# GRE Physics GR 1777 Problem Solution¶

## 037. Electrodynamics (Gauss's Law)¶

### 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

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

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