A unit positive point charge is taken slowly through an infinitesimally thin tube that is inside a charged dielectric sphere of radius R, having…

A unit positive point charge is taken slowly through an infinitesimally thin tube that is inside a charged dielectric sphere of radius $\displaystyle R$, having uniform positive charge density $\displaystyle \rho$, as shown in the figure. The initial and final positions of the charge are marked by $\displaystyle A$ and $\displaystyle B$ at distances $\displaystyle 2 R$ and $\displaystyle 3 R$ respectively, from the centre of the sphere. In this process, the magnitude of the total work done on the point charge is $\displaystyle \frac{\rho R^2}{n \epsilon_0}$. The value of $\displaystyle n$ is : ( $\displaystyle \epsilon_0$ is the permittivity of vacuum)