Lorentz Force: Does Velocity Still Matter?

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Discussion Overview

The discussion revolves around the Lorentz force and its implications regarding velocity, particularly in the context of parallel currents in wires and streams of electrons in space. Participants explore the nature of force, reference frames, and the effects of special relativity on charged particles.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • Some participants suggest that the Lorentz force implies an absolute velocity, questioning how velocity is defined in different contexts, such as in wires versus in space.
  • Others argue that the Lorentz force is dependent on relative velocity, emphasizing that measurements must consider the frame of reference of the observer.
  • A participant raises the question of what the "V" in the Lorentz force equation (F=QVB) is relative to, noting that it cannot be the relative speed between two electrons or the medium, as the force exists without a medium.
  • Some participants discuss the behavior of plasmas and the role of electric and magnetic fields, noting that the overall neutrality of plasmas affects the forces experienced by charged particles.
  • A later reply questions the applicability of the Lorentz force in scenarios involving parallel currents in wires, suggesting that if the electrons have the same drift velocity, they may not experience a measurable magnetic field from each other.
  • Another participant mentions that in extremely relativistic conditions, the attractive Lorentz force may be canceled by the repulsive Coulomb force, leading to no net force between parallel beams of electrons.

Areas of Agreement / Disagreement

Participants express differing views on the implications of the Lorentz force regarding absolute versus relative velocity, and there is no consensus on the nature of forces acting on parallel currents or streams of electrons. The discussion remains unresolved with multiple competing perspectives.

Contextual Notes

Participants highlight the complexity of defining velocity in different reference frames and the interplay between electric and magnetic forces in charged particle systems. There are unresolved questions about the effects of special relativity on the forces experienced by charged particles in various scenarios.

Who May Find This Useful

This discussion may be of interest to those studying electromagnetism, special relativity, or plasma physics, as well as individuals exploring the conceptual foundations of force and motion in charged particle systems.

  • #31
The electron mass also goes to infinity, Dick.
 
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  • #32
Phrak said:
The electron mass also goes to infinity, Dick.

Sure, Phrak. I'm just saying nothing here says you can't do the analysis in the beam rest frame and then translate to the lab frame. I had originally thought Bob S was saying in the 'highly relativistic' case the magnetic force would exceed or balance the Coulomb force. I don't think that's what being said.
 
  • #33
You know. This is something I asked in my freshman year. I was very disappointed to hear that it was due to both an increase in mass and a decrease in force. It seemed to messy. Acceleration of the beams (divergence) goes to zero in two ways.

Unless I'm missing some subte point, I think I know what you're asking. Not only are mass, length and time Lorentz tranformed, but force also transforms; the[/PLAIN] Faraday tensor is also transformed.
 
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  • #34
Yes, force is a messy concept in SR. And yes, everything else transforms as well. That's why it pays to find the right frame to express your question and then transform to another frame if you have to. You really can draw correct conclusions by just working in the beam frame. I'm not really asking anything. I'm just saying that the conclusion that opposite charges in the rest frame of the charges will repel is true, no matter how much you try to complicate it by frame change.
 
  • #35
OK. But we could despense with the force and just use the vector potential and Dirac equation for the vector potential's action on a charged particle. Now everything is nicely expressed in 4 dimensional tensors as it should be, and the result is the same.
 
  • #36
Sure you could. Or you could just find a simple frame. I'm glad everyone agrees.
 

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