### Problem 3: Electrostatic Force on a Central Charged Particle#### Problem StatementIn the figure, a central particle of charge \(-2q\) is surrounded by a square array of charged particles. These particles are positioned at distances either \(d\) or \(d/2\) along the perimeter of the square. Determine the magnitude and direction of the net electrostatic force on the central particle due to the other particles. (Hint: Consideration of symmetry can greatly reduce the amount of work required here.)#### Figure DescriptionThe figure illustrates a square configuration with a central particle of charge \(-2q\). The perimeter of the square has various particles located at each vertex and the midpoint of each side. The charge values of the particles are as follows:- Upper Left Vertex: \(+2q\)- Upper Midpoint: \(-7q\)- Upper Right Vertex: \(+4q\)- Right Midpoint: \(-3q\)- Lower Right Vertex: \(+2q\)- Lower Midpoint: \(-7q\)- Lower Left Vertex: \(+4q\)- Left Midpoint: \(-5q\)- Left Center between Midpoint and Central Particle: \(+3q\)Each charge is arranged symmetrically around the central particle, which simplifies the calculation of the net electrostatic force. The symmetry of the arrangement can be useful for reducing the complexity of solving the problem.### Approach to Solution1. **Identifying Coordinates and Charges:** - Coordinates are assigned to each charge, assuming the central particle is at the origin. - Charges are either at distance \(d\) (vertices) or \(d/2\) (midpoints).2. **Calculating Forces:** - Use Coulomb's Law to calculate the force exerted by each charge on the central charge. - Vector components of the forces need to be considered (x and y directions).3. **Summing the Forces:** - Sum the vector components of all forces to find the net force.4. **Symmetry Considerations:** - Leverage symmetry to simplify calculation: - Forces from particles at equal distances but opposite sides can cancel each other out or combine to simplify the net result.### Example CalculationFor any charge \(q_1\) at distance \(d_1\) from the central charge \(q

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