A capacitor is constructed from two square plates of sides and separation d. A material of dielectric constant 1 is inserted a distance x into

A capacitor is constructed from two square plates of sides ℓ and separation d. A material of dielectric constant 1 is inserted a distance x into the capacitor, as shown in Figure P26.64. Assume that d is much smaller than x.
(a) Find the equivalent capacitance of the device.
(b) Calculate the energy stored in the capacitor, letting ∆V represent the potential difference.
(c) Find the direction and magnitude of the force exerted on the dielectric, assuming a constant potential difference ∆V. Ignore friction.
(d) Obtain a numerical value for the force assuming that ℓ = 5.00 cm, ∆V = 2 000 V, d = 2.00 mm, and the dielectric is glass (1 = 4.50). (Suggestion: The system can be considered as two capacitors connected in parallel.)

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