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.