Answer
See answers.
Work Step by Step
a. The net flux through the surface of the cube is zero. The field is uniform, so there is no charge in this region. All of the electric field lines that enter the cube will exit the cube.
b. Assume that the field points in the positive x-direction, from left to right, and that we are looking at the “front” face of the cube. The “left” face has electric field lines entering it, and a negative flux.
$$\Phi_{left}=-EA=-(7500N/C)(0.085m)^2=-54.2\;Nm^2/C$$
The “right” face has electric field lines leaving it, and a positive flux.
$$\Phi_{right}=EA=(7500N/C)(0.085m)^2=54.2\;Nm^2/C$$
The other four faces - front, top, back, and bottom - have no flux through them, because there are no electric field lines that pass through any of them.
As expected, the net flux is zero.