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### Electrostatic Force Calculation for Multiple Charges on an Axis

In this exercise, we have two charges:
- A charge of +1 μC is placed at the origin (x = 0).
- A charge of +13 μC is placed at x = +1 m.

We are tasked with determining the magnitude and direction of the net force on a -8 nC charge at various positions on the xy-plane.

#### a) **Halfway Between the Two Charges:**
- **Position:** Midpoint between 0 m and +1 m, which is x = 0.5 m.
- **Required:** 
  - Magnitude of force in mN 
  - Direction of force (choose from provided options)

#### b) **On the x-axis at \(x = -0.5\) m:**
- **Position:** x = -0.5 m on the x-axis.
- **Required:** 
  - Magnitude of force in mN 
  - Direction of force (choose from provided options)

#### c) **At the Coordinate \((x, y) = (1 m, 0.5 m)\):**
- Located half a meter above the +13 μC charge in a direction perpendicular to the line joining the two fixed charges.
- **Hint for (c):** 
  - The direction is given as degrees below the -x axis.
- **Required:** 
  - Magnitude of force in mN 
  - Direction in degrees below the -x axis

This problem involves the application of Coulomb’s law to calculate the forces due to each charge at the specified positions. Ensure you use vector addition to find the net force.

---

For detailed calculations and steps, students are encouraged to revisit the principles of Coulomb’s law, vector addition, and trigonometry. Analyzing each position involves calculating the force exerted by each charge on the -8 nC charge and then combining these forces vectorially to determine both the magnitude and direction of the net force.
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Transcribed Image Text:### Electrostatic Force Calculation for Multiple Charges on an Axis In this exercise, we have two charges: - A charge of +1 μC is placed at the origin (x = 0). - A charge of +13 μC is placed at x = +1 m. We are tasked with determining the magnitude and direction of the net force on a -8 nC charge at various positions on the xy-plane. #### a) **Halfway Between the Two Charges:** - **Position:** Midpoint between 0 m and +1 m, which is x = 0.5 m. - **Required:** - Magnitude of force in mN - Direction of force (choose from provided options) #### b) **On the x-axis at \(x = -0.5\) m:** - **Position:** x = -0.5 m on the x-axis. - **Required:** - Magnitude of force in mN - Direction of force (choose from provided options) #### c) **At the Coordinate \((x, y) = (1 m, 0.5 m)\):** - Located half a meter above the +13 μC charge in a direction perpendicular to the line joining the two fixed charges. - **Hint for (c):** - The direction is given as degrees below the -x axis. - **Required:** - Magnitude of force in mN - Direction in degrees below the -x axis This problem involves the application of Coulomb’s law to calculate the forces due to each charge at the specified positions. Ensure you use vector addition to find the net force. --- For detailed calculations and steps, students are encouraged to revisit the principles of Coulomb’s law, vector addition, and trigonometry. Analyzing each position involves calculating the force exerted by each charge on the -8 nC charge and then combining these forces vectorially to determine both the magnitude and direction of the net force.
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