15. (II) An electric field greater than about 3 × 10° V/m causes air to break down (electrons are removed from the atoms and then recombine, emitting light). See Section 17-2 and Table 17-3. If you shuffle along a carpet and then reach for a doorknob, a spark flies across a gap you estimate to be 1 mm between your finger and the doorknob. Estimate the voltage between your finger and the doorknob. Why is no harm done?
15. (II) An electric field greater than about 3 × 10° V/m causes air to break down (electrons are removed from the atoms and then recombine, emitting light). See Section 17-2 and Table 17-3. If you shuffle along a carpet and then reach for a doorknob, a spark flies across a gap you estimate to be 1 mm between your finger and the doorknob. Estimate the voltage between your finger and the doorknob. Why is no harm done?
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Chapter1: Units, Trigonometry. And Vectors
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Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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![### Problem: Estimate the Voltage Between Finger and Doorknob
#### Problem Statement:
**(II)** An electric field greater than about \( 3 \times 10^6 \) V/m causes air to break down (electrons are removed from the atoms and then recombine, emitting light). See Section 17-2 and Table 17-3. If you shuffle along a carpet and then reach for a doorknob, a spark flies across a gap you estimate to be 1 mm between your finger and the doorknob. Estimate the voltage between your finger and the doorknob. Why is no harm done?
#### Solution Strategy:
1. **Calculate the voltage using the electric field and distance**:
- Given:
- Electric field \( E = 3 \times 10^6 \) V/m
- Distance \( d = 1\, \text{mm} = 0.001\, \text{m} \)
- Voltage \( V = E \times d \)
2. **Compute the Voltage**:
- Substitute the values into the formula:
\[
V = (3 \times 10^6\, \text{V/m}) \times (0.001\, \text{m}) = 3000\, \text{V}
\]
#### Explanation:
- **Why is no harm done?**
- The spark you experience when touching the doorknob is a discharge of static electricity. Although the voltage can be quite high (estimated at 3000 V), the energy involved is very small due to the extremely small amount of charge transferred. This results in a brief and harmless shock.
### Additional Context:
- **Breakdown of Air**: When the electric field exceeds \( 3 \times 10^6 \) V/m, it ionizes the air, causing a spark.
- **Static Electricity**: Commonly experienced after walking on synthetic carpets, this phenomenon demonstrates basic principles of electrostatics.
#### Note for Educators:
- Ensure students understand the relationship between electric field, voltage, and distance.
- Discuss the concept of dielectric breakdown of air in related topics for better grasp.
### References:
- **Section 17-2** and **Table 17-3** of the referenced textbook for detailed theoretical background.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8c08191f-4610-4f17-af7c-727bd3de0813%2Fb034bf3b-efc5-4523-b963-aa3233eb2a7a%2Fd0b9dewi_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem: Estimate the Voltage Between Finger and Doorknob
#### Problem Statement:
**(II)** An electric field greater than about \( 3 \times 10^6 \) V/m causes air to break down (electrons are removed from the atoms and then recombine, emitting light). See Section 17-2 and Table 17-3. If you shuffle along a carpet and then reach for a doorknob, a spark flies across a gap you estimate to be 1 mm between your finger and the doorknob. Estimate the voltage between your finger and the doorknob. Why is no harm done?
#### Solution Strategy:
1. **Calculate the voltage using the electric field and distance**:
- Given:
- Electric field \( E = 3 \times 10^6 \) V/m
- Distance \( d = 1\, \text{mm} = 0.001\, \text{m} \)
- Voltage \( V = E \times d \)
2. **Compute the Voltage**:
- Substitute the values into the formula:
\[
V = (3 \times 10^6\, \text{V/m}) \times (0.001\, \text{m}) = 3000\, \text{V}
\]
#### Explanation:
- **Why is no harm done?**
- The spark you experience when touching the doorknob is a discharge of static electricity. Although the voltage can be quite high (estimated at 3000 V), the energy involved is very small due to the extremely small amount of charge transferred. This results in a brief and harmless shock.
### Additional Context:
- **Breakdown of Air**: When the electric field exceeds \( 3 \times 10^6 \) V/m, it ionizes the air, causing a spark.
- **Static Electricity**: Commonly experienced after walking on synthetic carpets, this phenomenon demonstrates basic principles of electrostatics.
#### Note for Educators:
- Ensure students understand the relationship between electric field, voltage, and distance.
- Discuss the concept of dielectric breakdown of air in related topics for better grasp.
### References:
- **Section 17-2** and **Table 17-3** of the referenced textbook for detailed theoretical background.
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