Self-torque of a compressed rod?

1. Jan 15, 2010

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 Kâ, 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 âzâ. Since nothing rotates in Kâ, 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?

2. Jan 15, 2010

clem

3. Jan 16, 2010

GRDixon

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.

4. Jan 18, 2010

clem

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.

5. Jan 18, 2010

GRDixon

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.

6. Jan 18, 2010

clem

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