Final answer:
The electric flux through a rectangle in the xy-plane in a uniform electric field E pointing along the z-axis is 0, and in the xz-plane is E*a*b, where a and b are the sides of the rectangle.
Step-by-step explanation:
The question deals with the concept of electric flux through a surface in a uniform electric field. Specifically, it asks about the electric flux through a rectangle in different orientations relative to the electric field.
Answer to part (a): Since the rectangle lies in the xy-plane, and the electric field is along the z-axis, the angle between the field direction and the surface normal is 90°. The electric flux through a surface is given by the product of the field strength (E), the area (A), and the cosine of the angle (θ) between the field direction and the normal to the surface (Φ = E*A*cos(θ)). Here, cos(90°) is 0, so the flux is 0.
Answer to part (b): With the rectangle in the xz-plane, the angle between the electric field and the normal to the surface is 0°. Therefore, the electric flux is simply E*A because cos(0°) is 1. The area of the rectangle is a*b, so the electric flux is E*a*b.