Re: visualizing fields near charged objects

[John Denker <jsd@MONMOUTH.COM>]

At 11:01 PM 2/6/01 -0500, Ludwik Kowalski wrote:
> The cylindrical disk, at 100 V, would be represented by a
> flat rectangle (the cross section of the disk)

For a disk, we can do much better than a cross section.  We can write the
Laplacian in polar coordinates and get a good picture of the D=3 behavior
of anything with rotational symmetry.

This is implemented;  for further information see
  http://www.monmouth.com/~jsd/physics/laplace.html
The spreadsheet itself is at
  http://www.monmouth.com/~jsd/physics/laplace-cyl.xls

> The fact that you could do this in Excel is remarkable.

Think of it as a local cellular automaton.  The laws of classical physics
are local (I'm ducking any quantum EPR/Bell issues).  So you would expect
that a local finite-element approach should work for just about anything
you can think of.

At 12:48 AM 2/7/01 -0500, Ludwik Kowalski wrote:
> I hope John does the same thing for a disk at a good
> resolution (for example the diameter of 75 cells)
> and with the
> "infinity shield" pushed further away.

The D=3 rotational-symmetry case is done as mentioned above.  I leave it to
you to add more cells if you want.

> It seems to me that symmetry should help to reduce the calculation time by
> the factor of 4.

The way I implemented it you get a factor of 2, not 4.  I wanted to allow
objects with minimal symmetry C_infinity (rotation only, like a bowl or
pear) not D_infinity (rotation and reflection, like a barbell or donut).