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\begin{center}
\textbf{Vector Fields}

\textit{\textbf{Conservative Fields}}
\end{center}

\textbf{Question}

Calculate $\nabla \ln |\un{r}|$, with $\un{r} = x\un{i} + y\un{j} +
z\un{k}$.


\textbf{Answer}

\begin{eqnarray*}
\frac{\pa}{\pa x} \ln |\un{r}| & = & \frac{1}{|\un{r}|} \frac{\un{r}
\bullet \frac{\pa \un{r}}{\pa x}}{|\un{r}|} = \frac{x}{|\un{r}|^2}\\
\nabla \ln |\un{r}| & = & \frac{x\un{i} +y\un{j}
+z\un{k}}{|\un{r}|^2}\\
& = & \frac{\un{r}}{|\un{r}|^2}
\end{eqnarray*}


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