What is the electric flux through the hemispherical surface?

[physics231]

A uniform field E is parallel to the axis of a hollow hemisphere of radius R. a) What is the electric flux through the hemispherical surface? b) What is the result if E is instead perpendicular to the axis?

Here is what I've interpretted so far. If the field is parallel to the surface, then the electric flux = EA cos(theta). With the angle being 0, I came up with the answer as just EA Therefore that is my answer on part a).

On part b) if the field is perpendicular then the electric flux is just = EA, therefore making that my answer. But I know this isn't right. What step am I missing? Thank you

 

[quasar987]

Well the field is certainly not parallel to the surface in both cases. You'll have to evaluate the surface integral

$$\Phi_E=\int\vec{E}\cdot \hat{n}da$$

where $\hat{n}$ is the unit vector parallel to the surface element da.

Hint: If you chose a coordinate system in which the origin is on the center of the hollow sphere and in which the z-axis IS the axis of the hollow hemisphere, then what are $\vec{E}$ and $\hat{n}$?