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Homework Help: Showing a vector field is irrational on

  1. Mar 17, 2012 #1
    1. The problem statement, all variables and given/known data
    Let F = ( -y/(x2+y2) , x/(x2+y2) ) Show that this vector field is irrotational on ℝ2 - {0}, the real plane less the origin. Then calculate directly the line integral of F around a circle of radius 1.

    2. Relevant equations

    3. The attempt at a solution

    To show F is irrotational we must show curl v = 0. Although I'm unsure what it means by finding it on ℝ2 - {0} ?
  2. jcsd
  3. Mar 17, 2012 #2


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    It just means find the curl at a general point (x,y) where x and y aren't both 0. The vector field is undefined at (0,0).
  4. Mar 18, 2012 #3
    okay thanks.. I got it
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