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Math Help - Conservative?

  1. #1
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    Conservative?

    Is this vector field conservative? F(x)=(y+z, x+y, x+z)

    If it is, how do you find the potential field?
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  2. #2
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    Thsi vector field is conservative because when you calculate the curl (set up the Jacobian) it is equal to zero.

    This means there is a unique potential function whose differentiation yields the vector field that you mentioned.

    Now, to find the potential FUNCTION (not "field") you take the anti-derivative of each term.

    The final potential function according to my calculations is:
    F(x,y,z)=xy+zx+\frac{y^{2}}{2}+\frac{z^{2}}{2}

    Could somebody confirm?
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  3. #3
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    Quote Originally Posted by keysar7 View Post
    The final potential function according to my calculations is:
    F(x,y,z)=xy+zx+\frac{y^{2}}{2}+\frac{z^{2}}{2}
    Could somebody confirm?
    That is correct.
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