Problem 3.103

The space between the plates of a parallel-plate capacitor is filled consecutively with two dielectric layers 1 and 2 having the thicknesses $d_{1}$ and $d_{2}$ and the permittivities $\varepsilon_{1}$ and $\varepsilon_{2}$ respectively The area of each plate is equal to $S .$ Find: (a) the capacitance of the capacitor; (b) the density $\sigma^{\prime}$ of the bound charges on the boundary plane if the voltage across the capacitor equals $V$ and the electric field is directed from layer 1 to layer 2 .