
If we consider the coil to be moving and the magnet stationary, then it is pretty straightforward that the coil will experience resistance instantaneously.This is because the magnetic field is present where the coil is.
There's two things going on 1) the 'nudge' causes a wave, affecting the other object, which takes time. 2) there is how the already existing field affects the 'nudge'.

In the case where we nudge the magnet, 1) an electromagnetic wave travels from the magnet to the coil, induces a current, and a wave is sent back to the magnet, which causes a reaction force. (This is the delayed reaction, since it depends on whether the coil actually exists). and then there is 2) nudging the magnet means we are pushing a magnet through its own magnetic field, which causes a reaction on itself. This happens immediately, since the wave doesn't have to travel any distance.

In the case where we nudge the coil and the magnet is stationary: we have 1) the acceleration of charges in the coil through the stationary magnetic field causes an EM wave which travels from the coil to the magnet, which is affected, and sends a wave back to the coil, causing a reaction force on the coil. (Again this is the delayed reaction). And then there is 2) nudging the coil through the stationary magnetic field will cause a reaction on itself.
entropy15
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Dec31-12, 09:06 AM
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Quote Quote by BruceW View Post
There's two things going on 1) the 'nudge' causes a wave, affecting the other object, which takes time. In the case where we nudge the magnet

an electromagnetic wave travels from the magnet to the coil, induces a current, and a wave is sent back to the magnet
Are these waves real, like normal electromagnetic waves?
If the moving magnet is emitting an electromagnetic wave, it should do so only if the coil is present. Because if there was no coil there would be
nothing to absorb this wave. Also if there is no coil the magnet will not experience resistance meaning that it has not emitted the wave.
But how can the magnet know instantantaneously (as soon as it starts moving) that there is a coil at a distance x?
BruceW
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Dec31-12, 10:39 AM
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Well, when the magnet is given a 'nudge', this will cause a change in the surrounding EM field which will propagate at c. (Which is due to the theory of retarded potentials in the Lorenz gauge). (And by 'propagate at c', I simply mean that after time t, the furthest point at which the EM field is affected by the nudge is at distance ct).

This is true whether or not the coil is there. And if the coil is there, it will take time x/c after the nudge, for the EM field at the coil to be affected. So it is at this time that the current can be induced in the coil, Then the propagation of this effect will again travel at c, so it will take another time of x/c for the magnet to experience the field which is due to currents which have been induced in the coil.
BruceW
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Dec31-12, 11:10 AM
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I know I haven't immediately answered your questions, but I have not thought about this problem before, so I am trying to start with the principles that I am most certain should apply to this situation.

So, for the questions. Are they real waves? Um, I guess they satisfy the inhomogeneous wave equations. So yes? But then by this definition, every classical electromagnetic phenomena involves real waves. If we instead define a real wave as being oscillatory, then I guess generally the waves in this case would be partly real and partly not.

I would expect the accelerating magnet to emit EM energy even if the coil was not there. For example, if the magnet was made of a coil with current flowing through it, then when we nudge the magnet, we are accelerating charges, which generally gives off EM radiation.


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