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\begin{document}

\noindent \textbf{Een electrisch veld}
\\ \\
\noindent Het electrisch veld rond een puntlading heeft de (alom bekende) vorm:
\[
\vec{E}(\vec{r}) =  \frac{Q}{4 \pi \epsilon_0} \frac{\vec{r}}{r^3}
\]
De rotatie van dit veld (even de constanten buiten beschouwing gelaten) geeft:
\begin{eqnarray*}
	\vec{\nabla} \times \vec{E}(\vec{r}) &=& \left( \begin{array}{c} \partial_x \\ \partial_y \\ \partial_z \end{array} \right) \times \left( \begin{array}{c} 
		\frac{x}{\left( x^2 + y^2 + z^2 \right)^{\frac{3}{2}}} \\
		\frac{y}{\left( x^2 + y^2 + z^2 \right)^{\frac{3}{2}}} \\
		\frac{z}{\left( x^2 + y^2 + z^2 \right)^{\frac{3}{2}}}
	\end{array} \right) \\
&=&	\left( \begin{array}{c} 
		\partial_y \left( \frac{z}{\left( x^2 + y^2 + z^2 \right)^{\frac{3}{2}}} \right)
			- \partial_z \left(\frac{y}{\left( x^2 + y^2 + z^2 \right)^{\frac{3}{2}}}\right)\\
		\partial_z \left(\frac{x}{\left( x^2 + y^2 + z^2 \right)^{\frac{3}{2}}}\right) 
			- \partial_x \left(\frac{z}{\left( x^2 + y^2 + z^2 \right)^{\frac{3}{2}}}\right)\\
		\partial_x \left(\frac{y}{\left( x^2 + y^2 + z^2 \right)^{\frac{3}{2}}}\right) 
			- \partial_y \left(\frac{x}{\left( x^2 + y^2 + z^2 \right)^{\frac{3}{2}}}\right)
	\end{array} \right) \\	
&=&	\left( \begin{array}{c} 
		\frac{- 3 z y}{ \left( x^2 + y^2 + z^2 \right)^{\frac{5}{2}}} 
			- \frac{- 3 y z}{ \left( x^2 + y^2 + z^2 \right)^{\frac{5}{2}}} \\
		\frac{- 3 x z}{ \left( x^2 + y^2 + z^2 \right)^{\frac{5}{2}}} 
			- \frac{- 3 z x}{ \left( x^2 + y^2 + z^2 \right)^{\frac{5}{2}}} \\
		\frac{- 3 y x}{ \left( x^2 + y^2 + z^2 \right)^{\frac{5}{2}}} 
			- \frac{- 3 x y}{ \left( x^2 + y^2 + z^2 \right)^{\frac{5}{2}}} \\
	\end{array} \right) \\	
&=&	0
\end{eqnarray*}

\end{document}