- #1
Yeldar
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Separation Vector
Let [itex]\vec{r}[/itex] be the separation vector from a fixed point [itex](\acute{x},\acute{y},\acute{z})[/itex] to the source point [itex](x,y,z)[/itex].
Show that:
[tex]\nabla(\frac{1}{||\vec{r}||}) = \frac {-\hat{r}} {||\vec{r}||^2} [/tex]
Now, I've attempted this comeing from the approach that [itex]||\vec{r}|| = (\vec{r} \cdot \vec{r})^\frac {1} {2} [/itex] but it dosent seem to get me anywhere, am I missing something blatently obvious?
Thanks.
Let [itex]\vec{r}[/itex] be the separation vector from a fixed point [itex](\acute{x},\acute{y},\acute{z})[/itex] to the source point [itex](x,y,z)[/itex].
Show that:
[tex]\nabla(\frac{1}{||\vec{r}||}) = \frac {-\hat{r}} {||\vec{r}||^2} [/tex]
Now, I've attempted this comeing from the approach that [itex]||\vec{r}|| = (\vec{r} \cdot \vec{r})^\frac {1} {2} [/itex] but it dosent seem to get me anywhere, am I missing something blatently obvious?
Thanks.
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