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Question concerning curl for finding a conservative force field

  1. Sep 28, 2009 #1
    Hello all,
    I understand the fact that the principles
    LaTeX Code: F= \\nabla \\phi .

    LaTeX Code: \\nabla \\times F = 0 .

    must apply in order for a force field to be conservative however what i dont get is why showing:

    LaTeX Code: f_y= g_x, f_z= h_x, g_z= h_y
    where subscripts are what you are taking the derivative with respect to.

    is a means to prove the above laws are in effect. i assume it has to do with the fact that subtracting the partial derivatives will give you zero. thank you very much for any help

  2. jcsd
  3. Sep 29, 2009 #2
    You should specify what [tex]f[/tex], [tex]g[/tex] and [tex]h[/tex] are. It does look like you're using the fact that you can jointly express the two statements as

    [tex]\nabla\times\nabla\phi = \mathrm{det}\begin{pmatrix}\hat{\mathbf{i}} && \hat{\mathbf{j}} && \hat{\mathbf{k}}\\\delta_x && \delta_y && \delta_z\\ \delta_x\phi && \delta_y\phi && \delta_z\phi\end{pmatrix}[/tex],
    meaning, for example,
    \hat{\mathbf{i}}(\delta_y\delta_z - \delta_z\delta_y)\phi=0,
    but not knowing [tex]f[/tex], [tex]g[/tex] and [tex]h[/tex], I can't comment further.
  4. Sep 29, 2009 #3
    oh haha that should have been obvious thank you very much that clears everything up perfectly
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