Answer :
Final answer:
The magnitude of the electric field at the center of the square is [magnitude]. The direction of the electric field at the center of the square is towards the -38.8 C charge.
Explanation:
To calculate the magnitude of the electric field at the center of the square, we can use the principle of superposition. The electric field due to each individual charge can be calculated using Coulomb's law:
E = k * (|q| / r^2)
Where E is the electric field, k is the electrostatic constant (9 x 10^9 Nm^2/C^2), |q| is the magnitude of the charge, and r is the distance from the charge to the center of the square.
For the -38.8 C charge at one corner, the distance to the center of the square is half the length of a side, which is 21.25 cm. Plugging in the values, we get:
E1 = (9 x 10^9 Nm^2/C^2) * (38.8 C / (0.2125 m)^2)
For the -26.7 C charges at the other three corners, the distance to the center of the square is the diagonal of a square with side length 42.5 cm, which can be calculated using the Pythagorean theorem:
d = sqrt((42.5 cm)^2 + (42.5 cm)^2) = 60.1 cm
Plugging in the values, we get:
E2 = (9 x 10^9 Nm^2/C^2) * (26.7 C / (0.601 m)^2)
The total electric field at the center of the square is the vector sum of E1 and E2:
E_total = sqrt(E1^2 + E2^2)
Now, to determine the direction of the electric field at the center of the square, we need to consider the relative positions of the charges. Since the -38.8 C charge is at one corner, the electric field will be directed towards it. Therefore, the correct direction of the electric field at the center of the square is towards the -38.8 C charge.
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