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(A, C) According to Gauss's Law,the total electric flux $\phi_{	ext{total}}$ through any closed surface in a region with no enclosed charge is zero,i

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Total flux enclosed is zero.

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(A, C) According to Gauss's Law,the total electric flux $\phi_{	ext{total}}$ through any closed surface in a region with no enclosed charge is zero,i.e.,$\phi_{	ext{total}} = 0$.For the hemisphere,$\phi_{	ext{total}} = \phi_{	ext{curved}} + \phi_{	ext{flat}} = 0$.The flux through the flat circular surface is $\phi_{	ext{flat}} = -E \cdot A = -E(\pi R^2)$ (since the field lines enter the surface).Therefore,$\phi_{	ext{curved}} = -\phi_{	ext{flat}} = E \pi R^2$.Thus,statement $(A)$ is correct and $(C)$ is correct.Regarding the work done,for a uniform electric field,the potential difference $\Delta V = -\vec{E} \cdot \Delta \vec{r}$.Since points $A$ and $B$ lie on the same equipotential plane perpendicular to the electric field $\vec{E}$,the potential difference between $A$ and $B$ is $\Delta V = 0$.Therefore,the work done $W = q \Delta V = 0$,which is independent of the path and the radius $R$.

$A$ hemisphere of radius $R$ is placed in a uniform electric field $E$ so that its axis is parallel to the field. Which of the following statement$(s)$ is/are true?

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