Lorentz force between two moving charges

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Discussion Overview

The discussion centers around the Lorentz force experienced by two moving charges that are mutually perpendicular to each other. Participants explore the implications of this scenario on Newton's third law, particularly in the context of electromagnetic interactions and the role of the electromagnetic field in force dynamics.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant notes that when one charge crosses the path of another, the force on the first charge appears to be zero while the force on the second charge is non-zero, raising questions about the validity of Newton's third law.
  • Another participant suggests analyzing the situation from a frame where one of the charges is at rest to gain clarity on the forces involved.
  • It is proposed that the total electromagnetic force, rather than just the magnetic component, must be considered to understand the forces acting on the charges.
  • Some participants argue that Newton's third law does not always apply in the context of instantaneous forces in electromagnetic interactions, but it does hold in terms of overall momentum conservation when accounting for the momentum in the electromagnetic field.
  • An example involving two wires is provided, illustrating that a wire carrying current exerts a force on another wire that is initially at rest, highlighting the time delay in the magnetic field's effect and the importance of considering the momentum carried by the field.

Areas of Agreement / Disagreement

Participants express differing views on the applicability of Newton's third law in electromagnetic interactions, with some asserting that it does not hold in the instantaneous sense while others emphasize the importance of momentum conservation. The discussion remains unresolved regarding the implications of these viewpoints on the original scenario presented.

Contextual Notes

The discussion involves assumptions about the nature of electromagnetic forces and the frames of reference used to analyze the situation. There are unresolved aspects related to the definitions of forces and the treatment of electromagnetic fields in relation to classical mechanics.

Universeer
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Two charges are moving mutually perpendicular to each other in space with constant velocities.

The moment one charge crosses over the line of path of second charge the force on 1st charge (located just behind the 2nd charge moving away from it) appear to be zero (Magnetic field due to 2nd charge along its line of path is zero) while force on second charge due to 1st is non zero!
That violates Newton's 3rd law.

What am i missing here?
 
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It might be easier to see what is going on if you work in a frame in which one of the particles is at rest. Compare with the frame in which the other is at rest.
 
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Universeer said:
Summary: Lorentz force between moving Charges, violates Newton's 3rd law.

Two charges are moving mutually perpendicular to each other in space with constant velocities.

The moment one charge crosses over the line of path of second charge the force on 1st charge (located just behind the 2nd charge moving away from it) appear to be zero (Magnetic field due to 2nd charge along its line of path is zero) while force on second charge due to 1st is non zero!
That violates Newton's 3rd law.

What am i missing here?
1) You have to look at the total EM-force, not just the magnetic component.

2) Newton's 3rd law in the sense of instantaneous forces in fact doesn't always apply for EM-interactions. But it does apply in the more general sense of momentum conservation, if you account for the momentum in the EM-field.
 
A.T. said:
2) Newton's 3rd law in the sense of instantaneous forces in fact doesn't always apply for EM-interactions. But it does apply in the more general sense of momentum conservation, if you account for the momentum in the EM-field.

Can you Give an example?
I'll look for total EM force part

Thanks.
 
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Universeer said:
Can you Give an example?
Two wires, one carrying a current and one not. Turn on the current in the "off" wire. It immediately feels a force from the magnetic field of the other wire, but it takes finite time for the magnetic field from the new current to reach the other wire. If you don't account for the momentum carried by the field you get a short period where one wire is accelerating and the other isn't.

It's analogous to me throwing a ball to you. If you forget about the momentum of the ball then my reaction to throwing the ball and your reaction to catching it both apparently violate momentum conservation. But that's because you forgot about the momentum of the "force carrier".
 
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