Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: simple magnets question



Bill says:

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.
If one looks instead at the inertial frame in which the electron is
instantaneously stationary then the motion can be entirely understood
as a consequence of that electric field. At that instant of time the
magnetic field does not exert a force, and it is constant and uniform.
The electron itself is accelerated, but like a ball thrown upward it
is stationary at the instant in question, but is still accelerated.
It is possible (and feasible) to analyze the system completely by
considering the effects of sources (charges and currents) which act
on the electron, and all the fields produced will be static. I think
that, contrary to what Michael Edmiston suggests, the system is quite
understandable in this way. I would generate my uniform magnetic
field with a hypothetical infinite current sheet rather than a
hypothetical cyclotron, however. The sources are much easier to keep
track of with a current sheet. If this example will help you (an
electron moving in the uniform magnetic field generated by an
infinite planar current source instead of a cyclotron with its iron
and non-solenoidal windings) I'll be glad to explain the motion in
terms of sources. I'm sure that someone cleverer than I could do so
for the problem as stated, but it's just too shmutzig for my feeble
mind, and I really think the question underlying your question is:

How does one explain the motion of a charged particle in a uniform,
constant magnetic field in the frame of an observer moving with the
electron?

Since I agree that waving the relativistic field transformation flag
does not constitute a reasonable explanation unless one is already
comfortable with such transformations, let me do it all using only
time dilations and length contractions. Somehow many students seem to
be more comfortable with those.

Leigh