Which condition makes F⃗=P i⃗+Q j⃗\vec{F} = P\,\vec{i} + Q\,\vec{j}F=Pi+Qj conservative in a simply connected domain?
∂P∂y=∂Q∂x\dfrac{\partial P}{\partial y} = \dfrac{\partial Q}{\partial x}∂y∂P=∂x∂Q
∂P∂x=∂Q∂y\dfrac{\partial P}{\partial x} = \dfrac{\partial Q}{\partial y}∂x∂P=∂y∂Q
P=QP = QP=Q
curl F⃗≠0\text{curl}\,\vec{F} \neq 0curlF=0