An electric field \( \vec{E} \) is given by:
\[
\vec{E} =
\begin{cases}
+100\, \hat{i} \dfrac{\text{N}}{\text{C}} & \text{for } x>0 \\
-100\, \hat{i} \dfrac{\text{N}}{\text{C}} & \text{for } x<0
\end{cases}
\]
A right circular cylinder of length \( 10\, \text{cm} \) and radius \( 2\, \text{cm} \), is placed such that its axis coincides with the x-axis and its two faces are at \( x = -5\, \text{cm} \) and \( x = 5\, \text{cm} \). Calculate:
(a) the net outward flux through the cylinder, and
(b) the net charge inside the cylinder.