Re: Charge Distribution around pointed areas

[John Mallinckrodt <ajmallinckro@CSUPOMONA.EDU>]

On Tue, 16 Nov 1999, Bob Sciamanda wrote:

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

I think Bob may be right.  I didn't check Ludwik's results for 4 and 5
charges before.

Ludwik wrote:

> Here is a problem which should help. Four equally
> charged beads can slide without friction on a horizontal
> wire whose length is 20 cm. The charge on each bead
> is 10 microC. Two beads are immobilized at the ends
> of the wire, the other two are at a distance x from
> the center of the wire. How does the potential energy
> depend on x? Treat beads as point charges.
>
> The answer --> PE has a minimum of 45.01 J at
> x=3.333 cm, that is when the beads are equidistant.

I didn't read this carefully before, but now that I have I don't see how
that could possibly be right.  Indeed, I get 3.61 cm. In general, my
solution for four beads gives the answer as .361 of the way from the
center to the end of the wire.

> Solve the same problem for 5 beads (8 microC each). This
> time three beads are immobilized, one at the center and
> one at each end. Two beads are free to slide, as before.
> This time the minimum PE = 66.08 J occurs at x=5.28 cm.

Here I get a slightly different value--5.40 cm--or, in general, .540 of
the way from the center to the end.

I didn't debug the program, but it looks like Bob may be right.

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