On Aug 20, 2009, at 9:42 AM, Stephen A. Lawrence wrote:
Horace Heffner wrote:
It's hard to see how AM balances; that's true. However, take a
look at
the attached jpeg, which is a much simpler system:
It's a set of ball bearings in a race, just as you've been
using. The
balls are assumed to be NON-MAGNETIC. In fact, the balls may be
assumed
to be FLAT DISKS, which will make this simpler in some ways (make
'em
planetary gears if that's easier to picture).
The blue "current loop" is just that: it's a current loop, current
going clockwise, which provides a magnetic field, which goes "up"
outside the loop and "down" inside the loop, indicated with "o"s and
"x"s. If the "balls" are flat disks this is easy to do; if they're
actually 3-d balls it's a little harder but the basic field
arrangement
is surely realizable.
There is current through the balls, going radially out, as shown.
Surely there is a TORQUE on each ball, just as in your "model" of
the
ball bearing motor. This sort of thing is practical to realize; it
strikes me as a simple variant on the homopolar motor but I haven't
thought about the comparison a lot.
So.... WHY IS ANGULAR MOMENTUM CONSERVED IN THIS CASE?
I think the answer is that there is a return current segment (or are
current segments) not shown that goes from the outside race to the
inside race. If the sum of the ball currents is N*i = 5*i then the
return current is also exactly N*i. The torques exactly cancel. What
you have are two independent circuits acting on each other, which is
well known not to violate COAM.
But isn't the situation identical with the BB motor?
It is not identical without magnetic material. It is also not
identical because you show the big current ring as external to the
bearings and at the mid-line of the bearings. There is no such
external field producing current ring. There is however, such a set
of split fields generated by the current in the races, and only to
one side of each ball, but that is the topic of the theory I don't
seem to get time to document due to experiments and attempting to
answer questions.
It is only externally induced forces that can make the balls spin.
Forces purely internal to the ball, or internal to the races for that
matter, can not make the motor spin, at least not without violating
COAM.
The situation above is not identical to the theory proposed by either
Gruenberg nor myself. These theories are clearly wrong. Neither of
us include external currents or external fields in our theory of
operation, not even the influence of fields from very close current
segments, which is where I indeed now think the motivating force
comes from. When magnetic material is involved, with mu in the
thousands, any distant external circuit has no practical importance.
All the significant forces involve fields from magnetic dipoles, and
the fields from these decline as 1/r^3. The operative forces are
between current segments and magnetic material close to each other,
but in separate bodies.
Having some "distant" current segments balance the COAM can make
neither Gruenberg's nor my theory correct. Especially when magnetic
materials are involved, if COAM is balanced by distant things, then
these things have to be involved in the *cause* of the motor torque
itself, not just in an ancillary balancing of COAM. No theory
describing torque generated by EM force interactions strictly
internal to the balls or any other single component can conserve
angular momentum. It is only the interactions between components that
can cause the torque while still having COAM conserved. If I rev up
the motor in a vertical axis, hanging in torsion pendulum mode, but
don't turn on the current, the assembly spins wildly. If the current
is on and the motor runs at constant speed, no net torque is
produced. It is a tall order for forces from distance current
segments, not having magnetic material in the vicinity, to produce a
counter torque for that.
You have a magnetic field within the bearing which has similar
topology
to the field provided by the current loop in my diagram.
When the bearings are at rest the field in the bearings is not
similar. The field loop primarily goes around the current i. It is
only when the bearings move that the field lines that are due to mu *
M rotate into a configuration partly similar to the fields you show.
That was the point of my Fig. 4 here:
http://www.mtaonline.net/~hheffner/HullMotor.pdf
However, such rotated fields are *purely internal* to the ball. It is
true that B fields maybe a 1000 times smaller are generated to one
side of the ball by currents in the stationary outside race.
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.
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.
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.
I don't think so.
And you may also need to look at the current
flowing ALONG THE SHAFT, where the B field lines from the bearings are
curving around, so that the current in the shaft is *not* parallel to
the B field lines, and there will consequently be a Lorentz force
on it.
This I did in part, and discussed in regards to Fig. 4. The surface
of the shaft, if it is magnetic, is not different from an extension
of the outer race.
I think it is important to consider that (a) it is not necessary to
have a magnetic shaft because my magnetic motor works without a
magnetic shaft, and (b) the motor doesn't work at all if the bearings
are not magnetic. This then excludes from consideration the effect
of any fields on the shaft not originating from magnetic material
external to the shaft. I don't think forces on the shaft itself are
important to the analysis. OTOH, I do indeed think the H field
generated by the shaft and races plays a role in the magnetic
material in the bearings.
I don't see it, off the top of my head. But it surely is, and
whatever
the mechanism, the same thing may be at work in the ball bearing
motor.
For that matter COAM in the case of the homopolar motor is pretty
hard
to sort out, too!<horace-ball-bearing-motor-1.jpg>
Best regards,
Horace Heffner
http://www.mtaonline.net/~hheffner/
Best regards,
Horace Heffner
http://www.mtaonline.net/~hheffner/
