A uniformly charged disk with radius R = 45.0 cm and uniform charge density o = 8.10 × 10¬3 C/m² lies in the xy-plane, with its center at the origin. What is the electric field (in MN/C) due to the charged disk at the following locations? (a) z = 5.00 cm 24.97 X MN/C (b) z = 10.0 cm |47.34 X MN/C (c) z = 50.0 cm 76.23 X MN/C (d) z = 200 cm 10.76 X MN/C
A uniformly charged disk with radius R = 45.0 cm and uniform charge density o = 8.10 × 10¬3 C/m² lies in the xy-plane, with its center at the origin. What is the electric field (in MN/C) due to the charged disk at the following locations? (a) z = 5.00 cm 24.97 X MN/C (b) z = 10.0 cm |47.34 X MN/C (c) z = 50.0 cm 76.23 X MN/C (d) z = 200 cm 10.76 X MN/C
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Chapter1: Units, Trigonometry. And Vectors
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I also tried rounding to one decimal and that was still wrong plz help
![### Electric Field Due to a Uniformly Charged Disk
**Problem Statement:**
A uniformly charged disk with a radius \( R = 45.0 \) cm and a uniform charge density \( \sigma = 8.10 \times 10^{-3} \, \text{C/m}^2 \) lies in the xy-plane, with its center at the origin. What is the electric field (in MN/C) due to the charged disk at the following locations?
**Locations to Determine the Electric Field:**
**(a)** At \( z = 5.00 \) cm
**User Input:** 24.97 MN/C
**Result:** Incorrect (❌)
**(b)** At \( z = 10.0 \) cm
**User Input:** 47.34 MN/C
**Result:** Incorrect (❌)
**(c)** At \( z = 50.0 \) cm
**User Input:** 76.23 MN/C
**Result:** Incorrect (❌)
**(d)** At \( z = 200 \) cm
**User Input:** 10.76 MN/C
**Result:** Incorrect (❌)
### Explanation:
For a disk of charge density \(\sigma\) and radius \( R \), the electric field \( E_z \) at a distance \( z \) along the axis perpendicular to the disk can be calculated using the formula:
\[ E_z = \frac{\sigma}{2\epsilon_0} \left( 1 - \frac{z}{\sqrt{z^2 + R^2}} \right) \]
where \( \epsilon_0 \) is the permittivity of free space. The answers provided above for different \( z \)-values were incorrect based on this formula.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fec49f3dd-8736-4fbb-9af6-a16c8664e989%2F0baf0c94-fb83-4657-8b04-7cf33db9668c%2F6ua1mg.png&w=3840&q=75)
Transcribed Image Text:### Electric Field Due to a Uniformly Charged Disk
**Problem Statement:**
A uniformly charged disk with a radius \( R = 45.0 \) cm and a uniform charge density \( \sigma = 8.10 \times 10^{-3} \, \text{C/m}^2 \) lies in the xy-plane, with its center at the origin. What is the electric field (in MN/C) due to the charged disk at the following locations?
**Locations to Determine the Electric Field:**
**(a)** At \( z = 5.00 \) cm
**User Input:** 24.97 MN/C
**Result:** Incorrect (❌)
**(b)** At \( z = 10.0 \) cm
**User Input:** 47.34 MN/C
**Result:** Incorrect (❌)
**(c)** At \( z = 50.0 \) cm
**User Input:** 76.23 MN/C
**Result:** Incorrect (❌)
**(d)** At \( z = 200 \) cm
**User Input:** 10.76 MN/C
**Result:** Incorrect (❌)
### Explanation:
For a disk of charge density \(\sigma\) and radius \( R \), the electric field \( E_z \) at a distance \( z \) along the axis perpendicular to the disk can be calculated using the formula:
\[ E_z = \frac{\sigma}{2\epsilon_0} \left( 1 - \frac{z}{\sqrt{z^2 + R^2}} \right) \]
where \( \epsilon_0 \) is the permittivity of free space. The answers provided above for different \( z \)-values were incorrect based on this formula.
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