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

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1. Nov 20, 2014

A330NEO

1. The problem statement, all variables and given/known data

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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2. Nov 20, 2014

LCKurtz

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
3. Nov 20, 2014

A330NEO

I think the amount would be same, but will have negative value. But is that an enough explanation?

4. Nov 20, 2014

LCKurtz

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