Re: Question 07/02 CURRENT IN A WIRE

[Bob LaMontagne <rlamont@POSTOFFICE.PROVIDENCE.EDU>]

Hugh Haskell wrote:

> At 20:52 +0100 11/19/02, Mark Sylvester wrote:
> > But Hugh, just last week I was demonstrating to my class the mutual
> > attraction of two conductors carrying parallel currents!
> No problem there. The magnetic fields are real, and there is plenty
> of relative motion to account for it. But imagine two beams of
> identically charged particles in a vacuum, traveling parallel to each
> other (and in the same direction) and with the same velocity. Other
> than some random thermal motion which should cancel out, there is no
> relative motion of the charges in one beam with respect to the
> charges in the other beam, so can there be a magnetic interaction
> between these beams? I can't see how, but I am open to arguments that
> refute my claim.
>
> Hugh
> --

I think Hugh gets to the heart of the matter. In the lab frame, one can calculate the
magnetic forceof attraction per unit length between the two identically charged ion
beams - one can also calculate the electrostatic repulsive force per unit lenth. Very
nicely, the ratio of the magnetic force per unit length and the electric force per
unit length is v^2/c^2. If we now go to the frame traveling at speed v with the ions,
and properly account for the contraction factor in the lab frame, we find the
electrostatic force per unit length is reduced by just the required 1 - v^2/c^2
factor. We don't get a "pinch" - we get a reduced repulsion between the ions.

Obviously this doesn't apply to neutral plasmas or current carrying wires.

Bob at PC

This posting is the position of the writer, not that of SUNY-BSC, NAU or the AAPT.