Final answer:
To find the electric field at the center of a square with charges at its corners, use the principle of superposition to determine the net field direction and then use Coulomb's Law to calculate the magnitude of the field due to each charge, summing the vectors to find the net field.
Step-by-step explanation:
The question asks to calculate the electric field at the center of a square where charges are placed at its corners. Firstly, one must determine the direction of the electric field by using the principle of superposition and considering the symmetry of the charges. Because electric fields point away from positive charges and toward negative charges, the net electric field direction can be found by vector addition of the fields due to individual charges.
Once the direction is established, one can calculate the magnitude of the electric field (E) at the center using Coulomb's Law,
E = k_e * q / r^2, where 'k_e' is Coulomb's constant (approximately 8.99 x 10^9 N m^2/C^2), 'q' is the charge, and 'r' is the distance from the charge to the point of interest. For each charge, this calculation results in an electric field vector. The net electric field at the center is the vector sum of the individual fields.