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JEE Main 2022 · 27 Jun · Shift 2, Physics question 41

If a charge qq is placed at the centre of a closed hemispherical non-conducting surface, the total flux passing through the flat surface would be :

A closed hemisphere with its flat circular base shaded; the charge q sits at the centre of the flat face.
Choose one option
Answer and worked solution

Official answer: B

Keyed reading. By symmetry the charge's flux qε0\frac q{\varepsilon_0} splits equally between the two half-spaces, giving q2ε0\frac q{2\varepsilon_0} for the hemisphere, which the key gives.

Note. With the charge exactly at the centre of the flat face, the field lies in that face, so strictly the flux through the flat face is zero and the q2ε0\frac q{2\varepsilon_0} passes through the curved surface.

(B)

Topics:Electric flux and Gauss's law
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