"Harry" <harald.vanlintel@epfl.ch> wrote in message news:<4003ff4f$1@epflnews.epfl.ch>...
> "Bilge" <dubious@radioactivex.lebesque-al.net> wrote in message
> news:slrnc06a45.8e.dubious@radioactivex.lebesque-al.net...
> > Harry:
> >  >
> >  >"Bilge" <dubious@radioactivex.lebesque-al.net> wrote in message
> >  >news:slrnbvraov.dan.dubious@radioactivex.lebesque-al.net...
>  
> >  >>   The motion of a charge next to a wire can be found in a fairly
> >  >> straight-forward way just by finding the B-field from the wire and
> >  >> and using the lorentz force law. (Working in the frame in which the
> >  >> field from the wire is purely magnetic).
> >  >
> >  >True. So now we have:
> >  >
> >  >$(D??(B
> >  >$(D??(B  very long wire
> >  >$(D??(B
> >  >$(D??(B     <- -  o+    charged object , v<<c
> >  >$(D??(B
> >  >$(D??(B
> >  >^
> >  >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.
> 
> That doesn't really do, or does it?! I find no change of flux inside any
> wire loop, if we extend the picture to a large wire loop, and even if there
> was, a current does not directly equal a force.
> I still see nothing else but the magnetic field coming from the moving
> charge, resulting in curl B ~ dE/dt. And I already concluded that the
> resulting Lorentz forces on the nearby wire elements provide a counter clock
> turning moment (which is also needed for complete force balance), but the
> upward force is lacking...
> 
> >  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.
> 
> Ye. Still, explanation of how a wire functions is irrelevant for this
> problem.
> 
> > [...]
> >  >>  >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.
> 
> Yes - or not really at infinity, and integrating all the relevant parts. In
> this case, one does not have to extend very far to reach sufficient
> accuracy.
> 
> >  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.
> 
> Sorry, when I wrote it I did not put an effort in it, just wanted to
> identify the law. It's a bit complex to describe, and I haven't played with
> it myself. Phi is the angle between the current flow directions of each
> element, and alpha and beta are the angle of each current flow direction
> with the line between the current elements.
> 
> > [...]
> >
> >  >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.
> 
> Yes, obviously. Main point is that this paper also claims that the laws do
> make different predictions, with the Ampere force law more in agreement with
> observations than the Lorentz force law, and that the Ampere force law has
> "balanced action and reaction".
> 
> Harald


Dear Harald,

Long time I tried to catch from your discussion with Bilge, what
concern has the Ampere's law to my respond to Leo! And only now I
began understanding. This relates not to my respond to Leo but to our
experiments on induction with which you disagreed and remained the
standpoint of loop phenomenology of induction. And now you are
attempting to find the way, how to explain this through the Ampere's
law, i.e., through the interaction of two conductors with the current.

But first, you will not be able to manage it. You know, when I say so.
;-)

Second, to find efficiently the branching in existing formulas, one
has to be not mistaken in his reasoning. In particular, you wrote
about the paper attractive for you:

[Harald]
Main point is that this paper also claims that the laws do
make different predictions, with the Ampere force law more in
agreement with
observations than the Lorentz force law, and that the Ampere force law
has
"balanced action and reaction".

[Sergey]
Don't you think that you can derive the Lorentz force equation on the
basis of Ampere's law? ;-) Further, what it means in the Lorentz law
not "balanced action and reaction"? Balance of action and
counter-action is determined by the model. In the Lorentz law the idea
of magnetic field is used, but if you in your model consider not only
affection of this field on the moving charge but also reaction of the
charge to the source of magnetic field, this all will become balanced.

Thus, have a pleasant "disagreement". ;-)

Sergey