2. A belt is transferring charge to the high-potential inner shell of a Van de Graaff accelerator at the rate of 2.83 x 10-C/s. If the width of the belt carrying the charge is 50cm and the belt travels at a speed of 30 m/s[See Figure 2). (a) The statement of the problem implies that current is I = 2.83 x 10-3C/s. (True,False) (b) Assuming (a) is correct then the surface charge density on the belt follows as K 2.83 x 10-3C/s = 1.89 x 10-4C/m² (True, False) %3D %3D (0.5m)(30m/s)
2. A belt is transferring charge to the high-potential inner shell of a Van de Graaff accelerator at the rate of 2.83 x 10-C/s. If the width of the belt carrying the charge is 50cm and the belt travels at a speed of 30 m/s[See Figure 2). (a) The statement of the problem implies that current is I = 2.83 x 10-3C/s. (True,False) (b) Assuming (a) is correct then the surface charge density on the belt follows as K 2.83 x 10-3C/s = 1.89 x 10-4C/m² (True, False) %3D %3D (0.5m)(30m/s)
Transcribed Image Text:**Figure 2 Explanation:**
The diagram illustrates a configuration involving wires and a sheet of charge. The notation \( N i = I \) indicates a relationship between the number of wires (\( N \)), current per wire (\( i \)), and total current (\( I \)).
- **Wires Carrying Current:** Represented with circular symbols having dots, signifying current flowing out of the page.
- **Sheet of Charge:** Represented as a vertical rectangle moving downward, characterized by its width \( w \) and velocity \( v \).
The equation \( N i = I = K w \) and \( K = \sigma v \) denotes:
- \( K \) as the surface current density with the unit of A/m (amperes per meter).
- \( \sigma \) as the surface charge density.
**Problem Context:**
1. **Charge Transfer:** A belt transfers charge to a Van de Graaff accelerator's high-potential inner shell at \( 2.83 \times 10^{-3} \, \text{C/s} \).
2. **Belt Specifications:** Width of the belt is 50 cm, and it travels at 30 m/s.
(a) **Current Verification:**
- The problem states the current \( I \) as \( 2.83 \times 10^{-3} \, \text{C/s} \). Evaluation needed: True, False.
(b) **Surface Charge Density Calculation:**
- Expression:
\[
\sigma = \frac{K}{v} = \frac{L}{w \, v} = \frac{I}{w v} = \frac{2.83 \times 10^{-3} \, \text{C/s}}{(0.5 \, \text{m})(30 \, \text{m/s})} = 1.89 \times 10^{-4} \, \text{C/m}^2
\]
- Evaluation needed: True, False.
This information provides an in-depth understanding of the charge dynamics and mathematical verification for a belt-driven charge transfer system as seen in devices like Van de Graaff accelerators.
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![**Figure 2 Explanation:**
The diagram illustrates a configuration involving wires and a sheet of charge. The notation \( N i = I \) indicates a relationship between the number of wires (\( N \)), current per wire (\( i \)), and total current (\( I \)).
- **Wires Carrying Current:** Represented with circular symbols having dots, signifying current flowing out of the page.
- **Sheet of Charge:** Represented as a vertical rectangle moving downward, characterized by its width \( w \) and velocity \( v \).
The equation \( N i = I = K w \) and \( K = \sigma v \) denotes:
- \( K \) as the surface current density with the unit of A/m (amperes per meter).
- \( \sigma \) as the surface charge density.
**Problem Context:**
1. **Charge Transfer:** A belt transfers charge to a Van de Graaff accelerator's high-potential inner shell at \( 2.83 \times 10^{-3} \, \text{C/s} \).
2. **Belt Specifications:** Width of the belt is 50 cm, and it travels at 30 m/s.
(a) **Current Verification:**
- The problem states the current \( I \) as \( 2.83 \times 10^{-3} \, \text{C/s} \). Evaluation needed: True, False.
(b) **Surface Charge Density Calculation:**
- Expression:
\[
\sigma = \frac{K}{v} = \frac{L}{w \, v} = \frac{I}{w v} = \frac{2.83 \times 10^{-3} \, \text{C/s}}{(0.5 \, \text{m})(30 \, \text{m/s})} = 1.89 \times 10^{-4} \, \text{C/m}^2
\]
- Evaluation needed: True, False.
This information provides an in-depth understanding of the charge dynamics and mathematical verification for a belt-driven charge transfer system as seen in devices like Van de Graaff accelerators.](https://content.bartleby.com/qna-images/question/90ba196a-a4da-4c5b-97fd-f3d58be17337/ca6645c2-4a75-4b4f-98f9-edd6bc1294ad/wj11yxg_processed.jpeg)
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