Answer
$$0$$
Work Step by Step
Since, $n=\dfrac{2xi+2yj+2z k}{2 \sqrt {x^2+y^2+z^2}}=\dfrac{x}{a} i+\dfrac{y}{a} j + \dfrac{z}{a} k$
Thus, $F \cdot n=\dfrac{-x}{a}+\dfrac{-x}{a} \\ d \theta=\dfrac{2a}{2z} \ dA$
Solve the flux of $F$.
$$\iint_{S} F \cdot n \ d \theta =\iint_{R} (\dfrac{-x}{a}+\dfrac{-x}{a}) \times (\dfrac{2a}{2z}) \ dA \\=\iint_{R} (0) \times (\dfrac{a}{z}) \ dA \\=\iint_{R} (0) \ dA \\=0$$
