[SI-LIST] Re: Skin effect and Bessel function

  • From: Dazhao Liu <dlhbf@xxxxxxx>
  • To: Antonis Orphanou <orphanou@xxxxxxxxxxxx>
  • Date: Thu, 2 Aug 2012 17:47:50 -0700

Hi,
Thanks, Antonis. You showed me a good point.
I think, by definition, *current density* = sigma*E.
*current* = integral of *current density* over *area. *
*
*
So the *current* involves an integral of J0, while *current
density*doesn't. After integral,
*Current is*
*I = *sigma*Es*2*pi/A*r*J1(r). The current and current density cannot have
opposite trend.

Someone told me the current density may be related to the coefficient Es. I
will further take a look.
Thanks.


Regards
Dazhao

On Thu, Aug 2, 2012 at 4:09 PM, Antonis Orphanou <orphanou@xxxxxxxxxxxx>wrote:

> If you noticed, the Bessel equation of first kind zero order (Jo) is
> solved for the electric field.
> The current density involves an integral of Jo and from recurrence, it
> becomes first order, J1, which by definition is zero in the center.
>
>
>
>
> -----Original Message-----
> From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx]
> On Behalf Of tiancailuotuo
> Sent: Thursday, August 02, 2012 2:55 PM
> To: si-list@xxxxxxxxxxxxx
> Subject: [SI-LIST] Skin effect and Bessel function
>
> To solve the current density distribution within a solid copper wire
> cross-section, when only considering z-axial component Jz (current
> density), a Bessel differential equation can be solved.
> http://home.swipnet.se/swi/bessel/bessel.html
> <http://home.swipnet.se/swi/bessel/bessel.html>
> Then the solution is J0(A*r), where A=sqrt(-j*omega*sigma*mu), and J0 is
> the zero-th order Bessel function.  [./Form_7.png ac_currrent] Therefore,
> Current Density = sigma*Es*J0(A*r).  [./Form_7.png
> ac_currrent]   [Form_9.png E]
> We know that due to skin effect, current density is largest around the
> edge. But from the equation above, Current Density has max value when r=0.
> Can any one help me understand this?
> ThanksDazhao
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