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Re: Solving field equations in Excel



At 02:04 AM 2/11/01 -0500, Ludwik Kowalski wrote:

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?

It depends. If the world contained only conductors, i.e. equipotentials,
then sure, all the charge would be on the surface. And to make contact
with the spreadsheets: if we consider a cross-section of a conducting rod,
all the charge is on the perimeter of cross-section.

On the other hand, the world is full of stuff that isn't an
equipotential. A transistor wouldn't work very well if it were an
equipotential. Ditto for vacuum tubes. Ditto for the photosensitive drum
in a laser printer. All these critters have regions of space charge. And
the spreadsheet will propagate charge through the vacuum as necessary.

> .... sigmas are ....

For the reasons stated above, and in my note earlier today, be careful: I
think of these numbers as rho (coulombs per meter cubed), not sigma
(coulombs per meter squared). Otherwise there will be
problems. Dimensional analysis failures will be symptoms of these problems.

My code ignores charges which may be present in space

That's a pity. That forfeits a chance to demonstrate several principles of
physics:
-- global charge neutrality
-- local charge conservation
-- gauge invariance.