Find the electric flux through the surface in Figure below*1 point-6 C/εo-3 C/εo+3 C/εo+6 C/εo

To determine the electric flux through a given surface due to electric charges, we can apply Gauss's law, which states that the electric flux $\Phi_E$ through a closed surface is equal to the charge enclosed $Q_{\text{enc}}$ divided by the electric constant $\epsilon_0$:

$\Phi_E = \frac{Q_{\text{enc}}}{\epsilon_0}$

Step 1: Break Down the Problem

Identify the enclosed charge by reviewing the charges listed:

1. $-6 \, C$
2. $-3 \, C$
3. $3 \, C$
4. $6 \, C$

Step 2: Relevant Concepts

According to Gauss's law, we need to add all the enclosed charges to find $Q_{\text{enc}}$:

$Q_{\text{enc}} = Q_1 + Q_2 + Q_3 + Q_4$

Step 3: Analysis and Calculation

Calculate the total enclosed charge:

$Q_{\text{enc}} = (-6 \, C) + (-3 \, C) + (3 \, C) + (6 \, C)$

Calculating step-wise:

1. $-6 + -3 = -9 \, C$
2. $-9 + 3 = -6 \, C$
3. $-6 + 6 = 0 \, C$

Thus:

$Q_{\text{enc}} = 0 \, C$

Step 4: Verify and Summarize

Plugging the total enclosed charge back into Gauss's law:

$\Phi_E = \frac{Q_{\text{enc}}}{\epsilon_0} = \frac{0}{\epsilon_0} = 0$

Final Answer

The electric flux through the surface is:

$\Phi_E = 0 \, \text{N m}^2/\text{C}$