Re: Charge Distribution around pointed areas

[John Mallinckrodt <ajmallinckro@CSUPOMONA.EDU>]

On Tue, 16 Nov 1999, Ludwik Kowalski wrote:

> ...  Your idea of doing this with Interactive Physics was great. I do
> not have time to play with it now but I guess what you did. I suppose
> you started with an arbitrary positions and you waited till beads
> equilibrated. The gravity was turned off and charges were assigned. You
> used position meters to read the output accurately. Right?

Right.  Except you need to turn on some "air resistance" so that the
motion will damp to the equilibrium position.

> Knowing positions you can calculate PE at once.

I didn't bother calculating the PE since it isn't really of interest.

> No need to iterate till the minimum is found, as I did. Was this what
> you used Maple for?

I used Maple to find the equilibrium positions of seven charges (for which
two will be at the ends and one in the middle.) I simply wrote U(x,y),
where x is the distance of the second and sixth charges from the center
and y is the distance of the third and fifth, with k = Q = L/2 = 1 and
then had Maple solve the two equations, dU/dx = 0 and dU/dy = 0,
simultaneously (and numerically) for x and y.

John Mallinckrodt      mailto:ajm@csupomona.edu
Cal Poly Pomona          http://www.csupomona.edu/~ajm