Suppose that a uniform electric field exists in a certain region of space. Now consider a mathematical plane surface of area A. To maximize the flux through this surface, the face of the plane (not its normal)

Answer: The normal of the plane must be parallel to the electric field vector.

Explanation:

the normal to the surface is defined as a versor that is perpendicular to the plane.

Now, if the angle between this normal and the line of the field is θ, we have that the flux can be written as:

Φ = E*A*cos (θ)

Where E is the field, A is the area and θ is the angle already defined.

Now, this maximizes when θ = 0.

This means that the normal of the surface must be parallel to the electric field