spherical condenser has 10cm and 12 cm as the radii of inner and outer spheres. The space between the two is filled with a dielectric of dielectric constant 3. Find the capacity when the inner sphere is earthed.

$\frac{32}{15} \times 10^{-10} F$

By choice of reference potential at infinity and the potential of earthed conductor zero, the given system can be visualised as combination of two spherical capacitors, both being at same potential difference.

Connection wise these may be considered to be in parallel connection.

∴ $C=4 \pi \varepsilon_0 b+4 \pi k \varepsilon_0\left(\frac{a b}{b-a}\right)=\frac{32}{15} \times 10^{-10} F$