When does the permanent magnet begin to accelerate?

[zetetic56]

An electromagnet and a permanent magnet are at a distance from one another and are at rest relative to one another.

The electromagnet is off.

The electromagnet is turned on.

The turned-on electromagnet is within the permanent magnet's magnetic field, and so the electromagnet is attracted to the permanent magnet.

(The electromagnet and the permanent magnet are attractively aligned.)

And so, the electromagnet will begin to accelerate towards the permanent magnet.

When the electromagnet is turned on a magnetic field is created around the electromagnet.

The permanent magnet is within the electromagnet's newly created magnetic field, and so the permanent magnet is attracted to the electromagnet.

And so, the permanent magnet will also begin to accelerate towards the electromagnet.

---

When does the permanent magnet begin to accelerate?

At the same time as the electromagnet begins to accelerate

or

After the electromagnet begins to accelerate

---

(The curved lines in the drawings are just meant to be something symbolic of a field being present.  The electromagnet's magnetic field extends beyond the full body of the permanent magnet.)

[Genady]

I think, after a delay of (distance between them) / (speed of light).

[zetetic56]

2 minutes ago, Genady said:

I think, after a delay of (distance between them) / (speed of light).

I think you're right.  I was thinking the same thing.  But, if this is the case, then I end up in a different theoretical problem.

The two bodies start out at relative rest in this frame and so there is a total of 0 momentum.

When the electromagnet starts to accelerate (from left to right) there is an increase in positive momentum.

And if momentum is always conserved, which it is, then there must be an equal offsetting increase in negative momentum (from right to left) at the same time.

But if there is a delay between when the permanent magnet starts to accelerate and when the electromagnet starts to accelerate then, as far as I can tell, momentum is then not conserved.

There seems to be a problem here, and that's why I posted this question.

[Genady]

42 minutes ago, zetetic56 said:

I think you're right.  I was thinking the same thing.  But, if this is the case, then I end up in a different theoretical problem.

The two bodies start out at relative rest in this frame and so there is a total of 0 momentum.

When the electromagnet starts to accelerate (from left to right) there is an increase in positive momentum.

And if momentum is always conserved, which it is, then there must be an equal offsetting increase in negative momentum (from right to left) at the same time.

But if there is a delay between when the permanent magnet starts to accelerate and when the electromagnet starts to accelerate then, as far as I can tell, momentum is then not conserved.

There seems to be a problem here, and that's why I posted this question.

Momentum is conserved when there are no external forces, which is not the case here.

[zetetic56]

1 hour ago, Genady said:

Momentum is conserved when there are no external forces, which is not the case here.

I'm assuming the electromagnet and the permanent magnet are in the same closed system.

[Genady]

1 hour ago, zetetic56 said:

I'm assuming the electromagnet and the permanent magnet are in the same closed system.

I don't think it is possible to assume it a close system when taking relativistic effects in consideration. Because to assume the system to be closed we need to consider it all at once, but there is no simultaneity for the spatially separated bodies.

To analyze this condition, we don't need EM. We can consider a simple, purely mechanical system. Let's assume Alice and Bob are holding the ends of a stretched rope 1 light-hour long. Bob starts pulling himself along the rope, moving toward Alice. It will take an hour until Alice starts being pulled toward Bob. I don't think we can assume it to be a closed system.

[swansont]

I don't see an accounting of the magnetic field that will be present, and how it changes.

5 minutes ago, Genady said:

To analyze this condition, we don't need EM. We can consider a simple, purely mechanical system. Let's assume Alice and Bob are holding the ends of a stretched rope 1 light-hour long. Bob starts pulling himself along the rope, moving toward Alice. It will take an hour until Alice starts being pulled toward Bob. I don't think we can assume it to be a closed system.

The rope has mass, so it's not quite the same.

[Genady]

2 minutes ago, swansont said:

I don't see an accounting of the magnetic field that will be present, and how it changes.

I've suggested a purely mechanical system for this question, above.

5 minutes ago, swansont said:

I don't see an accounting of the magnetic field that will be present, and how it changes.

The rope has mass, so it's not quite the same.

Yes, but the rope doesn't move, so it doesn't change a momentum. The question of the momentum conservation is the same.

[zetetic56]

21 minutes ago, swansont said:

I don't see an accounting of the magnetic field that will be present, and how it changes.

There is momentum in the expanding magnetic field.

When the electromagnet is turned on the magnetic field surrounding the electromagnet expands to the left and the right.  There is an increase in positive momentum an there is an equal increase in negative momentum.  And so, these two momentum increases balance out, and momentum is conserved in this part of the overall system.

When the electromagnet is turned on the body the electromagnet begins to accelerate there is an increase in positive momentum in this part of the system.  And for momentum to be conserved there must be an equal increase in negative momentum to balance this out.

34 minutes ago, Genady said:

I don't think it is possible to assume it a close system when taking relativistic effects in consideration. Because to assume the system to be closed we need to consider it all at once, but there is no simultaneity for the spatially separated bodies.

If I understand you correctly, we would only be able to say that momentum is conserved when there is a direct collision between two bodies.  I don't think this is how the Law of Conservation of Momentum works.  I don't think it is limited in this way.

[studiot]

9 minutes ago, zetetic56 said:

There is momentum in the expanding magnetic field.

When the electromagnet is turned on the magnetic field surrounding the electromagnet expands to the left and the right.  There is an increase in positive momentum an there is an equal increase in negative momentum.  And so, these two momentum increases balance out, and momentum is conserved in this part of the overall system.

When the electromagnet is turned on the body the electromagnet begins to accelerate there is an increase in positive momentum in this part of the system.  And for momentum to be conserved there must be an equal increase in negative momentum to balance this out.

I think your analysi is too simplistic.

The permanent magent will already posses and exert a magnetic field which will encompass the dormant electromagent, but not affect it since copper coils are not magnetic of themselves.

As soon as the current starts changing (rising) in the electromagnet, the electromagnet will experience a force due to its immersion in the field of the permanent magnet.

This is before the electromagnet's own field has built up or reached the permanent magnet.

Edited April 4, 2022 by studiot

[Genady]

25 minutes ago, zetetic56 said:

If I understand you correctly, we would only be able to say that momentum is conserved when there is a direct collision between two bodies.  I don't think this is how the Law of Conservation of Momentum works.  I don't think it is limited in this way.

Yes, I think it is correct. A direct collision, or a system is small enough / our time scale is long enough that we can ignore time delays due to relativity.

[zetetic56]

20 minutes ago, studiot said:

I think your analysi is too simplistic.

The permanent magent will already posses and exert a magnetic field which will encompass the dormant electromagent, but not affect it since copper coils are not magnetic of themselves.

As soon as the current starts changing (rising) in the electromagnet, the electromagnet will experience a force due to its immersion in the field of the permanent magnet.

This is before the electromagnet's own field has built up or reached the permanent magnet.

Could this force push the electromagnet leftward and balance out the rightward force on the electromagnet (due to magnetic attraction) over the period of time it takes for the expanding magnetic field of the electromagnet to make it to the permanent magnet, so that the electromagnet stays in place until the permanent magnet starts accelerating?

If so, then momentum would be conserved (or so it seems to me).

[zetetic56]

I was thinking about the logic of this again.

If this force is what leads to momentum being conserved, in some ways it makes sense.  If the electromagnet, as its turned on, is further from the permanent magnet then there is less magnetic attraction and if the electromagnet, as its turned on, is closer to the permanent magnet then there is more magnetic attraction.  And so if there is a leftward force on the electromagnet as it is turned on, then it would need to be weaker the further the two magnets are apart and it would need to be stronger the closer the two magnets are together, to offset the different amounts of magnetic attraction with different amounts of distance between them.  And that the Physics could work out this way makes sense (to me).

But then there is also the question of duration.

The further the electromagnet is from the permanent magnet the longer it needs to be held in place (as the magnetic field of the electromagnet makes its way to the permanent magnet), and the closer the electromagnet is to the permanent magnet the less time it needs to be held in place (as the magnetic field of the electromagnet makes its way to the permanent magnet), for momentum to be conserved.  And this seems more conceptually problematic to me.

?

 

 

On 4/4/2022 at 8:23 AM, Genady said:

... but there is no simultaneity for the spatially separated bodies.

My understanding of the Law of Conservation of Momentum is that it applies to both push and pull.

And my understanding of Relativity, and of the Relativity of Simultaneity, is that "events which are simultaneous in one inertial frame of reference are not simultaneous in another inertial frame of reference".  If this is correct, this this means by definition Relativity allows for two events at a distance in the one same inertial frame of reference to be simultaneous.  My understanding is that the Relativity of Simultaneity applies between inertial frames of reference and not within one single inertial frame of reference.  Here, the turned off electromagnet and the permanent magnet are in the one same inertial frame of reference.

 

Edited April 6, 2022 by zetetic56

[Genady]

And what about Bob and Alice holding two ends of a stretched rope? The momentum of the system is 0. As soon as Bob pulls himself along the rope, he starts moving toward Alice. Nothing else moves until the other end of the rope pulls Alice. The system has a non-zero momentum all this time. Thus, the total momentum is not conserved. What is wrong here?

1 hour ago, zetetic56 said:

I was thinking about the logic of this again.

If this force is what leads to momentum being conserved, in some ways it makes sense.  If the electromagnet, as its turned on, is further from the permanent magnet then there is less magnetic attraction and if the electromagnet, as its turned on, is closer to the permanent magnet then there is more magnetic attraction.  And so if there is a leftward force on the electromagnet as it is turned on, then it would need to be weaker the further the two magnets are apart and it would need to be stronger the closer the two magnets are together, to offset the different amounts of magnetic attraction with different amounts of distance between them.  And that the Physics could work out this way makes sense (to me).

But then there is also the question of duration.

The further the electromagnet is from the permanent magnet the longer it needs to be held in place (as the magnetic field of the electromagnet makes its way to the permanent magnet), and the closer the electromagnet is to the permanent magnet the less time it needs to be held in place (as the magnetic field of the electromagnet makes its way to the permanent magnet), for momentum to be conserved.  And this seems more conceptually problematic to me.

?

 

 

My understanding of the Law of Conservation of Momentum is that it applies to both push and pull.

And my understanding of Relativity, and of the Relativity of Simultaneity, is that "events which are simultaneous in one inertial frame of reference are not simultaneous in another inertial frame of reference".  If this is correct, this this means by definition Relativity allows for two events at a distance in the one same inertial frame of reference to be simultaneous.  My understanding is that the Relativity of Simultaneity applies between inertial frames of reference and not within one single inertial frame of reference.  Here, the turned off electromagnet and the permanent magnet are in the one same inertial frame of reference.

 

You are correct. The relativistic effect here is not related (at least, not directly) to the relativity of simultaneity, but rather to speed limit of a signal. You are also correct that the electromagnet will not "wait" an indefinite time until the field reaches the permanent magnet. It will rather start moving quite soon, before the permanent magnet will. That's why I think it is simpler to analyze the conservation of momentum question in a system without EM involvement, e.g. Bob and Alice above. Certainly EM fields within the rope are involved in the "signal" transmission from Bob to Alice, but they have no connection to Bob's mass and velocity and thus to the total momentum of the system.

---

On the second thought, the EM fields in the rope "know" about Bob's momentum because they transfer this momentum to Alice. So, perhaps this is where the answer is...

[zetetic56]

55 minutes ago, Genady said:

And what about Bob and Alice holding two ends of a stretched rope? The momentum of the system is 0. As soon as Bob pulls himself along the rope, he starts moving toward Alice. Nothing else moves until the other end of the rope pulls Alice. The system has a non-zero momentum all this time. Thus, the total momentum is not conserved. What is wrong here?

If the rope has mass then as Bob pulls on the rope the mass of the rope moves towards Bob and Bob moves towards the mass of the rope, and so it seems to me that in this way momentum is conserved between Bob and the rope.  And then at some point later Alice is pulled by the moving rope and the pull on the rope by her will slow the moving rope down and accelerate her and then it seems to me that momentum will again be conserved.

If the rope is theoretically "massless" what will happen?  I don't know.  It's an interesting question and it may be a close analogy to what I'm asking here with a turned off and then turned on electromagnet.  I don't know.  I'll have to think about it.

---

(Sorry, I posted this before reading you "second thought".)

Edited April 6, 2022 by zetetic56
responded before seeing edit in previous post

[Genady]

2 minutes ago, zetetic56 said:

If the rope has mass then as Bob pulls on the rope the mass of the rope moves towards Bob and Bob moves towards the mass of the rope, and so it seems to me that in this way momentum is conserved between Bob and the rope.  And then at some point later Alice is pulled by the moving rope and the pull on the rope by her will slow the moving rope down and accelerate her and then it seems to me that momentum will again be conserved.

If the rope is theoretically "massless" what will happen?  I don't know.  It's an interesting question and it may be a close analogy to what I'm asking here with a turned off and then turned on electromagnet.  I don't know.  I'll have to think about it.

Yes, mass of the rope is one question. The other question is, how the rope can move when Bob starts pulling if it is stretched and Alice holds the other end?

Here is a related quote from The Feynman Lectures on Physics Vol. I Ch. 10: Conservation of Momentum (caltech.edu):

Quote

One of the propositions of Newton was that interactions at a distance are instantaneous. It turns out that such is not the case; in situations involving electrical forces, for instance, if an electrical charge at one location is suddenly moved, the effects on another charge, at another place, do not appear instantaneously—there is a little delay. In those circumstances, even if the forces are equal the momentum will not check out; there will be a short time during which there will be trouble, because for a while the first charge will feel a certain reaction force, say, and will pick up some momentum, but the second charge has felt nothing and has not yet changed its momentum. It takes time for the influence to cross the intervening distance, which it does at 186,000 miles a second. In that tiny time the momentum of the particles is not conserved. Of course after the second charge has felt the effect of the first one and all is quieted down, the momentum equation will check out all right, but during that small interval momentum is not conserved. We represent this by saying that during this interval there is another kind of momentum besides that of the particle, mv, and that is momentum in the electromagnetic field. If we add the field momentum to the momentum of the particles, then momentum is conserved at any moment all the time. The fact that the electromagnetic field can possess momentum and energy makes that field very real, and so, for better understanding, the original idea that there are just the forces between particles has to be modified to the idea that a particle makes a field, and a field acts on another particle, and the field itself has such familiar properties as energy content and momentum, just as particles can have. 

 

[zetetic56]

21 minutes ago, Genady said:

Here is a related quote from The Feynman Lectures on Physics Vol. I Ch. 10: Conservation of Momentum (caltech.edu):

So ... is the answer to my question simply that momentum is not always conserved?

I assumed that is always was.  And, perhaps that is wrong.

?

 

[Genady]

6 minutes ago, zetetic56 said:

So ... is the answer to my question simply that momentum is not always conserved?

I assumed that is always was.  And, perhaps that is wrong.

?

 

If we look deep inside, we get to interactions between particles, which are described by QFT. Momentum is always conserved in QFT. On the other hand, all interaction in QFT are "direct collisions", i.e. happen at a point. And then this momentum is carried by a particle to any distance. 

So, the momentum of the massive bodies, mv, is not necessarily conserved. But that momentum plus the momentum carried by the massless EM field is conserved.

[zetetic56]

On 4/6/2022 at 1:04 PM, Genady said:

If we look deep inside, we get to interactions between particles, which are described by QFT. Momentum is always conserved in QFT. On the other hand, all interaction in QFT are "direct collisions", i.e. happen at a point. And then this momentum is carried by a particle to any distance. 

So, the momentum of the massive bodies, mv, is not necessarily conserved. But that momentum plus the momentum carried by the massless EM field is conserved.

What you say makes perfect sense (and it makes sense with how I understand conservation of momentum).

However, the next step in the logic then, I having problems with.

If the massive body of the electromagnet begins to accelerate first and then if the massive body of the permanent magnet then begins to accelerate later and second, then we have a momentum imbalance between these two bodies (more positive momentum and less negative momentum).

If there is more momentum in the expanding newly created magnetic field around the electromagnet in the leftward direction (more negative momentum) and less momentum in the expanding newly created magnetic field in the rightward direction (less positive momentum) then this imbalance in the field could balance out the imbalance between the two massive bodies.

But this doesn't make any sense (and I'm sure you're not suggesting this, i'm just thinking things through out loud).

At some point after the electromagnet is turned on ( (distance between them ) / (speed of light) ) its expanding magnetic field, with its momentum, will collide with the permanent magnet.

If this collision resulted in the expanding field slowing down (a decrease in positive momentum) while not pushing the permanent magnet rightward (no corresponding increase in positive momentum) then this interaction could result in an overall (massive bodies and fields) balance and so then momentum would be conserved.

But, like my previous thinking out loud, this too seems not physically likely.

On 4/6/2022 at 11:12 AM, Genady said:

... the EM fields in the rope "know" about Bob's momentum because they transfer this momentum to Alice. So, perhaps this is where the answer is...

You may have suggested, and you may be thinking, that something different occurs in the rightward moving and expanding magnetic field.

As the magnetic field around the electromagnet expands rightward towards the permanent magnet, I can't see (at least not right now) how this field could carry the "information" with it of the electromagnet it is expanding from being in a state of acceleration.

Any ideas?

? 

 

Edited April 9, 2022 by zetetic56
i wrote "leftward" where i should i written "rightward"

[Genady]

1 hour ago, zetetic56 said:

What you say makes perfect sense (and it makes sense with how I understand conservation of momentum).

However, the next step in the logic then, I having problems with.

If the massive body of the electromagnet begins to accelerate first and then if the massive body of the permanent magnet then begins to accelerate later and second, then we have a momentum imbalance between these two bodies (more positive momentum and less negative momentum).

If there is more momentum in the expanding newly created magnetic field around the electromagnet in the leftward direction (more negative momentum) and less momentum in the expanding newly created magnetic field in the rightward direction (less positive momentum) then this imbalance in the field could balance out the imbalance between the two massive bodies.

But this doesn't make any sense (and I'm sure you're not suggesting this, i'm just thinking things through out loud).

At some point after the electromagnet is turned on ( (distance between them ) / (speed of light) ) its expanding magnetic field, with its momentum, will collide with the permanent magnet.

If this collision resulted in the expanding field slowing down (a decrease in positive momentum) while not pushing the permanent magnet rightward (no corresponding increase in positive momentum) then this interaction could result in an overall (massive bodies and fields) balance and so then momentum would be conserved.

But, like my previous thinking out loud, this too seems not physically likely.

You may have suggested, and you may be thinking, that something different occurs in the rightward moving and expanding magnetic field.

As the magnetic field around the electromagnet expands rightward towards the permanent magnet, I can't see (at least not right now) how this field could carry the "information" with it of the electromagnet it is expanding from being in a state of acceleration.

Any ideas?

? 

 

I'm not sure I follow. Let's make the discussion simpler by using symbols rather than pictures (simpler for me, anyway).

Here is my scenario. As soon as the electromagnet is turned on, it gets a momentum [+p] and the EM field goes off toward the permanent magnet carrying the momentum [-p]. After the specified time, the field reached the permanent magnet and interacts with it. As a result of this interaction, the field looses the momentum but the permanent magnet gets the momentum [-p]. The total momentum is 0 all the time, isn't it?

[zetetic56]

3 hours ago, Genady said:

I'm not sure I follow. Let's make the discussion simpler by using symbols rather than pictures (simpler for me, anyway).

Here is my scenario. As soon as the electromagnet is turned on, it gets a momentum [+p] and the EM field goes off toward the permanent magnet carrying the momentum [-p]. After the specified time, the field reached the permanent magnet and interacts with it. As a result of this interaction, the field looses the momentum but the permanent magnet gets the momentum [-p]. The total momentum is 0 all the time, isn't it?

Sorry if my pictures didn't help.

When the electromagnet is turned on it accelerates to the right [+p].

But the EM field moving towards the permanent magnet is also moving towards the right [and so it's momentum would also be +p not -p].

However , when the electromagnet is turned on it's field moves both to the left [-p] and to the right towards the permanent magnet [+p].  And I suspect that momentum is balanced in the field between the leftward moving field and rightward moving field itself.

When the rightward moving field [+p] collides with the resting permanent magnet [0] I suspect that the field slows down [-p] and the permanent magnet is initially moved to the right [+p] and here momentum would be conserved in this interaction.

And then after the permanent magnet is initially moved to the right [+p] due to the collision, the permanent magnet is now in the electromagnet's magnetic field and would then start to accelerate towards the electromagnet to the left [-p] due to magnetic attraction.

But, if I'm explained myself clearly enough (and maybe I haven't), and if I'm right (and maybe I'm not), then we end up with momentum being balanced everywhere except for the electromagnet itself accelerating to the right [+p] first and then the permanent magnet accelerating to the left second and later [-p], which would mean overall more rightward [>+p] momentum.

This is my problem.  If momentum overall is always conserved, which it must be, then somehow and somewhere I've gotten something wrong.

 

[Genady]

1 hour ago, zetetic56 said:

Sorry if my pictures didn't help.

When the electromagnet is turned on it accelerates to the right [+p].

But the EM field moving towards the permanent magnet is also moving towards the right [and so it's momentum would also be +p not -p].

However , when the electromagnet is turned on it's field moves both to the left [-p] and to the right towards the permanent magnet [+p].  And I suspect that momentum is balanced in the field between the leftward moving field and rightward moving field itself.

When the rightward moving field [+p] collides with the resting permanent magnet [0] I suspect that the field slows down [-p] and the permanent magnet is initially moved to the right [+p] and here momentum would be conserved in this interaction.

And then after the permanent magnet is initially moved to the right [+p] due to the collision, the permanent magnet is now in the electromagnet's magnetic field and would then start to accelerate towards the electromagnet to the left [-p] due to magnetic attraction.

But, if I'm explained myself clearly enough (and maybe I haven't), and if I'm right (and maybe I'm not), then we end up with momentum being balanced everywhere except for the electromagnet itself accelerating to the right [+p] first and then the permanent magnet accelerating to the left second and later [-p], which would mean overall more rightward [>+p] momentum.

This is my problem.  If momentum overall is always conserved, which it must be, then somehow and somewhere I've gotten something wrong.

 

You are correct, it was not accurate to say that "the field is moving to the right".

The EM field is there all the time. Before the electromagnet is turned on, the field is that of the permanent magnet. After the electromagnet is turned on, the field starts changing. What moves is the change, the EM wave. This wave is carrying the total momentum [-p].

The wave never slows down - being EM wave, it always travels with the speed of light. When the wave reaches the permanent magnet and interacts with it, the permanent magnet starts moving with the momentum [-p]. This causes another change in the field, making a new wave. This wave carries momentum [+p].

The stages of the process are like this:

1. Electromagnet at rest, permanent magnet at rest, no waves. Every component and the system have momentum 0.

2. Electromagnet moves to the right, momentum [+p]. Wave 1 goes out, momentum [-p]. Permanent magnet at rest.

3. Electromagnet moves to the right, momentum [+p]. Wave 1 goes out, momentum [-p]. Permanent magnet moves to the left, momentum [-p]. Wave 2 goes out, momentum[+p].

Does it make sense?

[zetetic56]

2 hours ago, Genady said:

You are correct, it was not accurate to say that "the field is moving to the right".

Did you mean to say "You are not correct ..."?  I have been saying that the field moves, and if I'm reading you right then I have been wrong to say this.  If I'm reading you right then I should have been saying "the EM wave moves" or I should have been saying "the change in the field moves".  If I have the terminology correct now, I still think I end up with my same question.  Please let me know if I still don't have this ("the EM wave moves") right.

But, there is a more basic question I have about the terminology of "+p" and "-p".  I thought I understood how you were using it and I thought you made a typo, but now I think I don't understand how you are using these terms.

When something moves to the right that is positive momentum and when something moves to the left that is negative momentum (as per convention).  And so I thought "+p" means momentum moving to the right and "-p" means momentum moving to the left.

When the massive body of the electromagnet moves to the right towards the permanent magnet you use "+p".

But when you talk about the EM wave moving towards the permanent magnet, which is also to the right, you use "-p".  If this isn't a typo, then I don't understand how you are using these terms/concepts.

If you don't mind, could you please explain.  

[Genady]

29 minutes ago, zetetic56 said:

Did you mean to say "You are not correct ..."?  I have been saying that the field moves, and if I'm reading you right then I have been wrong to say this.  If I'm reading you right then I should have been saying "the EM wave moves" or I should have been saying "the change in the field moves".  If I have the terminology correct now, I still think I end up with my same question.  Please let me know if I still don't have this ("the EM wave moves") right.

But, there is a more basic question I have about the terminology of "+p" and "-p".  I thought I understood how you were using it and I thought you made a typo, but now I think I don't understand how you are using these terms.

When something moves to the right that is positive momentum and when something moves to the left that is negative momentum (as per convention).  And so I thought "+p" means momentum moving to the right and "-p" means momentum moving to the left.

When the massive body of the electromagnet moves to the right towards the permanent magnet you use "+p".

But when you talk about the EM wave moving towards the permanent magnet, which is also to the right, you use "-p".  If this isn't a typo, then I don't understand how you are using these terms/concepts.

If you don't mind, could you please explain.  

You said that the field moves, but I said it first, and that leads to misunderstanding. That's why I said, you are correct - because I was wrong first

Now , to the subject. It is correct only about massive bodies, that "when something moves to the right that is a positive momentum ... etc." This does not apply to EM wave. It does apply to a moving massive body because its momentum is mv, so the momentum has the same direction as the velocity. But the momentum of a wave has nothing to do with mv.

Anyway, the wave doesn't move to the right, but is radiated away from the source. The momentum of the wave is not moving from electromagnet toward the permanent magnet. The wave radiating from the electromagnet has a total momentum [-p] (not a typo.) When the permanent magnet moves, its EM field is changing in a wave radiating from it. That wave has a total momentum [+p] (not a typo.) 

Does this explanation clarify what I mean?

Edited April 10, 2022 by Genady

[zetetic56]

11 hours ago, Genady said:

I've been studying Physics on my own, and for the most part this has worked out fine, but every now and then I find myself stumbling into something that I think I understand but it turns out there is a whole bunch of knowledge behind what I'm looking at that I do not have.

I appreciate you trying to help me but in reading your response I think this may be one of those times I thought I was playing in the shallow end but I didn't realize I swam out too far.

I haven't studied field theory yet and I thought that without knowing a lot about fields I could understand my "electromagnet / permanent magnet " question by staying away from the details of fields and just sticking to the concept of " momentum ".

11 hours ago, Genady said:

The momentum of the wave is not moving from electromagnet toward the permanent magnet. 

This makes no sense to me.  And I'm guessing it's because I don't understand fields and radiation and so on.

And so perhaps I need to just tuck away my little question for now and go back and finally get around to studying the basics of field theory.

Again, I appreciate you trying to help me, but I think I've swum out too far again on this one.

Thank you.