The parallel-plate air capacitor in Fig consists of two horizontal conducting plates of equal area A. The bottom plate rests on a fixed support, and the top plate is suspended by four springs with spring constant k, positioned at each of the four corners of the top plate as shown in the figure. When uncharged, the plates are separated by a distance Z0 A battery is connected to the plates and produces a potential difference V between them. This causes the plate separation to decrease to z. Neglect any fringing effects.
(a) Show that the electrostatic force between the charged plates has a magnitude є0Av2/2z2.
(b) Obtain an expression that relates the plate separation z to the potential difference V. The resulting equation will be cubic in z.
(c) Given the values A = 0.300 m2, Z0 = 1.20 mm, k = 25.0 N/m and V = 120 V, find the two values of z for which the top plate will be in equilibrium.
(d) For each of the two values of z found in part (c), is the equilibrium stable or unstable? For stable equilibrium a small displacement of the object will give rise to a net force tending to return the object to the equilibrium position. For unstable equilibrium a small displacement gives rise to a net force that takes the object farther away from equilibrium.

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A.