Curl Practice including Curvilinear Coordinates

  • Calculate the curl of each of the following vector fields. You may look up the formulas for curl in curvilinear coordinates.

    1. \begin{equation} \vec{F}=z^2\,\hat{x} + x^2 \,\hat{y} -y^2 \,\hat{z} \end{equation}
    2. \begin{equation} \vec{G} = e^{-x} \,\hat{x} + e^{-y} \,\hat{y} +e^{-z} \,\hat{z} \end{equation}
    3. \begin{equation} \vec{H} = yz\,\hat{x} + zx\,\hat{y} + xy\,\hat{z} \end{equation}
    4. \begin{equation} \vec{I} = x^2\,\hat{x} + z^2\,\hat{y} + y^2\,\hat{z} \end{equation}
    5. \begin{equation} \vec{J} = xy\,\hat{x} + xz\,\hat{y} + yz\,\hat{z} \end{equation}
    6. \begin{equation} \vec{K} = s^2\,\hat{s} \end{equation}
    7. \begin{equation} \vec{L} = r^3\,\hat{\phi} \end{equation}