Re: Park City Paradox ?

[Ludwik Kowalski <kowalskil@MAIL.MONTCLAIR.EDU>]

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. Wires would not interact
magnetically is all electrons had identical v in
the same direction. Magnetic interactions exist
because there is a wide distribution of v in each
wire, even when mean v are identical. Slow electrons
in one wire push fast electrons in another wire.
Fast electrons in that wire push slow electrons
of another wire. And vice versa. Was I the only
one who was not aware of this important nuance?

To make the analogy complete one needs several
skiers (long sticks) in each wire and they
should have different velocities. Then glass
pipes (properly charged to assure the overall
neutrality of each pipe with skiers) would attract
like two wires.

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.

By the way, what would happen in a long
superconducting wire loop connected to a
battery? Would electrons be accelerated to
v~c? Would the dissipation of energy (gained
in a battery) by radiation be significant?
I have no idea what to expect.
Ludwik Kowalski
*****************  Yesterday I wrote:

> > Is this a paradox or not? I was skiing down
> > on the left side of another skier this morning.
> > We were moving in the same direction with the
> > same speed. And I was speculating:
> >
> > 1) Suppose each of us was charged negatively.
> > Being at rest with respect to each other we
> > would repel each other by Coulomb's law.
> >
> > 2) But electrons drifting along two parallel
> > wires in the same direction produce an
> > attractive force between the wires.
> >
> > 3) This triggered my imagination. Suppose
> > each of us is skiing as specified above,
> > but intide a glass tube. Will our motion
> > produce an attractive force between the
> > two tubes? By analogy this should happen,
> > right? But this would contradict our
> > mutual repulsion, as in #1 above.
> >
> > Is it a paradox or not? The experiment is
> > of the gedanken type, allow any Q and any
> > v<<c [v->c is a non-classical problem] ...