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)
A charge $q$ is surrounded by a closed surface consisting of an inverted cone of height $h$ and base radius $R$, and a hemisphere of radius $R$ as shown in the figure. The electric flux through the conical surface is $\frac{n q}{6 \epsilon_{0}}$ (in SI units). The value of $n$ is _______.
![JEE Advanced 2021 Paper 1 Online Physics - Electrostatics Question 25 English](https://imagex.cdn.examgoal.net/1kuckukw8/c24bb5d1-c27d-4b77-9124-2c34dab330a0/4279cc80-2507-11ec-b291-1df06cb45b25/file-1kuckukw9.png)
The value of R is __________ meter.
![JEE Advanced 2021 Paper 1 Online Physics - Electrostatics Question 26 English](https://imagex.cdn.examgoal.net/1kuckukw8/c24bb5d1-c27d-4b77-9124-2c34dab330a0/4279cc80-2507-11ec-b291-1df06cb45b25/file-1kuckukw9.png)
The value of b is __________ meter.