Horace Heffner wrote: > > On Aug 20, 2009, at 9:42 AM, Stephen A. Lawrence wrote: > >> >> >> Horace Heffner wrote: >>
>> [sal] >> It's an ordinary magnetic field, and no matter what its cause, it must >> also have the usual properties of B-fields: The field lines never end, >> they just form loops. > [HH] > Yes. But, the field lines inside the balls are due primarily to the > current inside the balls, and are almost exclusively internal to the balls. > > >> [SAL] >> And you've got current going all the way around -- there is a current >> return path somewhere, outside the bearing, which you haven't shown. > > Yes, but it is likely mostly irrelevant. > > >> >> Even if (part of) your return path goes through a second bearing at the >> other end of the motor, you're still in the realm of something which can >> be simulated with my little current loop -- you just need a second loop >> for the second bearing (with current going CCW in the second loop). And >> when you try to think about what the fields must look like outside the >> two bearings in my "gedanken", you're also thinking about what the >> fields must look like outside the two bearings of a BB motor, because >> once again, the fields have roughly the same "shape". > > > Unlike your example, what happens even centimeters away from the > bearings is of no consequence. All the forces of consequence are from > nearby objects. > >> So, you may need to look to the *wires* bringing current to the motor, >> and their interaction with the B-field produced by the spinning ball >> bearings, to figure out where the "balancing" part of the angular >> momentum equation is. > > [HH] > I don't think so. > You are correct. The key to understanding why the proposed model doesn't work is to realize that the current going "straight up" through the ball creates a B field. The ball itself, through hysteresis, also has a B field, and the interactions between those fields is not a one-way street. The question to ask is, how does the current, with its field, interact with the ball, with its "hysterical" field? Maxwell's equations are correct without any reference to auxiliary fields; the H and D fields just simplify calculations in matter. The auxiliary fields are not necessary to understanding what's going on here (or anywhere). The ball, via its "hysterical" field, is acting like a permanent magnet (however transitory the effect may be). And we can model a permanent magnet as a collection of current loops (ignore the fact that the field is largely due to aligned electron spins, that doesn't change the conclusion). The effects of the current loops "cancel" everywhere except at the boundaries of the material, so we can, in fact, model a permanent magnet pretty well by just assuming it has a current flowing over its surface. Call that current a "VIRTUAL CURRENT". The attached JPEG shows the virtual current and induced B field in a ball bearing which is exhibiting "hysteresis" and "holding onto" its field as it turns. The "cause" of that field may be assumed to be a "virtual" current flowing diagonally UP through the center of the ball, and DOWN around the outside, as shown in the image. Now if we imagine a second current -- a "REAL" current this time -- flowing STRAIGHT UP through the ball between the bearing races, we realize two things: 1) There's a torque on the "REAL" current (and consequently on the current carriers, and on the ball itself). The torque is caused by the action of the "hysterical" field of the ball on the real current flowing through the ball from the inner to the outer race, and that's the torque you talked about in the paper. 2) There's a SECOND torque acting on the virtual currents supporting the "hysteresis field", caused by the B field generated by the "real" current acting on the virtual currents. And that torque must exactly balance the torque acting on the "real" current. And that is why COAM is not violated, and it's why the model in the paper doesn't work -- since the two torques balance, the net torque on the ball must be zero. I wish I could now reach into my hat and pull out a "correct" model (or at least one which seems to work) but I haven't got one. :-(
<<inline: horace-ball-bearing-field-1.jpg>>
