🚀 go-pugleaf

 Harry: 
 >
 >"Bilge" <dubious@radioactivex.lebesque-al.net> wrote in message
 >news:slrnbvraov.dan.dubious@radioactivex.lebesque-al.net...

 >>   The motion of a charge next to a wire can be found in a fairly
 >> straight-forward way just by finding the B-field from the wire and
 >> and using the lorentz force law. (Working in the frame in which the
 >> field from the wire is purely magnetic).
 >
 >True. So now we have:
 >
 >�
 >�  very long wire
 >�
 >�     <- -  o+    charged object , v<<c
 >�
 >�
 >^
 >Thus: I can see that the object is pushed downward, and, if I'm not
 >mistaken, that the wire is pushed counter clock wise.

   The field of a long wire is just given in MKSA by
   
B = \mu_0 I_enc/(2pi r)

   (in the \phi direction using cylindrical coordinates)

  The force comes from the lorentz force law, F = qv x B, so if the
motion of the charge is along the radial direction, the direction
of the force is along z. Balancing the forces requires the force
on the wire to be along z.

 >In order for the forces to balance I miss an upward longitudinal force on
 >the wire.

  That would be an induced current from the motion of the charge,

curl B = j + dE/dt.

 It should also be clear that currents in wires cannot be treated
as moving charges using maxwell's equations without additional
assumptions about the wire which requires quantum mechanics to
explain. The charges would repel each other if they were not
bound to the wire by a mechanism beyond the ability of maxwell's
equations to explain.

[...]
 >>  >Sorry, perhaps Ampere had several laws?!
 >>  >I meant the Ampere force law, which is very roughly:
 >>  >
 >>  >F = -i_m * i_n *(dm . dn / r^2) * (2 cos phi - 3 cos a cos b)
 >>
 >>   I didn't realize ampere had a "force law" other than what could
 >> be derived from the usual equations. In any case, that expression
 >> is written in a particular frame (which is okay). But, notice that
 >> because it's derived under the assumption of infinitely long wires,
 >> it's rather unphysical (at least from a relativistic standpoint),
 >> since the current can't ever begin flowing or stop flowing, but
 >> had to have existed and continue to exist for all time.
 >
 >In fact, no such assumption was made, it describes the force between two
 >individual charge elements.
 
  Yes, such an assumption _is_ made because the integral of ampere's
law, curl B = j, is a line integral over a closed path. Writing that
as current elements, is a convenient fiction which requires evaluating
the line integral over the entire _closed_ path. For a straight wire
(or any other wire which is not explicitly closed) the path is closed
at infinity.

  The biot-savart law is just a vector identity that allows you to
write an integral for B under the assumption that dl is a closed
path. I'm also not sure I understand the geometry of the wires for
which that force equation is derived. The angles \phi, a and b refer
to some assumption about the relative orientation of the configration.

[...]

 >Perhaps it's a paying website, sorry. My university has subscription on a
 >number of them...
 >It's IEEE trans. on Plasma Science, vol.21, no.6, dec.1993, pp. 701-713.
 >N. Graneau, "An electrodynamic vacuum arc ion acceleration mechanism based
 >on Ampere's force law".

  Plasmas are very messy and approximations abound. I would assume that
the article makes several either implicitly or explicitly.