[hamdani yusuf (OP)]

B field is observer dependent. What's like B field in one frame of reference, may be more like E field in another frame of reference.

This has some similarities with rainbow. It looks real because it can be seen with naked eye. But seen from different angle, the same rain drop looks to have different colors.

[hamdani yusuf (OP)]

Now we add another wire below the particle with the same direction of electric current but physically move in opposite direction to the first wire.



In the place where the particle resides, B=0 because the second wire produces magnetic fields with the same magnitude but opposite direction to the first wire. Nevertheless, the second wire gives down force as much as the first, thus the resultant force becomes twice. From here on it can be concluded that the idea about magnetic fields that fill the space is not adequate to explain electromagnetic phenomena.

I've shown the problem with magnetic field in the first page of this thread.

[hamdani yusuf (OP)]

Here's the referred video.

How Special Relativity Makes Magnets Work

Magnetism seems like a pretty magical phenomenon. Rocks that attract or repel each other at a distance - that's really cool - and electric current in a wire interacts in the same way. What's even more amazing is how it works. We normally think of special relativity as having little bearing on our lives because everything happens at such low speeds that relativistic effects are negligible. But when you consider the large number of charges in a wire and the strength of the electric interaction, you can see that electromagnets function thanks to the special relativistic effect of length contraction. In a frame of reference moving with the charges, there is an electric field that creates a force on the charges. But in the lab frame, there is no electric field so it must be a magnetic field creating the force. Hence we see that a magnetic field is what an electric field becomes when an electrically charged object starts moving.

I read the comments and found some interesting discussion.

If the cat isn't moving, wouldn't the electrons be length-contracted, and therefore the cat should feel a negative charge?

For those who ask themselves, why the electrons dont come closer together in the lab frame: I think its because only the electrons become contracted not the space in between. Hence, the density of charge doesn't change. When the cat moves, everything it sees is contracted, since everything (also the space between the postitiv charges) moves and the density of positive charges increases. Just my approach though

So why does the space between the electrons in the lab frame not contract, but the space between the protons in the moving cat's frame do? What's the difference?

In the lab frame the space does not move relative to the stationary observer. But relative to the moving Cat the space moves and ist therefore contracted

This line of reasoning isn't correct, even though it makes sense theoretically.

The reality of the situation is this: in the lab frame of reference, the protons in the wire are stationary while the electrons flow with a certain speed and with a certain charge density. Both of these variables (electron speed and electron density, or "how far apart the electrons are spaced") can be adjusted by the experimenter.

For the sake of this thought experiment, we say that the experimenter has calibrated the setup so that, from their frame of reference (I.E the lab frame), the wire appears electrically neutral. This is after the experimenter has accounted for the relativistic effects acting on the moving electrons (I.E length contraction causing the space between them to appear smaller and thus their density to be higher).
Put another way: imagine the experimenter starts off with the electrons not moving at all. Their speed is zero, and the experimenter adjusts the electron density to match the proton density, so that the wire is electrically neutral. Now the experimenter increases the electrons' speed; this causes length contraction, which causes the charge density of the electrons to increase from the perspective of the lab frame. Now the wire isn't electrically neutral because the density of electrons is higher than the proton density. So the experimenter decreases the electron density, so that now with the relativistic length contraction effect occurring, the densities of protons and electrons appear equal from the lab frame, and the wire appears neutral. The lab frame will still see a force acting on the charge however, since the charge appears to be moving and hence will be repelled by the wire (as the video explains, moving charges passing through a magnetic field like the one around the wire will experience a force).

But when we start moving with the positive charge, at the same speed as the electrons, they now appear stationary. Their length contraction is undone, so they appear to be spaced further apart. *At the same time*, the protons now ARE moving (from our new frame of reference), so they will experience length contraction, so their density will appear to be higher from our new frame.

The result? In our new moving frame of reference, electron density appears lower than before and proton density appears higher than before, and together, this means the wire appears positively charged from our new perspective. Hence, the moving charge experiences repulsion, as is shown in the video. This means the two frames of reference are in agreement, and the problem is solved.

If we wanted to, we could imagine that the experimenter changes the electron density so that now, in the moving frame of reference, the wire DOES appear electrically neutral. Hence, in the moving frame, the moving charge wouldn't experience any force. What would the stationary lab frame see? The wire would appear to be negatively charged (because we've increased electron density so that it'll appear neutral in the moving frame), so it should attract the moving positive charge. BUT since the lab frame also sees the positive charge as moving, it will seem to experience a repulsive force as a result.

Overall, the lab frame will see those two forces acting on the moving charge cancel out, so it moves alongside the wire without being accelerated. And as we said, the moving charge frame will arrive at the same result - the charge won't experience any force, so again, it'll keep moving alongside the wire without acceleration. The two frames of reference are in agreement again.

I hope this helps anyone that was confused by this.

[hamdani yusuf (OP)]

The discussion continues.

This whole video seems to imply that magnetic fields don't really exist, that they are but electric fields viewed from different reference frames, and that electric fields are somehow more fundamental.

But if you look at the equations for the magnetic field, like Biot?Savart law, or Ampere's law for simplicity, you'll see that they all depend on the current which induces them. So now, I think, it is only sensible to ask whether current depends on the frame of reference or not.

It may seem like it at first?when we move with the electrons in the wire, they appear stationary, so no current. But current is just charge over time, and in this case, it's the protons which are moving; moving in the opposite direction and holding opposite charge, so the current stays the same. Thus, there is a magnetic field in this frame of reference as well, of equal intensity as in the first. It doesn't exert any force on the cat because it's not moving (in this reference frame).

The electric field differs though. It's non-zero because of the length contraction of the protons. And it's also the reason behind the repulsive force acting on the cat.

This, of course, doesn't explain why stationary charges don't experience force from the magnetic field since it's present in both reference frames; however, I believe this is the correct interpretation, and it's also the reason why I think the video is wrong.

This discussion has led me to ask the question of what the velocity in the Lorentz force law actually is, and it turns out there's an article that tackles that specifically. It's called "On the Velocity in the Lorentz force Law" by A.K. T. Assis and RM. Peixoto, and it provides equations, derived from the Lorentz transformation, explaining how magnetic and electric fields change in different inertial reference frames. There's also the Wikipedia page "Classical electromagnetism and special relativity" with the same equations.

https://www.semanticscholar.org/paper/On-the-velocity-in-the-Lorentz-force-law-Assis-Peixoto/79a347acf9f264f04cffd3cecd0e3b36a8f027de

[hamdani yusuf (OP)]

The discussion below is more about how common has the relativistic explanation been taught in schools.

6 years of Electrical Engineering curriculum which included extensive study in EM and I was never taught this......  I'm somewhat disappointed in my university.  I actually think I asked this specifically: "I understand all the effects of a magnetic field, but what IS it fundamentally?"  and after some discussion of permeability and Maxwell's equations I lamented that no one in that class, professor included, actually knew.  We could all describe a magnetic field by its effects and influences and even the qualities and characteristics of materials that can support a magnetic field and the methods of inducing one, but not what it actually is.  Thank you so much for this video.  I can now (at least more fully) answer that question "What IS a magnetic field".

, I came across this in an intro EM textbook at Uni and it blew me away. It was like a "holy crap, of course" moment. But Maxwell's Eqns were like a beautiful derivation based on laws found from experiment, whereas the Relativity argument was more like a logical derivation from first principles.

This was a long time ago but I kept the book because it was so amazing. It is "Electromagnetic Fields and Waves" by Lorrain and Corson. It not only has a solid treatment of EM but it has plenty of examples with detailed explanations. Googling, it appears there is a pdf of the 3rd edition available on the internet.
The text gives an in-depth (intermediate level) intro to electrostatics and then before getting into magnetism it covers special relativity. I'm sure there are more up to date texts available but I don't know them.

As everyone else has pointed out, this is pretty much a physics thing as opposed to an EE thing... Now let me just say that if you don't have a good instructor for 3rd year physics E&M this will also be missed. I was pretty much in the same situation as you, I understand everything it does without knowing what it IS. I am a physics PhD student and didn't know this due to a teacher's neglect... The real lesson from this anecdote here is that if you want to know something don't rely on a program curriculum... do your own search based on your curiosity, after all that's how the real world is, you need initiative. Knowledge is rarely handed to you on a platter. Stay curious my friends~

[hamdani yusuf (OP)]

I?ve been teaching high school physics for 32 years, I and I?m still learning such cool things thanks to amazing videos like this one.

I know you meant it well, but tbh that's a bit sad (nothing against you!!). How aren't physics teachers required to know this, what kind of joke is uni degree for a highschool (that means right until university right?) teacher to not know this.. So confusing how bad "our" education is before uni and then you go to uni and everything is over 9000 and all profs are angry because you didn't learn it in highschool.. wtf:D

I do not know if it is good in the case of a pedagogical worker to admit this fatal ignorance. The relativistic consequence of the strength in your frame of reference is really the content of the universities you graduated from.

Don't start teaching this now please without reading:

"Is magnetic field due to an electric current a relativistic effect?" by Oleg D Jefimenko.

It shows it is impossible to interpret both the electric and the magnetic field as relativistic effects.

https://liceocuneo.it/oddenino/wp-content/uploads/sites/2/O.-D.-Jefimenko-Is-magnetic-field-due-to-an-electric-Eur.-J.-Phys.-17-180%E2%80%93182-1996.pdf

[hamdani yusuf (OP)]

Is magnetic field due to an electric
current a relativistic effect?
Oleg D Jefimenko
Physics Department, West Virginia University, PO Box 6315, Morgantown, WV 26506, USA

Abstract. Several authors have asserted that the magnetic
field due to an electric current is a relativistic effect. This
assertion is based on the fact that if one assumes that the
interaction between electric charges is entirely due to the
electric field, then the relativistic force transformation
equations make it imperative that a second field?the
magnetic field?is present when the charges are moving.
However, as is shown in this paper, if one assumes that the
interaction between moving electric charges is entirely due to
the magnetic field, then the same relativistic force
transformation equations make it imperative that a second
field?this time the electric field?is also present. Therefore,
since it is impossible to interpret both the electric and the
magnetic field as relativistic effects, one must conclude that
neither field is a relativistic effect. The true meaning of the
calculations demonstrating the alleged relativistic nature of
the magnetic field and of the calculations presented in this
paper is, therefore, that the idea of a single force field, be it
magnetic or electric, is incompatible with the relativity theory.

Perhaps this explains why the explanation in the Veritasium video isn't widely taught in high schools and electrical engineering.

[alancalverd]

Everything is relativistic. Physics just gets simpler if all the relative velocities are small compared with c.

[hamdani yusuf (OP)]

Everything is relativistic. Physics just gets simpler if all the relative velocities are small compared with c.

Drift velocity of electrons in copper wires, are small. Yet the force between two parallel current carrying wires can be significant.

[hamdani yusuf (OP)]

Imagine two parallel wires stationary in the lab frame. Electrons in both wires move to the right with average drift velocity v. Positive charges are stationary in both wires. Attractive Lorentz force F works on both wires. F is a combination of Lorentz force acting on both positive and negative charges on the wires.

According to relativistic explanation, electrons in first wire see positive charges in second wire length contracted, hence have higher charge density, and attract them. The wires are neutral in lab frame, thus both positive and negative charges have the same density.

Attractive forces on a wire depend on discrepancy of charge density in the other wire, which depend on length contraction by relative velocity of the charged particles. In this case, L=L0√(1-v^2/c^2)

[Eternal Student]

Hi.

Drift velocity of electrons in copper wires, are small. Yet the force between two parallel current carrying wires can be significant.

     The force on each charge carrier is small  BUT  there are quite a lot of these you need to add together  (approximately 10²⁹  free electrons per cubic metre of copper wire).

According to relativistic explanation, positive charges on first wire see moving electrons in second wire length contracted,......

    This line of reasoning and many of the comments you copied-and-pasted from a YT video just a little earlier are all based on the notion that length contraction should apply to the free electrons just as it applies to the metal ions.   So that in a lab frame where the metal ions were stationary, the electrons are then drifting, so they would have higher density due to length contraction and thus the wire should be of net negative charge.    This was discussed in an earlier post  (post # 406):

.....it is just not possible for the (current carrying) wire to be of overall neutral charge in every frame.....    For some reason the frame of reference where the wire is overall neutrally charged is the usual one, the one where the wire (the positive metal atoms in it rather than the free electrons) is stationary....
NOTE:   text in blue italics added to the original quote for clarity

    I haven't read the original paper / discussion you cited by Jefimenko, who died in 2009.   At a guess, this work is quite old and from a time when we were still sorting out the details of electromagnetism and relativity.
    This sentence you quoted seems most relevant:

The true meaning of the calculations demonstrating the alleged relativistic nature of the magnetic field and of the calculations presented in this paper is, therefore, that the idea of a single force field, be it magnetic or electric, is incompatible with the relativity theory.

   Indeed it is helpful to consider that there probably is only a combined electro-magnetic interaction and we cannot sensibly declare that a thing like an electric field (or a magnetic field) exists in isolation.   For example, Maxwells equations where a separate E and B field appear, starts to look more like a "hack" or convenient way of performing calculations involving 2 fields described as ordinary 3-vector fields.   3-vectors are basically the ordinary vectors we might associate with Newtonian mechanics and 3D space.   However, these 2 separate fields may very well be just fictitious artifiacts, useful for calculations but not representing anything that really exists. 
    It may be that the underlying nature of the interaction requires description using 4-vectors such as the Electromagnetic four-potential   (Reference:  https://en.wikipedia.org/wiki/Electromagnetic_four-potential ).   Specifcally, it seems that the more important and presumably more physically real field that may exist is a single 4-vector valued field (rather than 2 seperate 3-vector valued fields).

     About a year ago, the Aharanov-Bohm effect was discussed in this forum.   Here it seems that something can be affected by an electromagnetic field even where the Electric and Magnetic field are both 0 valued.   (Reference:  https://en.wikipedia.org/wiki/Aharonov%E2%80%93Bohm_effect  .   There's also an old forum post which had some diagrams and animation that still seem to be working  https://www.thenakedscientists.com/forum/index.php?topic=86694.msg722832#msg722832 ).    Anyway, this provides some evidence to support the idea that what physically exists and can exert physical effects may very well be a 4-vector valued field such as the  Elctromagnetic four-potential  rather than just 2 separate 3-vector valued fields like the E and B fields.

Best Wishes.

LATE EDITING:   I re-read the old forum post and it may cause some confusion when people read a sentence that said  ..... but back in the day it was important to imagine that magnetism (and possibly every other force) may demand that two fields existed throughout all of space..   That may seem to oppose the notion of needing to consider only ONE combined electro-magnetic object.
    The old forum thread emphasised that considering only a magnetic field (a B field) is not enough, we also need to consider a magnetic vector potential field.    That's why it was convenient to say we needed to consider 2 things (B field and a potential field).   There would be these two things to consider.   Note that both of these things (a B field and a magnetic vector potential field) are just ordinary 3-vector fields.   We get the next layer of complexity by considering 4-vector fields.
    In this post (this thread), you just need to be aware that we can recover ALL the information about EVERYTHING   (the E field, the scalar electric potential field, the B field and the magnetic vector potential field)  from just a single suitably defined 4-vector valued field we call the electromagnetic four-potential.   So if we're looking for the most fundamental description of electro-magnetism then we may need to be considering this object.  Specifically, the electromagnetic four-potential  seems to be a sufficiently integrated object to describe all the electro-magnetic effects that I am aware of.   Meanwhile a lesser set of objects such as:
  (i)  the B field on it's own.
   or (ii)  The B field plus a suitable potential for that B field,
 would NOT be sufficient.

    I hope that makes some sense.    Let's go back to your ( @hamdani yusuf ) original question and paraphrase all of the above comments.

What is the Origin of magnetic force?

I don't know but maybe the entire notion of a magnetic field existing as some sort of thing on its own is just a bit fictitious.
(i) We seem to need to have a E field with it.   We cannot adequately explain all effects with just a magnetic field.
(ii) We seem to need to consider potentials in addition to the forces.
(iii)  Overall we need to have an object like the electro-magnetic four-potential field in existance.   All of physics is just a model but considering the electromagnetic four-potential field as something that exists may be a good step closer to the truth rather than considering that we could attempt to identify and define a magnetic (or electric) field as something that could exist separately.

[alancalverd]

Drift velocity of electrons in copper wires, are small. Yet the force between two parallel current carrying wires can be significant.

Because the magnetic field, and hence the force,  depends on the current in the wire. Although the drift velocity is tiny, the number of electrons is enormous.

A current of 1 amp equals 1 coulomb, i.e 6.2 x 10¹⁸ electrons, per second. 

According to relativistic explanation, electrons in first wire see positive charges in second wire length contracted, hence have higher charge density, and attract them.

But since the drift velocity is of the order of 0.1 mm/s you can safely ignore any relativistic effect.

[hamdani yusuf (OP)]

According to relativistic explanation, positive charges on first wire see moving electrons in second wire length contracted,......

    This line of reasoning and many of the comments you copied-and-pasted from a YT video just a little earlier are all based on the notion that length contraction should apply to the free electrons just as it applies to the metal ions.   So that in a lab frame where the metal ions were stationary, the electrons are then drifting, so they would have higher density due to length contraction and thus the wire should be of net negative charge.    This was discussed in an earlier post  (post # 406):

.....it is just not possible for the (current carrying) wire to be of overall neutral charge in every frame.....    For some reason the frame of reference where the wire is overall neutrally charged is the usual one, the one where the wire (the positive metal atoms in it rather than the free electrons) is stationary....
NOTE:   text in blue italics added to the original quote for clarity

This constraint is based on the fact that electrically charged test particle doesn't seem to experience force when it's stationary to the current carrying wire, which implies that the wire is observed by the test particle as effectively electrically neutral, if we intend to perceive the  electrodynamic effects on the test particle as purely electrostatic one.

[hamdani yusuf (OP)]

But since the drift velocity is of the order of 0.1 mm/s you can safely ignore any relativistic effect.

Proponents of relativistic explanation for magnetic force disagreed, based on sheer number of free electrons in a wire, as described in Veritasium's video.

[alancalverd]

the wire is observed by the test particle as effectively electrically neutral, if we intend to perceive the  electrodynamic effects on the test particle as purely electrostatic one.

As noted by birds sitting on 400 kV grid wires. The field along the wire is negligible and the field perpendicular to the wire depends on the proximity of a surface at a different potential, so in an ideal case the E vector is negligible and the test charge has no inclination to move.

[hamdani yusuf (OP)]

the wire is observed by the test particle as effectively electrically neutral, if we intend to perceive the  electrodynamic effects on the test particle as purely electrostatic one.

As noted by birds sitting on 400 kV grid wires. The field along the wire is negligible and the field perpendicular to the wire depends on the proximity of a surface at a different potential, so in an ideal case the E vector is negligible and the test charge has no inclination to move.

The birds themselves are usually electrically neutral, unlike the test particle.

[hamdani yusuf (OP)]

There was shown that electric current in the wire is produced by the stream of positively charged particles,

"Conventional " current, in classical electromagnetism, flows from positive to negative. This gets the signs correct in Fleming, Ampere, Corkscrew and other Rules.

It seems like the Wikipedia article has been edited from when I referred to it in the OP.

This article is closer to the original source I referred to.
https://physics.weber.edu/schroeder/mrr/MRRhandout.pdf

Purcell Simplified : Magnetism, Radiation, and Relativity
 Anaheim,CA,14January1999
 Dan Schroeder, Weber State University, http://physics.weber.edu/schroeder
 Introductory Comments
 -There's almost nothing original in this talk; Purcell gets all the credit.
 -Don't use Purcell's book in an introductory course. If you're tempted, read the reviews in Amazon.com.)
 - I'm not presenting a complete curriculum; this material would occupy only 3?5 class sessions.
 - I have prepared a 39-page set of type set class notes, suitable for a calculus-based introductory course, which you can download from my website.
 -This material could also be adapted to an algebra-based course, with some loss of rigor.
 -Prerequisites:
1.An understanding of electrostatic fields, including either Gauss's law or equivalent rules for field lines.
2.Familiarity with basic magnetic phenomena, e.g., parallel currents attract.
3.The basics of special relativity, including reference frames, length contraction, and the cosmic speed limit but not including the Lorentz transformation equations or relativistic dynamics

Can you find the problems with this explanation?

[alancalverd]

Insert a realistic value for v and see if you get the right answer.

[hamdani yusuf (OP)]

Insert a realistic value for v and see if you get the right answer.

Is 1 mm/s realistic for you?

[hamdani yusuf (OP)]

Can you find the problems with this explanation?

The model of stationary current carrying wire in the first sentence is questionable. It uses conventional current, as if we didn't know about electron yet.