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A hemispherical surface (one half of a sphere) of radius R sits in a uniform electric field E directed parallel to the axis of the hemisphere. What is the magnitude of the electric flux passing through the curved hemispherical surface?

1. 0
2. 4*pi*R²*E/3
3. 2*pi*R²*E
4. pi*R²*E

Correct answer: pi*R²*E

Solution

For a uniform field, flux depends only on the projected area normal to the field. The curved hemisphere projects onto a flat circular disc of radius R and area pi*R² whose normal is along E. Hence the flux is E times pi*R² = pi*R²*E. (Equivalently, the closed surface formed by hemisphere plus flat cap encloses no charge, so flux in through the cap equals flux out through the curved part.)

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