Final answer:
To calculate the electric flux through a rectangle in the xy-plane, we need to know the electric field strength and the angle between the field and the normal to the rectangle. The flux is then found using Φ = E · A · cos(θ). Without specific values, we cannot determine the exact flux.
Step-by-step explanation:
To determine the magnitude of the electric flux through a surface, we use the formula Φ = E · A · cos(θ), where Φ is the electric flux, E is the electric field strength, A is the area through which the field lines pass, and θ is the angle between the electric field direction and the normal to the surface.
For the case of a rectangle lying in the xy-plane with an electric field in the direction given, since the problem does not specify the electric field strength, the angle, or any further details, we cannot calculate the exact flux without this information. However, I can show how this would be done if these values were known. Suppose the rectangle had an area (A) and was subjected to an electric field (E) with a perpendicular component (E₁) to the rectangle's plane (since it lies in the xy-plane), the flux would be simply the product of E₁ and A.
In the case where an angle is involved, such as when the normal to the rectangular area makes a specified angle with the electric field, the cosine of this angle would be used to determine the component of the electric field that is perpendicular to the surface.