Given an infinite volume charge $($extended to infinity in the $\backslash ($ x$-$y $\backslash )$ direction$)$ with a uniform positive volume charge density $\backslash (\backslash$rho $\backslash )($i$.$e$.$ the amount of positive charge per unit volume is $\backslash (\backslash$rho $\backslash ))$ and thickness $\backslash (2$ d $\backslash )$ in the $\backslash ($ z $\backslash )$ direction bisected by the $\backslash ($ x$-$y $\backslash )$ plane.

$($a$)$ By considering Gauss' law, find the magnitude of the electric field $\backslash (|\backslash$vec$\{$E$\}|\backslash )$ as a function of $\backslash ($ z $\backslash ).$ When applying Gauss' law, either draw or describe clearly the Gaussian surface. $(6$ pts$.)$

$($b$)$ Make a plot of the $\backslash ($ z $\backslash )$ component of the electric field $\backslash ($ E$\_\{$z$\}\backslash )$ as a function of $\backslash ($ z $.(4\backslash )$ pts$.)$