Homework Help: Conservative field over a domain

1. Sep 17, 2009

manenbu

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

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:
$$D: (x+5)^2 + y^2 \leq 9$$

2. Relevant equations

?

3. 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.

2. Sep 17, 2009

Staff: Mentor

Your field, the potential, and the partials Py and Qx 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.

3. Sep 17, 2009

manenbu

It doesnt't intersect.
ok, thanks.