# 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.