Re: A rotating disk PARADOX??

From: JM Albuquerque (jm.aREMOV.E_at_sapo.pt)
Date: 07/06/04 

Date: Tue, 6 Jul 2004 23:03:28 +0100

"sal" wrote:

> On Mon, 05 Jul 2004 22:10:53 +0100, JM Albuquerque wrote:

> > Between the mechanical and the electrical system there is a
> > magic pass.
>
> It's not magic. In the case of a straight wire moving perpendicular
> to its length in a B field, it's an electrostatic field inside the moving
> wire.

Hummm,...
Not magic?
So you have a new theory !

Since you agree that electrical energy comes from the mechanical torque
times disk angular displacement (energy) provided by the external motor,
and that between the mechanical and the electrical there is energy
conversion, the aim is to find the cause of the reaction torque on the
disk. It could be electrical or magnetic.

Your point is that the cause of the mechanical reaction torque on the disk
is an electrostatic field inside the moving wire, right?

At first I've presumed that the wire that you are talking about is the
external wire, which is the generator's load (resistance).
But it cannot be the torque exerted by the external wire,because the
external wire could be a small lamp in the lab frame, and the lamp
will blow up.

So it must be the "wire filament" which is the smallest path between
brushes on the copper disk (the disk radius length).

> Model the wire as a rather sparse positively charged rigid lattice. Then
> model the electrons in the wire as a negatively charged gas. The motor
> pushes the positively charged lattice along. The B field is exerting a
> force on the electron "gas" which is contrary to the motion of the wire.
> The consequence is that the wire, all along its length, acquires a
> negative charge on the trailing edge and a positive charge on the leading
> edge. The resulting E field, which is perpendicular to the wire and
> _inside_ the wire, is what actually imparts energy to the electrons.

Look carefully to what you said.
You said that the resulting E field... is the cause that imparts energy...

The cause cannot be the result !

> The electrons themselves accelerate through the "sparse lattice" without
> opposition until they collide with something, at which point they give up
> their energy to the lattice, and start accelerating again. The mean free
> path in real wire is typically pretty short so you can model the process
> as something like continuous friction and be pretty close to the right
> behavior.
>
> Pick up a textbook on solid state physics to get a more accurate,
> complete, and clear view of what happens inside a wire. Or ask a EE
> who's actually working in this area -- wires may be black magic as far as
> a physicist is concerned, but they're the bread and butter of electrical
> engineering. For real fun, if you find a knowledgeable EE ask him why
> the diode effect at the ends of the bonding wires on a silicon chip
> doesn't prevent computers from working.
>
> It's more than 10 years since I worked as a EE so I'm a little rusty.

I'm a mechanical. And mechanics is my best point of view.
I'm quit new in advanced electricity, but I'm doing my best.

> There's kind of a big difference between the homopolar generator and your
> mental model of a generator, though, isn't there?

Right.
There's a lot of difference.
That's why I made a mistake below.

> > The electrons don't flow. I'm quite sure that it has been proved that
> > electricity is not a flow of electrons.
>
> This is not correct. With direct current, which is what we're talking
> about here, electrons flow, and that's what the electrical current
> consists of. Current is measured in coulombs per second, which is a count
> of the number of electrons moving from one place to another. One coulomb
> is a _lot_ of electrons, and with DC, they move through the whole circuit,
> start to finish. More on what I think you're thinking of, below.

Coulombs is charge.
One Coulomb is the charge unit that is equivalent to a big number of
electrons.
It was assumed equivalent, it doesn't mean that electrons really flow.
Never heard about a difference between DC and AC speed.

> > Electricity flows, being charges or not, and what flows does it very
> > fast compared to the disk rotational speed.
>
> I think you are confusing the speed with which signals propagate with the
> speed with which electricity flows. Signal propagation velocity through a
> wire in a computer is typically equal to the speed of light in the
> insulator around the wire. Electricity flow rate, on the other hand, is a
> minuscule fraction of that.

At first glance I don't believe you.
Whatever electricity is it is something which accelerates and so has the
so-called time constant (tau = e^(L/R), or e^(R/L) I don't remember and also
the speed of light must be involved). After the transient effect had passed,
electricity flows at a speed close to the speed of light, no matter if it is
DC or AC.

I got you picture and I'm thinking about it.
One thing is voltage and another thing is current.
Electricity is current.
Voltage is the potential to do work.

DC current could be a low speed flow rate of electrons and AC current could
be electrons oscillation in a chain reaction at AC frequency. Maybe.

Then voltage must be the potential field travelling at the speed of light
and that is the speed at which the information travels in order to the
electrons know how to move.

Maybe, maybe...

> Signal propagation requires charges to move only a very small distance --
> just far enough to produce a charge imbalance. In fact, when modeling
> signal propagation in a wire, the actual motion of the charges is largely
> neglected; instead, it's modeled as a traveling EM wave, with the wire
> acting as a wave guide.
>
> But that's just what happens when you first turn the power on, or what
> happens when you're sending very high frequency alternating current
> through the wires. When you're sending DC, the flow is just exactly what
> you might expect: It's a bunch of electrons going from one place to
> another.

Maybe.
Do you have support for the above ?
This is very important.

> > So if you want to compute electricity speed you will find that
> > relative speeds makes the angle negligible.
>
> Neglecting the angle the electron paths make with the wire is equivalent
> to assuming the disk is stationary, or the wire is not moving.
>
> Sorry, you can't do that; the analysis will produce nonsense results if
> you do. The angle may be small, or it may be large, but it _can't_ be
> zero, and you can't neglect it and understand what's going on.

I agree.

> >> The B field causes a force perpendicular the path the electrons follow.
> >> Hence, <VxB, V> = 0, as usual, and it does no work.
> >
> > In the direction of the B field force there is the tangential motion of
> > the disk.
>
> B field is perpendicular to the disk, by the original assumptions, and by
> the design of a homopolar generator.

Here is my mistake.
In fact I got the wrong picture about the B direction.
That's because I'm always thinking in terms of the conventional generator
and the magnetic shear stress in the air-gap.

Magnetism is much more then a vector (It's a field).
There are two types of magnetic force, so to speak.
When you have a bar magnet N-S you will see that the axial magnetic force
(along B) depends on the distance squared. So the B vector changes
according to distance squared, like gravity does.
But there is also the "reluctance force", which is a transverse force that
you notice when you try to cut the flux lines. This shear force appears when
the flux linkage changes. The shear force is null when two magnets are
aligned and starts to develop when the magnets fall out of alignment
(sliding).

The magnetic force depends on the direction of the motion.
And a magnetic field creates force over any piece of wire or iron that moves
in any direction through the space. This boils down into a force normal to B
and a force transverse to B. The normal force depends on distance squared.
The transverse force is an exponential function of the distance followed by
an inverse exponential function of the distance (null at equilibrium,
increasing when sliding starts no matter the transverse direction in a
plane, then a maximum field strength is reached at some distance, then
decreasing).

Since the magnetic force can take any direction in space, I guess that I'm
always right.
The magnetic field does all the work, against the mechanical system.
I see the problem the other way around, starting from the mechanical
point of view, not the electrical point of view.

My point of view is that radial current flowing through the disk surface
disturbs the magnetic field and the magnetic field doesn't like to be
disturbed.
Since the disturbance is continuous (not changing) the current is DC.

How the current is pumped is a mystery. You have the same problem.
How does the E field builds in first place ?

> > Hence, you have a force (N) and you have a perimeter speed - m/s (or
> > else you have a torque - Nm and you have an angular displacement -
> > rad/s). Thus you have energy and energy is equal to work. That is the
> > mechanical energy that must be balanced by the magnetic field in order
> > to create and pump the electric field.
>
> In the laboratory's frame of reference, there's no electric field :-)

This one I cannot understand.
I'm using the generated voltage to light up a laboratory lamp, so...???

> Except, of course, for that E field _across_ the wire which I mentioned,
> if you're using wires rather than a solid disk. With a solid disk,
> there's not even that. No E field at all.

With a solid disk no E field at all ???
Very strange statement. Can you explain please ?

> This is _not_ your normal garden variety generator.

I've notice that.

> >> Note, however, that
> >> the force of the B field is _NOT_ perpendicular to the wire, because
> >> the motion of the electrons, in the lab frame, is not parallel to the
> >> wire, because the wire is moving relative to the lab!
> >
> > Two things to be notice:
> > 1 - If your believe that it is the electric field the responsible for
> > the force that produces mechanical energy you will find that radial
> > symmetry gives no torque.
>
> If you use a solid disk, then there is no electric field present. See
> below for what gives the actual "push" with a solid disk.
>
>
> > No torque means no force and no work. 2 - If
> > you compute the relative speed between electricity and the lab you will
> > find that the lab is at rest for any further calculations you want to
> > make.
>
> I don't know what you're trying to say here. As I said before, electron
> velocity in a wire, or in a copper disk, is a very small fraction of C.

Again I was pointing out the speed of light problem.
And I believe that you still have problems with the speed of electricity.

> >> The resistance of the wire, which can be viewed in a crude way as
> >> friction...
>
> [Replying to myself here...]
> In fact, for a solid disk, rather than one wire or a disk made of a radial
> sheaf of wires, the resistance _IS_ the driving force on the electrons.

Again I must point out that the result cannot be the cause.
First you get the electrons motion, then the resistance, not the other way
around.

> It's the collisions with the rotating lattice which impart motion to the
> electrons, and it's those collisions with the moving electrons which
> produce the "back torque" on the disk. The positively charged solid
> lattice moves only tangentially -- no radial component -- and so the only
> force on it from the B field is radial (no torque).

This is confusing and must be wrong, since you start from the result to
produce the cause. Can you explain please.

> > No, you must be wrong for several reasons: - The home energy meter looks
> > like a Faraday disk and there is no wire.
>
> See above - the resistance in the disk actually provides the "work" on the
> electrons.

I disagree.
The electrical resistance cannot be the cause for electricity.

> But really, I'm not familiar with home power meters, and without a
> schematic or clear description I can't comment intelligently on them.

It is exactly the same problem of the homopolar generator, but there is no
external wire, nor load resistor (just the disk and the B field). Instead of
a constant B you apply a sinusoidal B and the disk will spin like a motor.

> > - The wire can take any
> > direction and have any length you want. That won't change nothing.
>
> I don't understand this statement. The wire must move perpendicular to
> its length, and perpendicular to the B field, or nothing happens.

I'm talking about the external circuit with the load resistor, between
brushes.

> > - The
> > speed problem
>
> As I've said, you're confusing a couple different velocities here. (I
> wish I could quote the electron's exact velocity in a typical wire off
> the top of my head but unfortunately I've long since forgotten that
> number.)

Another problem with the speed of electricity is that according to your
theory the speed of electricity must be dependent on disk angular speed.
High rotation velocity means high speed electrons and low rotation must give
a low speed electricity.
That cannot be the case.

> > The motor applies torque over the disk axis and only a tangential force
> > can balance it.
> > The tangential force is the magnetic force. Hence the magnetic force
> > does all the work against the disk mechanical energy. It is impossible
> > to balance torque in the disk radial direction without involving the
> > magnetic force.
>
> I never denied that.

Then you cannot say that magnetic field does no work.

> I hope this has been of some help. The questions you are asking are not
> trivial. The answers are typically covered in E&M classes in the EE
> department, but they're probably not covered in the physics curricula of
> most schools below the graduate level.

This is nice talking and much better then nothing.

It is easy to see that most of your explanation is based on PMB paper:
http://www.geocities.com/physics_world/mag.htm

In fact it is a very nice article and it looks like a good explanation.
Nevertheless I must point out the following:
- There is no physical support to assume the direction of the magnetic force
(Fm)
in the way the paper shows it.
It was assumed that the direction of Fm is the complementary angle between
tangential speed and E field. This is very convenient for the explanation.

The B field vector points vertically to the disk and the resultant magnetic
force is
a transverse force whose direction in the disk plane is the complementary
angle.
Can you see the problem? First of all the magnetic force must know all the
involved directions and all vectors intensity to compute the complementary
angle in a given coordinate system which Fm must know in advance.

Complementary angle is very suspicious and for sure not natural.

I can solve the same problem noting that around the wire (perpendicular to
the main E field vector) there is a circular magnetic field that will
interact with the main B field in such a way that it works exactly like
conventional generators does.
Note that ahead the wire you will have repelling magnetic poles slowing down
the disk and behind the wire you will have attracting poles also slowing
down the disk. Hence it is quit obvious that from this point of view it is
the magnetic field that does all the work (the usual way - see stepper
motors and reluctance machines, as well as induction and synchronous).

So far we have discussed the generator problem.
And what about the motor?
Can you work out the same problem in the motor approach ?
I guess not.

If you apply a battery instead of the load the same disk must turn giving
mechanical energy out.
It is very easy to solve according to my explanation and straightforward.
You apply the E field and a circular E field is created around the wire
(radius).
Then circular B field will interact with the main B field.
Ahead the wire you will have repelling magnetic poles and behind the wire
you will have attracting poles, hence the disk goes nice and easy.

Loading