B How To Consistently Explain Electromagnetism With Relativity

[Geocentricist]

Superconducting Ring

In a superconducting ring does the contraction of space between electrons cause them to move inwards? Like in this animation.

Force Between Parallel Wires With Current

In the proton frame of two parallel wires with identical current, I've been told they attract and this is because the motion and length-contraction of the electrons increases the negative charge density. Is this correct? Because it seems this explanation accounts for the protons in one wire being attracted to the excess electrons in the other wire, but ignores the excess electrons being repulsed by the excess electrons in the other wire.

This animation shows a neutral wire becomes negatively charged when a current runs through it. So it's easy to see how two such wires would repel each other.

Veritasium's Video On Electromagnetism

I'm referring to this video:

Notice the separation in the electrons' rest frame at 1:17. Twelve electrons fit on the screen.

At 1:28 the electrons start moving but their separation remains the same.

At 2:08 the electrons' rest frame is again shown but the separation has increased so only 8 of them fit on the screen, and no explanation is provided for why this is.

Did Veritasium make a mistake with this video?

Another thing is at 1:28 when the electrons start moving, it seems their density should increase, and attract the cat-ion. Yet this density increase is not shown. In fact the narrator specifically says the density doesn't change.

I've posted all these questions to Reddit but response time is very, very slow there.

 

[A.T.]

the electrons start moving but their separation remains the same.

This is correct. There is no reason why the electron separation should change, when they start flowing. Even though the fields of the electrons are contracted, they are still repelling each other, so they still spread as far apart as possible within the same wire length.

Here is a good explanation by DrGreg:

https://www.physicsforums.com/threads/explanation-of-em-fields-using-sr.714635/page-2#post-4528480

 

[Dale]

Superconducting Ring

In a superconducting ring does the contraction of space between electrons cause them to move inwards? Like in this animation.

No, there is essentially nothing correct about that animation. In superconductivity electrons are no longer spatially localized.

 

[Geocentricist]

At 1:28 the electrons start moving but their separation remains the same.

This is correct. There is no reason why the electron separation should change, when they start flowing.

Okay. But what about the video showing electron spacing change while the electrons are at rest? Is that correct?

Even though the fields of the electrons are contracted, they are still repelling each other, so they still spread as far apart as possible within the same wire length.

Wouldn't "as far apart as possible" be contracted?

Would you happen to have a similar graphic explaining the force between two parallel, current-carrying wires?

No, there is essentially nothing correct about that animation. In superconductivity electrons are no longer spatially localized.

If the blue spheres represent electron probability clouds instead of actual electrons, would the animation be correct?

 

[Dale]

If the blue spheres represent electron probability clouds instead of actual electrons, would the animation be correct?

No, the animation is flat out wrong. The electrons are not localized, that means that their probability cloud is spread out throughout the entire superconductor. They don’t have a location, they don’t move around the wire, they don’t contract, and they certainly don’t jump off the inside of the superconductor! The animation is about as wrong as it can possibly get

 

[Ibix]

Does relativistic electromagnetism create and annihilate protons and electrons?

No. But you can't get a completely coherent picture if you ignore the return leg of the current loop. If you examine the whole loop you'll find that the electron and proton numbers are equal between frames. The balance of electrons between the out and return arms turns out to be different, as DrGreg's illustration shows.

 

[Geocentricist]

No. But you can't get a completely coherent picture if you ignore the return leg of the current loop. If you examine the whole loop you'll find that the electron and proton numbers are equal between frames. The balance of electrons between the out and return arms turns out to be different, as DrGreg's illustration shows.

Thanks for pointing this out. I actually noticed this after I posted and edited that part of my post out, but you seem to have caught it before I did so.

No, the animation is flat out wrong. The electrons are not localized, that means that their probability cloud is spread out throughout the entire superconductor. They don’t have a location, they don’t move around the wire, they don’t contract, and they certainly don’t jump off the inside of the superconductor! The animation is about as wrong as it can possibly get

Ok, thanks.

 

[A.T.]

Wouldn't "as far apart as possible" be contracted?

The number of electrons doesn't change when the current starts.
The length of the wire doesn't change when the current starts.
Why would the maximally possible distance between them change?

 

[Geocentricist]

The number of electrons doesn't change when the current starts.
The length of the wire doesn't change when the current starts.
Why would the maximally possible distance between them change?

I see what you're saying now. I guess I didn't before. But don't protons repel each other just like electrons? Why do they get to squeeze closer together when they move, since electrons don't?

 

[Ibix]

I see what you're saying now. I guess I didn't before. But don't protons repel each other just like electrons? Why do they get to squeeze closer together when they move, since electrons don't?

Because the electrons are the ones accelerating when the current turns on. The protons never change their state of motion. They're doing different things, so their behaviour is different.

 

[A.T.]

But don't protons repel each other just like electrons? Why do they get to squeeze closer together when they move, since electrons don't?

Unlike the free electrons, the protons are fixed in the lattice and have therefore constant proper distances (the distances in their rest frame). The proper distances of the free electrons can change, while their distance in the wire frame stay constant.

 

[Geocentricist]

Because the electrons are the ones accelerating when the current turns on. The protons never change their state of motion. They're doing different things, so their behaviour is different.

This explanation doesn't seem to work after the acceleration is over.

Unlike the free electrons, the protons are fixed in the lattice and have therefore constant proper distances (the distances in their rest frame). The proper distances of the free electrons can change, while their distance in the wire frame stay constant.

This also feels unsatisfactory for some reason but I will just accept it for now.

Moving on, here is an animation of two parallel wires with identical currents. In the proton frame, both wires are neutral, but in the electron frame, both wires are positive. This seems a contradiction to me because it seems like there would be no force between the wires in the proton frame but a repulsion in the second. What am I missing? If I performed this experiment in real life, what would actually happen?

 

[Dale]

What am I missing?

The magnetic force

 

[Geocentricist]

The magnetic force

What does it do?

 

[Ibix]

This explanation doesn't seem to work after the acceleration is over.

Yes it does.

When there is no current flowing, the electrons and protons are at rest with respect to one another. The electrons have the same spacing as the protons, and all frames agree on this although they will not agree on what the spacing is - frames where the wire is moving will see a smaller (length-contracted) spacing.

When the current is flowing, the wire remains uncharged in its rest frame. So the spacing of the electrons in this frame must be the same as the spacing of the protons. But this is not the rest frame of the electrons any more - we accelerated them. So this spacing must be a length-contracted version of the spacing in the rest frame of the electrons. But we haven't done anything to the protons. This is why the result is different for the electrons and the protons - we changed what the electrons are doing.

We are currently in the rest frame of the protons. If we change to any other frame, the spacing between the protons will length contract. But we are not in the rest frame of the electrons, so the spacing between them will either further length contract or will un-contract, depending if the frame change is to a frame closer to the electron rest-frame or further from it.

 

[Ibix]

What does it do?

Makes the two wires attract, more strongly than the magnetic force in the wire rest frame. The like-charges-repel effect counters that a bit, but the net interaction is still attractive.

 

[Dale]

What does it do?

It makes it so that the net electromagnetic force is attractive.

The reason the Purcell example (the one described by the Veritasium video) is chosen was to simplify the scenario and avoid electric forces in one frame and magnetic forces in the other frame. If you choose a different example then it won’t simplify the same way. With your example the magnetic force cannot be neglected in either frame.

 

[jartsa]

Moving on, here is an animation of two parallel wires with identical currents. In the proton frame, both wires are neutral, but in the electron frame, both wires are positive. This seems a contradiction to me because it seems like there would be no force between the wires in the proton frame but a repulsion in the second. What am I missing? If I performed this experiment in real life, what would actually happen?

The proton frame is the lab frame.

1: In the lab frame the forces between all protons are unchanged when current changes, obviously.

2: In the lab frame forces between protons and electrons are unchanged when current changes.

3: In the lab frame forces between the current carrying electrons are changed when current changes. The forces are decreased when the directions of the currents are the same.

Those are correct statements in the lab frame. Any questions about them?Let me guess: "But in number 2 the electrons see a contracted proton formation. And what is the reason for number 3?"I can answer the first part. Electrons' opinion about the force between the electrons and the protons is just an opinion. The opinion changes when the velocity of the electrons changes. Same logic applies to protons, their opinion about the force between the electrons and the protons does not change, as the velocity of the protons does not change. And the proton frame is the lab frame, so therefore in the lab frame there is no change of force between the electrons and the protons when the current changes.

 

[Geocentricist]

Okay, putting off replying to some comments for a bit while I learn about this magnetic force. I found this image from this Quora answer. Am I interpreting this correctly that an electron moving to the right at V will feel a magnetic force attracting it to another electron beside it also moving to the right at V?

 

[Dale]

Am I interpreting this correctly that an electron moving to the right at V will feel a magnetic force attracting it to another electron beside it also moving to the right at V?

Yes.

 

[Geocentricist]

Yes.

Okay, so if I consider the lab frame and simplify each wire to just one proton and one right-moving electron each, I can see how the magnetic force causes the two wires to attract. Both electrons move to the right, so they attract each other with a magnetic attraction greater than their electric repulsion, and I just ignore the protons since they aren't moving.

But what about in the electron frame, if I consider each wire to be two protons moving left and one stationary electron? Does a pair of left-moving protons attract to another pair of left-moving protons with an attraction strong enough to overcome their electrostatic repulsion? Would this mean magnetic force is stronger than electric force?

 

[Dale]

Does a pair of left-moving protons attract to another pair of left-moving protons with an attraction strong enough to overcome their electrostatic repulsion?

No, the net force is always repulsive for a pair of protons.

Would this mean magnetic force is stronger than electric force?

There is no universal answer to that question.

The quantity $E^2-B^2$ is an invariant. If that quantity is negative then in a sense the magnetic field is stronger than the electric field, and there is a frame where electric field is zero. If that quantity is positive then in the same sense the electric field is stronger, and there is a frame where the magnetic field is zero.

For a pair of charges the quantity is positive, and for a pair of current carrying wires the quantity is negative.

 

[Geocentricist]

No, the net force is always repulsive for a pair of protons.

So a pair of electrons moving together attract but a pair of protons moving together doesn't?

Then I'm back to having two left-moving protons and an electron, and another two left-moving protons and an electron. Since each of these two clusters are net positive, and therefore an electric force repels them, how do I explain why they actually attract?

I didn't comment on your answer to my second question because I don't understand it.

 

[Dale]

So a pair of electrons moving together attract but a pair of protons moving together doesn't?

For both a pair of electrons and a pair of protons the electric force is repulsive and the magnetic force is attractive and the net force is repulsive (the quantity is positive).

Then I'm back to having two left-moving protons and an electron, and another two left-moving protons and an electron. Since each of these two clusters are net positive, and therefore an electric force repels them, how do I explain why they actually attract?

Through the magnetic fields! In this case the magnetic force is stronger than the electric force (the quantity is negative). Yes, there is a net charge on the wire, but it is small compared to the current.

I didn't comment on your answer to my second question because I don't understand it.

To simplify, the question was if the electric field was stronger or the magnetic field. The answer is: it depends. In the case of two comoving charges the electric field is stronger. In the case of two parallel currents the magnetic field is stronger.

 

[Geocentricist]

For both a pair of electrons and a pair of protons the electric force is repulsive and the magnetic force is attractive and the net force is repulsive (the quantity is positive).

But I thought you said earlier a pair of moving electrons attract? Now you say they're repulsive? How am I going to explain why the wires on the left attract then?

Through the magnetic fields! In this case the magnetic force is stronger than the electric force (the quantity is negative). Yes, there is a net charge on the wire, but it is small compared to the current.

I'm so confused because now it seems you're contradicting what you just said, that a pair of a pair of protons repulse (the net force is repulsive because the quantity is positive).

To simplify, the question was if the electric field was stronger or the magnetic field. The answer is: it depends. In the case of two comoving charges the electric field is stronger. In the case of two parallel currents the magnetic field is stronger.

Okay so two comoving electrons, their electric force (repulsion) wins. So I'm at a loss as to how the wires attract in the lefthand scene, and I had thought I got that part down.

 

[Ibix]

Two isolated electrons will always repel. Two isolated protons will always repel. But you can't treat a wire as isolated protons and isolated electrons because that would be ignoring the interaction between the electrons and the protons.

If you analyse a pair of parallel current carrying wires in their rest frame then you will see only a magnetic field which causes an attractive force. If you view them in any other frame you will see a (different strength) magnetic field which causes an attractive force, but also an electric field which causes a repulsive force. The attractive magnetic force will always be stronger than the repulsive electric force so the net force will always be attractive.

You can analyse this in terms of pairs of streams of positive and negative charges with different velocities and rest charge densities, but you must remember both the electric and magnetic effect on one stream due to all three of the others. Sometimes you can short cut it and note that some effect cancels with another one - for example in the rest frame of the wire the electric effect of a proton stream cancels the electric effect of its electron stream. But that does not hold in every frame.

 

[Dale]

But I thought you said earlier a pair of moving electrons attract?

No, I said that the magnetic force between a pair of electrons is attractive. The electrostatic force is repulsive. In this case the electrostatic force dominates and the net force is repulsive.

How am I going to explain why the wires on the left attract then?

Through the magnetic force. In this case the magnetic force dominates and the net force is attractive.

I'm so confused because now it seems you're contradicting what you just said, that a pair of a pair of protons repulse (the net force is repulsive because the quantity is positive).

I am not contradicting what I said. You are asking different questions about different situations and they have different answers. As I said above, whether the magnetic force or the electric force is stronger depends on the situation. In the case of two co-moving charges of the same sign the electric force is stronger and the net force is repulsive. In the case of two parallel current carrying wires the magnetic force is stronger and the net force is attractive.

Okay so two comoving electrons, their electric force (repulsion) wins. So I'm at a loss as to how the wires attract in the lefthand scene, and I had thought I got that part down.

That should be pretty clear, I don't know how you are at a loss on that one. The wires are neutral, so the electric force is 0. The wires are carrying parallel currents so the magnetic force is attractive. In this case the magnetic force is clearly the dominant one, so the net force is attractive.

 

[jartsa]

But I thought you said earlier a pair of moving electrons attract? Now you say they're repulsive? How am I going to explain why the wires on the left attract then?

View attachment 215426

Well there a is really simple thing that you are ignoring:

The positive thing at the top left corner of the picture attracts the negative thing at the bottom left corner of the picture.

 

[Geocentricist]

Okay, thanks for all the responses. I've figured out that in the first situation, all forces cancel except for the magnetic attraction between the two moving electrons. But in the second situation, I'm still working on it. The two protons in each wire repel each other electrostatically, but also attract magnetically, right? But since electrostatic force is stronger than magnetic, this would mean there's a net repulsion yet this is not true so I must be wrong somewhere.

By the way, if the electrostatic force is 1, what would the magnetic force be?

 

[Ibix]

But since electrostatic force is stronger than magnetic

This statement is not true in general. It depends on the situation.

By the way, if the electrostatic force is 1, what would the magnetic force be?

In what setup, in what frame, between what objects?

 

[jartsa]

Okay, thanks for all the responses. I've figured out that in the first situation, all forces cancel except for the magnetic attraction between the two moving electrons. But in the second situation, I'm still working on it. The two protons in each wire repel each other electrostatically, but also attract magnetically, right? But since electrostatic force is stronger than magnetic, this would mean there's a net repulsion yet this is not true so I must be wrong somewhere.

Well now the two positive thighs at the top right corner of the picture attract the one negative thing at the bottom right corner of the picture. Just normal electrostatic attraction. Oh yes, the two positive things would be farther apart if they we not moving.If we make the positive things move together very fast, we can ignore net force between them, because the net force becomes very small. If the fast motion causes more positive things to get into the picture ... then it isn't so simple.

 

[Geocentricist]

In what setup, in what frame, between what objects?

In the frame of two wires with moving electrons, if a moving electron repels another moving electron with an electrostatic force of 1 then how strong is the magnetic attraction between them?

Well now the two positive thighs at the top right corner of the picture attract the one negative thing at the bottom right corner of the picture. Just normal electrostatic attraction.

Okay, but doesn't the top proton pair repel the bottom proton pair with double the force that it attracts the bottom electron? So the top wire is still, overall, repelling the bottom wire, contrary to the result I'm aiming for (the reality that the two wires attract).

Also I wanted to bump one of the original questions I had in the OP about Veritasium's video, which is, are they mistaken in portraying the electron-frame electron spacing different at different times?

 

[jartsa]

Okay, but doesn't the top proton pair repel the bottom proton pair with double the force that it attracts the bottom electron? So the top wire is still, overall, repelling the bottom wire, contrary to the result I'm aiming for (the reality that the two wires attract).

No. There's the 'magnetism' thing. Parallel currents attract.

But now that I thought about it I noticed that the contraction thing and the 'magnetism' thing cancel out in the electron frame. No matter how fast the protons move the net force between them is the always the same - which means it's the same as when the speed is zero. This is in the electron frame.

 

[Geocentricist]

No. There's the 'magnetism' thing. Parallel currents attract.

I know that if I put two wires with identical current side-by-side they will attract. But I want to know why this is by understanding the electrostatic and magnetic forces between the protons and electrons. That's why I'm confused as to how they can attract given they are both net positive (they each have 2 protons per electron). So there must be some magnetic force that overcomes this repulsion. Since the electrons aren't moving, they can have nothing to do with this magnetic force as it only involves moving charges. So does the magnetic attraction between two co-moving pairs of protons overcome their mutual electrostatic repulsion?

But now that I thought about it I noticed that the contraction thing and the 'magnetism' thing cancel out in the electron frame. No matter how fast the protons move the net force between them is the always the same - which means it's the same as when the speed is zero. This is in the electron frame.

I'm confused. When the protons don't move there's only one proton in the wire as opposed to two. So how could the net force between them be the same?

 

[jartsa]

I'm confused. When the protons don't move there's only one proton in the wire as opposed to two. So how could the net force between them be the same?

No motion - no contraction.
No motion - no 'magnetism'.

 

[jartsa]

I know that if I put two wires with identical current side-by-side they will attract. But I want to know why this is by understanding the electrostatic and magnetic forces between the protons and electrons. That's why I'm confused as to how they can attract given they are both net positive (they each have 2 protons per electron). So there must be some magnetic force that overcomes this repulsion. Since the electrons aren't moving, they can have nothing to do with this magnetic force as it only involves moving charges. So does the magnetic attraction between two co-moving pairs of protons overcome their mutual electrostatic repulsion?

Well that sounds correct - it's just that contraction causes complications.

An electron sees a contracted proton formation and is strongly attracted to that. That's the reason why the wires attract. That's the reason in the electron frame.

A proton sees a normal density of electrons, and protons. Protons repulse protons normally, electrons attract protons normally. But electrons repel electrons with smaller force than normally, because of 'magnetism'. That's the reason the wires attract, in the proton frame.

 

[jartsa]

Also I wanted to bump one of the original questions I had in the OP about Veritasium's video, which is, are they mistaken in portraying the electron-frame electron spacing different at different times?

They are correct.

And now I notice that I ignored that effect in the previous post.

 

[Dale]

Since the electrons aren't moving, they can have nothing to do with this magnetic force as it only involves moving charges.

But they do reduce the electrostatic repulsion substantially. In fact they reduce the electrostatic repulsion so that it is smaller than the magnetic attraction. You cannot neglect the electrons the way you are trying to.

So does the magnetic attraction between two co-moving pairs of protons overcome their mutual electrostatic repulsion?

No, it does not. But a wire is more than just protons.

 

[Geocentricist]

An electron sees a contracted proton formation and is strongly attracted to that. That's the reason why the wires attract. That's the reason in the electron frame.

This seems overly simplistic to me. Of course I don't mean you're wrong, but I don't understand how that can be correct. Sure, the top electron is attracted to the two protons it sees in the other wire. That's 2 units of attraction. But this electron is not far-sighted, so it must also see the two protons in its own wire, and conclude that these two protons both repulse the two protons in the other wire. That's 4 units of repulsion (top proton A repulses both bottom protons, and top proton B also repulses both bottom protons). So how do you explain that?

A proton sees a normal density of electrons, and protons. Protons repulse protons normally, electrons attract protons normally. But electrons repel electrons with smaller force than normally, because of 'magnetism'. That's the reason the wires attract, in the proton frame.

I understand the proton frame

 

[pervect]

[QUOTE="Geocentricist, post: 5886958, member: 636108"
Veritasium's Video On Electromagnetism

I'm referring to this video:

Notice the separation in the electrons' rest frame at 1:17. Twelve electrons fit on the screen.

At 1:28 the electrons start moving but their separation remains the same.

At 2:08 the electrons' rest frame is again shown but the separation has increased so only 8 of them fit on the screen, and no explanation is provided for why this is.

Did Veritasium make a mistake with this video?

Another thing is at 1:28 when the electrons start moving, it seems their density should increase, and attract the cat-ion. Yet this density increase is not shown. In fact the narrator specifically says the density doesn't change.

I've posted all these questions to Reddit but response time is very, very slow there.[/QUOTE]
[/quote]

The video is basically an adaptation of Purcell's approach to electromagnetism. I believe this is form his book "Electricity and Magnetism", https://www.amazon.com/dp/1107014026/?tag=pfamazon01-20, but I don't own that book so my impulse to look it up and make sure my memory is correct on the title will have to go unsatisfied.

Purcell's explanation is correct, but causes a lot of confusion. The thing people typically get confused about is more or less what you're confused about. That is the fact that a wire that is neutral in the lab frame stays neutral in the lab frame when you start a current flowing through it.

Because of this difficulty, I don't recommend Purcell's approach, though it is correct and in the literature. The two approaches I'd suggest are learning Maxwell's equations, or learning the four-vector treatment of special relativity.

About all I can say about why the wire stays neutral in the lab frame is that it is a consequence of the conservation of electric charge (which is formalized by Maxwell's equations). If the total charge of the wire + battery is zero before you hook the battery up to the wire and start the current flowing, the total charge remains zero after you connect the battery, though the charges do move.

This argument doesn't show why the charges stay uniformly distributed throughout the wire, though, but it does demonstrate that the total charge must remain zero.

Note that this seems to be contradicted by the video, when the wire picks up a positive charge in the "cat frame". But when one includes the fact that a wire carying a current does not exist in isolation, one realizes there must be another wire with a return path that's not shown on the diagram, and the charge on that wire that is not shown balances out the charge picked up by the wire that is shown.

This extra complication makes Purcell's approach rather unsatisfying. It avoid using the Lorentz transform of special relativity, but in my opinion that's it's downfall. The Lorentz transform contains an additional effect besides length contraction and time dilation. This effect is the relativity of simultaneity. Without this missing piece, the length contraction and time dilation expanations are not complete. The mathematical treatment using the Lorentz transform is complete, but it's not a pretty picture like the ones you have been drawing.

I have to run - I hope this helps some.

 

[Geocentricist]

They are correct.

They are correct that electron spacing changes in the electron rest-frame? Why would the electrons move further apart from each other? They haven't done anything. There's no cause for them to separate.

 

[Geocentricist]

Purcell's explanation is correct, but causes a lot of confusion. The thing people typically get confused about is more or less what you're confused about. That is the fact that a wire that is neutral in the lab frame stays neutral in the lab frame when you start a current flowing through it.

That's only one problem for me, but I can get over it by just accepting electron spacing doesn't contract when they move.

Because of this difficulty, I don't recommend Purcell's approach, though it is correct and in the literature. The two approaches I'd suggest are learning Maxwell's equations, or learning the four-vector treatment of special relativity.

I'm trying to understand the phenomena to the point where I can illustrate it graphically. I don't think Maxwell's equations or four-vector treatment is a shortcut to that goal, but rather a detour. I'm a visual person and I avoid math whenever possible. I'm not aware of any compelling reason why this phenomena can't be illustrated graphically and only mathematically.

Note that this seems to be contradicted by the video, when the wire picks up a positive charge in the "cat frame". But when one includes the fact that a wire carying a current does not exist in isolation, one realizes there must be another wire with a return path that's not shown on the diagram, and the charge on that wire that is not shown balances out the charge picked up by the wire that is shown.

This part actually doesn't bother me

The mathematical treatment using the Lorentz transform is complete, but it's not a pretty picture like the ones you have been drawing.

Surely there's nothing preventing me from illustrating the two frames graphically? Even if the protons and electrons aren't discrete particles (for whatever reason) that doesn't stop me from illustrating them as probability clouds, or whatever.

Thanks for your time.

 

[pervect]

Surely there's nothing preventing me from illustrating the two frames graphically? Even if the protons and electrons aren't discrete particles (for whatever reason) that doesn't stop me from illustrating them as probability clouds, or whatever.

Thanks for your time.

The video is from my brief inspection, correct. You can check it vs Purcell's textbook, or with online web resources (http://physics.weber.edu/schroeder/mrr/MRRtalk.html comes to mind), though of course it's much better to check it against the original source. Some web pages are correct and useful - others, not so much, and then there are the ones that are completely wrong and misleading.

Some of the "field line" approaches briefly mentioned in the article I linked to might be useful. They are very visual, though, and one can correctly get the electric part of the field of a moving charge simply by Lorentz-contracting the field lines.

You'll find plenty of illustrations of field lines if you look - the direction of the field lines gives the direction of the force, the density of the lines gives the magnitude of the force.

http://www.feynmanlectures.caltech.edu/img/FLP_II/f26-04/f26-04_tc_big.svgz

http://www.feynmanlectures.caltech.edu/img/FLP_II/f26-05/f26-05_tc_big.svgz

For example, the above, the field lines of a single charge taken from one of Feynman's lectures. Above are the electric field lines, one of a stationary charge, directly below it are the electric field lines of a moving charge. Below that is one of the magnetic field lines of a moving charge. You'll need to include the forces due to both the magnetic and electric fields to get the total force. The rules for interpreting electric field line diagram are that the field lines point in the direction of the force, and the density of the field lines gives the magnitude of the force. The rules for magnetic field lines are simila (but not quite the same). The magnetic force on a stationary charge is zero, only moving charges experience a magnetic force.

An explanation of why this approach works get quite deep, but if we avoid explaining why it works, it does seem to meet your visual criterion of a visual presentation.

The above gives the field lines for a single charge (moving and stationary). The field lines add together, but getting a correct diagram for a wire consisting of many charges without use of some of the applicable math (like Gauss' law, in particular) will be challenging. Gauss law isn't particularly hard to master and ties in well with the field line approach.

http://www.physicsclassroom.com/class/estatics/Lesson-4/Electric-Field-Lines also has some further explanations of the field line approach along with spelling out the applicable rules in detail, something I did not do in my short post which is mainly motivational and letting you know the approach exists.

 

[jtbell]

They are correct that electron spacing changes in the electron rest-frame? Why would the electrons move further apart from each other? They haven't done anything. There's no cause for them to separate.

This is just length contraction in reverse. Consider a rod (e.g. a meter-stick) that is stationary in your rest-frame. Now you start to move so that in your new reference rame, the rod is moving parallel to its length. The length of the rod that you measure in this frame is shorter than the length that you measure in your original frame. Why should the rod decrease in length? It hasn't done anything.

You need to come to grips with the true nature of length contraction, which is a space-time geometrical "perspective" effect determined by the relative velocity of the object in question and its observer, not a "physical" effect caused by interactions within the object.

 

[jartsa]

Why would the electrons move further apart from each other? They haven't done anything.

What is the frame of this question?

In the non-inertial frame of an accelerating electron distant things ahead move very fast, distant things include electrons and clock hands. It's because of relativity of simultaneity.

In some inertial frame an accelerating electron's electric field is getting contracted ... if an electron could hold a ruler, we could say the electron's ruler is contracting in this frame. The ruler would fit more easily between the electrons.

 

[Geocentricist]

This is just length contraction in reverse. Consider a rod (e.g. a meter-stick) that is stationary in your rest-frame. Now you start to move so that in your new reference rame, the rod is moving parallel to its length. The length of the rod that you measure in this frame is shorter than the length that you measure in your original frame. Why should the rod decrease in length? It hasn't done anything.

You need to come to grips with the true nature of length contraction, which is a space-time geometrical "perspective" effect determined by the relative velocity of the object in question and its observer, not a "physical" effect caused by interactions within the object.

I don't think you understand what I'm saying. I'm saying in the electron-frame at time A, their spacing is X. Then, still in the electron-frame, at time B the spacing has increased and is bigger than X. Yet the video provides no explanation for why this happens.

To paraphrase that, we are only dealing with one frame the entire time, the electron rest-frame. By definition, the electrons cannot move, so there can be no electron length contraction (again, the electrons are not moving) so why are the electrons moving further apart in their own rest-frame? That's what the video seems to be showing, and that's what I'm asking about.

What is the frame of this question?

The electron rest-frame. The video in the second instance calls it the cat frame but the cat is co-moving with the electrons so they share the same frame.

 

[Geocentricist]

An explanation of why this approach works get quite deep, but if we avoid explaining why it works, it does seem to meet your visual criterion of a visual presentation.

Thanks for your post. Unfortunately, your link uses a flow of positive charges and stationary negative charges. The opposite of my diagram, and the videos, so I fear I'm only going to confuse myself even more by trying to read that. Also, your images didn't work. I hope you can post them again for me to see.

 

[A.T.]

To paraphrase that, we are only dealing with one frame the entire time, the electron rest-frame. By definition, the electrons cannot move, so there can be no electron length contraction (again, the electrons are not moving) so why are the electrons moving further apart in their own rest-frame?

See:
https://en.wikipedia.org/wiki/Bell's_spaceship_paradox
Just replace rockets with electrons.

If you actually attach a frame to an electron, during it's acceleration, you have time running at different rates along the wire in that frame. This effectively delays the electrons in the back, and speeds up the electrons in the front, so their distances increase.

 

[jartsa]

The electron rest-frame. The video in the second instance calls it the cat frame but the cat is co-moving with the electrons so they share the same frame.

So, cat observes the rest density of electrons, it's 3 per cubic nanometer. Then cat calculates the rest density of protons, which means the density of protons in protons frame, it's 4 per cubic nanometer.

Then the cat wants to know a reason for the asymmetry. Well, the reason is in the past, when something happened to the electrons, while nothing happened to the protons. I mean acceleration. See my previous post for some details about the acceleration.

Oh yes, it was a deceleration in the cat frame. The electrons did not decelerate simultaneously in the cat frame, that caused some deformation of the electron formation in the cat frame.

 

[pervect]

Thanks for your post. Unfortunately, your link uses a flow of positive charges and stationary negative charges. The opposite of my diagram, and the videos, so I fear I'm only going to confuse myself even more by trying to read that. Also, your images didn't work. I hope you can post them again for me to see.

I don't understand why it is so hard to flip the sign, but I'd feel silly arguing about how easy it is. I do want to encourage you to do some more research, reading on the topic, taking full advantage of what's available, preferably not just you-tube videos (though those are better than nothing, I guess).