The formula for electric flux is as follows:
Electric flux = E*A (* E = electric field, A = area)
and if electric flux is at an angle from the normal (which is perpendicular) the formula is:
Electric flux = E*A*cos(theta) (* E = electric field, A = area, theta = angle between the normal of E and A)
For part A: First find the area of the rectangular surface.
Area of rectangle = length * width
A = 30cm * 10cm = 300 cm^2 = 0.03 m^2
and the electric field is given as
E = 6.74 104 N/C
Now, notice that since the electric field is entering the surface, it is at an angle of 180 degrees with the surface.
So plugging into the formula we get:
Electric flux = E*A*cos(theta)
Electric flux = (6.74 104 N/C)
* (0.03 m^2 )*cos(180) = -2022 N · m2/C
Electric flux = -2022 N · m2/C = -2.022 kN · m2/C