A positive, singly ionized atom of mass number $A_{\mathrm{M}}$ is accelerated from rest by the voltage $192 \mathrm{~V}$. Thereafter, it enters a rectangular region of width $w$ with magnetic field $\vec{B}_0=0.1 \hat{k}$ Tesla, as shown in the figure. The ion finally hits a detector at the distance $x$ below its starting trajectory.
[Given: Mass of neutron/proton $=(5 / 3) \times 10^{-27} \mathrm{~kg}$, charge of the electron $=1.6 \times 10^{-19} \mathrm{C}$.]
![JEE Advanced 2024 Paper 2 Online Physics - Magnetism Question 1 English](https://app-content.cdn.examgoal.net/fly/@width/image/6y3zli1lwpws4a7/cbba90e3-77ec-4288-acb0-204aa25d5dc6/546a73f0-1cac-11ef-a7f1-8b6b33c30c4d/file-6y3zli1lwpws4a8.png?format=png)
Which of the following option(s) is(are) correct?
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)