Use the result of Problem to determine the capacitance for each of the following configura...

Use the result of Problem to determine the capacitance for each of the following configurations:

(a) Conducting plates are on top and bottom faces of the rectangular structure in Fig. P

(b) Conducting plates are on front and back faces of the structure in Fig. P

(c) Conducting plates are on top and bottom faces of the cylindrical structure in Fig. P

Figure P: Dielectric section for Problems

Problem

Figure 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 ε1 and surface area A1 and another with ε2 and A2. The objective of this problem is to show that the capacitance C of the configuration shown in Fig. is equivalent to two capacitances in parallel, as illustrated in Fig. with

To this end, proceed as follows:

(a) Find the electric fields E1 and E2 in the two dielectric layers.

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(b) Calculate the energy stored in each section and use the result to calculate C1 and C2.

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(c) Use the total energy stored in the capacitor to obtain an

(a) Capacitor with parallel dielectric section, and. expression for C. Show that is indeed a valid result.