Electrostatic effect of a current carrying conductor

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Discussion Overview

The discussion centers on the electrostatic effects surrounding a current-carrying conductor, particularly the implications of special relativity on electric fields and charge density. Participants explore the relationship between stationary and moving reference frames and how these affect the perceived electric field at a test point outside the conductor.

Discussion Character

  • Debate/contested

Main Points Raised

  • Some participants assert that according to Maxwell's equations, the electric field at a test point outside a stationary conductor carrying current should be zero.
  • Others argue that when considering special relativity, the moving charges within the conductor experience Lorentz contraction, leading to a change in charge density and potentially creating an electric field at the test point.
  • A participant suggests that the apparent discrepancy can be resolved by noting that forces (electric and magnetic) cancel out in different reference frames, maintaining consistency across observations.
  • Another participant emphasizes that if the test charge is stationary, it experiences no magnetic force, but questions the implications of Lorentz contraction on the charge density of the conductor.
  • Some participants challenge the assumption that Lorentz contraction applies without considering multiple frames, arguing that in a single reference frame, the wire remains uncharged.
  • One participant posits that if the wire appears negatively charged due to Lorentz contraction, it would lead to a repulsion among electrons, contradicting the notion of a steady current.
  • Another participant questions the assumption about the distance between electrons in different states of motion, suggesting that the flexibility of electron spacing in conductors complicates the argument.

Areas of Agreement / Disagreement

Participants express differing views on whether there is a true discrepancy between the predictions of Maxwell's equations and the implications of special relativity. Some maintain that there is no discrepancy, while others argue that the implications of Lorentz contraction suggest an electric field should exist, leading to unresolved disagreements.

Contextual Notes

Participants highlight the importance of reference frames in understanding electric fields and charge distributions, noting that assumptions about charge density and the behavior of electrons may not align with experimental observations.

ashokanand_n
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Consider an infinitely long stationary conductor which carries a steady uniform current.

1. At an arbitrary Test Point outside the conductor the Electric Field should be ZERO according to Maxwell's Equation.
2. But if Special theory of Relativity is considered, the moving charges (electrons) inside the conductor is an inertial frame moving with a fixed velocity with respect to the Test Point. Hence there will be a Lorentz Contraction for the moving frame resulting in the change of (negative) charge density. This will give rise to an imbalance in the +ve and -ve charges in the conductor and hence an Electric Field will be experienced at the Test Point.

How is this discrepancy resolved?? And what does happen in reality??

Ashok
 
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ashokanand_n said:
Consider an infinitely long stationary conductor which carries a steady uniform current.

1. At an arbitrary Test Point outside the conductor the Electric Field should be ZERO according to Maxwell's Equation.
2. But if Special theory of Relativity is considered, the moving charges (electrons) inside the conductor is an inertial frame moving with a fixed velocity with respect to the Test Point. Hence there will be a Lorentz Contraction for the moving frame resulting in the change of (negative) charge density. This will give rise to an imbalance in the +ve and -ve charges in the conductor and hence an Electric Field will be experienced at the Test Point.

How is this discrepancy resolved?? And what does happen in reality??
Actually, it turns out that there is no discrepancy. Let's say in situation 1 that the test charge is at rest. There is no electrostatic force because the conductor is uncharged in this frame and there is no magnetic force because the velocity of the test charge is zero. In situation 2 there is, as you noticed, an electrostatic force, but here the test charge is moving so there is also a magnetic force. These forces always cancel each other out so that if one reference frame detects no force the same is true in all reference frames. Thus there is no experiment you can perform in different frames that will disagree on the measurable results, they will only disagree in what they call E and B.
 
Thanks for the reply.

DaleSpam said:
Actually, it turns out that there is no discrepancy.

But I think I have not put the question very clearly. Actually there are no different situations discussed in the question. There is only one situation. i.e., There is a TEST CHARGE at a fixed point away from a Steady Current Carrying Infinite Wire. Since the TEST CHARGE is not moving, there is no magnetic force on it. At the same time if the moving electrons (inside the wire) are considered with respect to the TEST CHARGE (The reference frame is still the Stationary TEST CHARGE) they will experience what is called Lorentz Contraction resulting in an increased -ve charge density and hence the TEST CHARGE will experience an Electrostatic Force. If this is true then it means that there is always an Electric Field around a current carrying wire which is against Maxwell's Laws. And that is what I was referring to as "discrepancy".
 
If you are only interested in a single reference frame (rest frame of wire and test charge) then I don't understand where you think there is a discrepancy. There is no Lorentz contraction unless you consider at least two frames. In the lab frame the wire is uncharged, so the distance between charge carriers (in the lab frame) is fixed by that condition.
 
DaleSpam said:
If you are only interested in a single reference frame (rest frame of wire and test charge) then I don't understand where you think there is a discrepancy. There is no Lorentz contraction unless you consider at least two frames. In the lab frame the wire is uncharged, so the distance between charge carriers (in the lab frame) is fixed by that condition.

In the Lab Frame the -ve charge carriers are moving whereas the +ve charge carriers are at rest (Supposing that the current is due to flow of electrons). So the -ve charge carriers can be treated as a second frame which will experience Lorentz Contraction because of which the wire should appear to be negatively charged.

Please correct me if i am wrong.
 
the wire should appear to be negatively charged.

Please correct me if i am wrong.
If it were negatively charged, the electrons would repel each other and drive away surplus electrons until the net charge is zero again.
 
Hi ashokanand,

I think you are making a mistaken assumption that the proper distance between the electrons is the same when they are at rest wrt the wire as when they are moving wrt the wire. This would be true if the free electrons in the wire formed a single very rigid object, but that is not the case at all. The distance between electrons is very flexible, particularly in a conductor.

The fact that the wire is uncharged in the lab frame is an experimental observation. Therefore that observed fact determines the distance between the flowing electrons. You are making an incorrect assumption about the distance between the electrons, recognizing that it implies a charged wire, and realizing that a charged wire goes against observed facts, but then you simply missed the conclusion that your assumption must therefore be incorrect.
 
Thank you DaleSpam,

I think i got your point.
 

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