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

[A330NEO]

Homework Statement

I have to explain why this vector field is not conservative.

Homework 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

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.

 

[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?

 

[A330NEO]

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

 

[LCKurtz]

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