- #1
Flux = Rad
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Homework Statement
This is from Griffiths' Intro to Electrodynamics. He is discussing the field of a polarized object of dipole moment per unit volume [tex] \vec{P} [/tex] viewed at [tex] \vec{r} [/tex].
He then states:
[tex] \nabla ' \left( \frac{1}{r} \right) = \frac{ \hat{r}}{r^2} [/tex]
Where [tex] \nabla ' [/tex] denotes that the differentiation is with respect to the source co-ordinates [tex] \vec{r}' [/tex]
Homework Equations
The Attempt at a Solution
Following from the definition of the gradient,
[tex] \nabla ' \left( \frac{1}{r} \right) = \frac{-1}{r^3} \left[ x \frac{ \partial x}{\partial x'} \hat{x}' + y \frac{\partial y}{\partial y'} \hat{y}' + z \frac{\partial z}{\partial z'} \hat{z} \right]
[/tex]
So I guess all would be well as long as
[tex] \frac{\partial x}{\partial x'} \hat{x}' = - \hat{x} [/tex]
However, this isn't clear to me at the moment