Three point charges are arranged as shown in the figure below. Find the magnitude and direction of the electric force on the particle q = 5.06 nC at the origin. (Let 12 = 0.275 m.) 9.33 Use Coulomb's law to find the force that each charge exerts on the charge at the origin and combine the forces to find the net force. N 255.2 magnitude direction O counterclockwise from the +x axis 6.00 nC 0.100 m

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Chapter19: Electric Forces And Electric Fields
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## Educational Exercise: Electric Force on a Point Charge

### Problem Statement:
Three point charges are arranged as shown in the figure below. Find the magnitude and direction of the electric force on the particle \( q = 5.06 \, \text{nC} \) at the origin. (Let \( r_{12} = 0.275 \, \text{m} \)).

### Figure Description:
In the provided figure:
- A coordinate system is depicted with the origin at position \( q \).
- Three point charges are arranged as follows:
  - A charge \( q \) positioned at the origin.
  - A charge of \( -3.00 \, \text{nC} \) located 0.100 meters directly below the origin (on the negative y-axis).
  - A charge of \( 6.00 \, \text{nC} \) positioned 0.275 meters to the right of the origin (on the positive x-axis).

\[  r_{12}  = 0.275 \, \text{m.} \]

\[  q  =  5.06 \, \text{nC.} \]

### Incorrect Attempt:
- **Magnitude:** 
  - Answer provided: 9.33 (This is marked incorrect).
  - Feedback on Magnitude: "Use Coulomb's law to find the force that each charge exerts on the charge at the origin and combine the forces to find the net force." The unit of force should be Newtons (N).
  
- **Direction:** 
  - Answer provided: 255.2° (This is marked correct).
  - Feedback on Direction: "Counterclockwise from the +x axis."

### Instructions:
1. **Use Coulomb’s Law:**
   \[
   F = k_e \frac{|q_1 q_2|}{r^2}
   \]
   where \( k_e \) is the Coulomb's constant (\( 8.988 \times 10^9 \, \text{Nm}^2/\text{C}^2 \)).

2. **Find the Forces:**
   - Calculate the force exerted by each charge on the charge at the origin.
   - Sum the vector components of these forces to find the net force.

3. **Combine Forces:**
   - Determine the x and y components.
   - Use
Transcribed Image Text:## Educational Exercise: Electric Force on a Point Charge ### Problem Statement: Three point charges are arranged as shown in the figure below. Find the magnitude and direction of the electric force on the particle \( q = 5.06 \, \text{nC} \) at the origin. (Let \( r_{12} = 0.275 \, \text{m} \)). ### Figure Description: In the provided figure: - A coordinate system is depicted with the origin at position \( q \). - Three point charges are arranged as follows: - A charge \( q \) positioned at the origin. - A charge of \( -3.00 \, \text{nC} \) located 0.100 meters directly below the origin (on the negative y-axis). - A charge of \( 6.00 \, \text{nC} \) positioned 0.275 meters to the right of the origin (on the positive x-axis). \[ r_{12} = 0.275 \, \text{m.} \] \[ q = 5.06 \, \text{nC.} \] ### Incorrect Attempt: - **Magnitude:** - Answer provided: 9.33 (This is marked incorrect). - Feedback on Magnitude: "Use Coulomb's law to find the force that each charge exerts on the charge at the origin and combine the forces to find the net force." The unit of force should be Newtons (N). - **Direction:** - Answer provided: 255.2° (This is marked correct). - Feedback on Direction: "Counterclockwise from the +x axis." ### Instructions: 1. **Use Coulomb’s Law:** \[ F = k_e \frac{|q_1 q_2|}{r^2} \] where \( k_e \) is the Coulomb's constant (\( 8.988 \times 10^9 \, \text{Nm}^2/\text{C}^2 \)). 2. **Find the Forces:** - Calculate the force exerted by each charge on the charge at the origin. - Sum the vector components of these forces to find the net force. 3. **Combine Forces:** - Determine the x and y components. - Use
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