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(A) According to Gauss's Law,the total electric flux through a closed surface is $\Phi = \frac{q_{enclosed}}{\varepsilon_0}$.In the given figure,the p

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$\frac{q}{2\varepsilon_0}$

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(A) According to Gauss's Law,the total electric flux through a closed surface is $\Phi = \frac{q_{enclosed}}{\varepsilon_0}$.In the given figure,the point charge $q$ is placed on the center of the flat circular base of the hemisphere.Since the charge lies on the boundary of the hemispherical surface,we can imagine a symmetric hemispherical surface on the other side of the flat base to form a complete sphere.Now,the charge $q$ is at the center of this Gaussian sphere.The total flux through the entire sphere is $\Phi_{total} = \frac{q}{\varepsilon_0}$.Due to symmetry,the flux through the original hemispherical surface and the flux through the imaginary hemispherical surface must be equal.Therefore,the flux through the original hemispherical surface is $\Phi = \frac{1}{2} \Phi_{total} = \frac{q}{2\varepsilon_0}$.

$A$ point charge $q$ is placed on the center of the flat circular base of a hemispherical surface as shown in the figure. The net flux of the electric field through the hemispherical surface is closest to:

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