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# Re: [femm] single wire -magnetic potential A problem

- To: femm@yahoogroups.com
- Subject: Re: [femm] single wire -magnetic potential A problem
- From: dcm3c@aol.com
- Date: Wed, 17 Oct 2001 12:21:42 EDT

    In a message dated 10/16/01 10:09:23 PM Eastern Daylight Time,
    tborzic@yahoo.com writes:

    > Hello everybody, My name is Tomislav and as You may assume
    > I'm new here and I am looking for some help regarding FEMM.
    > I am trying to solve some "simple" problem.It goes like this:
    > 1. Round wire,copper, infinite lenghth,we look at cross section
    > ,r=0.075m =7.5cm, I= 100 + j0 A,f= 50Hz, relative
    > permeability is 1.Working with old "pen and paper" i got some results
    > which are sure correct.Point is to get same thing in FEMM.
    > What I do is called "numerical callculations of eddy current in round
    > conductor".I nedd to obtain values of "A" in points r1=0, r2=0.25,
    > r3=0.5 and r4= 0.75. (In point r4 A = 0, boundary conditon,allready
    > given).
    > So what I need is that some one helps me to solve this,tell me
    > how to define parameters for my problem in FEMM,keeping in mind that I
    > am new here,but in near future i intend to use FEMM rather often.
    > My results are:
    > A1=0.9999951 x10-5 -j0.2109364 x10-7
    > A2=0.8888852 x10-5 -j0.1666658 x10-7
    > A3=0.5555543 x10-5 -j0.6510389 x10-8
    > A4=0.5169879 x10-22 -j0.6638621 x10-19 ( this should be 0 but
    > this is good enough)
    > So I need to obtain this rezults with FEMM.
    > Thanks
    >
    This problem is really similar to the example at <A HREF="http://femm.berlios.de/tube/tube.htm";>
    http://femm.berlios.de/tube/tube.htm</A> Following a similar chain of reasoning
    to this example, one can show that the solution for tangentially-directed H
    as a function of radius r is:

    H = i/(2 Pi R) BesselI[1,a*r]/BesselI[1,a*R]

    where a=(1+j)/d, and skin depth d is d = Sqrt[1/(Pi*freq*mu_o*sigma)] where
    freq is the frequency in Hz, mu_o is permeability of free space, and sigma is
    electrical conductivity. R is the outer radius of the wire, and i is the
    total current carried by the wire. In my notation, j = Sqrt[-1] and
    BesselI[1,x] is the modified Bessel function of order 1 of the first kind.

    I've attached a .fem solution for the same problem. The agreement with the
    analytical solution is pretty good.

    > P.S. To mr. David Meeker:
    > i am translating User's manual to Crotian,for my personal needs,and
    > for other students on University of Split, who may need it.When I am
    > done (about 20 days i guess), I can convert it to *.pdf and send it to you
    > if you want,and make it available for everybody on internet?
    >
    > Tomislav Borzic
    > tborzic@yahoo.com
    >

    Great! When you finish it, I'll post it on the web site.

    Dave
    --
    David Meeker
    <A HREF="http://members.aol.com/_ht_a/dcm3c";>http://members.aol.com/_ht_a/dcm3c</A>

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    <HTML><FONT FACE=arial,helvetica><FONT SIZE=2 FAMILY="SANSSERIF" FACE="Arial" LANG="0">In a message dated 10/16/01 10:09:23 PM Eastern Daylight Time, tborzic@yahoo.com writes:
    <BR>
    <BR>
    <BR><BLOCKQUOTE TYPE=CITE style="BORDER-LEFT: #0000ff 2px solid; MARGIN-LEFT: 5px; MARGIN-RIGHT: 0px; PADDING-LEFT: 5px">Hello everybody, My name is Tomislav and as You may assume
    <BR>I'm new here and I am looking for some help regarding FEMM.
    <BR>I am trying to solve some "simple" problem.It goes like this:
    <BR>1. Round wire,copper, infinite lenghth,we look at cross section
    <BR>,r=0.075m =7.5cm, I= 100 + j0 A,f= 50Hz, relative
    <BR>permeability is 1.Working with old "pen and paper" i got some results
    <BR>which are sure correct.Point is to get same thing in FEMM.
    <BR>What I do is called "numerical callculations of eddy current in round
    <BR>conductor".I nedd to obtain values of "A" in points r1=0, r2=0.25,
    <BR>r3=0.5 and r4= 0.75. (In point r4 A = 0, boundary conditon,allready
    <BR>given).
    <BR>So what I need is that some one helps me to solve this,tell me
    <BR>how to define parameters for my problem in FEMM,keeping in mind that I
    <BR>am new here,but in near future i intend to use FEMM rather often.
    <BR>My results are:
    <BR>A1=0.9999951 x10-5 &nbsp;-j0.2109364 x10-7
    <BR>A2=0.8888852 x10-5 &nbsp;-j0.1666658 x10-7
    <BR>A3=0.5555543 x10-5 &nbsp;-j0.6510389 x10-8
    <BR>A4=0.5169879 x10-22 &nbsp;-j0.6638621 x10-19 ( this should be 0 but
    <BR>this is good enough)
    <BR>So I need to obtain this rezults with FEMM.
    <BR>Thanks
    <BR></FONT><FONT COLOR="#000000" SIZE=3 FAMILY="SANSSERIF" FACE="Arial" LANG="0"></BLOCKQUOTE>
    <BR>This problem is really similar to the example at <A HREF="http://femm.berlios.de/tube/tube.htm";>http://femm.berlios.de/tube/tube.htm</A> &nbsp;Following a similar chain of reasoning to this example, one can show that the solution for tangentially-directed H as a function of radius r is:
    <BR>
    <BR></FONT><FONT COLOR="#000000" SIZE=3 FAMILY="SERIF" FACE="Times New Roman" LANG="0">H = i/(2 Pi R) BesselI[1,a*r]/BesselI[1,a*R]
    <BR>
    <BR>where a=(1+j)/d, and &nbsp;skin depth d is d = Sqrt[1/(Pi*freq*mu_o*sigma)] where freq is the frequency in Hz, mu_o is permeability of free space, and sigma is electrical conductivity. &nbsp;R is the outer radius of the wire, and i is the total current carried by the wire. &nbsp;In my notation, j = Sqrt[-1] and BesselI[1,x] is the modified Bessel function of order 1 of the first kind.</FONT><FONT COLOR="#000000" SIZE=3 FAMILY="SANSSERIF" FACE="Arial" LANG="0">
    <BR></FONT><FONT COLOR="#000000" SIZE=2 FAMILY="SANSSERIF" FACE="Arial" LANG="0">
    <BR>I've attached a .fem solution for the same problem. &nbsp;The agreement with the analytical solution is pretty good.
    <BR></FONT><FONT COLOR="#000000" SIZE=3 FAMILY="SANSSERIF" FACE="Arial" LANG="0">
    <BR></FONT><FONT COLOR="#000000" SIZE=2 FAMILY="SANSSERIF" FACE="Arial" LANG="0"><BLOCKQUOTE TYPE=CITE style="BORDER-LEFT: #0000ff 2px solid; MARGIN-LEFT: 5px; MARGIN-RIGHT: 0px; PADDING-LEFT: 5px">P.S. To mr. David Meeker:
    <BR>i am translating User's manual to Crotian,for my personal needs,and
    <BR>for other students on University of Split, who may need it.When I am
    <BR>done (about 20 days i guess), I can convert it to *.pdf and send it to you
    <BR>if you want,and make it available for everybody on internet?
    <BR>
    <BR>Tomislav Borzic
    <BR>tborzic@yahoo.com
    <BR></FONT><FONT COLOR="#000000" SIZE=3 FAMILY="SANSSERIF" FACE="Arial" LANG="0"></BLOCKQUOTE>
    <BR></FONT><FONT COLOR="#000000" SIZE=2 FAMILY="SANSSERIF" FACE="Arial" LANG="0">
    <BR>Great! &nbsp;When you finish it, I'll post it on the web site.
    <BR>
    <BR>Dave
    <BR>--
    <BR>David Meeker
    <BR><A HREF="http://members.aol.com/_ht_a/dcm3c";>http://members.aol.com/_ht_a/dcm3c</A></FONT></HTML>

    --part1_3e.13021d29.28ff0a16_alt_boundary--

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