Final answer:
The direction and magnitude of the net electrostatic force on a charge within a symmetrical arrangement, such as a square, are determined by using symmetry and Coulomb's Law. One must consider both the magnitude and sign of each charge as well as their distances from the point of interest to calculate the net force or the electric field at that point.
Step-by-step explanation:
The direction of the electrostatic force acting on a point charge in a square arrangement can be determined using the principle of superposition and symmetry. In the cases provided where charges are at the corners of a square, like-charge pairs will repel each other and opposite-charge pairs will attract. When charges are equal in magnitude but opposite in sign, the net force direction can often be straight towards the attractive charge or directly away from the repulsive charge if there is symmetry.
For a charge located at the center of a square (like q in Figure 18.52), with opposite signed charges at the corners, the net electrostatic force can be calculated by vectorially adding the forces due to each charge at the corners. If the charges are of equal magnitude and symmetrically placed, the force components along the diagonals will cancel, resulting in a net force along the line of symmetry. Furthermore, the magnitude of this force can be found using Coulomb's Law, considering the distance from the charge in question to each of the charges at the corners of the square.
For example, if a charge q is at the center of a square and each corner of the square has a charge Q, the force on q due to each Q can be calculated, and then the vector sum of these forces will give the net force on q. Also, the electric field at a particular location can be computed if all the charges and distances are known by calculating the electric field contribution from each charge and summing them vectorially.