Re: simple magnets question

["JACK L. URETSKY (C)1998; HEP DIVISION, ARGONNE NATIONAL LAB ARGONNE, IL 60439" <JLU@HEP.ANL.GOV>]

Hi all-
        Let me simplify Leigh's comment:
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> 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.

If one goes to the electron's instantaneous rest frame (which is not
inertial) the magnetic field does not affect the electron. Imagining
the field to be moving clearly misleads one in that case. In that
frame, however, there exists an electric field. It is that electric
field which is chiefly responsible for the deflection of the electron.
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        I imagine, in the inertial frame where the magnets are at rest,
two circular pole pieces with a uniform B-field between them.  There is
an axis of cylindrical symmetry; the electron moves with speed v at a
fixed radius R from the symmetry axis.  You know how t calculate the
speed v, knowing B, R, m and e.
        In the rest frame of the electron (non-inertial) there is a
centrifugal force mv^2/R.   This force is exactly balanced by an E-field
that resuls from the Lorentz transformation from the inertial frame to the
new frame.
        The electron therefore remains at rest in the new frame.

                                Regards,
                                                Jack

        "I scored the next great triumph for science myself,
to wit, how the milk gets into the cow.  Both of us
had marveled over that mystery a long time.  We had
followed the cows around for years - that is, in the
daytime - but had never caught them drinking fluid of
that color."
                Mark Twain, Extract from Eve's
                Autobiography