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Math Help - Calculate the line integral over a vector field

  1. #1
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    Calculate the line integral over a vector field

    Hello!
    I encountered the following problem in an exercise book for Electro magnethism. It is in a section that is used to refresh ones mathematical knowledge obtained in Calculus.

    Task:
    The vector field H = ( I / ( 2 pi * R) ) * phi is given in cylindrical coordinates.
    The curve C is the circumference to the circle: R = a, z = 0, 0 <= pi <= 2 pi.

    Calculate the line integral over the closed integral C of H* dl

    ----------

    Anyone that can give me some hints of the methodology to use? I have tried to solve it, but I do not succeed.

    Thanks!

    Anders Branderud
    bloganders.blogspot.com
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  2. #2
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    Quote Originally Posted by andersbranderud View Post
    Hello!
    I encountered the following problem in an exercise book for Electro magnethism. It is in a section that is used to refresh ones mathematical knowledge obtained in Calculus.

    Task:
    The vector field H = ( I / ( 2 pi * R) ) * phi is given in cylindrical coordinates.
    Do you mean \vec{H}= \frac{\phi}{2\pi R}\vec{i}?

    The curve C is the circumference to the circle: R = a, z = 0, 0 <= pi <= 2 pi.
    Parametric equations for the circle are x= a cos(\phi), y= a sin(\phi), z= 0 so that d\vec{s}= (-a sin(\phi)\vec{i}+ a cos(\phi)\vec{j})d\phi (Yes, 0\le \pi\le 2\pi but that doesn't make sense here. I presume you meant 0\le \phi\le 2\pi.)

    Calculate the line integral over the closed integral C of H* dl
    Take the dot product of \vec{H} and d\vec{s} and integrate with respect ot \phi from 0 to 2\pi.[/quote]
    ----------

    Anyone that can give me some hints of the methodology to use? I have tried to solve it, but I do not succeed.

    Thanks!

    Anders Branderud
    bloganders.blogspot.com[/QUOTE]
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  3. #3
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    HallsofIvy, Thanks alot for your help!

    Quote Originally Posted by HallsofIvy View Post
    Do you mean \vec{H}= \frac{\phi}{2\pi R}\vec{i}?
    Yes, that is correct.
    I saw now that they write: "Intensity is often denoted with the scalar <I>I</I>, but one should remember that it actually is a vector <B>I</B>.


    Anders Branderud
    bloganders.blogspot.com
    Last edited by andersbranderud; January 27th 2010 at 10:28 AM.
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