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 $\frac{Q}{{\epsilon }_0}$
• 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
$=-\frac{Q}{{\epsilon }_0}\times \frac{1}{4\pi }\times 2\pi \left(1-\frac{1}{\sqrt{2}}\right)$
$=-\frac{Q}{2{\epsilon }_0}\left(1-\frac{1}{\sqrt{2}}\right)$
Also all points of circumference are at equal distance from the charge