An uncharged spherical conductor of radius R=10r has two spherical cavities of radii ${\text{ R}}_{\text{1}}{\text{=2r\hspace{0.17em}\hspace{0.17em}and\hspace{0.17em}\hspace{0.17em}R}}_{\text{2}}\text{=3r}$ connected by an extremely narrow smooth tunnel. A, B are the centers of the cavities as shown. A point charge ‘q’ is arranged at B. Then it is transferred very slowly form B to A. which of the following statements is/aretrue?

 

Initial and final surface charge densities on the sphere at the point P are same

Initial and final energy densities at a distance $l(=16 r)$ from the centre of the sphere are same

The net electro static potential energy within the cavities increases as the charge is transferred from B to A

Work done by the agent in transferring the charge is $\frac{{\text{-q}}^{\text{2}}}{\text{48π}{\in }_{\text{0}}\text{r}}$