Consider a three$-$shell capacitor, where you have three concentric spherical shells $($of negligible thickness$)$ with radii R$,2$R$,$ and $3$R$.$ The inner and outer shells are connected by a wire $($passing through a tiny hole in the middle shell without touching it$),$ so they are always at the same potential.

The material between the shells is a linear dielectric of relative permittivity &r $=3.$

Find the capacitance of this capacitor. Hint: if you put a total charge $-$Q on the middle shell, an equal and opposite total charge Q must distribute itself over the inner and outer shells.