Force Between Moving Charge Particles: Does Speed Matter?

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Discussion Overview

The discussion centers on the effects of speed on the force between moving charged particles, specifically electrons and positrons, as they approach or move apart from each other. Participants explore theoretical implications and calculations related to the Lienard-Wiechert potentials and the Lorentz force, with a focus on specific geometries and scenarios.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant questions whether the opposing force between two electrons remains constant when they move apart or approach each other, specifically at a fixed distance.
  • Another participant asserts that speed does affect the force and references the Lienard-Wiechert potentials for calculations, providing specific examples of forces based on charge positions and velocities.
  • A follow-up inquiry asks if the reduction in force would be the same if the particles were moving apart at the same rate as in the previous example.
  • It is confirmed that the reduction in force is dependent on the specified geometry, indicating that non-linear motion could yield different results.
  • A participant speculates that in a scenario where the particles are slightly off a direct line, the decrease in force when moving apart would be less than when moving towards each other.
  • Another participant encourages practical experimentation with calculations using math software or manual methods to explore the Lienard-Wiechert potentials.
  • One participant reflects on their calculations and suggests they may have misunderstood the relationship between the scenarios discussed.
  • Another participant expresses interest in verifying results through their own calculations, indicating a collaborative exploration of the topic.
  • Specific force calculations are shared, showing results for different velocities and positions, with one participant noting no difference in the outcomes.
  • A final inquiry is made regarding the alignment of the results with empirical data, leaving the question open-ended.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the effects of speed on force between moving charges, with multiple competing views and interpretations of the scenarios presented. The discussion remains unresolved regarding the implications of their calculations and the relationship to empirical data.

Contextual Notes

Limitations include the dependence on specific geometries and the potential for different outcomes based on the motion of the charges. The discussion does not resolve the mathematical steps involved in the calculations or the implications of the results.

Chris Frisella
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You have two electrons held at a fixed distance X from each other. You measure the opposing force is Y. Now you bring the electrons closer to each other, and then let them go so they can fly apart. As the electrons move apart and reach distance X, will the opposing force still be Y, or will it be less/more than that? Similarly, if you reserves it so you had the particles approaching each other (let's say electron & positron pair), what would happen with the force between them at distance X?

Put simply, does the speed towards or away from each other effect force?
 
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Yes, the speed does affect the force. If you want to calculate this the Lienard Wiechert potentials will let you calculate the fields, and then the Lorentz force will give you the force.

So, in units where c=1 and q=1, if you have a charge A at x=-1 and a charge O at the origin then the force on O is f=(1,0,0). Now, if charge A is moving uniformly towards the origin at v=0.6 then f=(0.64,0,0). In that moving case, because you specified motion exactly towards the other charge there is no magnetic field at O, so the force on O does not depend on the speed of O, only the speed of A. (That is not a general result, but a very specific result only for the geometry specified)
 
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Thanks! I think I get the math, but I'm a little unfamiliar, so if the particles were moving apart at the same rate in your example, the reduction in force would be the same as well?
 
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Yes, it works out the same, but again that is dependent on the geometry specified. If they are not moving on a direct line then towards or away can make a difference.
 
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Ok, cool! Now comparing them moving apart vs moving towards each other, but in both cases not on a perfectly direct line (just slightly off). If my understanding of the fields is correct, the moving apart scenario wouldn't experience as much a decrease in force as the moving towards, yes?
 
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At this point you may want to try working this out for yourself. Do you have any math software? If so, then you can write a little routine to calculate the Lienard Wiechert potentials. If not, then use pencil and paper but look for very simple scenarios.
 
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Was just doing that :) SO actually it looks like I had that backwards, yea?
 
That is good! I will have to check later, I don't know that result off the top of my head so I will have to run it through my own routine.
 
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Cool, thanks! I'm interested to see what you get!
 
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OK, so for O at the origin A at (-1,0,0) and for velocity of O = v and velocity of A = -v with v = (.6,.1,0) I get f=(0.633174, 0.0383742, 0.) and with v=(-.6,.1,0) I get f=(0.633174, -0.0383742, 0.)
 
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  • #11
So, no difference. Do you know if that aligns with empirical data?
 

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