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Math Help - How to test if a vector field is conservative for a F(x,y,z)

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    How 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
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    (\frac{\partial P}{\partial y}-\frac{\partial N}{\partial z})=0

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

    (\frac{\partial N}{\partial x}-\frac{\partial M}{\partial y})=0
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    I edited my original post to make it more clear.
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    Senior Member AllanCuz's Avatar
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    Quote Originally Posted by wizrd54 View Post
    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
    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.
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