Two paralel streams of electrons.

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Discussion Overview

The discussion centers on the interaction between two parallel streams of electrons in vacuum, specifically examining the forces acting between them as described by classical electrodynamics and the implications of relativistic effects. Participants explore the nature of attraction and repulsion in this context, considering both classical and relativistic perspectives.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant notes that classical electrodynamics states that parallel currents attract each other, but questions how relativistic length contraction affects this attraction.
  • Another participant suggests that the attractive force may equal the repulsive force as the speed of electrons approaches the speed of light, referencing the transformation of forces in relativity.
  • A different participant seeks clarification on whether the discussion pertains to electron beams in vacuum or electrons in a conductor.
  • One participant argues that while classical electrodynamics predicts attraction, relativistic effects imply that the Lorentz force cannot become attractive, only less repulsive as velocity increases.
  • Another participant acknowledges the oversight of the observer's perspective, noting that the sum of the Coulomb repulsive force and magnetic attractive force remains non-attractive as electron velocity increases.

Areas of Agreement / Disagreement

Participants express differing views on the nature of the forces between the electron streams, with some asserting that attraction is impossible under relativistic conditions, while others propose that relativistic effects may alter the balance of forces. The discussion remains unresolved regarding the implications of these forces.

Contextual Notes

Participants highlight the dependence on the definitions of force and the frames of reference involved, as well as the unresolved mathematical steps related to force transformations in relativistic contexts.

alpha358
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Consider two parallel streams of electrons in vacuum. Each stream moves with constant velocity and carries a current. According to classical electrodynamics parallel and same direction currents attract each other.
The problem is that I can't see how relativistic length contraction can cause attraction in this situation.

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Does classical electrodynamics perhaps say the attractive force becomes equal to the repulsive force when the electrons are moving at the speed of light?


Because in relativity:

Transformed repulsive force = repulsive force / gamma.

Transformed repulsive force approaches zero, when speed of electrons approaches speed of light.
 
alpha358 said:
Consider two parallel streams of electrons. Each stream carries a current.

Ate you asking about two parallel electron beams in a vacuum, or streams of electrons flowing through a current-carrying wire or other conductor?
 
alpha358 said:
Consider two parallel streams of electrons. Each stream carries a current. According to classical electrodynamics parallel and same direction currents attract each other.
The problem is that I can't see how relativistic length contraction can cause attraction in this situation.
In this circumstance the Lorentz force will never be attractive. As v increases it will become less repulsive, but never attractive. I encourage you to work it out for yourself to confirm.

To understand length contraction's role in reducing the attraction consider the following. Let's say that the spacing between electron's is constant in our frame so that the charge density is constant and I is proportional to v. As v increases the distance between electrons in the electron's frame increases. This is required so that it will length contract down to the correct distance in our frame. That effect causes the acceleration in the electron's rest frame to reduce. Then, that acceleration is further reduced in our frame due to time dilation.
 
jartsa said:
Does classical electrodynamics perhaps say the attractive force becomes equal to the repulsive force when the electrons are moving at the speed of light?

Thanks now I see. I have overlooked the fact that observer at rest will see dominating Coulomb repulsive force and magnetic attractive force increasing with electrons velocity. Sum of these forces is never attractive in this case.
 
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