Problem 3.104

The gap between the plates of a parallel-plate capacitor is filled with isotropic dielectric whose permittivity $\varepsilon$ varies linearly from $\varepsilon_{1}$ to $\varepsilon_{2}\left(\varepsilon_{2}>\varepsilon_{1}\right)$ in the direction perpendicular to the plates. The area of each plate equals $S,$ the separation between the plates is equal to $d$. Find: (a) the capacitance of the capacitor; (b) the space density of the bound charges as a function of $\varepsilon$ if the charge of the capacitor is $q$ and the field $\overrightarrow{\mathrm{E}}$ in it is directed toward the growing $\varepsilon$ values.