Conservative field over a domain

[manenbu]

Homework Statement

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

Homework Equations

?

The Attempt at a Solution

Well,
$$\frac{\partial P}{\partial y} = \frac{\partial Q}{\partial x} = \frac{-2xy}{(x-y)^3}$$
So is it conservative.
Also, the potential is:
$$f = \frac{xy}{x-y}$$
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.

 

[Mark44]

Your field, the potential, and the partials P_y and Q_x 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.

 

[manenbu]

It doesnt't intersect.
ok, thanks.