Question concerning curl for finding a conservative force field
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