Re: What is the electric field near a rotating wire, and why doesn't it follow logic of moving individual sections?
- From: Neil Bates <neil_delver@xxxxxxxxxxxxxxx>
- Date: Tue, 24 Jul 2007 20:26:10 +0000 (UTC)
"Lorentz" <drosen0000@xxxxxxxxx> wrote in message
news:1184722044.912776.258330@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
On Jun 29, 2:15 am, "Neil Bates" <neil_del...@xxxxxxxxxxxxxxx> wrote:<snip>
Hi, I'm not getting enough response elsewhere:
What is the electric field near a rotating wire section rotating like a
baton? (Let's say, close to the relevant side and axis of a slowly
rotating
rectangular current loop.) I am wondering why the use of some valid
field
rules conflicts with what we expect from this apparently reasonable
assumption: to pretend that each piece of the wire "projected" the effect
it's magnetic field would have, if the segment is considered separate and
moving in a straight line at its velocity.
The Maxwell equation curl E =I note that the A field of a segment can not by its nature be
- @B/@t doesn't give the E field directly. We can use the A field
(magnetic
vector potential) instead, which is parallel to the current producing it
and
decays as 1/r. The electric field projected from sources can be given
as:
parallel to the segment. The segment is infinitesmally short.
Therefore, there are regions far in front of the segment where the A
field will not be parallel to the wire segment. What you unconsciously
did was impose the cylindrical symmetry of the wire on the
infinitesmal segment of wire. This is a no-no. The reason the A field
is parallel to the wire with electric current is that perpendicular to
the wire cancel out, but only under conditions where that electric
current is constant. However, if the electric charges in the different
segments were accelerating at different rates, these perpendicular
components couldn't possibly cancel out.
I think you made a mistake up there. Look at formulas for A field: the A
vector is parallel to the current section, regardless of position relative
to the current segment (yes, even parallel to the current!) It isn't like
electric or magnetic field. But I do think you made a decent explanation of
why not we couldn't trust the inferrence from treating segments of the
rotating wire as if they were separable entities moving at constant velocity
for that moment. There would instead, have to be a curl around a loop next
to the rotating wire, since the B from the wire increases and decreases
through that loop. If there's a curl, then there's an E field one place and
a weaker one farther away. I just wondered why the two approaches gave
different results.
That 1/r dependence looks like a quantity derived using the
cylindrical symmetry of the wire. This is a pretty good assumption if
one is looking at a long length of wire. But it probably doesn't work
for an infinitesmal segment. At the very least, you need a retardation
delay to modify the 1/r dependence. I am guessing, as I am not sure
exactly how you came up with these formulas. It would be helpful if
you describe exactly which electromagnetic gauge you are working in.
To summarize: Your analysis is working for your potential
calculation rather than your field calculation because in the
potential calculations you are using the symmetry of the total system
to cancel out the acceleration terms. I suspect that you can probably
do that in a field calculation provided you somehow include special
relativity in it.
.
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