Self-torque of a compressed rod?

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Discussion Overview

The discussion centers on the concept of self-torque in the context of a dielectric rod subjected to Lorentz forces from two charges. Participants explore the implications of these forces on the rod and the charges, particularly when viewed from different inertial reference frames. The conversation touches on theoretical considerations, mechanical effects, and the Trouton-Noble experiment.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant questions whether the torque exerted by the rod on the charges can be classified as a self-torque and seeks to understand the parameters that influence its direction and magnitude.
  • Another participant expresses a preference for the views of Panofsky and Phillips, suggesting that additional mechanical considerations are necessary and that stress tensors in a resting body may transform into self-torques when the body is in motion.
  • It is proposed that self-torques cannot influence the motion of the object itself, as they are considered reaction forces to externally applied forces.
  • A participant argues that the self-torque experienced by the rod is balanced by the external Lorentz force couplet, resulting in a net torque of zero on the charges.
  • One participant challenges the reasoning presented, suggesting that the explanation does not adequately address the relationship between the forces and torques involved.

Areas of Agreement / Disagreement

Participants express differing views on the nature and implications of self-torques, with no consensus reached regarding their effects or the underlying mechanics involved. The discussion remains unresolved with competing perspectives on the topic.

Contextual Notes

The discussion involves complex interactions between forces and torques, with references to specific experiments and theoretical frameworks. Limitations include the dependence on definitions of self-torque and the unresolved nature of the mechanical considerations raised.

GRDixon
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Two charges, q1=q2=q>0, are held apart by a dielectric rod of length L. Everything is at rest in the xy-plane of IRF K, with x1=y1=0 and x2=L cos(theta), y2=L sin(theta), 0<theta<pi/2.

Viewed from frame K’, moving in the positive x-direction of K at speed v, the Lorentz forces on the two charges constitute a force couplet that is manifest as a torque toward –z’. Since nothing rotates in K’, the rod presumably exerts a counteracting torque on the charges. Is this a self-torque, and if so, what parameters explain its direction and size?
 
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clem said:

Thanks, Clem. I must confess that I'm more sympathetic with the view of Panofsky and Phillips, that other mechanical considerations must be taken into account. Another thread in these forums has included a derivation of the non-constancy of the spring "constant" when springs move parallel and transverse to their longitudinal axes, relative to an IRF. I'm inclined to believe that stress tensors in a resting body transform to self-torques when the body moves. But the self-torques only exist in the presence of an external stress-causing agent. In any case, the author of your cited article correctly points out that many texts avoid the Trouton-Noble experiment altogether ... possibly because there is no consensus about why the charges don't rotate in response to the Lorentz torque.
 
GRDixon said:
I'm inclined to believe that stress tensors in a resting body transform to self-torques when the body moves.
The first thing I learned on the first day of my first physics course was that "self-torques" cannot affect the motion of the object itself.
 
clem said:
The first thing I learned on the first day of my first physics course was that "self-torques" cannot affect the motion of the object itself.

In my opinion they taught you right. Everything I've read and written about to date indicates that self-forces and self-torques are REACTION forces and torques, the reaction being to externally applied forces/torques. The point I was trying to make in the thread is that the motion of the rod is affected by neither the external Lorentz force couplet nor by the hypothetical self-torque, as these are equal but oppositely directed and sum to zero. (The self-torque experienced by the rod is passed through to the charges, and thus the net torque on them is also zero.) Within the context of the Trouton-Noble experiment, the counteracting torque would be provided by the chassis that holds the capacitor plates at a constant separation.
 
Now you are trying to use the harness to explain the cart and the horse.
It won't work.
 

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