On the Reaction Torque in a Homopolar Generator
Fig. 1 depicts a conducting rod driven by an axle in such a manner as to cut across the B lines of a stationary, disc-shaped magnet. Although the conduction electrons, like the molecules of a gas, move in every direction in the rodís atomic lattice, they are swept along with the same nominal velocity as their containing "vessel."
In the presence of the external B field, Lorentz magnetic forces drive the conduction electrons toward the axle. A resting return wire provides a return path to the stationary outer collection ring. The return wire slides on the axle, and the rod slides on the collection ring. Heat is dissipated in the load, and some mechanical agent (not shown) must apply a torque to the axle. The question is, what explains the equal and opposite reaction torque that the axle exerts on the driving agent?
Homopolar Generator (Side View)
Fig. 2 shows an individual conduction electron in the conducting rod. Along with the rodís atomic lattice it is swept along in the positive x direction.
Conduction Electron in Rod
Now as pointed out, in the absence of any B field the conduction electrons would be moving in all directions, colliding elastically with lattice atoms. They would collectively exert zero torque on the atomic lattice. However, when a nonzero B field exists as shown then the electron experiences a deflecting force in the negative y direction. The resulting motion biases the impulses, delivered to the moving lattice, toward negative x. These myriad, biased impulses are passed (via the rigid lattice) to the drive axle and hence to the driving agent, resulting in a reaction torque that points opposite to w in Fig. 1.