1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Greens theorem direction of line integral

  1. Jun 11, 2010 #1
    My course notes said that in greens theorem

    where the closed line integral of F.r = the double integral (....)dxdy

    the curve c is taken once anti-clockwise, why does it matter which way you take the line integral? Does it matter at all?

  2. jcsd
  3. Jun 11, 2010 #2
    Green theorem tells that we can transform a closed line integral of curl to a surface integral. As we know, the curl of a vector will still be a vector, so the line integral of curl will have its direction, and it points to the direction of the surface. So if you change the circular as a clockwise one, the direction will change, and you will obtain a minus.
  4. Jun 11, 2010 #3


    User Avatar
    Science Advisor

    Note that in Stoke's theorem, which generalizes Green's theorem to the boundary of a surface in three dimensions, the direction of the path integral dependes upon the direction the normal to the surface points. For example, if you surface is a sphere, whether the normal is pointing inward or outward. As ben.zhang98 said, changing the the direction changes the sign.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook