An electric field with a magnitude of 3.50 kN/C is applied along the x axis. Calculate the electric flux through a rectangular plane 0.350 m wide and 0.7 m long assuming that

(a) the plane is parallel to the yz plane;
(b) the plane is parallel to the xy plane;
(c) the plane contains the y axis, and its normal makes an angle of 40.0° with the x axis.

To calculate the electric flux through a rectangular plane, we can use the formula:

Flux = E * A * cos(theta)

Where:
- Flux is the electric flux through the plane
- E is the magnitude of the electric field
- A is the area of the plane
- theta is the angle between the electric field and the normal to the plane.

Let's calculate the electric flux for each case:

(a) The plane is parallel to the yz plane:
In this case, the plane is perpendicular to the x-axis and has an area of A = length * height = 0.7 m * 0.350 m = 0.245 m^2.
Since the plane is parallel to the electric field, the angle between the field and the normal to the plane is 90 degrees.
Therefore, cos(theta) = cos(90°) = 0.

Flux = E * A * cos(theta) = 3.50 kN/C * 0.245 m^2 * 0 = 0 Nm^2/C = 0 Nm^2/C.

(b) The plane is parallel to the xy plane:
In this case, the plane is perpendicular to the z-axis and has an area of A = length * width = 0.7 m * 0.350 m = 0.245 m^2.
Since the plane is parallel to the electric field, the angle between the field and the normal to the plane is 90 degrees.
Therefore, cos(theta) = cos(90°) = 0.

Flux = E * A * cos(theta) = 3.50 kN/C * 0.245 m^2 * 0 = 0 Nm^2/C = 0 Nm^2/C.

(c) The plane contains the y-axis, and its normal makes an angle of 40.0° with the x-axis:
In this case, the plane has an area of A = width * height = 0.350 m * 0.7 m = 0.245 m^2.
The angle between the electric field and the normal to the plane is 40.0 degrees.
Therefore, cos(theta) = cos(40.0°).

Flux = E * A * cos(theta) = 3.50 kN/C * 0.245 m^2 * cos(40.0°).
Using a calculator, cos(40.0°) ≈ 0.766.

Flux = 3.50 kN/C * 0.245 m^2 * 0.766
≈ 0.639 Nm^2/C.

So, the electric flux through the rectangular plane is approximately 0.639 Nm^2/C when the plane contains the y-axis and its normal makes an angle of 40.0° with the x-axis.