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Re: Current in a wire

thanks, Michael, this is basically what I realized as I was making my other
post. You worded it more succinctly than I would've. (As my thoughts were
stuck on integral forms of Maxwell's equations, rather than the differential
forms.) Matters are of course more subtle on the surfaces themselves.

Joel Rauber

If a steady state exists, then the time derivative of the
charge density
is zero. Then, the equation of continuity requires that the
divergence
of the current density is also zero. If Ohm's law applies, the
divergence of the electric field is then zero. Gauss's law
(differential form) then implies that the charge density is zero.

Michael Burns-Kaurin
Physics Dept.
Spelman College
mburns-k@spelman.edu


Joel Rauber wrote:

I'm troubled by an aspect of what Don Boys and Beatty wrote:

Don Boys wrote:

These
electrons see a non-zero electric field *due to some excess charge
distributed in a non-uniform way on the surface of the
metals*. Articles
should appear shortly
in Physics Teacher and AJP showing the actual distribution of
the charges on the
wires for a few specific circuits.

Beatty wrote:

the idea that because
net-charge *only exists on the surface of the wire*, then
CURRENT can only
exist on the surface of the wire, since electric current
is a flow of
charge, and there is no charge in an uncharged region of metal.

(N.B. asterisks are my emphasis in the above quotes)

The troubling part is the implication/claim that net charge
only resides on
the surfaces of the wire and can not reside to the interior
of the wire.
This may be the case for conventional situations but:

My understanding is that that the claim that non-zero net
charge only
resides on the surfaces is based on a Gauss' Law arguement
that hinges
crucially on the idea that the E field is zero to the interior of a
conductor. The E field is of course manifestly *not* zero
to the interior
of the conductor where we have non-zero current.
Consequently I see no
fundamental reason why one can not have net charge as well
as non-zero
current to the interior of a wire.

Joel Rauber