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Re: simple magnets question

On Thu, 24 Jun 1999, John Mallinckrodt wrote:

I think you are perhaps confusing the *generation* of E-fields by time
changing B-fields a la Faraday's law with the E-fields that appear as a
natural result of the Lorentz transformation when you change reference
frames.

Nope, I'm only looking at situations where there are no time-changing
B-fields at all: as when a disk magnet spins on axis, or when an electron
is flying through the uniform field between the pole-pieces in a
cyclotron.

I see that one point of confusion is that:

1. *I'M* saying that each small portion of a spinning disk-magnet
resembles a magnet in uniform motion, and therefor a spinning
disk-magnet should behave differently than a non-spinning disk
magnet.

2. OTHERS are saying that, because the strength of the spinning magnet's
field does not change, then there can be no force on the electron,
and therefor the spinning motion of a disk magnet does nothing.

3. Then *I* say that No. 2 is wrong, because stationary electrons can be
affected by b-fields which do not change, for example, by the
uniform field within a moving cyclotron.

So there are two questions here: does a spinning magnet do weird things,
and if not, then why does a uniformly moving cyclotron cause a stationary
electron to move? I say that a spinning disk-magnet *must* create an
e-field as a consequence of its spinning motino. I insist that, since a
uniformly moving cyclotron DOES cause a stationary electron to move, then
a rotating disk-magnet should also cause a stationary electron to move.
(...as long as that electron is not on the axis of the disk.)


For instance, in another message you wrote:

Since an electron which moves relative to a large, flat magnet pole
will see a perpendicular e-field, will the electron still see that
perpendicular e-field if we reverse the situation so the electron stays
still and the magnet moves?

Yes, because these are one and the same thing. The E-field that the
electron sees *is* the E-field that exists in the frame in which the
electron is at rest. This E-field is not the result of time changing
B-fields.

OK, then you're saying the same thing as I am, I think: when a magnet
moves, it can push an electron, even if the electron is in a region where
the strength of the b-field is not changing.


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.

Right, because in the frame of the electron (which is the only one that
really matters) there is no electric field. As I said earlier and as John
Denker's post nicely explains, electrons "see" only electric fields. But
there is nothing "strange" about this from your viewpoint; in *your* frame
there *is* an electric field and the electric force precisely cancels the
magnetic force due to the motion of the electron. This is what the
Lorentz transformation was built to do!

OK, now we're getting somewhere. The "strangeness" I mentioned was
regarding an earlier assertion that, when an electron is near the surface
of a rotating disk-magnet, it sees no e-field. I wonder how this could
be, because when an electron is near the surface of a moving cyclotron
magnet, it definitely does see an e-field. Why would the moving rim of a
rotating disk-magnet be different than the pole-pieces of a
uniformly-moving cyclotron magnet? If the radius of the disk-magnet is
very large, then portions of the disk should be almost identical to that
uniformly-moving cyclotron magnet. In both cases an e-field should
appear.


... 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.

Yes, because now there is an electric field in the frame of the electron
which now happens to be the same as yours.

And therefor if I place an unmoving electron near the flat surface of a
disk-magnet which rotates on axis, and if this electron is off-axis from
the disk, then the electron should see an e-field which is caused by the
rotation of the disk. This e-field should be directed radially across the
surface of the rotating disk, either pointing inwards or outwards
depending on the sense of rotation.

And presumably if I place an entire cloud of electrons near a rotating
disk-magnet, those electrons would experience the e-field, and either be
attracted towards the axis of the disk, or towards the rim of the disk.

... 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.

It responds differently because the electric field that it sees depends on
its motion, again, because of the Lorentz transformation and not because
of Faraday's law.

Right. I'm trying to get to the bottom of the radial e-fields which are
apparantly created by the "Faraday's Disk" or homopolar generator. If a
disk-magnet starts rotating on axis, so that the b-field is nowhere
changing, then when observed from the frame of a nearby non-moving
electron, portions of the rotating disk-magnet should become
Lorentz-contracted, and this should generate an e-field.


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