Re: Current in a wire

[Bob Sciamanda <trebor@VELOCITY.NET>]

Allow me to correct an over simplification in 1), below:

Change the phrase "require that Div E (and therefore the volume charge
density) be non-zero . . ."   to "allow Div E (and therefore the volume
charge density) to be non-zero ...".
The quantitative expression is rho = E (dot) Grad sigma / sigma.    IE.,
there must not only be a conductivity gradient - there must also be an E
field component in the direction of that gradient.

Bob

Bob Sciamanda (W3NLV)
Physics, Edinboro Univ of PA (em)
trebor@velocity.net
http://www.velocity.net/~trebor

----- Original Message -----
From: "Bob Sciamanda" <trebor@VELOCITY.NET>
To: <PHYS-L@lists.nau.edu>
Sent: Saturday, March 25, 2000 2:05 PM
Subject: Re: Current in a wire


> Sorry to enter this fray so late - I was "away".
>
> Re: the distribution of unbalanced charge in a current carrying
conductor
> (arises perennially on Phys-L) :
>
> 1) The continuity equation and (the point version of) Ohms "law" require
> that Div E (and therefore the volume charge density be non-zero wherever
> there is a (spatial) gradient in the conductivity.  This occurs at the
> wire surfaces, wire bends, tapered wire sections, junctions of different
> conductors, etc.
>
> 2) The above predicts that the interior of a straight, homogeneous,
right
> circular conductor would be neutral.  An AJP article by Peters added the
> (pinch) effect of the current's own magnetic field on the charge
carriers
> to show that there must be a balancing interior radial E field and so an
> interior charge density which is a function of the cylindrical radial
> coordinate.  If necessary I can recover the reference to Peter's paper.
> (This interior radial field and charge density are weak effects under
> normal circumstances.)
>
> Bob