Final answer:
To calculate the electric flux through a non-perpendicular planar surface, one must consider the surface's area and its inclination angle relative to the field. The electric flux is then determined by the component of the surface area perpendicular to the field lines.
Step-by-step explanation:
To represent the electric flux through a planar surface that is not perpendicular to the field, let's consider surface S2 with area A2 inclined at an angle to the xz-plane. The projection of this surface in the xz-plane is surface S1, with area A1. The relationship between the areas is described by A2 cos θ = A1. Given that the same number of field lines crosses both surfaces, their electric fluxes are equal. Consequently, the electric flux through surface S2 is given by Φ = EA1 = EA2 cos θ. If η2 is designated as a unit vector normal to S2, the electric flux through it is represented as Φ = E · η2 A2.