Self-torque of a compressed rod?

[GRDixon]

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?

 

[Meir Achuz]

http://arxiv.org/abs/physics/0603110

 

[GRDixon]

http://arxiv.org/abs/physics/0603110

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.

 

[Meir Achuz]

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.

 

[GRDixon]

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.

 

[Meir Achuz]

Now you are trying to use the harness to explain the cart and the horse.
It won't work.