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(B) According to Gauss's Law,the total electric flux through a closed surface is $\phi_{total} = \frac{q_{enclosed}}{\varepsilon_0}$.In this problem,t

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$\frac{4q}{\varepsilon_0}$

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(B) According to Gauss's Law,the total electric flux through a closed surface is $\phi_{total} = \frac{q_{enclosed}}{\varepsilon_0}$.In this problem,the charges $3q$ and $5q$ are placed on the planar surface of the hemisphere. Since they are on the boundary,we can imagine a complete sphere by placing an identical hemisphere on top of the given one.The total charge enclosed by this complete sphere is $Q_{enclosed} = 3q + 5q = 8q$.By symmetry,the flux through the original hemisphere is half of the total flux through the complete sphere.Therefore,the electric flux over the curved surface is $\phi = \frac{1}{2} 	imes \frac{Q_{enclosed}}{\varepsilon_0} = \frac{1}{2} 	imes \frac{8q}{\varepsilon_0} = \frac{4q}{\varepsilon_0}$.

The figure shows a hollow hemisphere of radius $R$ in which two charges $3q$ and $5q$ are placed symmetrically about the centre $O$ on the planar surface. The electric flux over the curved surface is

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