Regrading the Lorentz force between two currenbt carrying wires Bill Hobba
wrote:
I have carefully worked through the math many times. I have examined
texts
that do the same eg page 488 of Griffiths - Introduction to
Electrodynamics
where the derivation of this well known fact is given in full detail.
The
analysis depends entirely on the existence of length contraction - the
force
between two current carrying wires is zero if length contraction does
not
occur and matches exactly what is observed if it does. AFAICS the only
attack that can reasonably be leveled is that electrons moving at
constant
velocity though a wire is not really a good model for the complex QM
dependant process that is really occurring - but to my that is not
really
germane to the point.


Richard relied:
Why isn't it? It is exactly these complexities that make your
interpretation contradictory. Consider once again: If the
'electrostatic' field density increases, and this causes the observed
force between the conductors, then the motions (the complexities that
you referred to) of the charge quanta must also cause the same
generation of force between the components of charge in the conductor
even when no currents are flowing in them, that is, the electrostatic
field is itself due to the relative motion of the charges.

I think your logic is askew. First the exact experiment that is considered
is the force experienced by a single moving charge caused by a current
carrying wire and the Lorentz force is deduced. It is later in the analysis
that the existence of the Lorentz force is used to predict the force between
two current carrying wires. Hence for the first part of the analysis your
objection that we are ignoring the density imbalance between the moving
electrons and the nuclei in the current carrying wire is a not an issue.
For the second part (ie where we deduce the force between the current
carrying wires) we consider the nuclei at rest and the electrons as moving
it is not an issue either. Of course from the POR we could have done all
our calculations from the viewpoint of the moving electron - but all the
calculations I have done and have seen done do not do that - for obvious
calculational convenience. But the POR guarantees the results will be the
same - if not you have found a violation of the POR and your place in
history is assured. As an exercise it might be illuminating to do this
calculation but I must admit I have not done so because the POR tells me it
is not really an interesting thing to do.

Hence I consider the existence of a force between 2 current carrying wires
as strong evidence of the existence of length contraction.

Thanks
Bill