Chapter 24, Problem 24.62P

An air capacitor is made by using two flat plates, each with area A, separated by a distance d. Then a metal slab having thickness a (less than d) and the same shape and size as the plates is inserted between them, parallel to the plates and not touching either plate (Fig. P24.62). (a) What is the capacitance of this arrangement? (b) Express the capacitance as a multiple of the capacitance C₀ when the metal slab is not present, (c) Discuss what happens to the capacitance in the limits a → 0 and a → d.

Figure P24.62