Answer:
E_total = 1.39 x 10^5 N/C
Step-by-step explanation:
We can calculate the electric field at the center of the square using the principle of superposition. We will treat each charge as a point charge and calculate the electric field due to each charge, and then add them up vectorially.
Let's assume that the positive charge is located at the bottom-left corner of the square, and the negative charges are located at the other three corners. The distance from the charges to the center of the square is:
r = 60 cm / 2 = 30 cm
The electric field due to a point charge is given by Coulomb's law:
E = k*q / r^2
where k is the Coulomb constant, q is the charge, and r is the distance between the charge and the point where we want to calculate the electric field.
For the positive charge, we have:
E1 = k*q1 / r^2
E1 = (9 x 10^9 Nm^2/C^2)(45 x 10^-6 C) / (0.3 m)^2
E1 = 4.50 x 10^5 N/C
The electric field due to the negative charges is:
E2 = k*q2 / r^2
E2 = (9 x 10^9 Nm^2/C^2)(-31 x 10^-6 C) / (0.3 m)^2
E2 = -3.11 x 10^5 N/C
Since the negative charges are at opposite corners, the direction of the electric field due to each charge cancels out, so we only need to consider the magnitude of the electric field due to the negative charges.
The total electric field at the center of the square is:
E_total = E1 + E2
E_total = 4.50 x 10^5 N/C - 3.11 x 10^5 N/C
E_total = 1.39 x 10^5 N/C
The direction of the electric field at the center of the square is the direction of the net electric field due to the two charges, which is from the positive charge to the negative charges. This direction is along the diagonal of the square, at a 45 degree angle with respect to the sides of the square.