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

On Tue, 29 Jun 1999, Bob Sciamanda wrote:


I was screwed up about VxB earlier. Are we now on the same page?

Welcome aboard, William!
-Bob


Now my terminology is closer to correct, but my original questions haven't
changed. :)



NNNNNNNNNNNNNNNNNNNNNNNNNNNNN
___________________________
| magnet | Flat magnet having N and S poles on
|___________________________| its large, flat faces.
fig. 1
SSSSSSSSSSSSSSSSSSSSSSSSSSSSS


The other shoe falls: what is the cause of the e-field which we detect in
the region above a wide flat magnet in uniform motion? From past
messages, I gather that the answer is this: adopt a frame in which the
magnet appears stationary, measure the EM field above it, then go back to
the first frame again (from which the magnet appears to be moving) and
predict that an e-field should appear because of "Lorentz Transformation"
performed on the EM field as we leap between frames.


NNNNNNNNNNNNNNNNNNNNNNNNNNNNN
___________________________
| magnet | --------->
|___________________________|
Flat magnet in uniform motion. Above
SSSSSSSSSSSSSSSSSSSSSSSSSSSSS the magnet, we would measure an e-field
directed out of the page.
fig. 2

Does leaping between inertial frames cause us to begin seeing an e-field?
To me it seems equivalent to say that the cause of the e-field is the
velocity of the sources relative to the frame in which the measurement is
made. If each microscopic dipole in the above magnet is moving with
respect to my frame, then I would discover that each dipole has a tiny
e-field associated with it. These small regions of e-field superpose, and
the little e-fields add up to an extended region of fairly uniform e-field
which exists in the space above the face of the moving magnet.


N N N N N N
_ _ _ _ _ _ ---------->
| | | | | | | | | | | |
|_| |_| |_| |_| |_| |_| Many small dipoles moving together, each
contributes to the measured e-field
S S S S S S fig. 3


In other words, a cyclotron can deflect an electron because, in the
inertial frame where the electron is (momentarily) stationary, all the
little dipoles in the cyclotron magnet are moving, and together they are
creating an e-field which the electron can experience. Is this an
incorrect model?

My conclusion: if we move a large, flat magnet in a direction along the
plane of its pole faces, then in the region above the pole face we will
detect an e-field. The direction of the e-field will be perpendicular to
the magnet's direction of motion (this assumes that the b-field above the
magnet is everywhere perpendicular to the pole face.) If we dangled a
stationary, very strong test-charge above this moving magnet, the
test-charge would be visibly deflectd by this e-field. Also, an observer
who moves along with the magnet will not measure any e-field, but would
explain the force on the test-charge as arising from the Lorentz force
qVxB. All OK so far?

Finally, what happens when we dangle a test charge above the flat face of
a *rotating* disk-magnet, where the plane of the disk is horizontal, the
b-field points upwards, and the test-charge is not aligned with the axis
of the disk? Won't this test-charge experience an e-field and therefor a
force? After all, that test-charge is close to billions of tiny moving
dipoles within the magnet, and in the frame of that stationary
test-charge, each of those dipoles creates an e-field. If this is wrong,
where does my error lie?


((((((((((((((((((((( ( ( ( ( (O) ) ) ) ) )))))))))))))))))))))
William J. Beaty SCIENCE HOBBYIST website
billb@eskimo.com http://www.amasci.com
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