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Calculating the Vector Field from a curl function

  1. Apr 7, 2012 #1
    1. The problem statement, all variables and given/known data
    Consider the intersection,R, between two circles : x2+y2=2 and (x-2)2+y2=2
    a) Find a 2-Dimensional vector field F=(M(x,y),N(x,y)) such that ∂N/∂x - ∂M/∂y=1

    2. Relevant equations
    none.
    3. The attempt at a solution
    There are other parts to the main question but I don't think I will have a problem with them. I know how to calculate the curl of F but I'm unsure of how to go about it so that the vector field relates to the intersection as we use F in an integral later on. What I thought of doing was integrating the curl function with respect to x or y in turn and trying to find M and N. I cant quite see how to involve the equations of the circles in all of this, if someone could point me in the right direction?
    Thanks
     
    Last edited: Apr 7, 2012
  2. jcsd
  3. Apr 9, 2012 #2
  4. Apr 9, 2012 #3

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    What was the full statement of the problem? There doesn't see, to be any statement as to what the "two circles" has to do with the vector you are trying to find.

    If the problem were just "Find a two dimensional vector [itex]\underline{F}= (M(x,y),N(x,y))[/itex] such that [itex]\partial N/\partial x- \partial M/\partial y= 1[/itex] then M= y, N=2x so that [itex]\underline{F}= (y, 2x)[/itex] is an obvious solution.
     
  5. Apr 9, 2012 #4
    Part b) of the question asks "Using this F and Greene's theorem, write the area integral ∫∫RdA as a line integral"

    Does that help?
     
  6. Sep 17, 2012 #5
    How can I solve the
    ∇×A(r,θ,φ)=B,A(r)=?,A(θ)=?,A(φ)=?
    where B is constant.
    please help me? :(
     
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