Derive expression for capacitance of a spherical conductor.

A parallel-plate capacitor of area $A$, plate separation $d$ and capacitance $C$ is filled with four dielectric materials having dielectric constants$k_1$, $k_2$, $k_3$ and $k_4$ as shown in the figure below. If a single dielectric material is to be used to have the same capacitance $C$ in this capacitor, then its dielectric constant $k$ is given by

Half of the space of a parallel plate capacitor is filled with a dielectric as shown. A potential difference $V_0$ is applied across the plates. The electric field between the plates in the space with dielectric is $E_1$ and in the space without dielectric is ${\mathrm{E}}_2$ then