$(24$ pts$)$ Given the two charged plates shown below, determine the expression for the electric field intensity anywhere in the $xy$ plane $($i$.$e$.,$ assume $z=0).$ Also, calculate the electric field at the points specified below and sketch the vector field for $E.$ Assume the right plate $(+y$ half plane$)$ has surface charge density ${}_s^{+}=2\frac{nC}{m^2}$ and the left plate $(-y$ half plane$)$ has surface charge density ${}_s^{-}=-2\frac{nC}{m^2}.$

Calculate the electric field intensity at the following points $($all dimensions in mm $)$:

$($a$)x=8,y=5,z=0$

$($b$)x=8,y=0,z=0$

$($c$)x=8,y=-5,z=0$

$($d$)x=0,y=5,z=0$

$($e$)x=0,y=0,z=0$

$($f$)x=0,y=-5,z=0$

$($g$)x=-8,y=5,z=0$

$($h$)x=-8,y=0,z=0$

$($i$)x=-8,y=-5,z=0$