Re: simple magnets question

[John Mallinckrodt <ajmallinckro@CSUPOMONA.EDU>]

On Thu, 24 Jun 1999, William Beaty wrote:

> 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.

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.

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.

>   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!

>   ...  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.

>     ... 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.

John
----------------------------------------------------------
 A. John Mallinckrodt        http://www.csupomona.edu/~ajm
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