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 ρ, as shown in the figure. The initial and final positions of the charge are marked by A and B at distances 2R and 3R resp…

Question

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 ρ, as shown in the figure. The initial and final positions of the charge are marked by A and B at distances 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 (ρ R²)/(nε₀). The value of n is : (ε₀ is the permittivity of vacuum)

Accepted Answer

(4) 18. The work done on the charge depends only on the end points, not on the path through the tube: W=q(V_B-V_A) with q=1. A and B are outside the sphere, where it acts as a point charge Q=4/3π R³ρ. |W|=kQ(1/(2R)-1/(3R))=(kQ)/(6R)=1/(4πε₀)·(4π R³ρ)/(3×6R). |W|=(ρ R²)/(18ε₀), so n=18.

Step-by-step solution

Why the other options are wrong