$(20$ points$)$ Consider two infinite parallel slabs having equal thickness $W$ and equal charge densities. Slab $1$ is parallel to the $xy-$plane and extends from $z=-2W$ to $z=-W$ while slab $2$ extends from $z=W$ to $z=2W.$ Both slabs have a negative uniform charge density $-{}_0\frac{C}{m^3}.$ The charge density is zero everywhere else.

$($a$)(10$ points$)$ Determine the electric field component $E_z$ in terms of ${}_0$ over the region $-3W.$