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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 [if?] 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.
...
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.