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.

 

[entropy15]

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]

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]

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]

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]

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]

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.

 

[Drakkith]

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?

I would guess that EM waves would be created by the acceleration, but I really don't know. I know accelerating a single charge will do this, but I don't know about a magnet. IF it emits EM waves then it must feel a small amount of "resistance" from the emission. This would be separate resistance from the resistance felt due to induction in the coil, and would only happen during the acceleration. Once it was moving steadily it would not emit EM radiation since it isn't accelerating. (That of course is IF it emits EM radiation in the first place)

 

[entropy15]

IF it emits EM waves then it must feel a small amount of "resistance" from the emission. This would be separate resistance from the resistance felt due to induction in the coil, and would only happen during the acceleration. Once it was moving steadily it would not emit EM radiation since it isn't accelerating. (That of course is IF it emits EM radiation in the first place)

The energy transfer here should be taking place due to the induction and not through radiation (which even if present should be small and can be neglected as well).

The delay for the magnet to experience resistance due to the current in the coil seems to be
2x/c.

Indeed, If we follow the classical approach the delay seems to be 2x/c. But if we look at it from QED perspective it seems to be 0. (Wheeler Feynman absorber theory)

Can we throw more light on it looking at it from the relativity perspective?
After all magnetic field can be explained as an effect due to the "length contraction" involving moving charges using theory of relativity.

I have seen papers which explain the origin of magnetic fields using relativity. Most of them have to do with the forces of attraction/repulsion between two wires carrying current.
But I have not come across any which explain electromagnetic induction with the same approach.

I know it would be too complicated, but in case any of you have come across it, please help.

 

[BruceW]

Drakkith has got a good point. There are two different situations 1) considering a magnet which is being given a 'nudge' by some person. 2) considering a magnet which is moving toward the coil, with no 'outsider' forces.

I have mostly been talking about what happens when the magnet is given a 'nudge' i.e. acceleration. In this case, there is a delay before the effect is felt by the coil. I am pretty sure that Wheeler Feynman absorber theory also predicts that there is a time delay. But because I don't know much QFT, I can't say with complete certainty.

Now in the case when the magnet is moving freely (not being 'nudged'), then I am not so sure about whether there is a delay in the reaction force being felt, because in this case, at any particular time, there is already a magnetic field traveling between the magnet and the coil (which is due to the magnet moving at an earlier time).

 

[Jano L.]

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?

It is just normal electromagnetic wave. When the magnet is nudged, the surface currents on it get nudged too and electromagnetic waves start to propagate out of the surface. In standard theory with retarded fields, there is no immediate effect of the coil on the magnet; this comes only later, after time 2x/c.

However, the magnet will feel small resistance immediately. This is due to the fact that one part of the surface current will act on another, an in case the magnet is accelerated, these forces do not cancel each other but tend to act against the acceleration. This is sort of a "self-inductance" effect.

Later, after time 2x/c, the wave from the coil will come and damp the magnet as well. This will be typically much greater effect (sort of "mutual inductance").

 

[entropy15]

However, the magnet will feel small resistance immediately. This is due to the fact that one part of the surface current will act on another, an in case the magnet is accelerated, these forces do not cancel each other but tend to act against the acceleration. This is sort of a "self-inductance" effect.

Later, after time 2x/c, the wave from the coil will come and damp the magnet as well. This will be typically much greater effect (sort of "mutual inductance").

Since the self inductance effect is very small let's consider only the mutual inductance.

Suppose that the magnet is initially at rest.
It is given a push at time t=t1. Let's assume that the kinetic energy transferred to the magnet due to this push is E_k.
This kinetic energy may decrease immediately due to radiation or self inductance but the effect is negligible.

Now at time t=t1+(x/c) we have the current induced in the coil and it has gained energy due to this induced current.

Now since the magnet does not experience any resistance till t1+(2x/c) i.e any considerable resistance we can see that the magnet does not lose the kinetic energy acquired by it during the initial push till t1+(2x/c).

So between t1+(x/c) and t1+(2x/c) we have this energy in the coil as well as in the kinetic energy of the magnet.

The kinetic energy of the magnet is the cause for the current to be induced in the coil.
The magnet just transfers its kinetic energy to the coil through mutual induction.
So should not the kinetic energy of the magnet decrease before the current is induced in the coil?

 

[Jano L.]

The kinetic energy of the magnet is the cause for the current to be induced in the coil.

Not exactly. It is better to say that the electromagnetic forces due to the magnet drive the currents in the coil.

The magnet just transfers its kinetic energy to the coil through mutual induction.

This is also not accurate enough. If we want to use the energy concept, we can, but we have to keep in mind all contributions to the energy. In this case, besides the magnet and the coil, there is also energy distributed throughout the remaining space. It is better to say that when the wave hits the coil, the field in the vicinity of the coil and inside it supply the energy for the animation of the currents.

So should not the kinetic energy of the magnet decrease before the current is induced in the coil?

It should not. Again, try to think of this in terms of the force - the response from the coil has not arrived yet, so there is no force acting on the magnet in the time interval x/c,2x/c.

You are probably worried about conservation of energy, but I think there is no problem. The currents in the coil get their energy from the field near the wires. Eventually, the magnet will lose some kinetic energy, but this is merely an after-effect.

 

[entropy15]

You are probably worried about conservation of energy, but I think there is no problem. The currents in the coil get their energy from the field near the wires. Eventually, the magnet will lose some kinetic energy, but this is merely an after-effect.

The current strength is proportional to the velocity of the magnet. The faster the magnet moves, more is the current.
The energy stored inside the magnetic field is constant. If the current gets energy from the field surrounding the coil, how can it obtain more and more energy from this field as the velocity of the magnet increases.

If the magnet is moving with a sufficiently high velocity the current induced in the coil may increase beyond what the surrounding magnetic field can provide.

 

[entropy15]

It should not. Again, try to think of this in terms of the force - the response from the coil has not arrived yet, so there is no force acting on the magnet in the time interval x/c,2x/c.

If we consider the Wheeler Feynman absorber theory the response from the coil arrives as advanced waves from the future to the instant when the magnet starts to move.
So this should get rid of the energy conservation problems.

In this case the resistance is felt immediately rather than 2x/c.

 

[Jano L.]

If the current gets energy from the field surrounding the coil, how can it obtain more and more energy from this field as the velocity of the magnet increases.

The energy of the field is not just magnetic; it has electric component as well. This has to be so, for pure magnetic field could not induce currents in the coil.

The energy of the field is the higher the higher is the velocity of the magnet. We can be sure that there is always enough energy present to maintain the energy conservation, because we have the Poynting theorem; this shows that the energy is conserved locally, and moves through space like fluid..

I agree it is difficult to imagine this in such complicated process, but there is an alternative way of description, via EM forces, which makes this much more clear. According to the Faraday law, the magnitude of the electric field due to magnet animating the currents is the higher the higher is the velocity of the magnet; the higher the electric field, the stronger currents get induced.

 

[Dale]

The current strength is proportional to the velocity of the magnet. The faster the magnet moves, more is the current.
The energy stored inside the magnetic field is constant. If the current gets energy from the field surrounding the coil, how can it obtain more and more energy from this field as the velocity of the magnet increases.

When you have a moving magnetic field then you also induce an E field according to Faraday's law. This E field also contains energy. As you push the magnet faster your dB/dt is greater and therefore the induced E field is also greater. The extra energy you are worried about is in this induced E field.

I see the scenario as follows:
1) magnet and coil at rest wrt each other, no forces
2) force on magent to accelerate magnet (extra force required in order to generate E field)
3) EM wave propagates at c to coil
4) changing current induced in coil
5) changing field produced by coil
6) EM wave propagates at c to magnet
7) coil field opposes motion of magnet

I recommend against throwing unnecessary quantum concepts into any discussion which can be done purely classically. Generally it adds more confusion than understanding.

 

[BruceW]

Now since the magnet does not experience any resistance till t1+(2x/c) i.e any considerable resistance we can see that the magnet does not lose the kinetic energy acquired by it during the initial push till t1+(2x/c).

No, the point is that when we give the magnet a 'nudge', we are putting energy into the electromagnetic field. So there is an immediate resistance, but not due to mutual inductance. (We will feel a resistance even if there is no coil). And if there is a coil, then we also get a delayed resistance due to mutual inductance.

Edit: So I guess I'm saying that if we only considered mutual inductance, then energy is not conserved when we give the magnet a nudge. (But this is because we are not considering the whole picture).

 

[BruceW]

If the magnet is moving with a sufficiently high velocity the current induced in the coil may increase beyond what the surrounding magnetic field can provide.

I don't understand what you mean here.

 

[entropy15]

No, the point is that when we give the magnet a 'nudge', we are putting energy into the electromagnetic field. So there is an immediate resistance, but not due to mutual inductance. (We will feel a resistance even if there is no coil). And if there is a coil, then we also get a delayed resistance due to mutual inductance.

Hi Bruce,
Thanks for replying to my queries.

One more thing here, suppose that we replace the magnet with an electromagnet. The current in the electromagnet is controlled by a switch. Also we will remove the coil.(which was originally placed at a distance x)

Initially the electromagnet is not powered on and hence no magnetic field would be present.
Now we nudge this electromagnet so that it starts moving at a constant velocity.

Next the electromagnet is switched on so that it produces a magnetic field. Now since it is moving, it should try putting energy to the electromagnetic field.

So won't this oppose the current flowing in the electromagnet itself? trying to decrease the magnetic field.

 

[entropy15]

I don't understand what you mean here.

I was assuming that the energy in the electric field was constant, but as DaleSpam has pointed out the faster the magnet moves more the energy in the electric field, so this should not be a problem.