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Homework Help: Green's theorem

  1. Apr 13, 2009 #1
    1. The problem statement, all variables and given/known data

    http://img5.imageshack.us/img5/8295/capturewmw.th.jpg [Broken]

    2. Relevant equations

    3. The attempt at a solution

    I tried to find the curl first and what i got is y - 3 and then I multiply that by the area of the circle which is 4pi.. am I doing something wrong?
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Apr 14, 2009 #2


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    The circulation of a vector field [itex]\vec G[/itex] around a curve C is given by
    [tex]\operatorname{circ}_C(\vec G) = \iint_A \operatorname{curl}(\vec G) \, \mathrm d\vec a[/tex]
    Since the curl is not a constant on the disk, the integral is not as trivial as integrand * surface area.

    You could have easily seen that your answer is wrong because 4pi(y - 2) still depends on y, while it should be a number.
  4. Apr 14, 2009 #3
    well..how do I get around to solve this? I know the curl is y-3...
  5. Apr 15, 2009 #4


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    If you have to solve this question I assume you have learned how to integrate a function over some area.

    I suggest integrating from y = -2 to y = 2 so that the x integral will be trivial (you only need to worry about the integration boundaries):

    [tex]\operatorname{circ}_{C}(\vec G) \propto \int_{-2}^{2} \int_{\cdots}^{\cdots} (y - 2) \, dx \, dy[/tex]
    up to some proportionality factors... see the image below.

    I hope that I have provided you with enough clues to solve the question now...

    Attached Files:

  6. Apr 15, 2009 #5
    so the curl is -4? I don't get it why it's -2 to 2
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