Re: visualizing fields near charged objects

[John Denker <jsd@MONMOUTH.COM>]

I wrote:
> > The formula for the Laplacian
> > that gives the charge density in this second step is essentially the same
> > formula used in the relaxation algorithm in the previous step, so at the
> > very least there should be excellent consistency. Checking to see that
> > overall charge is conserved is a good diagnostic. See
> >    http://www.monmouth.com/~jsd/physics/laplace.html
> > for more on this.

Then at 10:03 AM 2/8/01 -0800, Leigh Palmer wrote:

> Since I set potential boundary conditions in my technique charge
> is not conserved.

Huh?????  I set potential boundary conditions, too .... whereupon my code
conserves charge (to better than 1%).  If it doesn't conserve charge there
is something severely unphysical about your model.

> I don't see how you accommodated to azimuthal
> symmetry in your relaxation calculation, John. It looks like you
> have used the rectangular form of the Laplacian everywhere,

What are you looking at?  There are two different spreadsheets,
  http://www.monmouth.com/~jsd/physics/laplace.xls
  http://www.monmouth.com/~jsd/physics/laplace-cyl.xls

One of them is rectangular D=2 everywhere, and the other is D=3
rotationally invariant everywhere.

> That will surely lead to funniness. Why do
> you not use the cylindrical Laplacian? The calculation is still
> two dimensional when you do so.

I did.  Read the instructions and/or look at the code.

> having progressed from
> v.1.0 -> v.3.0 -> Excel 98 without having really ever read a
> manual*.

I have never even seen such a manual.