https://file.aiquickdraw.com/mathbot/file/1729170806703dfqesmx5.jpg

The image shows a diagram of a Gaussian surface, along with electric field lines passing through it, and the associated question is in Persian. Here's a translation of the question:

**Translation**:
1. The figure shows a Gaussian surface and the electric field lines passing through it. What can you say about the sign of the enclosed electric charge inside the surface?

### Answer:
According to **Gauss's Law** in electrostatics:

\[
\Phi_E = \frac{Q_{\text{enc}}}{\epsilon_0}
\]

Where:
- \( \Phi_E \) is the electric flux through the surface,
- \( Q_{\text{enc}} \) is the charge enclosed by the Gaussian surface,
- \( \epsilon_0 \) is the permittivity of free space.

In this diagram, the electric field lines are pointing inward, which implies that the flux is negative. Since the flux through the surface is proportional to the enclosed charge, this means the charge inside the surface is **negative**.

So, the enclosed charge within the Gaussian surface is negative based on the direction of the electric field lines.

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Do you need more details or further clarifications on this?

Here are some relative questions to deepen understanding:
1. What is the relationship between electric flux and enclosed charge for non-symmetric surfaces?
2. How would the flux change if the charge inside were positive?
3. Can you describe how Gauss's Law applies to spherical and cylindrical symmetries?
4. What role does the permittivity of free space (\( \epsilon_0 \)) play in these calculations?
5. How would the electric field lines differ if the enclosed charge was neutral?

**Tip**: Always check the direction of electric field lines to determine the nature (positive or negative) of the enclosed charge.

شکل مقابل یک سطح گوسی و خطوط میدان الکتریکی گذرنده از آن را نشان می‌دهد. در مورد علامت بار الکتریکی محصور در سطح چه می‌توانید بگویید؟

Learn how to determine the sign of the enclosed electric charge in a Gaussian surface by analyzing the direction of electric field lines. This electrostatics problem explores key concepts such as electric flux and Gauss's law, suitable for students in Grades 10-12.

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