Hi, Doug This is not a coincidence and can be proved mathematically. Also this is exactly the reason why we can approximate that all the current travel in 1 skin depth when computing Rac. Please see below, Remember for exponential function, integral{exp^(a*x)}=1/a*integral{exp^(a*x)}, Let a=-1/s, where s is the skin depth. Then the integral = -s * [exp^(-x/s) |x=inf - exp^(-x/s)|x=0]=-s*(-1)=s; Thus this is valid independent of s. Jingbo > Date: Mon, 4 Jun 2012 14:20:16 -0700 > To: cristian.torres@xxxxxxxxxxxxxx; si-list@xxxxxxxxxxxxx > From: dbrooks9@xxxxxxxxxxxxxxx > Subject: [SI-LIST] Re: Skin Effect question > > Very good point. > > OK then, does anyone have an exact expression for the current density > (under skin effect conditions)? Or does such an expression even exist? > > Doug > > > > > At 10:18 AM 6/4/2012, Cristian Torres wrote: > >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 > > > >------------------------------------------------------------------ > >To unsubscribe from si-list: > >si-list-request@xxxxxxxxxxxxx with 'unsubscribe' in the Subject field > > > >or to administer your membership from a web page, go to: > >//www.freelists.org/webpage/si-list > > > >For help: > >si-list-request@xxxxxxxxxxxxx with 'help' in the Subject field > > > > > >List forum is accessible at: > > http://tech.groups.yahoo.com/group/si-list > > > >List archives are viewable at: > > //www.freelists.org/archives/si-list > > > >Old (prior to June 6, 2001) list archives are viewable at: > > http://www.qsl.net/wb6tpu > > > > > > > >------------------------------------------------------------------ > >To unsubscribe from si-list: > >si-list-request@xxxxxxxxxxxxx with 'unsubscribe' in the Subject field > > > >or to administer your membership from a web page, go to: > >//www.freelists.org/webpage/si-list > > > >For help: > >si-list-request@xxxxxxxxxxxxx with 'help' in the Subject field > > > > > >List forum is accessible at: > > http://tech.groups.yahoo.com/group/si-list > > > >List archives are viewable at: > > //www.freelists.org/archives/si-list > > > >Old (prior to June 6, 2001) list archives are viewable at: > > http://www.qsl.net/wb6tpu > > > > Check out our resources at http://www.ultracad.com > > ------------------------------------------------------------------ > To unsubscribe from si-list: > si-list-request@xxxxxxxxxxxxx with 'unsubscribe' in the Subject field > > or to administer your membership from a web page, go to: > //www.freelists.org/webpage/si-list > > For help: > si-list-request@xxxxxxxxxxxxx with 'help' in the Subject field > > > List forum is accessible at: > http://tech.groups.yahoo.com/group/si-list > > List archives are viewable at: > //www.freelists.org/archives/si-list > > Old (prior to June 6, 2001) list archives are viewable at: > http://www.qsl.net/wb6tpu > > ------------------------------------------------------------------ To unsubscribe from si-list: si-list-request@xxxxxxxxxxxxx with 'unsubscribe' in the Subject field or to administer your membership from a web page, go to: //www.freelists.org/webpage/si-list For help: si-list-request@xxxxxxxxxxxxx with 'help' in the Subject field List forum is accessible at: http://tech.groups.yahoo.com/group/si-list List archives are viewable at: //www.freelists.org/archives/si-list Old (prior to June 6, 2001) list archives are viewable at: http://www.qsl.net/wb6tpu