11. (II) Particles of charge +65, +48, and -95 μC are placed in a line (Fig. 16-52). The center one is 0.35 m from each of the others. Calculate the net force on each charge due to the other two. +65 μC +48 μC -95 μC 0.35 m 0.35 m FIGURE 16-52 Problem 11.
11. (II) Particles of charge +65, +48, and -95 μC are placed in a line (Fig. 16-52). The center one is 0.35 m from each of the others. Calculate the net force on each charge due to the other two. +65 μC +48 μC -95 μC 0.35 m 0.35 m FIGURE 16-52 Problem 11.
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![### Problem 11: Calculating Net Forces on Charged Particles
#### Description
Particles with charges of \( +65 \, \mu\text{C} \), \( +48 \, \mu\text{C} \), and \( -95 \, \mu\text{C} \) are aligned in a straight line, with the distances between adjacent charges being 0.35 meters (Fig. 16–52). The objective is to compute the net force exerted on each charge by the other two charges.
#### Diagram Explanation
- **Figure 16-52** displays three charged particles in a linear arrangement:
- A particle with charge \( +65 \, \mu\text{C} \) is positioned on the left.
- Next to it, to the right, is a particle with charge \( +48 \, \mu\text{C} \). The distance between these two particles is 0.35 meters.
- The third particle, with charge \( -95 \, \mu\text{C} \), is placed to the right of the \( +48 \, \mu\text{C} \) charge, at another 0.35-meter distance.
The visual representation helps in understanding the physical setup for calculating the forces.
#### Objective
Calculate the net force on each of the three charges as a result of the other two charges.
### Solutions Steps:
1. **Identify Forces Acting on Each Charge**:
- Use Coulomb’s Law, which states that the force \( F \) between two point charges \( q_1 \) and \( q_2 \) separated by a distance \( r \) is given by:
\[
F = k_e \frac{|q_1 q_2|}{r^2}
\]
where \( k_e \) is Coulomb's constant (\( 8.99 \times 10^9 \frac{\text{Nm}^2}{\text{C}^2} \)).
2. **Calculate Force Between Pair of Charges**:
- Compute the individual forces for each pair of charges taking both magnitude and direction (attraction or repulsion) into account.
3. **Determine Net Force on Each Charge**:
- Sum the forces vectorially to get the net force on each charge from the other two charges.
4. **Account for Directions**:](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcaea1532-9bca-456b-84fc-9594bcc8dc11%2Fdc1cbfa7-01c4-4433-987d-2e84d1cd34a6%2F2mi9q8_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem 11: Calculating Net Forces on Charged Particles
#### Description
Particles with charges of \( +65 \, \mu\text{C} \), \( +48 \, \mu\text{C} \), and \( -95 \, \mu\text{C} \) are aligned in a straight line, with the distances between adjacent charges being 0.35 meters (Fig. 16–52). The objective is to compute the net force exerted on each charge by the other two charges.
#### Diagram Explanation
- **Figure 16-52** displays three charged particles in a linear arrangement:
- A particle with charge \( +65 \, \mu\text{C} \) is positioned on the left.
- Next to it, to the right, is a particle with charge \( +48 \, \mu\text{C} \). The distance between these two particles is 0.35 meters.
- The third particle, with charge \( -95 \, \mu\text{C} \), is placed to the right of the \( +48 \, \mu\text{C} \) charge, at another 0.35-meter distance.
The visual representation helps in understanding the physical setup for calculating the forces.
#### Objective
Calculate the net force on each of the three charges as a result of the other two charges.
### Solutions Steps:
1. **Identify Forces Acting on Each Charge**:
- Use Coulomb’s Law, which states that the force \( F \) between two point charges \( q_1 \) and \( q_2 \) separated by a distance \( r \) is given by:
\[
F = k_e \frac{|q_1 q_2|}{r^2}
\]
where \( k_e \) is Coulomb's constant (\( 8.99 \times 10^9 \frac{\text{Nm}^2}{\text{C}^2} \)).
2. **Calculate Force Between Pair of Charges**:
- Compute the individual forces for each pair of charges taking both magnitude and direction (attraction or repulsion) into account.
3. **Determine Net Force on Each Charge**:
- Sum the forces vectorially to get the net force on each charge from the other two charges.
4. **Account for Directions**:
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