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Re: [Phys-l] Force on a charged particle from a magnetic field



Perhaps Eisberg * is not an intro - text, as he (and Lerner) devote 12 pp. [pp. 1129 ff.] to the "Relativistic Origin of the Magnetic Force". During their development they derive the Lorentz contraction and point out that "... the present argument is much closer to that originally followed by Einstein." [p. 1134], as opposed to the usual text book mechanical derivation. Their last paragraph [p. 1138] is: "It is fair to ask, How can relativistic effects be significant at such tiny speeds as that of an electron drifting through a copper wire? The answer is suggested by Example 24-3." [Actually very well answered.]

Comparison of Eqs. ... in the light of this discussion leads to the conclusion that IT IS THE LORENTZ FORCE -- AND NOT THE ELECTRIC OR THE MAGNETIC FORCE INDIVIDUALLY -- WHICH IS FUNDAMENTAL." [P. 1134]


bc




* Physics, Foundations and Applications (1981)

Bob LaMontagne wrote:

Your answer, and those of others, is a direct response to my question. The
last post by John D. provides a neat way to go from this simple problem
through a series of plausible steps into a full relativistic treatment.

I was never in doubt that this was purely a relativistic effect, I was
convinced of this many years ago as a student when I had to demonstrate how
the Lorentz transforms made Maxwell's equations valid in all inertial frames
of reference. This same example that I brought up in this thread is what
prompted my instructor to assign me the task of preparing this demonstration
for the rest of the class. It made me a true believer.

I agree with you that it is best not to bring up this example in an
introductory class unless you are using it as a stepping stone to
relativity. Otherwise, it would make the students doubt Maxwell's equations
- which is not the intent because the equations are still valid in
relativity. My concern is that so many introductory texts bring up this
example in the end-of-the-chapter problem sets. They then leave the students
hanging, with the implication that Maxwell's equations are incorrect. There
is no clear statement that the full resolution to this asymmetry requires us
to change our approach to space and time itself - not Maxwell's equations.

Again, thanks to all for the responses - they were very useful.

Bob at PC



-----Original Message-----
From: phys-l-bounces@carnot.physics.buffalo.edu [mailto:phys-l-
bounces@carnot.physics.buffalo.edu] On Behalf Of Jack Uretsky
Sent: Wednesday, November 29, 2006 12:27 AM
To: Forum for Physics Educators
Subject: Re: [Phys-l] Force on a charged particle from a magnetic field

Hi Bob-
I don't think you've been directly answered, so here's my take.
You point out that a certain field is purely magnetic in a certain frame.
Call it frame M. In a frame moveing with respect to frame M, you point
out, the field is a mixture of magnetic and electric. You ask, how do I
explain this fact to an introductory class?
My answer is that you are describing a relativistic effect, as you
have noted. I would not want to get into relativistic effects in an
introductory class. So, unless there is a pressing need to do so that you
have not told us about, I would not bring up this particular effect.
Note, by the way, that there is no frame where the field is purely
electric. It is characterized by the fact that there is a particular
frame where it is purely magnetic. This is analogous to a timelike
vector; there is one frame where it has no spacelike component and no
frame where it has no timelike comonent.
Regards,
Jack

On Tue, 28 Nov 2006, Bob LaMontagne wrote:



-----Original Message-----
From: phys-l-bounces@carnot.physics.buffalo.edu [mailto:phys-l-
bounces@carnot.physics.buffalo.edu] On Behalf Of John Mallinckrodt
Sent: Tuesday, November 28, 2006 2:01 PM
To: Forum for Physics Educators
Subject: Re: [Phys-l] Force on a charged particle from a magnetic field


But there is time varying flux in the frame of the proton. The only
way to avoid that involves using an infinitely large magnet.


That's why I carefully defined the magnetic field to be uniform, so

there is

no change in flux with time (classically). Specifically, how do you get

the

time varying flux that ultimately produces an electric field to move the
proton? (Again, without an appeal to relativity.)


Maxwell's equations have relativity built into them so they are, in
principle, fully capable of answering the question.


I thought that the Lorentz transformations came about through Einstein's
attempt to make Maxwell's equations apply to any inertial frame of
reference.

Anyway, I agree with most of the responder's claims that relativity is
required - and, as Skip said, that was what Einstein was trying to do a
hundred years ago. I am just uneasy with the way various textbook

author's

present this example (or a variation of it) before relativity is

introduced,

and then expect students to be comfortable with the answer. And yes, it

does

seem to provide a great segway into relativity.

Thanks to all who took the time to respond.

Bob at PC

_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
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--
"Trust me. I have a lot of experience at this."
General Custer's unremembered message to his men,
just before leading them into the Little Big Horn Valley



_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l


_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l