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Re: Park City Paradox ?



Thanks to those who responded so far.
I will think about the comments at home
and will probably ask for help. Clearly
my understanding of the relativistic
nature of the magnetic effect is very
limited. It is a topic worth discussing.
Ludwik Kowalski

----- Original Message -----
From: John Mallinckrodt <ajmallinckro@CSUPOMONA.EDU>
Date: Sunday, January 6, 2002 6:26 pm
Subject: Re: Park City Paradox ?

On Sun, 6 Jan 2002, Ludwik Kowalski wrote:

What was a paradox yesterday (see below) is no longer a
paradox to me. Item #1 was OK. But the "analogy" in item #3
was not OK. This is because a wire with electrons is
electrically neutral while a glass pipe containing a charged
skier is not neutral. To make the analogy valid let me
represent each skier by a long uniformly charged rod. The
linear charge density is negative. Each pipe is positively
charged (also uniformly with the same linear density). The net
electric force on each skier is now zero.

Suppose the skiers move side by side with the same v. In that
case, as indicated in item #1, the magnetic force is zero.

The magnetic force between the skiers may be zero, but not the
force between the two "wires". Even in the frame of the skiers
the "wires" carry current due to the motions of the positive
pipes.

Wires would not interact magnetically is [if?] all electrons
had identical v in the same direction.

This is not correct for the reason stated above.

Magnetic interactions exist because there is a wide
distribution of v in each wire, even when mean v are
identical.

No. The magnetic interactions exist because there are currents.
No distribution of speeds is necessary (although it surely
exists.)

...

Another misconception surfaced as I was trying to resolve the
paradox. One can often read that "magnetic interactions are
only relativistic manifestations of electric interactions."
This is true, but the word "relativistic" does not refer to
special relativity. It refers to "relative motion" of two
charged particles, nothing else. Classical physics alone (v in
the Lorentz formula) explains magnetic interactions between
wires; under ordinary conditions.

Again I think you are mistaken. The reference *is* to
Relativity not simply "relative motion."

Consider an electron near and moving parallel to a long and
strictly neutral current carrying wire. For concreteness, assume
that it is 1 m away and moves in the direction of the conventional
current which is 1 A at a speed of 1 m/s. The electron *will* be
deflected *away* from the wire with an acceleration of about 35
km/s^2 due to its motion through the wire's magnetic field. That
is to say, its distance from the wire *will* (rapidly!) begin to
increase.

Now consider what all this looks like in the frame of the
electron. There is still a magnetic field but since the electron
is not moving it does not experience a magnetic force. So why
does it *start* moving and why, in particular, does it begin
moving *away* from the wire?

The answer lies in the Lorentz contraction which minutely alters
the densities of the positive and negative charge carrying
constituents of the wire due to their differing motions.

Can you show that the linear charge density of the wire in the
(initial) frame of the electron is about -1.1 x 10^-17 C/m as
would be required to give the electron the same observed
acceleration in both frames?

John Mallinckrodt
Cal Poly Pomona