A charge is kept at the central point $\mathrm{P}$ of a cylindrical region. The two edges subtend a half-angle $\theta$ at $\mathrm{P}$, as shown in the figure. When $\theta=30^{\circ}$, then the electric flux through the curved surface of the cylinder is $\Phi$. If $\theta=60^{\circ}$, then the electric flux through the curved surface becomes $\Phi / \sqrt{n}$, where the value of $n$ is ___.
![JEE Advanced 2024 Paper 2 Online Physics - Electrostatics Question 2 English](https://app-content.cdn.examgoal.net/fly/@width/image/6y3zli1lwpwz485/37aa84bd-f29d-4048-be41-27e03c06328f/17092550-1cad-11ef-a7f1-8b6b33c30c4d/file-6y3zli1lwpwz486.png?format=png)
Two equilateral-triangular prisms $\mathrm{P}_1$ and $\mathrm{P}_2$ are kept with their sides parallel to each other, in vacuum, as shown in the figure. A light ray enters prism $\mathrm{P}_1$ at an angle of incidence $\theta$ such that the outgoing ray undergoes minimum deviation in prism $\mathrm{P}_2$. If the respective refractive indices of $\mathrm{P}_1$ and $\mathrm{P}_2$ are $\sqrt{\frac{3}{2}}$ and $\sqrt{3}$, then $\theta=\sin ^{-1}\left[\sqrt{\frac{3}{2}} \sin \left(\frac{\pi}{\beta}\right)\right]$, where the value of $\beta$ is ____.
![JEE Advanced 2024 Paper 2 Online Physics - Geometrical Optics Question 2 English](https://app-content.cdn.examgoal.net/fly/@width/image/6y3zli1lwpx4jkd/771b8365-f2ad-4f6c-8cf9-cf2ccef72a53/adee4bd0-1cad-11ef-a7f1-8b6b33c30c4d/file-6y3zli1lwpx4jke.png?format=png)
An infinitely long thin wire, having a uniform charge density per unit length of $5 \mathrm{nC} / \mathrm{m}$, is passing through a spherical shell of radius $1 \mathrm{~m}$, as shown in the figure. A $10 \mathrm{nC}$ charge is distributed uniformly over the spherical shell. If the configuration of the charges remains static, the magnitude of the potential difference between points $\mathrm{P}$ and $\mathrm{R}$, in Volt, is ________.
[Given: In SI units $\frac{1}{4 \pi \epsilon_0}=9 \times 10^9, \ln 2=0.7$. Ignore the area pierced by the wire.]
![JEE Advanced 2024 Paper 2 Online Physics - Electrostatics Question 1 English](https://app-content.cdn.examgoal.net/fly/@width/image/6y3zli1lwpx6vn9/578e82d5-01e8-4528-9808-19d31dc92cc0/eee17e50-1cad-11ef-a7f1-8b6b33c30c4d/file-6y3zli1lwpx6vna.png?format=png)