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A point charge $+Q$ is placed just outside an imaginary hemispherical surface of radius $R$ as shown in the figure. Which of the following statements is/are correct?
(IMAGE)
$[A]$ The electric flux passing through the curved surface of the hemisphere is $-\frac{\mathrm{Q}}{2 \varepsilon_0}\left(1-\frac{1}{\sqrt{2}}\right)$
$[B]$ Total flux through the curved and the flat surfaces is $\frac{Q}{\varepsilon_0}$
$[C]$ The component of the electric field normal to the flat surface is constant over the surface
$[D]$ The circumference of the flat surface is an equipotential
$A,C$
$A,B$
$A,C,D$
$A,D$
Solution
Solid angle subtended by flat surface at position of charge
$ =2 \pi(1-\cos \theta)$
$=2 \pi\left(1-\cos 45^{\circ}\right)$
$=2 \pi\left(1-\frac{1}{\sqrt{2}}\right)$
Flux entering through curved surface $=$ flux leaving through flat surface
$\Rightarrow$ Flux entering through curved surface $=-\frac{\mathrm{Q}}{\varepsilon_0} \times \frac{1}{4 \pi} \times 2 \pi\left(1-\frac{1}{\sqrt{2}}\right)$
$=-\frac{Q}{2 \varepsilon_0}\left(1-\frac{1}{\sqrt{2}}\right)$
Also all points of circumference are at equal distance from the charge
