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 correct options are
A The electric flux passing through the curved surface of the hemisphere is $-\frac{Q}{2{\in }_0}(1-\frac{1}{\sqrt{2}})$
D The circumference of the flat surface is an equipotential

$\varphi =\frac{q}{2{ϵ}_0}(1-cos\varphi )$

$Here,\varphi =\frac{\pi }{4}$

So, $\varphi =\frac{q}{2{ϵ}_0}(1-\frac{\pi }{4})$

$\varphi =\frac{-q}{2{ϵ}_0}(1-\frac{1}{\sqrt{2}})$

Also the circumference of the flat surface is an equipotential.