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Curl and path independence.

  1. Nov 30, 2008 #1
    1. The problem statement, all variables and given/known data

    F(r) = r/!!r!!^3 (Sorry but the !! is supposed to imply that its scalar)

    I found the curl using the cartesian coordinate definition of curl. It came out to be zero. Now the question is, is F path independent? Its silly, becuase if the curl is zero then it does imply that its path independent, however F is not defined when r is zero. So i m confused here. Any help will be deeply appreciated.
  2. jcsd
  3. Nov 30, 2008 #2


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    Since r=0 is the only place that r/|r|^3 is undefined, you can check if it's path independent by checking that the integral around any closed path enclosing r=0 is zero. You can check any particular path you want. If one vanishes, they all do.
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