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part d (last subpart)

part d (last subpart)

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part d (last subpart)

### E&M 1: Electric Fields in a Square Configuration Consider a square of side length \( a \) with a positive point charge \( +Q \) fixed at the lower-left corner and negative point charges \( -Q \) fixed at the other three corners of the square. Point \( P \) is located at the center of the square. #### Diagram: The diagram shows a square with points at each corner and the center, labelled as follows: - Top-left corner: \( -Q \) - Top-right corner: \( -Q \) - Bottom-left corner: \( +Q \) - Bottom-right corner: \( -Q \) - Center: \( P \) - Midpoint of the bottom side: \( R \) - Side length: \( a \) #### Problem Statements: (a) **Indicating Direction of Electric Field at Point \( P \):** - On the diagram, indicate with an arrow the direction of the net electric field at point \( P \). (b) **Deriving Expressions:** - Derive expressions for each of the following in terms of the given quantities and fundamental constants. - i. The magnitude of the electric field at point \( P \). - ii. The electric potential at point \( P \). (c) **Work Done by Electric Field:** - A positive charge is placed at point \( P \). It is then moved from point \( P \) to point \( R \), which is at the midpoint of the bottom side of the square. As the charge is moved, is the work done on it by the electric field positive, negative, or zero? - Options: - Positive - Negative - Zero - Explain your reasoning. (d) **Adjusting Charge Configuration:** - i. Describe one way to replace a single charge in this configuration that would make the electric field at the center of the square equal to zero. Justify your answer. - ii. Describe one way to replace a single charge in this configuration such that the electric potential at the center of the square is zero but the electric field is not zero. Justify your answer. This problem encourages students to apply their understanding of electric fields and potentials within a symmetric charge distribution. Through this exercise, they will explore the behaviors of electric fields in a structured, theoretical model and provide justifications for their reasoning. Use appropriate principles and formulas to derive the required expressions and
Transcribed Image Text:### E&M 1: Electric Fields in a Square Configuration Consider a square of side length \( a \) with a positive point charge \( +Q \) fixed at the lower-left corner and negative point charges \( -Q \) fixed at the other three corners of the square. Point \( P \) is located at the center of the square. #### Diagram: The diagram shows a square with points at each corner and the center, labelled as follows: - Top-left corner: \( -Q \) - Top-right corner: \( -Q \) - Bottom-left corner: \( +Q \) - Bottom-right corner: \( -Q \) - Center: \( P \) - Midpoint of the bottom side: \( R \) - Side length: \( a \) #### Problem Statements: (a) **Indicating Direction of Electric Field at Point \( P \):** - On the diagram, indicate with an arrow the direction of the net electric field at point \( P \). (b) **Deriving Expressions:** - Derive expressions for each of the following in terms of the given quantities and fundamental constants. - i. The magnitude of the electric field at point \( P \). - ii. The electric potential at point \( P \). (c) **Work Done by Electric Field:** - A positive charge is placed at point \( P \). It is then moved from point \( P \) to point \( R \), which is at the midpoint of the bottom side of the square. As the charge is moved, is the work done on it by the electric field positive, negative, or zero? - Options: - Positive - Negative - Zero - Explain your reasoning. (d) **Adjusting Charge Configuration:** - i. Describe one way to replace a single charge in this configuration that would make the electric field at the center of the square equal to zero. Justify your answer. - ii. Describe one way to replace a single charge in this configuration such that the electric potential at the center of the square is zero but the electric field is not zero. Justify your answer. This problem encourages students to apply their understanding of electric fields and potentials within a symmetric charge distribution. Through this exercise, they will explore the behaviors of electric fields in a structured, theoretical model and provide justifications for their reasoning. Use appropriate principles and formulas to derive the required expressions and
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