1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Stoke's thrm

  1. May 6, 2009 #1
    1. The problem statement, all variables and given/known data

    Let [tex] \vec{F} = (z - y)\vec{i} + (x - z)\vec{j} + (y - x)\vec{k} [/tex] . Let C be the rectangle of width 2 and length 5 centered at (9, 9, 9) on the plane x + y + z = 27, oriented clockwise when viewed from the origin.

    [tex] \int\limits_C \vec{F} d\vec{r} [/tex] ?
    2. Relevant equations



    3. The attempt at a solution

    I've already computed the curl F and so now I need to solve the dA. What is the dA here?
     
    Last edited: May 7, 2009
  2. jcsd
  3. May 7, 2009 #2
    anyone??
     
  4. May 7, 2009 #3

    dx

    User Avatar
    Homework Helper
    Gold Member

    Do you mean F = (z - y)i + (x - z)j + (y - x)k? Also, please write out the question completely; don't make us guess. You did this in another recent thread too where you left out an important part of the question because you "didn't think it was relevant".
     
  5. May 7, 2009 #4
    yes, sorry.. I've edited it now
     
  6. May 7, 2009 #5

    dx

    User Avatar
    Homework Helper
    Gold Member

    You should get a constant vector of length 2 for the curl. Did you? It is also perpendicular to the rectangle and pointing outwards, so the circulation is just 2(area of rectangle).
     
  7. May 7, 2009 #6
    you mean [tex] \int\limits_C \vec{F} d\vec{r} = 20 [/tex] ?
     
  8. May 7, 2009 #7

    dx

    User Avatar
    Homework Helper
    Gold Member

    CFdr = 2 x (area of rectangle) = 2 x 10 = 20.
     
  9. May 7, 2009 #8
    hmm.. the answer is wrong for some reason
     
  10. May 7, 2009 #9

    dx

    User Avatar
    Homework Helper
    Gold Member

    Oops, sorry. The magnitude of the curl is √(2² + 2² + 2²) = √12. So the circulation is (√12)(10).
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook