Re: Question 07/02 CURRENT IN A WIRE

["John S. Denker" <jsd@MONMOUTH.COM>]

At 11:10 -0500 11/19/02, Bob Sciamanda wrote:
>
> The laboratory observer sees moving charges which
> interact via magnetic forces, even though their
> relative velocity is zero.

Yes, that's what the laboratory observer sees.

Hugh Haskell wrote:

> > They interact with each other via magnetic forces?
> > How is this possible?

Why not?  We see charge A moving and hence creating
a magnetic field.  We charge B moving through this
magnetic field, and hence being deflected.  What's the
problem?

>  My understanding of this is that the only reason we see a
> magnetic field around a moving charge is that it is moving *relative
> to us.*

Yes, that's what we see in our frame (the laboratory
frame).

>  The moving charges in a wire feel a magnetic field because
> they see the opposite charges moving relative to them.

1)  The presense of opposite charges if by no means
the whole story.

2) There are two ways to parse that sentence.  We
can calculate _in our frame_ what the moving charges
feel.  Or we can calculate the same physics in a frame
comoving with the charges.  The physics is the same.
The vectors (and bivectors) are the same.  But if we
pick apart the vectors (and bivectors) into components,
the components will be different.

> In a plasma,
> there is motion between the opposite charged particles (IIRC a plasma
> is only a "plasma" if it is at least approximately neutrally charged,

Mostly irrelevant.  Certainly not the whole story.

> in otherwise empty space, a beam of charged
> particles will not sense a magnetic field due to the presence of
> other charges in the beam,

That's a frame-dependent statement.
The physics is frame-independent.
The correct frame-independent statement is that the
particles interact via the electromagnetic field.
Deciding whether the field is "electric" or "magnetic" is
frame-dependent and not particularly important.

Specifically:  the electromagnetic field is a bivector.
If Joe is in a frame where this bivector is oriented in
the t /\ x direction, he calls it a purely electric field.
If Moe is moving relative to Joe in the y direction, he
deals with the !!same!! physical bivector but in his frame
it has a projection in the x /\ y direction, which he calls
a magnetic component.  Draw the picture.

This posting is the position of the writer, not that of Trevor,
Scabbers, or Crookshanks.

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