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Re: simple magnets question



On Thu, 24 Jun 1999, John Denker wrote:

Hi Folks --

Some points that might clarify things:

1) This question cuts to the core of what electromagnetism is. At any
nonzero velocity, you can't discuss magnetic fields separately from
electric fields.

Hi John. I agree. What I don't understand is, nonzero velocity relative
to what? Relative velocity between the electron and the field? Relative
velocity between the electron and the atoms of the cyclotron pole-pieces?
If an electron is flying through the cyclotron's magnet gap, then we must
insert a *stationary* cyclotron and a *stationary* b-field into the
problem without noticing that we've done so. From my viewpoint this is a
serious error.

2) As various people have pointed out, it's not clear what it means to
speak of a field that moves. If you rotate the *source* of a magnetic
field, such as a piece of magnetized iron, all sorts of weird effects
occur, such as centrifugal effects on the electrons in the iron,
centrifugal effects on the iron ions, plus the intrinsically
electromagnetic effects discussed below.

Yes, and I'm wondering if these other weird effects just happen to
perfectly cancel out the radial e-field that's caused by the rotation of
the magnet. Maybe the rotating magnet cannot affect a nearby electron,
but not because the rotating b-field has no effect. Maybe there are two
separate phenomena here (i.e. the centrifugal e-field and the induced
radial e-field,) phenomena which create two opposing forces upon a
test-charge which always sum to zero.

Yet they certainly don't sum to zero in a homopolar generator.

3) If I understand the spirit of the question correctly, the centrifugal
effects in the previous paragraph are unnecessary complications. If we
disregard centrifugal effects, then at any single point, circular motion is
indistinguishable from straight-line motion along the tangent at that
point. So let's discuss the straight-line case.

Accordingly, we can rephrase the question: imagine that in the lab from an
electron is moving through a magnetic field.

Right there is my confusion. Is the electron moving through a field
that's created by *stationary* magnets, or by magnets which are moving
uniformly at the same velocity as the electron? It makes a big
difference.

At any given point, it feels a force transverse to its motion.

Yes, but only if the magnets are *not* stationary with respect to the
electron. If the magnets and the electron move together, the electron
will still continue in a straight line, even though the electron is
immersed in a b-field, and even though the electron is moving with respect
to the lab frame. Yes, from our lab frame we will measure an e-field
caused by the moving magnets, but obviously the electron does not respond
to this e-field. The electron doesn't care about the e-field that we see,
apparantly it only cares about relative motions between itself and the
cyclotron magnets (or maybe between itself and the 'lines of flux' of the
b-field.)

So the question is, what happens in some
other reference frame, such as one comoving with the electron?

Answer: The electron sees an electric field. You can easily calculate the
details of this field by Lorentz transforming the electromagnetic field
tensor from the one frame to the other.

OK? --- jsd

Then why, if the magnets and the electron are moving uniformly together,
does the electron not see the same induced e-field that we see? I mean,
suppose we are on a uniformly-moving train which passes by a cyclotron.
Suppose that in the cyclotron's frame there is an unmoving electron
sitting between the pole-pieces. From the frame of the train, we will see
a moving cyclotron, a moving b-field with a transverse e-field, and an
electron that *doesn't* respond to the transverse e-field. What the heck
is going on? Somehow the electron "knows" that it is stationary with
respect to the cyclotron, and therefor it isn't deflected when the
cyclotron, the b-field, and the electron all move uniformly past our
train.

Hence I conclude that the linear motion of the magnets is important. And
I wonder if, since linear motion of the magnets (or of the field) can
affect an electron, what will rotary motion do? If shooting an entire
cyclotron at an unmoving electron will cause the electron to accelerate
perpendicular to the moving cyclotron, what will a rotating cyclotron do
to an unmoving electron?


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