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- https://phys.libretexts.org/Bookshelves/University_Physics/Book%3A_Introductory_Physics_-_Building_Models_to_Describe_Our_World_(Martin_Neary_Rinaldo_and_Woodman)/08%3A_Potential_Energy_and_Conservation_of_Energy/8.01%3A_Conservative_Forces\[\begin{aligned} \frac{\partial F_{z}}{\partial y}-\frac{\partial F_{y}}{\partial z} &= \frac{\partial }{\partial y}\left(\frac{-kz}{(x^2+y^2+z^2)^\frac{3}{2}}\right)-\frac{\partial}{\partial z}\left...\[\begin{aligned} \frac{\partial F_{z}}{\partial y}-\frac{\partial F_{y}}{\partial z} &= \frac{\partial }{\partial y}\left(\frac{-kz}{(x^2+y^2+z^2)^\frac{3}{2}}\right)-\frac{\partial}{\partial z}\left( \frac{-ky}{(x^2+y^2+z^2)^\frac{3}{2}}\right)\\ &=\frac{3kz(2y)}{2(x^2+y^2+z^2)^\frac{5}{2}}-\frac{3ky(2z)}{2(x^2+y^2+z^2)^\frac{5}{2}} = 0\\ \frac{\partial F_{x}}{\partial z}-\frac{\partial F_{z}}{\partial x} &= \frac{\partial}{\partial z}\left(\frac{-kx}{(x^2+y^2+z^2)^\frac{3}{2}}\right)-\frac{\…
- https://phys.libretexts.org/Courses/Berea_College/Introductory_Physics%3A_Berea_College/08%3A_Potential_Energy_and_Conservation_of_Energy/8.01%3A_Conservative_Forces\[\begin{aligned} \frac{\partial F_{z}}{\partial y}-\frac{\partial F_{y}}{\partial z} &= \frac{\partial }{\partial y}\left(\frac{-kz}{(x^2+y^2+z^2)^\frac{3}{2}}\right)-\frac{\partial}{\partial z}\left...\[\begin{aligned} \frac{\partial F_{z}}{\partial y}-\frac{\partial F_{y}}{\partial z} &= \frac{\partial }{\partial y}\left(\frac{-kz}{(x^2+y^2+z^2)^\frac{3}{2}}\right)-\frac{\partial}{\partial z}\left( \frac{-ky}{(x^2+y^2+z^2)^\frac{3}{2}}\right)\\ &=\frac{3kz(2y)}{2(x^2+y^2+z^2)^\frac{5}{2}}-\frac{3ky(2z)}{2(x^2+y^2+z^2)^\frac{5}{2}} = 0\\ \frac{\partial F_{x}}{\partial z}-\frac{\partial F_{z}}{\partial x} &= \frac{\partial}{\partial z}\left(\frac{-kx}{(x^2+y^2+z^2)^\frac{3}{2}}\right)-\frac{\…
