Re: Capacitor and Force

On Tue, 16 Oct 2007 04:51:13 GMT, "Jon Slaughter"
<Jon_Slaughter@xxxxxxxxxxx> wrote:

<snip>
But the main point is, I'd like to see you find the closed form solution to
it by hand since, again, you seem to think computing integrals by hand is
easy. Remember, its not the same on that page because they did not compute
any integeral for the general case of two 2d parallel plate... or, if you
think they did, then do it for arbitrary charge densities.. doesn't quite
matter because you say they are easy.

Jon, I'd already thought just a little bit about the integral before
looking at the web page that The Phantom pointed at and had already
come to exactly the same approach that the web page mentions, using
annular rings with an infinitesimal width and integrating, as the
right simplifying approach. I didn't go further, as their description
about the approach matched my own initial impression about it and the
solution they gave appeared, without spending time, to be correct.

Do you have any reason to imagine that the author of the page didn't
actually solve the integral correctly? Why also do you bring up the
complicating idea of 'arbitrary charge densities' when, in the case of
idealized parallel plates I'd imagine that the charge was distributed
to minimize the required work and thus uniformly spread (except
perhaps at the edges of the plates, where closer thinking may be
required, but probably wouldn't much impact the final result?)

You mentioned you were off by a factor of two (I'm not accepting or
rejecting that.) The web page that The Phantom mentioned said that
folks often jump initially to imagine a result that is, in fact, a
factor of two off the actual mark. Is that coincidence?

Jon
.

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