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Math Help - Circulation

  1. #1
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    Circulation

    Find circulation
    F(x,y) = (x+2xy)i + (y+x^2)j around the

    \alpha : |x| + |y| = 1
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  2. #2
    Super Member Random Variable's Avatar
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    Use Green's Theorem which says the circulation of a vector field around a simpled closed curve in the xy-plane is equal to the line integral of the vector field evaluated around the curve. In ths problem the curve is diamond-shaped. So you have to parametrize each side and evaluate four separate line integrals.

    BTW, is the answer to that flux problem in your textbook?
    Last edited by Random Variable; June 3rd 2009 at 06:46 PM.
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  3. #3
    Super Member Random Variable's Avatar
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    Starting at (1,0) and and going counterlcockwise

     \int \int_{D} (\nabla \times F) \cdot \hat{k} \ dA =  \int_{C} F \cdot dr = \int_{0}^{1} \Big( F(1-t,t) \cdot (-1,1) \Big) dt + \int_{0}^{1} \Big(F(-t,1-t) \cdot (-1,-1) \Big) dt  + \int_{0}^{1} \Big(F(t-1, -t) \cdot (1,-1) \Big) dt + \int_{0}^{1} \Big( F(t, t-1) \cdot (1,1) \Big) dt
    Last edited by Random Variable; June 3rd 2009 at 07:47 PM.
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