Re: Toward the equilibrium

[brian whatcott <inet@INTELLISYS.NET>]

 At 17:28 1/3/01 -0500, Ludwik wrote:
> > Suppose that at t=0 a charge of 1 microC is deposited at one
> > point of a copper sphere whose diameter is one meter.
/snip/
> > 1) Do charges travel to final destinations through the entire
> > volume or do they travel mostly near the surface?

At 09:26 1/4/01 -0600, Tim Folkerts responded:

> Neither!  The +1 uC doesn't travel through the conductor at all!

I am largely in agreement with this: steep electric wavefronts are
confined to a relatively thin surface skin of a conductor.


> You need to start before t=0.  As the +1 uC is brought close to the
> conductor, the electrons in the copper are already rearranging themselves.
> The point on the conductor nearest the external charge will have a -1 uC
> charge, while the rest will have a +1 uC surface charge.

Aw shucks - starting out on a good note by observing an induced surface
 charge, Tim supposes that the induced charge equals the charge being
transported.
  This is easily shown to be untrue - the electric field mediates charge
induction - and you are well aware that field is highly dependent on
geometry: consider a charged point compared with a charged sphere carrying
1 microcoulomb - their effects will be different, I submit.


> No significant travel of electrons will be needed to establish equilibrium.

If Tim concurs on the magnitude of the potential on the 1 meter sphere in
the steady state - about 13 kV for the room size I had in mind -
 he will presumably agree that there is a surface displacement of electrons
to comply with this field.
Is this 'insignificant' or 'significant'? the distances certainly are
minute....   But I am quite certain he cannot be confusing bulk transport
of electrons with a travelling electric field.

> Other than a little "ringing", it seems that equilibrium is established AT
> t=0.

Perhaps it would be harder to hold out this position, if one morphed
the charged sphere to a circle of coaxial cable - and visualized Ludwik
adding charge to a stub conductor (a 'tee') connected to the center
coax conductor.
   I expect there is nobody who would hold out that the center conductor
would instantaneously equilibrate within 1E-19 seconds?
 It is so easy to demonstrate the progress of a travelling wave in coax.

 Come to think of it, perhaps the "ridiculous" answer that someone
> quoted and I already deleted :-(  of something like 10^-18 s actually is
> correct.
>
> Tim Folkerts
> FHSU


Bob again reminded us of this position - and how it is "echoed in E&M texts."
   He did mention he visualized the charge is added from inside the sphere
like in a Van de Graaff. I think he has a different situation in mind.

A sphere charged at one point is essentially a fat short antenna - expect
a travelling wave - and expect some radiation thereby - Hertz did!  <grin>




brian whatcott <inet@intellisys.net>  Altus OK
                Eureka!