FreeLists / si-list / [SI-LIST] Re: Question: Reverse current layers? in the skin effect

[Paul Levin <levinpa@xxxxxxxxxxxxx>]

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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