Re: Toward the equilibrium

[Ludwik Kowalski <KowalskiL@MAIL.MONTCLAIR.EDU>]

Referring to this:

>  >Suppose that at t=0 a charge of 1 microC is deposited at one
>  >point of a copper sphere whose diameter is one meter. I used
>  >to say that "the equilibrium is going to be established very
>  >quickly, perhaps in a couple of nanoseconds or so. Why?
>  >Because it can not be faster than  3.3 ns; the time light
>  >needs to cover the distance of 1 m in air.
>  >
>  >1) Do charges travel to final destinations through the entire
>  >volume or do they travel mostly near the surface?

Tim Folkerts wrote:

> Neither!  The +1 uC doesn't travel through the conductor at all!  (But I'll
> admit I never thought about it until you asked ....)
>
> 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.  When the external
> charge finally reaches the conductor at t=0, it only needs to travel to the
> -1 uC of electrons waiting at the nearest side.
>
> No significant travel of electrons will be needed to establish equilibrium.
> Other than a little "ringing", it seems that equilibrium is established AT
> t=0.  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.

I am not sure that this is correct. It is true that the sphere is strongly
polarized before it is touched and that the injected +Q mixes with the
-Q nearby. But the net charge +Q, at time zero, is on the other side of
the diameter. In other words, the distribution at t=0 is not uniform
over the sphere, as it becomes when the equilibrium is established.
How long does it take to equilibrate charges? Anything less than
1 ns would be unrealistic for the sphere of one meter.
Ludwik Kowalski