Cylinder E-Field (Part 2)

A uniform cylinder has an area charge density of $1$ . It is parametrized as follows:

$x^2 + y^2 = 1 \\ -1 \leq z \leq 1$

If the magnitude of the electric field at test point $(T_x,T_y,T_z) = \Big ( 0,0,1 \Big)$ is $E_T$ , and the electric permittivity of free space is $\epsilon_0$ , determine the value of $\epsilon_0 \, E_T$ .

Note: The symmetry of this problem makes it easier than Part $1$