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

On Thu, 1 Jul 1999, Bob Sciamanda wrote:

From the hip: If a circular loop of current rotates about its own axis,
there is no definable up-down direction in which it can develop a charge
separation and an electrical dipole moment, as there is when it is
translated in a linear direction (as I indicated above).

I'm reasoning like so: if an uncharged straight wire contains a current,
and if that wire is moving with respect to an observer in a direction
parallel to the current, then the observer will detect an e-field, and the
wire will appear to be charged. If that wire is made into a rotating
circle, and if the observer is very close to the wire, then locally the
wire will be approximately straight. I conclude that the observer will
still see the small, local part of the wire as being charged. (Can
distant parts of the rotating circle reach out and cancel the charge on
the portion of wire near the tiny observer?)


It would seem that
there is thus reason to speculate that the rotating magnet does NOT develop
an electrical polarization (and its E' field) as does a translating magnet.
This may be another instance of the pitfalls inherent in assuming that one
can apply SR to a rotating frame by considering an infinity of inertial
frames, each co-moving with a particular point fixed in the rotating frame.

I'm doing a similar thing: assuming that the (very thin) disk magnet is
composed of many small rectangular segments, each of which is moving
tangentially, and each of which has an e-field because of this uniform
motion. Together, the e-fields superpose to produce a field which is
directed inwards across the face of the disk. But each tiny magnet is
accelerating inwards at the same time that it is moving tangentially, and
I suppose that the magnets should radiate as a consequence of this
acceleration. This is "DC" radiation?! Maybe it cancels out the e-field.


I do not object to looking at phenomena from various frames, this is often
very helpful; but you somehow seem to ALWAYS prefer the rest frame of q as
preferred for purposes of understanding. F=q(E+VxB) is valid in any frame.

I am taking an obvious route based on my central question: "what happens
to a test charge near a rotating magnet?" and for this reason I keep
coming back to a "stationary" test charge which is next to a disk-shaped
cloud of tangentially "moving" magnet-elements. I keep asking how the
"moving" magnets would affect the charge. Hmmm. You're right, I could
ignore the e-fields of the moving magnets and instead go to the inertial
frame of each tangentially-moving piece of the disk-magnet, calculate the
qVxB force each one produces upon the test-charge, and then sum up all of
these forces. Wouldn't the net force be the same as when the test-charge
is stationary and all of the magnet-segments are moving?


The frame in which V=0 is not to be preferred.

But if moving magnets are surrounded by "motional" e-fields, then neither
should we perfer a frame where the magnets are stationary and the
test-charge is moving.


If I (now) understand things correctly, the qVxB force depends on the
frame of the observer: the force q(E + VxB) is "real" and unchanging, but
if the observer jumps to a different inertial reference frame, then E and
VxB will vary (although their sum will not.)

You fell off the wagon again, Bill! In F=Q(E+VxB) , only Q is numerically
the same in all inertial frames; V, E, B AND F transform into different
values V', E', B', AND F'.

Even when I'm spinning a physical magnet on my physical lab bench? The
force-pair between the test-charge and the magnet is the same whether we
say that the magnet is moving and the test-charge is stationary, or vice
versa. Oh, I get it. Observers who are travelling at 50% of c with
respect to my lab bench would *not* see the E, V, and B as producing the
same F force that I measure. F is only constant when all relative motions
are << c. I think.


True. When discussing an electron which moves between the cyclotron's
poles, we must focus on the forces felt by an electron *at a particular
instant.* Either that, or assume that we could restrain the electron so
it moves uniformly, and then we could measure the perpendicular force.

F=q(VxB) is valid in the (inertial) LAB frame, EVEN THOUGH THE ELECTRON IS
ACCELERATING IN THAT FRAME. There is no need to stop it, or jump onto its
frame.

If F=q(VxB) is still valid when the electron takes a circular path within
the cyclotron, then perhaps F = q(E) is valid when a stationary
electron is adjacent to a rotating cyclotron (where E is the net field
created by the tangential motion of each tiny piece of the rotating
magnet.) Obviously I still want to know if a rotating disk-magnet can
apply a constant force to a stationary test-charge. :)


I think this person is wrong. To generate a current, relative rotation
between the "conductor disk" and the "external circuit" is necessary. If
we keep the "external circuit" stationary and ignore that we have done so,
then it will *appear* we can detect the absolute rotation of the
conductive disk. If we hold the conductive disk stationary and rotate the
brushes, the meter, and the external circuit, we still obtain a current.
This shows that the Homopolar Generator does not rely on absolute
rotation. The rotation is always a relative motion between a "rotor" and
a "stator" section. The meter and its leads are the "stator". Hold the
"rotor" still and spin the "stator" around it, and the generator still
functions.


The rotating conducting magnet, all by its lonesome,

Whoa. I don't like to make the magnet a conductor. Conductive-magnet
HPGs have greatly confused people in the past, so I adopted the habit of
imagining the magnet as separate from the disk. This keeps separate
concepts separated. If we want to rotate the magnet and the metal disk
together, that's OK. But if we want to keep all the metal parts
stationary and rotate just the magnet, then the conductor-disk had better
be separate from an insulating magnet. And if we want to keep the magnet
from aquiring its own charge distribution, then the magnet needs to take
the form of a separate insulating disk.

will develop a charge
separation, from the Q(VxB) motional magnetic force on its moving carriers
if brushes are added, a current will be available). Again, the rotating
frame is more complicated than an infinity of inertial frames.


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