- #1
TheGreatDeadOne
- 22
- 0
- Homework Statement
- calculate the function gradient with respect to r
- Relevant Equations
- gradient in spherical coordinates
Doing R=|r-r'|, i get the expected result: [tex] \nabla \frac{1}{|r-r'|} = -\frac{1}{R^2}\hat r=-\frac{(r-r')}{|r-r'|^3}[/tex]
But doing it this way seems extremely wrong, as I seem to be disregarding the module. So I tried to do it by the chain rule, and I got:
[tex] \nabla \frac{1}{|r-r'|}=-\frac{1}{2}(r-r')^{-\frac{3}{2}}[/tex]
but that doing so looks much more correct using Cartesian coordinates. So, does anyone have any tips?
But doing it this way seems extremely wrong, as I seem to be disregarding the module. So I tried to do it by the chain rule, and I got:
[tex] \nabla \frac{1}{|r-r'|}=-\frac{1}{2}(r-r')^{-\frac{3}{2}}[/tex]
but that doing so looks much more correct using Cartesian coordinates. So, does anyone have any tips?