### You should know¶

#### Gauss's Law¶

$$ \large \Phi_E = \oint_S \vec{E} \cdot d \vec{a} = \frac{Q_\text{enc}}{\epsilon_0} $$where

$\Phi_E$: electric flux through a closed surface $S$ enclosing any volume $V$

$Q_\text{enc}$: total charge enclosed within $V$

$\epsilon_0$: electric constant

### Solution¶

Since the half of the total electric flux passes through the $yz$-plane, the total electric flux passes through the $yz$-plane is

$$ \large \Phi_\text{E,yz} = \frac{1}{2} \Phi_\text{E,tot} = \frac{Q}{2\epsilon_0} $$### Answer¶

(D) $ \large \frac{Q}{2\epsilon_0}$