(b) What If? What is the minimum electric field magnitude that could be obtained at the center of the circle by moving one or more of the charges along the circle, with minimum separation of 8.70° between each of the charges? Express your result as the ratio of this new electric field magnitude to the magnitude of the electric field found in part (a). Eminimum Epart (a)
(b) What If? What is the minimum electric field magnitude that could be obtained at the center of the circle by moving one or more of the charges along the circle, with minimum separation of 8.70° between each of the charges? Express your result as the ratio of this new electric field magnitude to the magnitude of the electric field found in part (a). Eminimum Epart (a)
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Need help in part (b) please
![### Problem Description
#### (a) Three point charges are located on the circumference of a circle of radius \( r \), at the angles shown in the figure below:
[Diagram Description]
- The diagram depicts a circle centered at the origin of an \( xy \)-coordinate system.
- Three point charges are marked:
- A charge \( +q \) at 150°.
- A charge \( -2q \) at 270°.
- A charge \( +q \) at 30°.
##### Question:
1. What is the electric field at the center of the circle due to these point charges? (Express your answer in vector form. Use the following as necessary: \( k_e \), \( q \), and \( r \).)
\[ \vec{E} = \frac{3k_e q}{r^2} (-\hat{j}) \]
(Answer confirmed with a checkmark)
#### (b) What If?
1. What is the minimum electric field magnitude that could be obtained at the center of the circle by moving one or more of the charges along the circle, with a minimum separation of 8.70° between each of the charges? Express your result as the ratio of this new electric field magnitude to the magnitude of the electric field found in part (a).
\[ \frac{E_{\text{minimum}}}{E_{\text{part (a)}}} = \]
### Graph Diagram Details
- The diagram with the circle:
- The circle is oriented with 0° at the positive \( x \)-axis, increasing counterclockwise.
- The charge \( +q \) at 30° lies in the first quadrant.
- The charge \( +q \) at 150° lies in the second quadrant.
- The charge \( -2q \) at 270° lies along the negative \( y \)-axis.
This problem explores the calculation of the electric field at the center of a circle due to point charges placed on its circumference and extends to find the minimal possible electric field configuration with given constraints. This scenario is common in electrostatics problems where symmetry and point charge contributions are analyzed.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1e0e1ba5-7eb8-4b1c-b696-d9174b598130%2F30ceece9-d19e-4623-a8f1-68fd48aaf436%2Foio2prs_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem Description
#### (a) Three point charges are located on the circumference of a circle of radius \( r \), at the angles shown in the figure below:
[Diagram Description]
- The diagram depicts a circle centered at the origin of an \( xy \)-coordinate system.
- Three point charges are marked:
- A charge \( +q \) at 150°.
- A charge \( -2q \) at 270°.
- A charge \( +q \) at 30°.
##### Question:
1. What is the electric field at the center of the circle due to these point charges? (Express your answer in vector form. Use the following as necessary: \( k_e \), \( q \), and \( r \).)
\[ \vec{E} = \frac{3k_e q}{r^2} (-\hat{j}) \]
(Answer confirmed with a checkmark)
#### (b) What If?
1. What is the minimum electric field magnitude that could be obtained at the center of the circle by moving one or more of the charges along the circle, with a minimum separation of 8.70° between each of the charges? Express your result as the ratio of this new electric field magnitude to the magnitude of the electric field found in part (a).
\[ \frac{E_{\text{minimum}}}{E_{\text{part (a)}}} = \]
### Graph Diagram Details
- The diagram with the circle:
- The circle is oriented with 0° at the positive \( x \)-axis, increasing counterclockwise.
- The charge \( +q \) at 30° lies in the first quadrant.
- The charge \( +q \) at 150° lies in the second quadrant.
- The charge \( -2q \) at 270° lies along the negative \( y \)-axis.
This problem explores the calculation of the electric field at the center of a circle due to point charges placed on its circumference and extends to find the minimal possible electric field configuration with given constraints. This scenario is common in electrostatics problems where symmetry and point charge contributions are analyzed.
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