## Thomas' Calculus 13th Edition

$0$
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, $=0$