GRE Physics GR 1777 Problem 037 Solution

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}$

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