Final answer:
The electric flux through a square in the xy-plane with side length 0.560 m, in the z-direction electric field with magnitude E = (881 N/(C·m))x, is 276 N·m²/C to three significant figures.
Step-by-step explanation:
To calculate the electric flux through a square in the xy-plane, we need to apply the definition of electric flux (Φ) which is Φ = E · A · cos(θ), where E is the magnitude of the electric field, A is the area of the surface through which the field is passing, and θ is the angle between the field direction and the normal (perpendicular) to the surface.
Given the electric field E has a magnitude of (881 N/(C·m))x and is in the z-direction, and the square is in the xy-plane at z = 0 with side length of 0.560 m, the angle θ between the field direction and the normal to the surface is 0 degrees because the field is perpendicular to the plane of the square.
The area A of the square is A = side length · side length = (0.560 m) x (0.560 m). This gives us an area of 0.3136 m².
Since the cosine of 0 degrees is 1, and the field is uniform over the square, the electric flux through the square is simply Φ = E · A. Substituting the given values, we find that Φ = (881 N/(C·m)) · 0.3136 m² · 1 = 276.22416 N·m²/C. Therefore, the electric flux through the square to three significant figures is 276 N·m²/C.