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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

    sleventh
     
  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,
    [tex]
    \hat{\mathbf{i}}(\delta_y\delta_z - \delta_z\delta_y)\phi=0,
    [/tex]
    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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