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!

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

    CompuChip

    User Avatar
    Science Advisor
    Homework Helper

    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

    CompuChip

    User Avatar
    Science Advisor
    Homework Helper

    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
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Green's theorem
  1. Green's Theorem (Replies: 8)

  2. Greens theorem (Replies: 10)

  3. Green's Theorem (Replies: 4)

  4. Green's Theorem (Replies: 9)

  5. Green's Theorem (Replies: 2)

Loading...