Question

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?

• A. The electric flux passing through the curved surface of the hemisphere is $-\frac{Q}{25_{0}}\left(1-\frac{1}{\sqrt{2}}\right)$
• 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

Answer 1

Answer: (A), (D)

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
$=-\frac{ Q }{\varepsilon_{0}} \times \frac{1}{4 \pi} \times 2 \pi\left(1-\frac{1}{\sqrt{2}}\right)$
$=-\frac{ Q }{2 \varepsilon_{0}}\left(1-\frac{1}{\sqrt{2}}\right)$
Also all points of circumference are at equal distance from the charge