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A plastic disk of radius R = 46.3 cm is charged on one side with a uniform surface charge density 8.73 fC/m, and then three quadrants of the disk are removed. The remaining quadrant is shown in the figure. With V= 0 at infinity, what is the potential in volts due to the remaining quadrant at point P, which is on the central axis of the original disk at distance D= 0.246 cm from the original center?

A plastic disk of radius R = 46.3 cm is charged on one side with a uniform surface charge density 8.73 fC/m, and then three quadrants of the disk are removed. The remaining quadrant is shown in the figure. With V= 0 at infinity, what is the potential in volts due to the remaining quadrant at point P, which is on the central axis of the original disk at distance D= 0.246 cm from the original center?

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
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**Electrostatics Question** **Problem Statement:** A plastic disk of radius \( R = 46.3 \) cm is charged on one side with a uniform surface charge density \( 8.73 \, \mu C/m^2 \), and then three quadrants of the disk are removed. The remaining quadrant is shown in the figure. With \( V = 0 \) at infinity, what is the potential in volts due to the remaining quadrant at point \( P \), which is on the central axis of the original disk at distance \( D = 0.246 \) cm from the original center? **Visualization:** The image accompanying the problem shows a circular disk from which three quadrants have been removed, leaving one quadrant of the circular disk remaining. The remaining segment is a quarter of the disk, illustrating its shape and orientation. The point \( P \) is placed on the central axis of the original disk at distance \( D \) from the center. The radius of the original disk is marked as \( R \). **Diagram Explanation:** - **Original Disk Radius \( R \):** 46.3 cm - **Remaining Quadrant:** Highlighted in green, showing a 90-degree arc of the original disk. - **Point \( P \):** Positioned along the central vertical axis at distance \( D = 0.246 \) cm from the center of the original disk. - **Central Axis:** Represented by a dotted line extending through the center of the original and removed parts of the disk, indicating the line along which point \( P \) lies. **Calculation Requirement:** Determine the electric potential at point \( P \) due to the charge on the remaining quadrant, using provided parameters and the electrostatic concept of potential \( V \) at infinity being zero. **Answer Input Fields:** - **Number:** Text box for numerical answer. - **Units:** Dropdown to select the unit "V" (volts). This question aims to test the understanding of electrostatics, specifically the calculation of electric potential due to a segment of charged surface. **Expected Knowledge:** To solve this problem, students should apply principles of electrostatics, considering the configuration of the charge distribution, potential due to surface charge density, and symmetry arguments for simplifying the integration process.
Transcribed Image Text:**Electrostatics Question** **Problem Statement:** A plastic disk of radius \( R = 46.3 \) cm is charged on one side with a uniform surface charge density \( 8.73 \, \mu C/m^2 \), and then three quadrants of the disk are removed. The remaining quadrant is shown in the figure. With \( V = 0 \) at infinity, what is the potential in volts due to the remaining quadrant at point \( P \), which is on the central axis of the original disk at distance \( D = 0.246 \) cm from the original center? **Visualization:** The image accompanying the problem shows a circular disk from which three quadrants have been removed, leaving one quadrant of the circular disk remaining. The remaining segment is a quarter of the disk, illustrating its shape and orientation. The point \( P \) is placed on the central axis of the original disk at distance \( D \) from the center. The radius of the original disk is marked as \( R \). **Diagram Explanation:** - **Original Disk Radius \( R \):** 46.3 cm - **Remaining Quadrant:** Highlighted in green, showing a 90-degree arc of the original disk. - **Point \( P \):** Positioned along the central vertical axis at distance \( D = 0.246 \) cm from the center of the original disk. - **Central Axis:** Represented by a dotted line extending through the center of the original and removed parts of the disk, indicating the line along which point \( P \) lies. **Calculation Requirement:** Determine the electric potential at point \( P \) due to the charge on the remaining quadrant, using provided parameters and the electrostatic concept of potential \( V \) at infinity being zero. **Answer Input Fields:** - **Number:** Text box for numerical answer. - **Units:** Dropdown to select the unit "V" (volts). This question aims to test the understanding of electrostatics, specifically the calculation of electric potential due to a segment of charged surface. **Expected Knowledge:** To solve this problem, students should apply principles of electrostatics, considering the configuration of the charge distribution, potential due to surface charge density, and symmetry arguments for simplifying the integration process.
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