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Consider two separate systems with four charges of the same magnitude q = 16 µC arranged in the vertexes of a square of length h = 35 cm, see the picture below. Calculate the electric potential at the center of the square (points A and C) and at the middle of the bottom side of the square (points B and D).

Consider two separate systems with four charges of the same magnitude q = 16 µC arranged in the vertexes of a square of length h = 35 cm, see the picture below. Calculate the electric potential at the center of the square (points A and C) and at the middle of the bottom side of the square (points B and D).

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
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Title: Calculating Electric Potential for Charged Particles Arranged in a Square Description: This exercise involves two separate systems, each with four charges of the same magnitude \( q = 16 \, \mu C \), arranged at the vertices of a square with a side length \( h = 35 \, \text{cm} \). **Diagram Explanation:** 1. **System A:** - Charges are placed at the corners of a square. - Point A is at the center of the square. - Point B is at the middle of the bottom side. 2. **System C:** - Similar configuration with charges placed at the corners. - Point C is at the center of the square. - Point D is at the middle of the bottom side. **Tasks:** 1. Calculate the electric potential at the center of the square (points A and C) and at the middle of the bottom side (points B and D). 2. Determine the amount of work required to move a \(-12 \, \mu C\) charge between specified points. **Calculations:** - **Potential at Point A, \( V_A \):** \( 2320457.1 \, \text{V} \) - **Potential at Point B, \( V_B \):** \( 2373880.6 \, \text{V} \) - **Potential at Point C, \( V_C \):** \( 0 \, \text{V} \) - **Potential at Point D, \( V_D \):** \(-208380.8 \, \text{V} \) **Work Calculation:** - **From A to B:** - Work \( W_{A \rightarrow B} \): \( -0.7948 \, \text{J} \) (incorrect answer, requires recalculation) - **From C to D:** - Work \( W_{C \rightarrow D} \): \( 10.90 \, \text{J} \) This problem helps in understanding the concepts of electric potential and work done in electric fields, crucial for comprehending electrostatics and electric field theory.
Transcribed Image Text:Title: Calculating Electric Potential for Charged Particles Arranged in a Square Description: This exercise involves two separate systems, each with four charges of the same magnitude \( q = 16 \, \mu C \), arranged at the vertices of a square with a side length \( h = 35 \, \text{cm} \). **Diagram Explanation:** 1. **System A:** - Charges are placed at the corners of a square. - Point A is at the center of the square. - Point B is at the middle of the bottom side. 2. **System C:** - Similar configuration with charges placed at the corners. - Point C is at the center of the square. - Point D is at the middle of the bottom side. **Tasks:** 1. Calculate the electric potential at the center of the square (points A and C) and at the middle of the bottom side (points B and D). 2. Determine the amount of work required to move a \(-12 \, \mu C\) charge between specified points. **Calculations:** - **Potential at Point A, \( V_A \):** \( 2320457.1 \, \text{V} \) - **Potential at Point B, \( V_B \):** \( 2373880.6 \, \text{V} \) - **Potential at Point C, \( V_C \):** \( 0 \, \text{V} \) - **Potential at Point D, \( V_D \):** \(-208380.8 \, \text{V} \) **Work Calculation:** - **From A to B:** - Work \( W_{A \rightarrow B} \): \( -0.7948 \, \text{J} \) (incorrect answer, requires recalculation) - **From C to D:** - Work \( W_{C \rightarrow D} \): \( 10.90 \, \text{J} \) This problem helps in understanding the concepts of electric potential and work done in electric fields, crucial for comprehending electrostatics and electric field theory.
Expert Solution
Step 1

Expression of potential at point A.

VA=q4πε0h2+q4πε0h2+q4πε0h2+q4πε0h2=4q4πε0h2

Substitute the values.

VA=4×16×10-64π×8.85×10-12×0.352=2325272.16 V

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