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Green's theorem

  • Thread starter -EquinoX-
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  • #1
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Homework Statement



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

Homework Equations





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?
 
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Answers and Replies

  • #2
CompuChip
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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.
 
  • #3
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well..how do I get around to solve this? I know the curl is y-3...
 
  • #4
CompuChip
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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...
 

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  • #5
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so the curl is -4? I don't get it why it's -2 to 2
 

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