$\text { Let } \mathbf { E } = x \mathbf { i } + y \mathbf { j } + 2 z \mathbf { k }$

Multiple Choice

$\text { Let } \mathbf { E } = x \mathbf { i } + y \mathbf { j } + 2 z \mathbf { k }$ be an electrostatic field. Use Gauss's Law to find the total charge enclosed by the closed surface consisting of the hemisphere $z = \sqrt { 1 - x ^ { 2 } - y ^ { 2 } }$ and its circular base in the $x y$ -plane.

A) $10 \pi$
B) $\frac { 8 } { \pi }$
C) $\frac { 8 \pi } { 3 }$
D) $12 \pi$
E) $\frac { 10 \pi } { 7 }$