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Re: simple magnets question



On Wed, 23 Jun 1999, Leigh Palmer wrote:

Yes, so the question becomes: "does an axially-spinning disk magnet create
a motional e-field which can attract/repel a stationary charged particle?"

I guess the answer is, simply, no, it does not. If the field and its
source are axially symmetric then spinning the source about its axis
will affect nothing outside. As John Mallinckrodt emphasizes, one
should never think of a field (electric or magnetic) as "moving".

I'm still confused about this. I think I'm having trouble communicating
why this is so. I'm talking about situations where the intensity of
fields does not change, yet electrons are still affected. I'm ignoring
any situations where the intensity of the b-field is changing. A simple,
non-rotating example: if an electron is flying across the *uniform* field
between the cyclotron pole-pieces, then that electron does not encounter
changing field intensity. Yet it is deflected sideways.

In the cyclotron, if the relative motion between an electron and the
b-field is a meaningless concept, and if a "stationary" b-field is the
same as a "moving" b-field, then I have a problem: why is an electron
deflected sideways if the electron moves *differently* than the cyclotron,
but an electron is *not* deflected sideways if the electron and the
cyclotron move together? Let me put it this way:

Suppose an entire cyclotron is moving uniformly with respect to my
frame. I should see a b-field between the pole-pieces, but because of
the relative motion, I should also see a transverse e-field. If I put
an electron between the cyclotron's pole-pieces, and if the electron is
moving but is NOT moving with respect to the cyclotron, then from my
viewpoint the electron is strangely unaffected by the transverse
e-field, and the electron moves in a straight line. (This makes some
sense, because in the cyclotron's frame, the electron is sitting
stationary between the pole pieces.) Now for the important part. If
instead I place an unmoving electron between the pole-pieces of the
moving cyclotron, then I see the electron get accelerated sideways. I
have now observed that the electron responds differently depending on
the relative motion between it and the cyclotron, EVEN THOUGH THE
B-FIELD BETWEEN THE POLE-PIECES IS UNIFORM AND THE ELECTRON DOESN'T
ENCOUNTER CHANGING FIELD STRENGTHS. I conclude that, for uniform
b-fields, the motion of the field is *not* a meaningless concept.
Either that, or the uniform motion of the POLE-PIECES is important to
the electron, and the electron will only be deflected if it moves across
the pole-pieces or if the pole-pieces move past the electron.

I find that it is frequently illuminating in such questions to
consider the interactions directly in terms of the sources. Given
the fact that there exist no monopoles, the only sources possible
are the elementary electric charges which make it up. If the
disc magnet is spun, the only source that can change is the current
source. If the magnet is electrically neutral and nearly homogeneous
then the resulting currents will also vanish, and with them any
magnetic fields which might have otherwise resulted.

Yet if this reasoning is applied to the uniform field inside a cyclotron,
we would incorrectly predict that a moving electron would experience the
same forces as a stationary electron. After all, the electron doesn't
encounter any non-uniform spots in the field.

The central issue: if the pole-pieces of a uniformly moving cyclotron
appear to generate a transverse e-field, then I conclude that the relative
motion of the field (or of the pole-pieces) is important, and I predict
that a cyclotron which rotates on axis will appear to generate a radial
e-field. Is my reasoning clear?

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