Re: Solving field equations in Excel

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

Not being able to follow the details I can only applaud,
learn and ask questions, very timidly. JohnD, in the
tutorial on his website

   http://www.monmouth.com/~jsd/physics/laplace.html

wrote:

> ... Farther right is a third grid that calculates the charge
> density (charge per unit volume). In D=2, charge per unit
> volume means the same thing as charge per unit area. ...
The numbers from the third grid are shown below.

           43
   38  10   5
   31   5   -   5   8  12  35
            5              15
            8              15
           12   7   8   7  16
           45              49

Up to this time I was thinking and calculating distributions
of sigma only in terms of surface charge densities (C/m^2).
My understanding of the above (without checking it numerically
with numbers in previous grids) was that numbers are charges
per unit area along the infinitely long rods. These areas are
perpendicular to the screen. The numbers are facing us but
charges to which they refer reside in planes perpendicular
to the screen. I was comfortable with this and started to
write my own code.

But JohnD refers to these numbers as charge densities per
unit volume (C/m^3). This is new to me and here is my
question. Is it necessary to deal with volume densities in
solving static problems? Is it not true that free charges,
after the equilibrium is established, reside only on surfaces?

My code ignores charges which may be present in space and,
like Leigh I see that the total charge on the surface of the disk
changes when potentials in the "vacuum cells" are changing.
Many iterations are necessary to reach a configuration in
which sigmas are practically unchanging.
Ludwik Kowalski