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An electric field is uniform, and in the positive x direction for positive x, and uniform with the same magnitude but in the negative x direction for negative x. It is given that $E = 200 \hat i N/C$ for $x > 0$ and $E = –200 \hat i N/C$ for $x < 0$. A right circular cylinder of length $20\; cm$ and radius $5\; cm$ has its centre at the origin and its axis along the x-axis so that one face is at $x = +10 cm$ and the other is at $x = –10 cm$ (see the figure given below). What is the net charge inside the cylinder?

$q= \in_0 \phi$
$\quad= 3.14 \times 8.854 \times 10^{-12}$
$\quad =2.78 \times 10^{-11}$