Re: Toward the equilibrium (and getting close)

[brian whatcott <inet@INTELLISYS.NET>]

At 10:12 1/6/01 -0500, Bob wrote:
> Ohanian (AJP, Nov 1983, pg 1020) treats the approach to equilibrium as a
> three-step process:
> 1) the "expulsion" of unbalanced free charge from the interior volume of
> the conductor,
> 2) the "expulsion" of fields and currents from the interior,
> 3) the damping out of oscillating surface currents and wave fields.
>
> 1) follows a relaxation equation with time constants like10^-14 sec (for
> Cu when finite mean free paths are taken into account )
> 2) follows a diffusion equation, with damping times of the order of 10^-4
> sec for Cu.
> 3) is geometry dependent.
>
> Regarding 3) Ohanian remarks (referring to a specific "beer-can"
> geometry ) :
>
> " . . . the relaxation time will be shorter than the light-travel time
> h/c.  This is not in conflict with causality because no signal needs to
> travel from one end of the conductor to the other - the signal is already
> present at the initial instant, in the electric fields of the initial
> charge configuration."
>
> Bob Sciamanda (W3NLV)


Ohanian's piece is a rousing good read. One would not argue with his
introduction:
"Many textbooks claim that the relaxation time for the approach to
electrostatic equilibrium is epsilon sub 0 /rho. We show that for a
good conductor, this claim is false. For such a conductor, the approach
to the electro- and magneto-static [sic] equilibrium hinges on the damping
of the induced electric and magnetic fields. The relaxation time
depends on the conductivity, the geometry of the conductor, and the
details of the initial charge distribution."

In the body of the text, he is somewhat hampered by his starting
assumptions which include the sudden apparition of excess charges
spread through the volume of the conductor. This is what you would
call a 'physicist's model'   :-)

He knocks down the resulting expression for relaxation time
(ca 1E-19sec) like this:
"But a bit of thought immediately convinces us that this expression
for the relaxation time cannot be right - it has a nonsensical
 dependence on the relevant physical parameters."

 [He got *that* right!]     This is Bob's item 1)

He offers two or three inch columns of footnotes with e/m text
citations including that particular fallacy such as
Corson & Lorrain, Reitz & Milford, P Tipler, Wangsness, Marion,
Panovsky & Philipps, J D Jackson, even J Jeans - though he
largely excuses him on the basis he was exploring dielectric
behavior.  Moreover he notes later editions of Corson & Lorrain
 and Reitz & Milford fess up that their naive derivations are
 not applicable in conductors.
He says, "This is a step in the right direction, but the claim
that the relaxation time is anywhere near the collision time is
competely false."

You will easily conclude that mistakes are carried from text
to text - a practice that in students, is called copying.

I cannot do better than comment that though his intuition into
the dominance of the electromagnetic field (This is Bob's item 3)
is supported by the experimental evidence, his assertion about
superluminal effects (that Bob quoted) is simply an artifact
of these wonderful magical charges which suddenly appear
throughout the conductor's volume, and which can safely be
disregarded in any situation of practical interest.

 He does offer a characteristic time around 1100 nanoseconds
 for a beer can which is in the right order.  On the other hand,
 he offers a diffusion time constant of 100 microseconds for
a 1 mm thick copper sheet which would provide a time constant
 for the sphere under consideration of 25 seconds.
This can be categorized with the magical charge apparitions as
far as I can tell....     Bob's item 2)

Having had my share of fun with Ohanian's paper, I will give
him credit for reminding us that Ohm's law is a statistical result
of momentum gain in an electric field being lost by collision
on a trajectory lasting abt 2E-14 seconds (0.02 picoseconds).
At timescales shorter than this, Ohm's Law is not valid.
brian whatcott <inet@intellisys.net>  Altus OK
                Eureka!