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!

Greens theorem on a circle

  1. Nov 26, 2011 #1
    1. The problem statement, all variables and given/known data
    Use greens theorem to solve the closed curve line integral:
    [itex]\oint[/itex](ydx-xdy)

    The curve is a circle with its center at origin with a radius of 1.

    2. Relevant equations
    x^2 + y^2 = 1

    3. The attempt at a solution
    Greens theorem states that:
    Given F=[P,Q]=[y, -x]=yi-xj

    [itex]\oint[/itex]F*dr=[itex]\oint[/itex]Pdx+Qdy=[itex]\int[/itex][itex]\int[/itex]([itex]\frac{dQ}{dx}[/itex]-[itex]\frac{dP}{dy}[/itex])dA

    From the circle equation i find:
    x=[itex]\sqrt{1-y^2}[/itex]
    y=[itex]\sqrt{1-x^2}[/itex]

    Which means that:
    [itex]\frac{dQ}{dx}[/itex]=0 and [itex]\frac{dP}{dy}[/itex]=0

    Obviously, I am doing something wrong... but which rules am I breaking??

    I did find the answer the "normal" way, without greens, which was -2[itex]\pi[/itex].

    I think a lot of my difficulties originates from lack of knowledge about different coordinate systems and the conversion between these.
    One could write:
    x=cos t and y=sin t, but do I have to? (btw, i used that for solving the normal way).
     
  2. jcsd
  3. Nov 26, 2011 #2
    Oh wait... I think I got the vector field F mixed up with the circle that I am integrating over.
    I shouldn't insert for x and y before I have applied greens theorem... I think.
     
  4. Nov 26, 2011 #3
    It's [itex]Q = -x, P= y[/itex], so [itex]\frac{dQ}{dx} = -1[/itex], etc...
     
  5. Nov 26, 2011 #4
    Solved, used polar coordinates on the integral after greens theorem.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Greens theorem on a circle
  1. Green's Theorem (Replies: 9)

  2. Green's Theorem (Replies: 2)

Loading...