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Suppose an electron outside a wire is moving with the same velocity as the electrons inside, then due to length contraction, there would be excess positive charges per unit area causing attraction of the election towards the wire, and the positive charges moving in this frame of reference with the same velocity of the electrons but in the opposite direction will create a magnetic field that wouldn't affect the electron that is not moving in this frame of reference. Now, if a grounded shield is placed around this wire, the electric field would not penetrate it and therefore there should be no attraction but then why is the electron attracted to the wire in spite of this shield?

User2956
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  • Which velocity are you writing about -- drift-velocity, Fermi-velocity or something else? – RedGrittyBrick Nov 03 '15 at 16:24
  • By "length contraction" are you speaking of Lorentz contraction? None of the velocities involved in electrical current are close enough to $c$ to make the geometric difference needed for your argument. – Daniel Griscom Nov 03 '15 at 20:54
  • @DanielGriscom: Actually, the speeds are enough, see this question and the corresponding section in the Feynman lectures. – Martin J.H. Nov 04 '15 at 12:41
  • @DanielGriscom There are enough electrons in a wire for even the miniscule effects of Lorentz contraction at those speeds to produce a noticeable force. – User2956 Nov 04 '15 at 13:48
  • But, why does it matter if the electrons contract? It looks like the OP is suggesting that you get more charges per area because of Lorentz contraction; why would contracting electrons cause that effect? – Daniel Griscom Nov 04 '15 at 15:04
  • @DanielGriscom: In the reference frame that moves with the electrons in the wire, the positive charges of the wire are moving and subject to Lorentz contraction. This increases their density. – Martin J.H. Nov 04 '15 at 18:28
  • Well, the consensus seems to be that this question makes sense; if so then someone should probably answer it. – Daniel Griscom Nov 04 '15 at 22:02
  • Doesn't look like I'm gonna get an answer. Should I repost? – User2956 Nov 05 '15 at 10:19
  • Stack Exchange discourages repeated postings of the same question. I'd instead try to edit it in place to clarify it. For instance, you mention magnetic fields as if they attract electrons; perhaps you mean electric fields? It also isn't clear why Lorentz contraction is important here. – Daniel Griscom Nov 05 '15 at 16:26
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    Magnetic fields are just electric fields viewed from a different frame of reference. From the FOR(frame of reference) of the electron outside, it and the electrons inside are at rest(both moving with velocity v in the lab FOR) and it is the wire and positive charges that are moving(with velocity -v in their FOR), causing a Lorentz contraction in their frame, giving the wire a positive charge per unit area. Hence, in the frame of reference of the electron, it is getting attracted by an electric field, but in the lab frame of reference, we explain this phenomenon by calling it a magnetic field. – User2956 Nov 06 '15 at 03:27

2 Answers2

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In the frame of the now stationary electron you could put a cylindrical shell of conducting material around the wire.

Since the wire has a net charge and has an electric field pointing from it, the conductor, if isolated will redistribute its charge to have an equal and opposite charge on the inside surface of the shell and an equal charge on the outside surface. And the electric field will continue outside just the same as inside.

And the stationary electron outside will feel that electric field. Charges outside a Faraday cage still feel an electric field from the amount of charge inside.

If you try to ground the conducting shell then you are grounding in a frame.

And scalar potential is gauge dependent, and you can pick a gauge for statics, but statics is frame dependent. If you looked at that result of just charge on the inner surface and moved back to the original frame you see an equal and opposite current on that surface and see a moving person saying that to them it looks grounded.

Magnetic fields are not just electric fields in a different frame, that would not explain travelling electromagnetic waves.

Timaeus
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  • Addressing your last sentence, how does it not explain it? As stupid as it sounds, why not call it an electric field with an oscillating frame of reference? – Zach Johnson Dec 25 '15 at 06:23
  • @ZachJohnson The electromagnetic force could be due solely to the electric field in the frame of the particle feeling it. But with a situation as simple as a neutral current carrying wire, you would have to have two or more different frames at the same place to compute forces. Picking a single frame allows you to talk about grounding and such. Even so, you'd still need dynamical laws. If you didn't want to use Maxwell as dynamical laws and wanted only electric fields you would still need to assign energy and momentum (and stress) to the field to preserve conservation of energy and momentum. – Timaeus Dec 25 '15 at 07:20
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U need a second ground wire or your shield is not high enough for defense as the magnetic or electical field penetrating.

Jason Bauer
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    Hello and Welcome to Stack Exchange! Sadly, I can't make sense of this sentence - could you please check the grammar and elaborate more? Additionally, please note that we generally don't like the use of colloquial abbreviations. – Martin Nov 03 '15 at 15:55
  • What don't u understand? – Jason Bauer Nov 03 '15 at 15:58
  • I can't parse the sentence beyond "defense" - and I don't see why the first part is true. – Martin Nov 03 '15 at 17:15