Explanation of EM-fields using SR

Nugatory
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Narrator slips up a few times and says "moving" instead of "moving relative to", but other than that it's pretty good.

I don't immediately get why the separation of the negatively charged particles doesn't contract from the man's reference frame, as they are moving relative to him, and therefore there would be a negative overall charge.

pervect
Staff Emeritus
It seems like an attempt to popularze Purcell.

I have a suspicion that it will confuse it's target's audience , but I'm not sure if that can be helped, considering that it's an attempt to reach as many people as possible (and hence put the "target" as low as possible).

Personally, I'd save this sort of explanation for someone who is sophisticated enough to work out what charge densities are required (as measured in the lab and comoving frames, the comoving frames of the electrons being different from the lab frame) to ensure electrical neutrality in the lab frame. Perhaps I'm being pessemistic, perhaps not.

Dale
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I don't immediately get why the separation of the negatively charged particles doesn't contract from the man's reference frame, as they are moving relative to him, and therefore there would be a negative overall charge.
That tends to be the point that confuses most of the people that actually understand the argument being presented, so kudos on understanding the argument.

The spacing of the electrons in the wire frame is determined by the observed fact that the wire is uncharged in the wire frame. This is a "boundary condition" that can be experimentally controlled.

For example, instead of having an uncharged wire you could give the wire an excess positive charge by putting it at a very high voltage. If you did that then the spacing between electrons in the wire frame would be greater than the spacing between protons.

Once the spacing is determined in the wire frame, then it is determined in all frames.

As for Noyhcat, take a look here: http://physics.weber.edu/schroeder/mrr/MRRtalk.html as it explains things in a much more lucid manner than does the video commenter in my opinion.
Thanks for the link, but I don't think it adresses Noyhcat's point, as it also starts out with the current already flowing and the wire being neutral in the lab frame.

Let's start with a wire without a current. It is neutral too, so the distances between pos. and neg. charges are equal here. Now what happens when a current starts flowing? Judging by the video and your link only one type of charge starts moving and gets contracted in the lab frame. So the wire should become charged in the lab frame, which is not the case.

Shouldn't both charge types move in opposite directions in the lab frame? Then they are contracted by the same amount, and the wire remains neutral in the lab frame. Only when you move relative to the wire the contractions become different, and the wire becomes charged. The problem is of course that they identify positive charges with protons which cannot move in the lab frame, instead with the electron holes that are moving opposite to the electrons in the lab frame.

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pervect
Staff Emeritus
I don't immediately get why the separation of the negatively charged particles doesn't contract from the man's reference frame, as they are moving relative to him, and therefore there would be a negative overall charge.

That tends to be the point that confuses most of the people that actually understand the argument being presented, so kudos on understanding the argument.

The spacing of the electrons in the wire frame is determined by the observed fact that the wire is uncharged in the wire frame. This is a "boundary condition" that can be experimentally controlled.

This is related to what I was trying to say earlier.

There are three possibilities:

1) Ignore the issue, which is what the video has done. Then you'll get questions like Noyhcat's.
2) Try to explain this in the video - which will raise the bar on the target audience
3) Raise the bar on the target as far as the "target audience" is concerned.

Overall, I favor 3, because ignoring the issue doesn't really work, and I'm afraid I don't know how to do 2) (explain the issue) without violating 3) (raising the height of the target audience).

WannabeNewton
You're right A.T. in that the link doesn't answer that particular question in a straightforward manner. Do you have access to Griffiths book? Perhaps his explanation would be to your liking. Check out section 12.3.1.

I'm afraid I don't know how to do 2) (explain the issue) without violating 3) (raising the height of the target audience).
What do you think about my idea in post #7, with both charge types moving in opposite directions in the wire's frame? Does it work out quantitatively? I don't think it would make the video more difficult to understand.

WannabeNewton
That's what Griffiths does in the aforementioned section.

That's what Griffiths does in the aforementioned section.
What is the title of the book?

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atyy
I like the video and DaleSpam's answer. One has to specify what is happening in one frame of reference, eg. there is a current in the wire, and the wire containing the current is uncharged in the lab frame. Relativity is a relationship between frames of reference, so if you specify what happens in one frame, it tells you what happens in another frame.

I like the video and DaleSpam's answer. One has to specify what is happening in one frame of reference, eg. there is a current in the wire, and the wire containing the current is uncharged in the lab frame. Relativity is a relationship between frames of reference, so if you specify what happens in one frame, it tells you what happens in another frame.

Yes, with the clarifications mentioned by DaleSpam it makes sense. But otherwise many will try to extrapolate the presented mechanism, to see what happens when a current starts/stops flowing.

atyy
Maybe something like this:

We know that in the lab frame we can set up a wire with a current in it. We know we can do this in a way such that the wire is electrically neutral, because the wire neither attracts nor repels a charged particle that is stationary in the lab frame. Since we have set up the wire to be electrically neutral in the lab frame, the distance between positive charges is the same as the distance between negative charges in the lab frame. Now, will the wire attract or repel a charged particle that is moving in the lab frame? If the only force that affects charged particles is the electric force, since the wire is electrically neutral in the lab frame, it will neither attract nor repel a moving charged particle.

WannabeNewton
Thanks, I will try to check it out. But the idea with both charge types moving is basically correct?

Yeah.

Thanks, I will try to check it out. But the idea with both charge types moving is basically correct?

Yeah.

And how do you explain, if the current carrying wire is made of highly doped n-type semiconductor, when you don't have any holes to go by.

The spacing of the electrons in the wire frame is determined by the observed fact that the wire is uncharged in the wire frame. This is a "boundary condition" that can be experimentally controlled.
Once the spacing is determined in the wire frame, then it is determined in all frames.

I think role of physics is in finding relations(mostly logical) between observations, for example what should we observe if we stop the current, and we all know it is an observed fact that the wire still remains electrically neutral. The point is, according to the SR length contraction explanation, it should not be neutral when we stop the current if it were to be neutral when there was a current.

Dale
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I think role of physics is in finding relations(mostly logical) between observations, for example what should we observe if we stop the current, and we all know it is an observed fact that the wire still remains electrically neutral. The point is, according to the SR length contraction explanation, it should not be neutral when we stop the current if it were to be neutral when there was a current.
That would only be true if the electrons were rigidly attached to each other, which they are not. Charge carriers in a conductor are, by definition, very mobile and able to change their position and spacing in response to any fields.

In the wire frame the wire is electrically neutral. The spacing of the charges must reflect that boundary condition.

Dale
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What do you think about my idea in post #7, with both charge types moving in opposite directions in the wire's frame? Does it work out quantitatively?
Yes, it works out quantitatively. Using units where c=1 the current four-vector or four-current is ##J=(\rho,\mathbf{j})## where ρ is the charge density and j is the current density.

Suppose that we have a flow of unit charges (no opposite charges) each separated by a distance of 0.5 and travelling at a speed of 0.5 c. That gives a four-current of J=(2,1,0,0). Now, if we boost that to .5 c we find J'=(1.732,0,0,0), which corresponds to unit charges at rest with a spacing of 0.577. The γ factor at .5 c is 1.155, and so the spacing of 0.577 at rest transforms to a spacing of .5 at .5 c. You can play around with other speeds, charges, and distances to convince yourself that the four-current is a proper four-vector. Regardless of the combination of charge, separation, and velocity, the four-current always transforms correctly.

Once you have convinced yourself of that then it follows from linear algebra that if A and B are vectors (e.g. the four-current) and L is a linear transform (e.g. the Lorentz transform) then A+B=C implies that ##L \cdot A+L \cdot B=L \cdot (A+B)=L \cdot C## so it doesn't matter how you split up your current four-vector into positive charges moving one way and negative charges moving another way, as long as the sum is correct, the Lorentz transform will give you the correct four-current in any other frame.

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That would only be true if the electrons were rigidly attached to each other, which they are not. Charge carriers in a conductor are, by definition, very mobile and able to change their position and spacing in response to any fields.

In the wire frame the wire is electrically neutral. The spacing of the charges must reflect that boundary condition.

So if it is the spacing of the electrons that keeps changing while switching on and off the current, what do you suggest happens for a closed loop of current wire! ,where does the extra electrons go or come from ?

Dale
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So if it is the spacing of the electrons that keeps changing while switching on and off the current, what do you suggest happens for a closed loop of current wire! ,where does the extra electrons go or come from ?
If any additional electrons are required then they would come from the battery or other power source. However, usually no additional electrons are required. Usually, charge is just redistributed around the loop.

If any additional electrons are required then they would come from the battery or other power source. However, usually no additional electrons are required. Usually, charge is just redistributed around the loop.
How does a particular redistribution of charges(electrons), as a result of the presence or absence of net electric field in the wire in a single direction, cancels out the effect of length contraction due to motion of electrons everywhere. A particular redistribution can only cancel out the effects at a particular point and not everywhere.

And you already know we don't always need the batteries to produce the current !!

Dale
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How does a particular redistribution of charges(electrons), as a result of the presence or absence of net electric field in the wire in a single direction, cancels out the effect of length contraction due to motion of electrons everywhere. A particular redistribution can only cancel out the effects at a particular point and not everywhere.
Consider an uncharged square loop of unit length (units where c=1) and width carrying a unit current clockwise. In the top wire the four-current is Jt=(0,1,0,0). In the right wire the four-current is Jr=(0,0,-1,0). In the bottom wire the four-current is Jb=(0,-1,0,0). And in the left wire the four current is Jl=(0,0,1,0).

Now, if we go to a frame moving at .6 c wrt the wire then the four-currents become Jt'=(-.75,1.25,0,0), Jr'=(0,0,-1,0), Jb'=(.75,-1.25,0,0), Jl'=(0,0,1,0). So the excess negative charge density on the top is balanced by an excess positive charge density on the bottom, with no net charge for the whole loop.

And you already know we don't always need the batteries to produce the current !!
Clearly not. I just mentioned it because there are times when there is a net charge and in such cases the charge comes from the power source. I never said that batteries are always needed, and in fact, I specifically said that usually the power source is not needed for the explanation.

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DrGreg
Gold Member
So if it is the spacing of the electrons that keeps changing while switching on and off the current, what do you suggest happens for a closed loop of current wire! ,where does the extra electrons go or come from ?

In the rest frame of the wire, the spacing of electrons does not change, so no extra electrons are needed.

In an inertial frame in which the wire is moving and the electrons along one straight part of the wire are at rest, electrons in a different part of the closed loop (the return wire, if you like) are not at rest. So, in this frame, the electron density isn't constant: it's lower where the electrons are at rest and higher where the electrons are moving. Averaged out over the whole loop, the total number of electrons is unchanged.

I posted the diagram below over 18 months ago in a thread you took part in:

Consider an uncharged square loop of unit length (units where c=1) and width carrying a unit current clockwise. In the top wire the four-current is Jt=(0,1,0,0). In the right wire the four-current is Jr=(0,0,-1,0). In the bottom wire the four-current is Jb=(0,-1,0,0). And in the left wire the four current is Jl=(0,0,1,0).

Now, if we go to a frame moving at .6 c wrt the wire then the four-currents become Jt'=(-.75,1.25,0,0), Jr'=(0,0,-1,0), Jb'=(.75,-1.25,0,0), Jl'=(0,0,1,0). So the excess negative charge density on the top is balanced by an excess positive charge density on the bottom, with no net charge for the whole loop.
Seriously! I thought we were discussing switching the current on and off, what you are describing is Lorentz invariant nature of current in two different frames.
Clearly not. I just mentioned it because there are times when there is a net charge and in such cases the charge comes from the power source. I never said that batteries are always needed, and in fact, I specifically said that usually the power source is not needed for the explanation.
I think i was rather vague in my last post, what I meant was where do you get the extra electrons when the current is produced by the changing magnetic field, or let's say a current carrying superconducting wire, where current is due to changing magnetic field.

Dale
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Seriously! I thought we were discussing switching the current on and off, what you are describing is Lorentz invariant nature of current in two different frames.
Your posts are rather vague. You should carefully specify what you are interested in including the reference frame. I believe that I answered the question you asked.

Regarding switching a current on or off, there is no net charge without current. There is no net charge with current. So what is the confusion?

what I meant was where do you get the extra electrons when the current is produced by the changing magnetic field, or let's say a current carrying superconducting wire, where current is due to changing magnetic field.
What extra electrons? The point of the exercise is to show that there aren't any extra electrons.

In the rest frame of the wire, the spacing of electrons does not change, so no extra electrons are needed.

In an inertial frame in which the wire is moving and the electrons along one straight part of the wire are at rest, electrons in a different part of the closed loop (the return wire, if you like) are not at rest. So, in this frame, the electron density isn't constant: it's lower where the electrons are at rest and higher where the electrons are moving. Averaged out over the whole loop, the total number of electrons is unchanged.

I posted the diagram below over 18 months ago in a thread you took part in: