JEE Advanced · 2017 · 21 May 2017 · Paper 2 · Electrostatics

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?

1. (A)The electric flux passing through the curved surface of the hemisphere is $-\frac{Q}{2{\epsilon }_0}\left(1-\frac{1}{\sqrt{2}}\right)$✓ Correct
2. (B)Total flux through the curved and the flat surfaces is $\frac{Q}{{\epsilon }_0}$
3. (C)The component of the electric field normal to the flat surface is constant over the surface
4. (D)The circumference of the flat surface is an equipotential✓ Correct

Answer: (A), (D)

Solution

The solid angle subtended by the flat surface at the charge position is $2\pi (1-\cos 45°)=2\pi (1-\frac{1}{\sqrt{2}})$. The flux through the flat surface (and hence entering through the curved surface) is $-\frac{Q}{{\epsilon }_0}\cdot \frac{2\pi (1-1/\sqrt{2})}{4\pi }=-\frac{Q}{2{\epsilon }_0}(1-\frac{1}{\sqrt{2}})$. All points on the circumference are equidistant from the charge, making it an equipotential. The normal component of electric field varies over the flat surface, and the total flux is not $Q/{\epsilon }_0$.

JEE Advanced · 2017 · 21 May 2017 · Paper 2 · One or more correct options