Potential due to a uniformly charged sphere

2026 Re-NEET 1 question

1. A unit positive point charge is taken slowly through an infinitesimally thin tube that is inside a charged dielectric sphere of radius R, having uniform positive charge density $\rho$, as shown in the figure. The initial and final positions of the charge are marked by A and B at distance 2R and 3R respectively, from the centre of the sphere. In this process, the magnitude of the total work done on the point charge is $\frac{\rho R^2}{n\varepsilon_0}$. The value of n is: ($\varepsilon_0$ is the permittivity of vacuum)