Problem 3.84

Initially the space between the plates of the capacitor is filled with air, and the field strength in the gap is equal to $E_{0}$. Then half the gap is filled with uniform isotropic dielectric with permittivity $\varepsilon$ as shown in Fig. $3.12 .$ Find the moduli of the vectors $\mathbf{E}$ and $\mathbf{D}$ in both parts of the gap $(1$ and 2$)$ if the introduction of the dielectric (a) does not change the voltage across the plates; (b) leaves the charges at the plates constant.