[SI-LIST] Re: Skin Effect question
- From: "Cristian Torres" <cristian.torres@xxxxxxxxxxxxxx>
- To: <dbrooks7@xxxxxxxxxxxxxxx>, <si-list@xxxxxxxxxxxxx>
- Date: Mon, 4 Jun 2012 13:18:52 -0400
Doug,
It's not even a coincidence. It just happens to be almost equal.
The integral of y=8*e^(-x/.125) between 0 and x0 is this mathematical
function of x0: -8*0.125*(e^(-x0/0.125)-1)
In this case, when x0=1, the integral equals 0.9997, which is just close to
1. If x0=+inf, the integral equals 1.
--Cristian
-----Original Message-----
From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx] On
Behalf Of Doug Brooks
Sent: 3-Jun-12 10:45 PM
To: si-list@xxxxxxxxxxxxx
Subject: [SI-LIST] Skin Effect question
This question relates to skin effect.
Consider a current density function with (surface density) Io=8 and skin
depth = .125, unity radius.
consider the current density function y=8*e^(-x/.125) integrate the area
under this function between 0=<x=<1. The answer is
.9997 (according to the tool I am using!)
Consider the rectangle formed by the points 0,0, 0,8, .125,8, .125,0 (Note
that x=.125 [i.e. at the skin depth] is where the exponent of e in the
current density function is -1.) the area under this rectangle is 1.0 (same
as the area under the current density function.)
Here is my question. Is this a fortunate coincidence or can this identity be
proven mathematically?
Doug has a new e-mail address dbrooks7@xxxxxxxxxxxxxxx
check out the free resources at http://www.ultracad.com
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