Suppose you have enough linear dielectric material, of dielectric constant r, to half-fill a parallel-plate capacitor (Fig. 4.25). By what fraction is the capacitance increased

Suppose you have enough linear dielectric material, of dielectric constant εr, to half-fill a parallel-plate capacitor (Fig. 4.25). By what fraction is the capacitance increased when you distribute the material as in Fig. 4.25(a)? How about Fig. 4.25(b)? For a given potential difference V between the plates, find E, D, and P, in each region, and the free and bound charge on all surfaces, for both cases.

(a) (b)