Current: the speed of charges vs the number of charges past a point

[hutchphd]

The drift velocity is indeed very small, but remarkably the relativistic effects are still significant - Purcell's first year E&M textbook uses them to derive the velocity-dependent transformation betwen electrical and magnetic fields around a current-carrying wire. Neglecting these effects may introduce errors of the same magnitude as the magnetic field itself.

Yes. Consider two identical charged particles moving past each other in their CM frame. Their magnetic interaction force is smaller than the electric by a ratio of (v/c)² where v is their relative speed.
In a wire we have eliminated the strongest electric interaction because the conductor is not charged.
It is therefore not surprising the leading order correction to the electric field and the magnetic field itself are of equivalent magnitude.

 

[sophiecentaur]

I was well impressed by that alternative idea. The electrons in two current carrying wires ‘see’ a different density of + and - charges due to Relativistic effects for even a very slow mean velocity. The force is the same (calculation) as if you use Ampere’s law and magnetic fields.
So much for ‘what really happens’

 

[vanhees71]

I was talking about the rest frame of the electrons drifting along the wire. In this case the electrons are stationary and the protons are moving. In fact, the movement of protons is the source of the current in this frame.

I've just written an FAQ article about this case. I've to still proof-read it tomorrow once more. Then I'll put it up as an Insights article too:

https://itp.uni-frankfurt.de/~hees/pf-faq/relativistic-dc.pdf

 

[Ibix]

Is there a lot of point in the 'frame game' here?

The OP specifically asked (in #7 and again, more clearly, in #13) about the current measured by a moving ammeter. In that case, changing frames is the easiest way of answering. The answer is in #9. The discussion since has been about the various traps in naive electron counting and when and why you have to use relativity.

 

[jartsa]

So the wire looks c

You've forgotten the proton current, which is non-zero in the train frame.

Oh. The train moving in the same direction as the electrons sees a positively charged wire.

I guess both trains see the same current passing by then.

If we assume that the wire is neutral in its rest frame, then the train moving against the electron current sees a negatively charged wire, from which the electrons do not feel any particular need to leave. So this kind of wire can not be transmitting any energy anywhere.

 

[vanhees71]

The wire is neutral in the frame, where the conduction electrons are at rest, not in the wire rest frame! See my new FAQ article (which I hope I can also post to the Insights section, which seems not to work right now):

https://itp.uni-frankfurt.de/~hees/pf-faq/relativistic-dc.pdf

 

[jartsa]

The wire is neutral in the frame, where the conduction electrons are at rest, not in the wire rest frame! See my new FAQ article (which I hope I can also post to the Insights section, which seems not to work right now):

https://itp.uni-frankfurt.de/~hees/pf-faq/relativistic-dc.pdf

I have read the first chapter.

A classical physicist standing next to a wire where current in ramping up sees conducting electrons rearranging themselves, she explains that by the self induced Hall effect.

A classical physicist co-moving with the conducting electrons also sees conducting electrons rearranging themselves. He can not explain it. Some electrons even move against the force of gravity - without any reason that a classical physicsist is aware of.Only relativity can explain it.

 

[David Lewis]

Current is determined as the amount of charge moving past a certain point of reference... in 1 second.

To calculate current, the amount of charge that passes may be measured over any amount of time.

For every electron entering the locomotive via the overhead wire, there is an electron leaving via the ground or the other overhead wire so how would that affect your model?

To avoid charge imbalance, the entering and leaving must happen at the same time, and not all frames will agree on simultaneity.