Electric flux through a hemisphere with uniform field

[uchicago2012]

Homework Statement

(a) Calculate the electric flux through the hemispherical surface shown in the figure. (The surface is an open shell, with no bottom.) The electric field is uniform: E = E₀ khat.
(b) If the electric field is instead E = E₀ ihat, what is the flux?

Homework Equations

Gauss' Law

The Attempt at a Solution

I was just wondering, for b), since ihat dot khat = 0, does that mean the electric flux is zero? Because it seems like the electric flux will always be perpendicular to the normal force if it is E = E₀ khat

 

[cupid.callin]

the net field lines entering the surface are sae as not lines coming out so yes flux will be 0