Answer
$0$
Work Step by Step
We have: $n=\dfrac{2xi+2yj+2z k}{2 \sqrt {x^2+y^2+z^2}}=\dfrac{xi+yj+z k}{a}$
Thus, $F \cdot n=\dfrac{-x}{a}+\dfrac{-x}{a}$ and $d \theta=\dfrac{2a}{2z} \ dA$
We set up the integral and solve the flux of $F$ as follows:
$\iint_{S} F \cdot n \ d \theta =\iint_{R} (\dfrac{-x}{a}+\dfrac{-x}{a}) (\dfrac{2a}{2z}) \ dA$
or, $=\iint_{R} (0) (\dfrac{a}{z}) \ dA$
or, $=\iint_{R} (0) \ dA$
or, $=0$
