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Re: visualizing fields near charged objects



At 2:33 PM -0800 2/9/01, John Mallinckrodt wrote:
On Fri, 9 Feb 2001, Leigh Palmer wrote:

At 6:02 AM -0800 2/9/01, John Mallinckrodt wrote:
>Once the calculation is finished, finding the Laplacian for those
>cells whose value was specified as a part of the boundary
>condition gives the charge density (times some appropriate
>constant) in those cells.

Do you mean the Laplacian or the gradient? It is the potential
gradient that is proportional to the charge density.

Oh, Leigh! You know better than that. The gradient of the
potential is a vector. It's called ... um ... er... Dang. Well,
I know that it *does* have a name!

I must be out of step with everyone except Ludwik. Yes, the
potential gradient *is* a vector, but that is trivial! The
normal component of the potential gradient is a scalar, and
the potential gradient has *only* a normal component at the
surface of a conductor.

|E| = |grad V|

|sigma| = eps0 |E|

What could be simpler?

Perhaps I should have called it the Poissonian?

No, I think you meant the laplacian (div grad), but that's
an unnecessarily complicated way to calculate *surface*
charge density. Why would one want to take another spatial
derivative in this geometrically simple case where the
E field is always normal to the surface?

Leigh