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## Homework Statement

Consider the intersection,R, between two circles : x

^{2}+y

^{2}=2 and (x-2)

^{2}+y

^{2}=2

a) Find a 2-Dimensional vector field

__F__=(M(x,y),N(x,y)) such that ∂N/∂x - ∂M/∂y=1

## Homework Equations

none.

## The Attempt at a Solution

There are other parts to the main question but I don't think I will have a problem with them. I know how to calculate the curl of

__F__but I'm unsure of how to go about it so that the vector field relates to the intersection as we use

__F__in an integral later on. What I thought of doing was integrating the curl function with respect to x or y in turn and trying to find M and N. I cant quite see how to involve the equations of the circles in all of this, if someone could point me in the right direction?

Thanks

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