The figure shows a closed cylinder of length $0.50\ \text{m}$ and radius $0.10\ \text{m}$, with its axis along the $x$-axis and its left face at $x = 0$. In this region the electric field points along $+x$, and its magnitude is $E = E_0 + bx$, where $E_0 = 600\ \text{N C}^{-1}$ and $b = 400\ \text{N C}^{-1}\text{m}^{-1}$. Take $\varepsilon_0 = 8.85 \times 10^{-12}\ \text{C}^2\text{N}^{-1}\text{m}^{-2}$. What is the net charge inside the cylinder?

Fig. 1: A closed cylinder of length 0.50 m and radius 0.10 m lying on its side, its axis along the x-axis. Its left face is at x equal to zero. Horizontal arrows above and below the cylinder point in the positive x direction and grow steadily longer from left to right, showing a field along x that increases with x. The x-axis is drawn below the cylinder with the origin at the left face.