The net electrostatic force on a charge placed at the center of a square with equal charges at three of its corners can be calculated using Coulomb's Law and vector addition of the forces due to each corner charge.
The student is asking about the net electrostatic force acting on a 6.0 µC charge placed at the center of a square with three of its corners having a 5.0 µC charge each. To solve for the magnitude and direction of the net force, we utilize Coulomb's Law which states that the electric force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.
Since the charges are identical and symmetrically placed, the forces on the center charge due to the charges at the corners will point directly towards each corner. The distances from the center to each corner of the square are equal, and thus the magnitudes of the forces due to each corner charge will be the same. The resultant force can be found by vector addition of these three forces.
We first find the force between the center charge and one of the corner charges using Coulomb's Law, and then use trigonometry to resolve the forces into horizontal and vertical components. The components along the same direction can be added algebraically to obtain the total force in that direction. Due to symmetry, some components will cancel out, leaving only the resultant force's magnitude and direction to be calculated.