Final answer:
The magnitude of the electric field due to four equal +6.00 uC point charges placed at the corners of a square 2.00m on each side at the center of the square is 2.16 x 10^5 N/C.
Step-by-step explanation:
The electric field due to the charges at the corners of a square can be calculated by considering each charge individually and then adding up their contributions. Since all the charges are equal, we can use the formula for the electric field due to a point charge, which is given by E = kQ/r^2, where E is the electric field, k is Coulomb's constant, Q is the charge, and r is the distance. In this case, the distance from each corner charge to the center of the square is equal to half the length of a side, which is 1.00m. Therefore, the magnitude of the electric field due to each charge is given by E = (9.00 x 10^9 Nm^2/C^2)(6.00 x 10^-6 C)/(1.00m)^2 = 5.40 x 10^4 N/C. Since there are four charges, we add up their contributions to get a total electric field of 4 times this value, which is 2.16 x 10^5 N/C.