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Help. Find electric potential at the origin.
The provided diagram displays a ¾ section of a circle over a Cartesian coordinate system with the origin at the center. The radius of the circle section extends from -10 cm to +10 cm along both the x-axis and y-axis. The charge distribution is indicated with a label of +30μC on the left side of the circle section.
#### Diagram Details:
- **Axes Description:**
- The horizontal axis is labeled as x (cm).
- The vertical axis is labeled as y (cm).
- **Circle Segment:**
- The red semi-circular arc starts from the point (-10,0) on the x-axis, traverses through the second quadrant, and ends at the point (10,0) on the x-axis, covering ¾ of a circle.
- The radius values for the circle increment are marked as -10 and 10 along both axes.
- **Charge Notation:**
- A label, “+30μC,” indicates the total amount of charge distributed along the arc.
#### Instructions:
To solve this problem:
1. **Understand Uniform Charge Distribution:**
- The charge is uniformly distributed along the length of ¾ of the circle’s perimeter.
2. **Calculate Linear Charge Density (λ):**
- Determine the linear charge density λ = Total charge / Length of arc.
3. **Find Differential Elements:**
- Break the arc into infinitesimal charge elements dq.
4. **Use Electric Field Formula:**
- Use the principle of superposition to calculate the net electric field due to all the infinitesimal charges at the origin.
- Consider both x and y components of the electric field vectors.
5. **Integrate to Find Total Electric Field:**
- Integrate the contributions of dq over the given arc to find the total electric field at the origin.
This problem encourages students to delve into principles of electrostatics, applying concepts such as charge distribution, superposition, and integration to find the electric field at a specific point.](https://content.bartleby.com/qna-images/question/73881bad-35e9-478f-80dc-30ed83e5c525/ccb715df-19ed-4aed-bd42-586af14336f7/e8mrr8d_processed.jpeg)
Transcribed Image Text:### Physics Problem: Electric Field Calculation
#### Problem Statement:
A total charge of +30 micro Coulombs is uniformly distributed along this shape (¾ of a circle). Calculate the electric field at the origin. You must show ALL steps involved for credit, not just the answer.
#### Diagram:
The provided diagram displays a ¾ section of a circle over a Cartesian coordinate system with the origin at the center. The radius of the circle section extends from -10 cm to +10 cm along both the x-axis and y-axis. The charge distribution is indicated with a label of +30μC on the left side of the circle section.
#### Diagram Details:
- **Axes Description:**
- The horizontal axis is labeled as x (cm).
- The vertical axis is labeled as y (cm).
- **Circle Segment:**
- The red semi-circular arc starts from the point (-10,0) on the x-axis, traverses through the second quadrant, and ends at the point (10,0) on the x-axis, covering ¾ of a circle.
- The radius values for the circle increment are marked as -10 and 10 along both axes.
- **Charge Notation:**
- A label, “+30μC,” indicates the total amount of charge distributed along the arc.
#### Instructions:
To solve this problem:
1. **Understand Uniform Charge Distribution:**
- The charge is uniformly distributed along the length of ¾ of the circle’s perimeter.
2. **Calculate Linear Charge Density (λ):**
- Determine the linear charge density λ = Total charge / Length of arc.
3. **Find Differential Elements:**
- Break the arc into infinitesimal charge elements dq.
4. **Use Electric Field Formula:**
- Use the principle of superposition to calculate the net electric field due to all the infinitesimal charges at the origin.
- Consider both x and y components of the electric field vectors.
5. **Integrate to Find Total Electric Field:**
- Integrate the contributions of dq over the given arc to find the total electric field at the origin.
This problem encourages students to delve into principles of electrostatics, applying concepts such as charge distribution, superposition, and integration to find the electric field at a specific point.
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