Part (a)  Write an expression for the electric flux Φ1 through S1.  Φ1 = ______ Part (b)  Write an expression for the electric flux Φ2 through S2.  Φ2 = ______ Part (c)  Write an expression for the electric flux Φ3 through S3.  Φ3 = ______ Part (d)  Write an expression for the electric flux Φ5 through S5.  Φ5 = ______

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Chapter1: Units, Trigonometry. And Vectors
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Part (a)  Write an expression for the electric flux Φ1 through S1. 

Φ1 = ______

Part (b)  Write an expression for the electric flux Φ2 through S2. 

Φ2 = ______

Part (c)  Write an expression for the electric flux Φ3 through S3. 

Φ3 = ______

Part (d)  Write an expression for the electric flux Φ5 through S5. 

Φ5 = ______

**Problem 13:**
Three electric charges, \( Q_1 = -2 \ \text{C} \), \( Q_2 = 4 \ \text{C} \), and \( Q_3 = -8 \ \text{C} \), are presented in the figure, as well as 5 surfaces, \( S_1 \) through \( S_5 \).

*Graph/Diagram Explanation:*
The figure accompanying the problem displays three points, each representing the charges \( Q_1 \), \( Q_2 \), and \( Q_3 \). These points are enclosed by five different surfaces, labeled \( S_1 \), \( S_2 \), \( S_3 \), \( S_4 \), and \( S_5 \):

- **\( Q_1 \)** is positioned towards the lower right and is colored red, located at the center of surface \( S_4 \) (green ellipse).
- **\( Q_2 \)** is positioned towards the lower left and is also colored red, located at the center of surface \( S_3 \) (gray ellipse).
- **\( Q_3 \)** is positioned towards the upper center and is colored red, located at the center of surface \( S_2 \) (black ellipse).

Surfaces \( S_1 \) (purple ellipse) and \( S_5 \) (orange ellipse) are larger and encompass the regions that include the charges:

- **\( S_1 \)** is the largest surface, covering the entire area containing all three charges \( Q_1 \), \( Q_2 \), and \( Q_3 \).
- **\( S_5 \)** is an intermediate surface that also encompasses all three charges. 

This representation visually contextualizes the placement of electric charges and their surrounding surfaces within the problem framework.
Transcribed Image Text:**Problem 13:** Three electric charges, \( Q_1 = -2 \ \text{C} \), \( Q_2 = 4 \ \text{C} \), and \( Q_3 = -8 \ \text{C} \), are presented in the figure, as well as 5 surfaces, \( S_1 \) through \( S_5 \). *Graph/Diagram Explanation:* The figure accompanying the problem displays three points, each representing the charges \( Q_1 \), \( Q_2 \), and \( Q_3 \). These points are enclosed by five different surfaces, labeled \( S_1 \), \( S_2 \), \( S_3 \), \( S_4 \), and \( S_5 \): - **\( Q_1 \)** is positioned towards the lower right and is colored red, located at the center of surface \( S_4 \) (green ellipse). - **\( Q_2 \)** is positioned towards the lower left and is also colored red, located at the center of surface \( S_3 \) (gray ellipse). - **\( Q_3 \)** is positioned towards the upper center and is colored red, located at the center of surface \( S_2 \) (black ellipse). Surfaces \( S_1 \) (purple ellipse) and \( S_5 \) (orange ellipse) are larger and encompass the regions that include the charges: - **\( S_1 \)** is the largest surface, covering the entire area containing all three charges \( Q_1 \), \( Q_2 \), and \( Q_3 \). - **\( S_5 \)** is an intermediate surface that also encompasses all three charges. This representation visually contextualizes the placement of electric charges and their surrounding surfaces within the problem framework.
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