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 $-\frac{Q}{2{\in }_0}(1-\frac{1}{\sqrt{2}})$
• B. The component of the electric field normal to the flat surface is constant over the surface
• C. Total flux through the curved and the flat surface is $\frac{Q}{{\in }_0}$
• D. The circumference of the flat surface is an equipotential

Answer 1

Answer: (A), (D)

The circumference of the flat surface is an equipotential

The circumference of the flat surface is an equipotential because the distance of each point on the circumference is equal from $+Q$

$\therefore$ option D is correct.
The component of electric field normal to flat surface is $Ecos\theta$.
Here $E$ as well as $\theta$ changes for diffrent point on the flat surface.
$\therefore$option B is incorrect
The total flux through the curved and the flat surface should be less than $\frac{Q}{{ϵ}_o}$. Therefore option B is incorrect.
The solid angle subtended by the flat surface at
$P=2\pi (1-\frac{1}{\sqrt{2}})$

$\therefore$ Flux passing through curved surface
$=-\frac{Q^{\prime }}{{ϵ}_o}\frac{2\pi (1-\frac{1}{\sqrt{2}})}{4\pi }=-\frac{Q}{2{ϵ}_o}(1-\frac{1}{\sqrt{2}})$
option A is correct.