How do you determine if a vector field is conservative for a fuction of x,y, and z?

For F(x,y) I know you can determine this if Py= Qx

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- Apr 9th 2010, 09:58 AMwizrd54How to test if a vector field is conservative for a F(x,y,z)
How do you determine if a vector field is conservative for a fuction of x,y, and z?

For F(x,y) I know you can determine this if Py= Qx - Apr 9th 2010, 10:03 AMdwsmith
$\displaystyle (\frac{\partial P}{\partial y}-\frac{\partial N}{\partial z})=0$

$\displaystyle (\frac{\partial M}{\partial z}-\frac{\partial P}{\partial x})=0$

$\displaystyle (\frac{\partial N}{\partial x}-\frac{\partial M}{\partial y})=0$ - Apr 9th 2010, 10:05 AMwizrd54
Thanks.

- Apr 9th 2010, 10:06 AMdwsmith
I edited my original post to make it more clear.

- Apr 9th 2010, 10:07 AMAllanCuz
It is conservative if we can find the conditions bellow to be true:

dF1/dy = dF2/dx : dF1/dz = dF3/dx : dF2/dz = dF3/dy

Remember that there is a vector function such that

F(x,y,z) = F1(x,y,z)i + F2(x,y,z)j + F3(x,y,z)K

Fairly simple. If you want to make a non conservative field conservative, simply add in a constant infront of your F1/F2/F3, and find the value that satisfies the above equation.