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Thread: Curl of Vector Field

  1. #1
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    Curl of Vector Field

    Find the curl of vector field.

    F(x, y, z) = xyz i - x^2 y k

    ∇xF = 0

    No curl in this vector field.

    The book's answer is

    ∇xF = -x^2 i + 3xy j - xz k

    Who is right and why?
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  2. #2
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    Re: Curl of Vector Field

    Quote Originally Posted by USNAVY View Post
    Find the curl of vector field.
    F(x, y, z) = xyz i - x^2 y k
    ∇xF = 0
    No curl in this vector field.
    The book's answer is
    ∇xF = -x^2 i + 3xy j - xz k
    Who is right and why?
    $\nabla\times F=\left| {\begin{array}{*{20}{c}} {\partial x}&{\partial y}&{\partial z} \\ {xyz}&0&{ - {x^2}y} \end{array}} \right| = - {x^2}i + 3xyj - xzk$

    It appears that the textbook is correct.
    Thanks from USNAVY
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  3. #3
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    Re: Curl of Vector Field

    It is very easy to make simple sign errors when calculating the determinant for the curl F. I believe this to be my problem.
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