Capacitance of an Isolated Spherical Capacitor

A spherical capacitor has an inner sphere of radius $12 \mathrm{cm}$ and an outer sphere of radius $13 \mathrm{cm}$. The outer sphere is earthed, and the inner sphere is given a charge of $2.5 \mathrm{\mu C}$. The space between the concentric spheres is filled with a liquid of dielectric constant $32$. Determine the capacitance of the capacitor. Also, what is the potential of the inner sphere. Compare the capacitance of this capacitor with that of an isolated sphere of radius 12 cm. Explain why the latter is much smaller.

A spherical capacitor consists of two concentric spherical conductors, held in position by suitable insulating supports. Show that the capacitance of a spherical capacitor is given by $C=\frac{4\pi {\epsilon }_0{r}_1{r}_2}{r_1-r_2}$where $r_1$and $r_2$are the radii of outer and inner spheres, respectively.