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How can I explain that this vector field is not conservative?

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  1. Nov 20, 2014 #1
    1. The problem statement, all variables and given/known data

    upload_2014-11-21_0-12-36.png I have to explain why this vector field is not conservative.
    2. Relevant equations
    Maybe it is: if ##\frac{\partial P}{\partial y} = \frac{\partial Q}{\partial x}## then F(x, y) = p(x, y)i + Q(x, y)j is a conservative field. I tried to figure out what P and Q is, but that

    3. The attempt at a solution
    I tried to figure out what P and Q is, but that was unsuccessfu. By book says that when I can draw a closed, continuous curve that always goes with where the vector field goes, that field is not conservative. But, I don't think it's enough.
     

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  3. Nov 20, 2014 #2

    LCKurtz

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    Suppose those arrows represent force of a water current. Do you think you would do the same amount of work swimming in a circle clockwise about the origin as swimming counterclockwise? Zero in both cases?
     
    Last edited: Nov 20, 2014
  4. Nov 20, 2014 #3
    I think the amount would be same, but will have negative value. But is that an enough explanation?
     
  5. Nov 20, 2014 #4

    LCKurtz

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    Surely you can word it more completely and carefully than that.
     
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