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Re: "Faraday's Disk" which started it all

On Sun, 27 Jun 1999, Bob Sciamanda wrote:

(The E field of the surface charges will of course also exist inside
the armature, but this is a "secondary" effect, and in fact will
oppose the current - all exactly as in a "standard" armature
generator) There is no "mystery" here (or there) [:)<

Aha, then I've found a big fuzzy spot in my understanding. . .

Aha, this is why I emphasized: "I speak in YOUR lab frame."

But which is "my" lab frame? There are many, and I'm trying to understand
this system from all these various frames in various experiments. When I
adopt one of the following frames, it becomes my lab frame.

MAGNET AND TEST CHARGE IN UNIFORM RELATIVE MOTION

1. the frame of a magnet, while a test charge moves past it

2. the frame of a test charge, while we move a magnet past it


SPINNING DISK-MAGNET ADJACENT TO A STATIONARY TEST CHARGE

3. the frame of a test charge which is adjacent to a disk-magnet which
is spinning (with the axis of the magnet stationary with respect to
the test charge.)

4. the (non inertial) frame of the surface of a rotating disk-magnet
which is spinning adjacent to a test charge (with the test charge
stationary with respect to the axis of the magnet)


SPINNING DISK-MAGNET WITH A TEST CHARGE MOVING TANGENTIALLY

5. The frame of a test charge as we move a spinning magnet past it,
such that an adjacent spot on the magnet is momentarily stationary
with respect to the test charge.

6. The (non-inertial) frame of a rotating disk-magnet as a test charge
is moved with respect to the axis of the magnet such that the
test-charge is momentarily stationary with respect to a spot the
pole-face of the magnet.


I want all of the above frames of reference to make sense according to the
relativity of electrodynamics. If a moving magnet creates a large e-field
in one experiment, then a portion of a rotating magnet should do the same
in a different experiment. If it doesn't, then I want to know why.


. . . It was my
understanding that VxB is itself an e-field: it is the same as the
relativistic e-field that an electron sees as it flys between the
poles of a cyclotron magnet. Wrong?

This (YOUR) language is not speaking from YOUR lab frame, but from a
frame attached to an anthropomorphized electron!

No, the electron is at rest in my lab frame. If I "follow an electron" as
it approaches a distant magnet, then in the lab frame, the electron (the
test charge) is stationary, and the magnet is being moved uniformly
towards it. In this lab frame, I should measure an e-field when the
magnet passes by, and my test charge should experience a force. However,
we had been discussing a rotating disk-magnet, not a uniformly moving
nonrotating magnet. Why am I talking about uniform motion all of a
sudden? Because No. 2 in my above list seems to be very similar to No. 3.
If the test-charge in No. 2 experiences a large e-field, while in No. 3
the e-field is somehow constrained inside the volume of the magnet, then I
need a clear explanation of where this major difference originates. How
does rotation cause the e-field to be limited to the inside of the magnet?

The lab observer measures no such E field.

He/she certainly does if the magnet is moving *uniformly* with respect to
the lab frame. "Following the electron" is the same as observing a
stationary test charge and then putting the magnet into uniform motion
with respect to the lab. We would measure a strong e-field. Why, if we
"follow the electron" as it sits next to the edge a spinning magnet, would
we *not* detect a significant e-field? We *do* detect an e-field when our
electron sits next to the edge of a uniformly-moving magnet!

Obfuscation and confusion result from a
description which leaps from frame to frame! Physics is designed to
describe reality from one frame at a time. Lose this maddening habit!

Yes, I'm trying to account for all six of the frames in my list, in order
to detect any incorrect reasoning. Mistakes are easily exposed if we look
at things from one frame, and then verify that this makes sense when we
switch to another. But I've been doing this as a mental double-check
all along, without describing my thought processes in detail. If
something seems screwy when viewed from some other frame, then I leap to
that frame and start describing the contradictions that I see.


If we build a spinning disk-magnet device and sit it on the lab bench,
and the magnet is ceramic (nonconductor), then, in the lab frame,
won't a stationary test-charge "see" an e-field caused by the spinning
magnet? [In a plane at the surface of the spinning disk,] won't this
e-field be radial?

A magnetic volume polarization M will transform into a different M' and
an electrical volume polarization P', in a different frame. If in one
frame the disk has only an M, in the rotating frame it will have an M'
and a P', producing a radial internal E' field.

Why *internal*? I think this is wrong. Look at my #2 above. If I move a
magnet uniformly past a test charge, the test-charge should see a
significant e-field, and this e-field is *not* internal to the magnet.
The external b-field of a stationary magnet leads to an external e-field
when that magnet is moving with respect to the lab frame.

Since (in relation to me) any uniformly-moving magnet creates an
*external* e-field, then I would assume that each small piece of a
rotating disk-magnet would do something similar. Why would the e-field be
external for a uniformly-moving magnet, but internal for a rotating disk
magnet? This needs further explanation. (Again, I'm assuming that the
magnet is a ceramic insulator, so that there are no free charges which
could redistribute and mess things up.)

It will look like a
charged cylindrical capacitor/magnet. The EXTERNAL E' will be weak, due
only to fringing.

Yet a uniformly-moving magnet, although it also looks like a charged
capacitor/magnet, creates a significant external e-field. Why is this
not the case for a rotating magnet? I'm convinced that a rotating magnet
*does* create a significant external e-field.

Forget the second disk; put brushes on the spinning magnet itself, and
you will have a generator (now using a conducting magnet).

True. However, those free charges in the rotating conductive magnet,
since they rotate with the magnet, will have no reason to see a VxB field.
They are in a frame which is very similar to my number 6 in the list
above. Yet the generator does create a potential difference and a current.
Why? Because in the frame of the non-rotating brushes and the wires of
the external circuit, there is a magnet moving past! The wires and
brushes contain mobile charges. It is *they* which see the e-field which
surrounds a rotating conductive magnet, while the electrons in the magnet
itself would not. (The electrons in the external circuit are in frame 3
in my list above.)


In the lab
frame, the EMF is provided by the motional, magnetic QVxB force, inside
the magnet. In the rotating frame the EMF is caused by the radial QE
electric force, inside the magnet.

This is demonstrably wrong through experiment. If we place a copper disk
on the face of a disk-magnet, but with an insulating spacer so the copper
disk is outside of any "weak fringe e-fields", we can still create a
generator. Spin the magnet and the copper disk together as one unit.
Touch a voltmeter lead to the edge of the spinning copper disk (sliding
contact) and to the center of the disk, and we measure a voltage. This
shows that conductors will respond to e-fields at a considerable distance
from a spinning magnet.


If we place a metal plate close to the spinning magnet and parallel to
its face, won't this radial e-field cause the charges of the metal
plate to redistribute themselves until they produce a cancelling
e-field and thus cease their motion?

Yes, a small effect of the weak fringe E field.

The experiment where the metal disk spins *with* the magnet apparantly
shows that this e-field is not weak.



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