Question 289 of 311

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

A$\dfrac{q}{{\epsilon }_{0}}$B$\dfrac{q}{2{\epsilon }_{0}}$C$\dfrac{q}{4{\epsilon }_{0}}$D$\dfrac{q}{2\pi {\epsilon }_{0}}$

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Answer: (B) $\dfrac{q}{2{\epsilon }_{0}}$

Assume a complete sphere, then flux due to a charge placed at the center of sphere is $\phi =\dfrac{q}{{\epsilon }_{0}}$
Flux through hemisphere surface is equal to flux passing through flat surface $\phi =\dfrac{1}{2}\times \dfrac{q}{{\epsilon }_{0}}=\dfrac{q}{2{\epsilon }_{0}}$

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