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Homework Help: Integration of vectors

  1. Mar 13, 2010 #1
    1. The problem statement, all variables and given/known data

    [tex]\int_{S}[/tex][tex]\int[/tex] n dS = 0 for any closed surface S.

    2. Relevant equations



    3. The attempt at a solution
    I can't solve this because I don't have any idea in Vector intregrals.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Mar 13, 2010 #2
    It should only equal zero if it is conservative since the partial of n with respect to x equals the partial m with respect to y. I am not sure if this what you are looking for since I am not sure what your question is.
     
  4. Mar 13, 2010 #3

    LCKurtz

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    Hint: The result is a vector, so look at its components. The x component of a vector V is [itex] V \cdot i[/itex]. So look at, for example:

    [tex] i \cdot \int\int_S \hat n\ dS = \int\int_S i\cdot \hat n\ dS[/tex]
     
  5. Mar 13, 2010 #4
    What is i there???

    n is normal line, I think
     
  6. Mar 13, 2010 #5

    LCKurtz

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    i is the unit vector in the x direction, the usual i,j,k notation. n is the unit outward normal.
     
  7. Mar 13, 2010 #6

    Matterwave

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    If the vector field is always tangential to the surface (and therefore perpendicular with the normal of the surface), this relation is trivially true. If the vector field is 0 everywhere, then this relation is also trivially true. What is the question exactly? Find all such vector fields n for which this relation holds?
     
  8. Mar 13, 2010 #7
    So, will you help me to make a proof?
     
  9. Mar 13, 2010 #8
    is there any proof you can show??

    that's the question..
     
  10. Mar 14, 2010 #9

    gabbagabbahey

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    As LCKurtz already pointed out, [itex]\textbf{n}[/itex] is the outward unit normal to whichever closed surface is integrated over. The problem is to show that this integral is zero for any closed surface.
     
  11. Mar 14, 2010 #10

    gabbagabbahey

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    We don't make proofs for you here. LCKurtz has given you a very good hint in his first reply, try using it and show us what you get. You should find that the divergence theorem is very useful to you here:wink:
     
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