456 figure p456a depicts a capacitor consisting of two parallel conduc

Question

4.56 Figure P4.56(a) depicts a capacitor consisting of two parallel, conducting plates separated by a distance d. The space between the plates contains two adjacent dielectrics: one with permittivity & and surface area A1 and another with & and A2. The objective of this problem is to show that the capacitance C of the configuration shown in Fig. P4.56(a) is equivalent to two capacitances in parallel, as illustrated in Fig. P4.56(b),with C=C1+C2, where \begin{array}{l}
C_{1}=\frac{\varepsilon_{1} A_{1}}{d} \\
C_{2}=\frac{\varepsilon_{2} A_{2}}{d}
\end{array} To this end, proceed as follows: