Re: Charge Distribution around pointed areas

[John Mallinckrodt <ajmallinckro@CSUPOMONA.EDU>]

On Tue, 16 Nov 1999, Ludwik Kowalski wrote:

> For seven beads (three of them being fixed as above)
> the potential energy becomes the function of two
> parameters (due to symmetry) and I would expect the
> minimum to occur when the consecutive distances
> between beads become progressively smaller as one
> moves away toward the end point beads.

Just to confirm your expectation, Maple tells me (and Interactive Physics
confirms) that the equilibrium positions for seven beads include beads
.365 and .711 of the way to the ends on each side of the center.

For 21 beads, Interactive Physics is my tool of choice and it puts the nine
intermediate beads on each side at the following fractional positions:

  .110, .219, .327, .435, .540, .644, .744, .840, and .928

further confirming the expectation.

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