### E&M 1 The image presents a physics problem related to electric fields and potentials in a square setup. The square of side length \( a \) has a positive point charge \( +Q \) at the lower-left corner and negative point charges \( -Q \) fixed at the other three corners of the square. The point \( P \) is located at the center of the square. #### Problem Breakdown: **Part (a)** On the diagram, indicate with an arrow the direction of the net electric field at point \( P \). **Part (b)** 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 \( P \). **Part (c)** 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. #### Diagram Description: The diagram depicts a square with charges at each corner: - The top-left, top-right, and bottom-right corners have a negative charge \( -Q \). - The bottom-left corner has a positive charge \( +Q \). - The center point is labeled \( P \). - The midpoint of the bottom side is labeled \( R \). The side length of the square is labeled \( a \). The problem involves determining the net electric field and electric potential at point \( P \), and analyzing the work done when moving a positive charge from \( P \) to \( R \). This problem is typical in the study of electrostatics, where understanding the principles of electric fields and potentials in various geometries is essential.

### E&M 1 The image presents a physics problem related to electric fields and potentials in a square setup. The square of side length \( a \) has a positive point charge \( +Q \) at the lower-left corner and negative point charges \( -Q \) fixed at the other three corners of the square. The point \( P \) is located at the center of the square. #### Problem Breakdown: Part (a) On the diagram, indicate with an arrow the direction of the net electric field at point \( P \). Part (b) 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 \( P \). Part (c) 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. #### Diagram Description: The diagram depicts a square with charges at each corner: - The top-left, top-right, and bottom-right corners have a negative charge \( -Q \). - The bottom-left corner has a positive charge \( +Q \). - The center point is labeled \( P \). - The midpoint of the bottom side is labeled \( R \). The side length of the square is labeled \( a \). The problem involves determining the net electric field and electric potential at point \( P \), and analyzing the work done when moving a positive charge from \( P \) to \( R \). This problem is typical in the study of electrostatics, where understanding the principles of electric fields and potentials in various geometries is essential.