# vector field and curl

• May 16th 2009, 07:20 PM
yzc717
potential vector
The vector field F(x,y)=( $y^2$ +cosx i )+ 2xy j in the plane is conservative.

can I conclude this statement is right if I found the potential f(x,y)=x $y^2$ + sinx ?
• May 16th 2009, 08:51 PM
mr fantastic
Quote:

Originally Posted by yzc717
The vector field F(x,y)=( $y^2$ +cosx i )+ 2xy j in the plane is conservative.

can I conclude this statement is right if I found the potential f(x,y)=x $y^2$ + sinx ?

Yes.

$\nabla \times F = 0 \Longleftrightarrow F = \nabla f$