Re: [Phys-L] charge distribution leading up to a capacitor

[Todd Pedlar <pedlto01@luther.edu>]

The ratio r of N_neg, plate / N_pos, plate is quite useless actually, as
John points out, but if one is forced to think about it, and to compare it
to r_wire, the similar ratio that you asked about, Robert,  r_wire could be
> r, < r or exactly = r, depending on the size (volume) of the wire
relative to that of the plates, the geometry of the situation, and probably
other factors that I am not thinking of off the top of my head.  What we do
know is that the electrons in the battery+wires+plates system arrange
themselves so that we have an electrostatic situation.  This will, in
normal situations, mean that the majority of the free electrons are on one
of the plates, and the holes left behind by electrons are on the other
plate.  Because no real system is ideal, there will be some excess
electrons in the negative plate's lead wire, and some holes in the positive
plate's lead wire, but other than that, without specifics, you cant' say
much without making a very detailed calculation, and you certainly can't
say anything about the ratio r_wire relative to r_plates.  In addition, we
return to the fact that there's really nothing helpful that this ratio
reflects (at least that I can think of).

Todd

On Fri, Jul 29, 2016 at 8:06 PM, John Denker <jsd@av8n.com> wrote:

> On 07/29/2016 04:21 PM, Robert Cohen wrote:
>
> > I understand and agree that the ratio is essentially 1.
> >
> > However, it is not exactly 1 on the plate.  If it was, it would be
> neutral.
>
> On the third hand, the ratio still has no physical significance.
>
> Using notation where
>    r := N_pos / N_neg
>
> we can also define
>    q := N_pos - N_neg.
>
> where q is the /charge/.
>
> AFAICT the thing that appears in the Maxwell equations is q, not r.
>
> Furthermore, r alone is not sufficient to determine q.  There are ways of
> changing r by several orders of magnitude without changing q.
>
> I cannot imagine any practical and/or pedagogical reason for introducing
> the concept of r.  It's just not a good way to organize the thoughts or
> the calculations.
>
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-- 
Todd K. Pedlar
Associate Professor of Physics
Luther College, Decorah, IA
pedlto01@luther.edu