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Jack,
Feynman is not conning you here. He is teaching the well known, non
Newtonian, behavior of the Lorentz interaction of charged particles.
Newton knew nothing about magnetic forces. All the forces he observed
followed N3. Today we recognize N3 as a corollary to the conservation
of linear momentum, as applied to an otherwise isolated two particle
interaction. Two interacting electrons are not isolated in the
general case - their fields can influence distant matter. Ascribing
momentum/energy to the fields allows us to treat many such situations
as tractable, localized situations. In the last paragraph of 26-2
Feynman introduces the "problem":
***
"We would like to point out, in passing, something interesting for you
to think about. (We will come back to discuss it again later.) Imagine
two electrons with velocities at right angles, so that one will cross
over the path of the other, but in front of it, so they don't collide.
At some instant, their relative positions will be as in Fig. 26-6(a).
We look at the force on q1 due to q2 and vice versa. On q2 there is
only the electric force from q1, since q1 makes no magnetic field
along its line of motion. On q1, however, there is again the electric
force but, in addition, a magnetic force, since it is moving in a
B-field made by q2. The forces are as drawn in Fig. 26-6(b). The
electric forces on q1 and q2 are equal and opposite. However, there is
a sidewise (magnetic) force on q1 and no sidewise force on q2. Does
action not equal reaction? We leave it for you to worry about."
***
In the next chapter (27) Feynman goes on for 11 pages to develop the
Poynting vector and the required field momenta (linear and angular)
and energy required to locally conserve energy/momenta. He finally
fulfills his promise ("We will come back to discuss it again later.")
and re-visits the two electron situation. In the penultimate
paragraph of section 27-5 :
***
"We will mention two further examples of momentum in tne
electromagnetic field. We pointed out in Section 26-2 the failure of
the law of action and reaction when two charged particles were moving
on orthogonal trajectories. The forces on the two particles don't
balance out, so the action and reaction are not equal; therefore the
net momentum of the matter must be changing. It is not conserved. But
the momentum in the field is also changing in such a situation. If you
work out the amount of momentum given by the Poynting vector, it is
not constant. However, the change of the particle momenta is just made
up by the field momentum, so the total momentum of particles plus
field is conserved."
***
Finally, the last paragraph of Feynman's section 27-5 resolves a
related, earlier introduced, problem by ascribing ANGULAR momentum to
the field. Cf section 17-4 for the referenced ANGULAR momentum
problem.
Bob Sciamanda
Physics, Edinboro Univ of PA (Emeritus)
www.winbeam.com/~trebor
trebor@winbeam.com
----- Original Message -----
From: "Jack Uretsky" <jlu@hep.anl.gov>
To: "Forum for Physics Educators" <phys-l@carnot.physics.buffalo.edu>
Sent: Sunday, August 05, 2007 5:05 PM
Subject: Re: [Phys-l] interaction
| Hi Bob-
| I'd forgotten the discussion. Did we come out in agreement?
| Sorry, the animated illustration didn't help me. And, although
| the Feynman reference is in point, I don't think that it supports
your
| statement. Feynman, the great con artist, is presenting us with a
puzzle;
| how can it be that the forces between two electrons on the
prescribed
| paths are not equal and opposite? Didn't Newton claim that they
would
| have to be?
| Regards,
| Jack
|
|
| On Sun, 5 Aug 2007, Bob Sciamanda wrote:
|
| > Jack,
| > You and I had an off-list discussion of this the last time this
| > subject came up. Now I find a neat animated illustration of the
very
| > example which I then suggested to you as a clear violation of N3
when
| > only the mechanical momenta (mv) of the particles are considered.
| > Please go to:
| >
| > http://jlnlabs.imars.com/lifters/lorentz/index.htm
| >
| > Also consult the Feynman Vol II references.
| >
| > Bob Sciamanda
| > Physics, Edinboro Univ of PA (Emeritus)
| > www.winbeam.com/~trebor
| > trebor@winbeam.com
| >
| > ----- Original Message -----
| > From: "Jack Uretsky" <jlu@hep.anl.gov>
| > To: "Forum for Physics Educators"
<phys-l@carnot.physics.buffalo.edu>
| > Sent: Saturday, August 04, 2007 5:50 PM
| > Subject: Re: [Phys-l] interaction
| >
| >
| > | Hi Bob-
| > | I don't understand "the linear momentum is not conserved"
(unless
| > | you're including brehmstrahlung). Have I forgotten something?
| > | Regards,
| > | Jack
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