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Homework Help: Conservative field over a domain

  1. Sep 17, 2009 #1
    1. The problem statement, all variables and given/known data

    prove that:
    [tex]\vec{F} = \frac{-y^2}{(x-y)^2}\vec{i} + \frac{x^2}{(x-y)^2}\vec{j}[/tex]
    is a conservative field, and find the potential in the domain:
    [tex]D: (x+5)^2 + y^2 \leq 9[/tex]

    2. Relevant equations


    3. The attempt at a solution

    [tex]\frac{\partial P}{\partial y} = \frac{\partial Q}{\partial x} = \frac{-2xy}{(x-y)^3}[/tex]
    So is it conservative.
    Also, the potential is:
    [tex]f = \frac{xy}{x-y}[/tex]
    which is correct according to my answer.

    My question is - where does the domain come in? Why do I have it? I didn't use it while solving the problem.
  2. jcsd
  3. Sep 17, 2009 #2


    Staff: Mentor

    Your field, the potential, and the partials Py and Qx are undefined on the line y = x. Your domain D is a disk of radius 3, centered at (-5, 0). Does the line y = x intersect D? If not, your field is conservative over all of D. If so, the field is not conservative over all of D.
  4. Sep 17, 2009 #3
    It doesnt't intersect.
    ok, thanks.
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