[SI-LIST] Re: Question: Reverse current layers? in the skin effect
- From: Paul Levin <levinpa@xxxxxxxxxxxxx>
- To: ikanno@xxxxxxxxxxxxxxxx
- Date: Tue, 03 Dec 2002 04:28:55 -0800
Dear Izuru,
You are not mistaken that the Jo function is oscillatory.
However, for this problem you are using mag[Jo(sqrt(j)*v)],
where j = sqrt (-1). That result ends up with an exponential
like characteristic.
Regards,
Paul
ikanno@xxxxxxxxxxxxxxxx wrote:
> Dear ,
>
> I have a silly question about the skin effect of conductive
> currnt in cylindrical wires ( for over 20 years).
> My textbook shows the skin effect using Bessel function
> to describe the E,H in the conductor.
>
> The result is terrible to understand, should be ok, must be.
> but I wonder the bouncing area of Bessel function.
> It seems to me very strange as if reverse current layers
> exist pararell to the surface where the J0(kr) /J1(ka)
> have the minus value, at a moment.
>
> I am very willing to be advised,
>
> Regards,
>
> Izuru Kanno
> Sun Corp.
> -----------------------------------------------
> I have two text books , almost same results as follows,
> One is electromagnetics, the others is a Math book.
> They start discussion from
> Maxwell & J=sigma*E (sigma is not infinite)
>
> assuming Ez, Hphi are only left non-zero,
> and others are all zero. Then separate
> forms into r-dependent and time-dependent
> portions as follows;
>
> Ez(r,t) = Ez(r) * exp(j*omega*t)
> Hphi(r,t) = Hphi(r) * exp(j*omega*t)
> :
> d2Ez/dr2 + 1/r dEz/dr + k*k*Ez=0
> Mr. Besell's result is available with n=0.
> :
> using sylindrical location (r, phi, z) ,
> 2a:diameter.
> k = root( -j*sigma*mu*omega )
> I: total current
> J0 ( ), J1( ) : Bessel function
> :
> the ( terrible ) results are listed as;
>
> Ez(r)= (kI/2pi*a*sigma ) * J0(kr)/J1(ka)
> Hphi(r)= (I/2pi*a )* J1(kr)/J1(ka)
> iz(r)=sigma*Ez(r)
>
> QQQ. J0(kr) , J1(kr) have strange shapes that bounces
> and goes below 0 level according to r at a moment..
> Is this means reverse current layers in the skin effect?
> or J1(ka) cancells the bounces which goes below zero?
>
> My shameful idea is , its a footprint left by the invasion,
> energy invasion from surface to internal conductor.
> AC conductive current is powered from air side?
> Or am I confused to understand Bessel?
> Thanks for reading silly question. Have a nice day!
>
>
>
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--
Paul Levin
Senior Principal Engineer
Logic Innovations, a Xyratex company
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