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

Related Introductory Physics Homework Help News on Phys.org

quasar987

Homework Helper
Gold Member
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 $\hat{n}$?

Last edited:

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving