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Force Fields and Curl

  1. Jan 20, 2009 #1

    bfr

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    1. The problem statement, all variables and given/known data

    Suppose that f is a vector field such that curl f=(1,2,5) at every point in R^3. Find an equation of a plane through the origin with the property that [tex]\oint_{C}[/tex]f dot dX = 0 for any closed curve C lying in the plane.

    2. Relevant equations

    [​IMG]

    3. The attempt at a solution

    With Stokes' theorem and a bit of algebra I get: [tex]\int\int[/tex] ( 1,2,5) dot [tex]\nabla[/tex]g dy dx) = 0 . So, 1*dx+2*dy+3*dz=0; let dx=1; let dy=1; dz=-1. The resulting plane is x+y-z=0. Is this right?
     
  2. jcsd
  3. Jan 20, 2009 #2

    Dick

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    You want curl(F)=(1,2,5) to be normal to the plane, right? I don't think that gives you x+y-z=0.
     
  4. Jan 20, 2009 #3

    bfr

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    Er, oops :eek:.

    Then I guess x+2y+5z=0 would simply be the answer?
     
  5. Jan 20, 2009 #4

    Dick

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    Seems so to me.
     
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