Energy transfer in electromagnetic induction

[entropy15]

Consider a magnet moving towards a coil.
We know that the motion of the magnet will induce a current in the coil and the direction of this induced current is to oppose the motion of the magnet.

Now does the magnet experience resistance to its motion immediately as soon as it starts moving?

Since the magnet and coil are physically separated, it would take a time t (which is equal to the time taken by light to travel from the magnet to the coil)
to induce a current in the coil and an equal amount of time for the effect of this current to travel back to the magnet and oppose its motion.
Hence the total delay appears to be 2t.

So does the magnet experience resistance immediately or does it have to wait for time 2t?

 

[Drakkith]

I'm with you, as it looks to me like 2t. Anyone else know?

 

[davenn]

Consider a magnet moving towards a coil.
We know that the motion of the magnet will induce a current in the coil and the direction of this induced current is to oppose the motion of the magnet.

Now does the magnet experience resistance to its motion immediately as soon as it starts moving?
Since the magnet and coil are physically separated, it would take a time t (which is equal to the time taken by light to travel from the magnet to the coil)
to induce a current in the coil and an equal amount of time for the effect of this current to travel back to the magnet and oppose its motion.
Hence the total delay appears to be 2t.

for what to travel at the speed of light from the magnet ??
Nothing is traveling from the magnet
Why ? ... because the magnetic field already exists around the magnet whether its moving or not
As soon as the wire encounters the field lines, a current will start to flow in the wire
bringing the magnet even closer just has the effect of more field lines "moving through" the wire and generating a larger current

The 2 velocities would be
1) the velocity that YOU move the magnet towards the coil, then
2) the velocity of the expanding field around the wire ( over a short distance you would be lucky to measure this)

So does the magnet experience resistance immediately or does it have to wait for time 2t?

I would suspect any delay you measured would be more related to the times it takes for the mangetic field around the wire to grow strong enough to have a measurable interaction with the magnets field

as said above... The magnetic field around the wire doesn't just suddenly appear, it progressively grows stronger as the magnet comes closer

Dave

 

[Drakkith]

Dave, imagine we place the magnet there stationary first. That way the field is not changing until we start to move it again. We can imagine a very sudden *bump* that accelerates it. Does this change in the field due to the movement of the magnet move at c?

 

[davenn]

hey Drakkith :)
seasons greetings to you buddy ... have you moved ranch yet ?

...the field is still only going to move at the speed/velocity at which the magnet is moved
bearing in mind that we are not going to be able to move it at c anyway
But I don't see where the OP was asking about moving the magnet at c, just moving it by hand or mechanically towards the coil
He/she was assuming the magnets field was suddenly appearing and moving out from the magnet at c
but of course this isn't the case, the field is present all the time

Dave

 

[entropy15]

"The magnetic field around the wire doesn't just suddenly appear, it progressively grows stronger as the magnet comes closer"

Initially the magnet is at rest. Now there is a certain amount of magnetic flux linking the coil.
But since the flux is constant there is no current induced.

Now suppose that we start to move the magnet at instant t=t1. The flux linking the coil will increase since the magnet is moving closer. The question is when does it start to increase?

Certainly it cannot be t1 since that would be mean faster than light information travel.
So there should be a delay and will it not be equal to the time taken for the effect of the changing magnetic field to reach the coil.

As an example, if the sun were to disappear at this instant of time, we would not notice it for the next eight minutes after which we will plunge into darkness.

 

[Andrew Mason]

hey Drakkith :)
...the field is still only going to move at the speed/velocity at which the magnet is moved

Since the field extends outward from the magnet, the question relates to the ability of the physical magnet, as it begins to accelerate, to instantaneously communicate that acceleration to its field lines at the conductor a distance s away: there must be a delay (Δt≥ c/s) before the conductor feels the change in magnetic field and the resultant induced electric field; and since there is that delay, there must be a similar delay in the magnet feeling the opposing magnetic field from the induced current in the conductor. That seems to be the question.

Feynman studied the interaction of fields of approaching electrons. The effect should be similar. He discovered that it did not matter whether you assumed that the field traveled in advance, was retarded or was instantaneous. The reaction force was always the same. You may wish to google the "Wheeler-Feynman absorber theory"

AM

 

[entropy15]

I'm with you, as it looks to me like 2t. Anyone else know?

Hi Drakkith,

That is fine. But suppose say the magnet starts moving at instant t=t1.
So the current would be induced in the coil at t=t1+t and the magnet will start experiencing
resistance only at t=t1+2t.

But what about the total energy of the system at time t=t1+t. At this time we have a moving magnet which has not experienced any resistance and has not lost any energy and also the current induced in the coil.

Should not the whole process act as a way of energy transfer between the motion of magnet and the coil? should not the moving magnet lose energy as soon as the current is induced in the coil.

 

[entropy15]

Feynman studied the interaction of fields of approaching electrons. The effect should be similar. He discovered that it did not matter whether you assumed that the field traveled in advance, was retarded or was instantaneous. The reaction force was always the same. You may wish to google the "Wheeler-Feynman absorber theory"
AM

What exactly do you mean by the reaction force in this case? Is it the resistance experienced by the magnet and does it feel the reaction instantaneously as it starts to move?

 

[Andrew Mason]

What exactly do you mean by the reaction force in this case? Is it the resistance experienced by the magnet and does it feel the reaction instantaneously as it starts to move?

Yes. It appears that it does. But it is complicated.

Feynman's work led to a very successful theory of quantum electrodynamics and earned him the Nobel prize. Here is a bit of an explanation of the reaction force: http://physics.fullerton.edu/~jimw/general/radreact/index.htm

AM

 

[BruceW]

The maximum speed at which information can be transmitted is the speed of light. So if I decide to push the magnet towards the coil, it will take an amount of time at least x/c before a current is induced in the coil. (where x is distance from magnet to the coil).

Now does this mean that there will necessarily be an amount of time at least 2x/c before the magnet feels the force caused by the moving charges in the coil? No way. Remember that in this situation, the 'choice' we made was to give the magnet a nudge. So if we want to consider the region of spacetime which can be effected causally by this action, then at the same position at which the action happened (i.e. at the magnet), it will be causally linked immediately after the action has happened, so there is no necessary delay between the actions of nudging the magnet, and the magnet feeling a reaction force.

Edit: I should also specify, this explanation is for the least possible time delay. So the time delay could be greater, for example if I shot someone in the foot, that person could decide to shoot me in the foot (as vengeance), and so the time delay could be quite large.

 

[entropy15]

Yes. It appears that it does. But it is complicated.
AM

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 traveling 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.

 

[davenn]

of course...
a magnetic field needs to be generated in "something" so that it will oppose the field of your magnets field so you/it feels/measures a resistance

Dave

 

[davenn]

Initially the magnet is at rest. Now there is a certain amount of magnetic flux linking the coil.
But since the flux is constant there is no current induced.

Now suppose that we start to move the magnet at instant t=t1. The flux linking the coil will increase since the magnet is moving closer. The question is when does it start to increase?

instantly because the field is already in contact with the coil

D

 

[BruceW]

eh? Surely, if I nudge the magnet, there is a time delay before a current is induced in the coil.

 

[davenn]

eh? Surely, if I nudge the magnet, there is a time delay before a current is induced in the coil.

and where would the delay be coming from ??

the field is already around the coil, the moment the field moves a current is induced

D

 

[Andrew Mason]

and where would the delay be coming from ??

the field is already around the coil, the moment the field moves a current is induced

D

The time delay would occur because of the distance between the magnet and the conductor. The effects from the sudden acceleration of the magnet cannot instantaneously propagate out to the position of the conductor. Special relativity says it cannot propagate faster than c.

AM

 

[Jano L.]

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.

 

[davenn]

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]

Yes. It appears that it does. But it is complicated.
AM

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 traveling 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]

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:

AM

 

[BruceW]

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]

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]

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]

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/applets/retard/Retard_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]

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]

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/applets/retard/Retard_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]

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]

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]

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.