Re: Charge Distribution around pointed areas

[Ludwik Kowalski <KowalskiL@MAIL.MONTCLAIR.EDU>]

Bob Sciamanda wrote:

> Are you sure you have included all interaction energy
> terms among all possible pairs of 5 charges?
> You seem to have too few terms!

Possible. Let me see. Draw 5 beads and connect them to
make a pentagon. This make five links. Then add more
links till everybody is dirctly connected with everybody
else. This adds five more links. So there should be 10
links. How many were there in my little program?

1 with 4
1 with 5 twice (to account for 4 with 5)
2 with 3
3 with 4 twice (to account for 1 with 2)
5 with 2 twice (to account for 5 with 3)

You are right, two are missing, 1 with 3 and its
symmetric couterpart, 2 with 4.

Here is the corrected program. The new minimum is
at x=5.409 cm and EP=73.59 J (instead of x=5.28 cm
and PE=66.08 J). The tendency of concetrating toward
the end points is slightly stronger. Thanks for correcting.
Ludwik Kowalski

let L=0.2                    ! wire length (meters)
let Q=8e-6                  ! charge on each bead (C)
let PE14=9e9*Q*Q/L                 ! end to end
let PE15=9e9*Q*Q/(0.5*L)       ! center to end
for x=0.0539 to 0.0541 step 0.00001
   let PE23=9e9*Q*Q/(2*x)
   let PE34=9e9*Q*Q/(0.5*L-x)
   let PE52=9e9*Q*Q/x
   let PE13=9e9*Q*Q/(0.5*L+x)  ! added term
   let PE=PE14+PE23+2*(PE34+PE15+PE52+PE13)
   print "x=";x;"meters.   Pot. Energy=";PE;" joules"
next x
end