Re: mag field of infinite wire

["RAUBER, JOEL" <JOEL_RAUBER@SDSTATE.EDU>]

> -----Original Message-----
> From: Carl E. Mungan [mailto:mungan@USNA.EDU]
> Sent: Tuesday, March 26, 2002 2:21 PM
> To: PHYS-L@lists.nau.edu
> Subject: mag field of infinite wire
>
>
> When I first use Gauss' law to derive the E field outside an infinite
> uniformly charged rod, I like to take a few minutes to go through
> some symmetry arguments to show that E can only point in the radial
> direction and can only vary in magnitude with the radial coordinate.
>
> I would like to do the analogous thing for Ampere's law to derive the
> B field outside an infinite straight wire carrying a current.

<snip>

> You may use Maxwell's equations in their integral or differential
> form and you may use symmetry arguments. You may not use Biot-Savart
> law nor appeal to experiment.
>
> Is there a solution? Carl

Carl,

When you use Gauss' law for the "cylindrically" distribution to argue its
radial nature, do you avoid any use of knowledge of the direction of E field
from point charges (Coulomb expression for E field)?

I know when I spend the few minutes to go through the symmetry arguement,
I'm looking at pairs of charge elements (line charge pairs on either side of
a perpendicular line extending from the field point through the symmetry
axis;and note that if you choose the pairs symmetrically their non-radial
components of E field cancel.

I consider this using the coulomb expression for E field (its direction in
particular and the fact that magnitude is proportional to charge density and
inverse distance square) in addition to Gauss' Law and symmetry.

I suspect that you may have to use the Biot-Sarvart Law to the same extent
(to obtain some minimal directional information).

Nice arguement for the radial component, I've always used the Biot-Sarvart
law to rule out that component as well.  My Ampere's Law lecture in a couple
of weeks will change!

Joel R