Two particles are fixed to an x axis: particle 1 of charge q1 = 2.91 × 10*8 C at x = 23.0 cm and particle 2 of charge 92 = -5.29q, at x = 70.0 cm. At what coordinate on the x axis is the electric field produced by the particles equal to zero? Number i Units cm
Two particles are fixed to an x axis: particle 1 of charge q1 = 2.91 × 10*8 C at x = 23.0 cm and particle 2 of charge 92 = -5.29q, at x = 70.0 cm. At what coordinate on the x axis is the electric field produced by the particles equal to zero? Number i Units cm
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![### Example Problem in Electromagnetism
#### Electric Field Zero Point Calculation
Two particles are fixed on an x-axis:
- **Particle 1**: Charge \( q_1 = 2.91 \times 10^{-8} \) C, located at \( x = 23.0 \) cm.
- **Particle 2**: Charge \( q_2 = -5.29q_1 \), located at \( x = 70.0 \) cm.
#### Problem Statement
At what coordinate on the x-axis is the electric field produced by these particles equal to zero?
**Enter your answer:**
- **Number:** [ ]
- **Units:** [cm]
---
#### Explanation
For an observer to understand how to determine the point at which the electric field produced by the charges is zero, we follow the steps outlined below:
1. **Understanding Electric Fields**:
- The electric field (\(E\)) produced by a point charge (\(q\)) at a distance \( r \) is given by Coulomb's law:
\[
E = \frac{kq}{r^2}
\]
where \( k \) is the Coulomb constant (\( k \approx 8.99 \times 10^9 \, \text{N} \cdot \text{m}^2 \cdot \text{C}^{-2} \)).
2. **Setting up the Equation**:
- Let \( x \) be the point on the x-axis where the electric field is zero.
- The distance from particle 1 to \( x \) is \( x - 23.0 \) cm.
- The distance from particle 2 to \( x \) is \( 70.0 - x \) cm.
- The electric field produced by particle 1 at point \( x \) is:
\[
E_1 = \frac{kq_1}{(x - 23.0)^2}
\]
- The electric field produced by particle 2 at point \( x \) is:
\[
E_2 = \frac{kq_2}{(70.0 - x)^2}
\]
3. **Finding the Zero Point**:
- For the electric fields to cancel out, \( E_1 = |E_2| \):](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe462800b-ac16-4590-bafb-82d68c005ec5%2F075583bf-b055-48ca-a76f-e96455e830ca%2Fvnd1a5_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Example Problem in Electromagnetism
#### Electric Field Zero Point Calculation
Two particles are fixed on an x-axis:
- **Particle 1**: Charge \( q_1 = 2.91 \times 10^{-8} \) C, located at \( x = 23.0 \) cm.
- **Particle 2**: Charge \( q_2 = -5.29q_1 \), located at \( x = 70.0 \) cm.
#### Problem Statement
At what coordinate on the x-axis is the electric field produced by these particles equal to zero?
**Enter your answer:**
- **Number:** [ ]
- **Units:** [cm]
---
#### Explanation
For an observer to understand how to determine the point at which the electric field produced by the charges is zero, we follow the steps outlined below:
1. **Understanding Electric Fields**:
- The electric field (\(E\)) produced by a point charge (\(q\)) at a distance \( r \) is given by Coulomb's law:
\[
E = \frac{kq}{r^2}
\]
where \( k \) is the Coulomb constant (\( k \approx 8.99 \times 10^9 \, \text{N} \cdot \text{m}^2 \cdot \text{C}^{-2} \)).
2. **Setting up the Equation**:
- Let \( x \) be the point on the x-axis where the electric field is zero.
- The distance from particle 1 to \( x \) is \( x - 23.0 \) cm.
- The distance from particle 2 to \( x \) is \( 70.0 - x \) cm.
- The electric field produced by particle 1 at point \( x \) is:
\[
E_1 = \frac{kq_1}{(x - 23.0)^2}
\]
- The electric field produced by particle 2 at point \( x \) is:
\[
E_2 = \frac{kq_2}{(70.0 - x)^2}
\]
3. **Finding the Zero Point**:
- For the electric fields to cancel out, \( E_1 = |E_2| \):
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