Two square air-filled parallel plates that are initially uncharged are separated by 1.2 mm, and each of them has an area of 190 mm². How much charge must be transferred from one plate to the other if 1.1 nJ of energy are to be stored in the plates? (ε₀₀ = 8.85 × 10^-12 C²/N ∙ m²) A) 56 pC B) 39 pC C) 78 pC D) 3.5 µC

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Quizplus · Accepted Answer

The energy stored in a capacitor is given by U = 1/2 CV^2, where C is the capacitance and V is the voltage. The capacitance of a parallel-plate capacitor is given by C = εA/d, where ε is the permittivity of the material between the plates, A is the area of the plates, and d is the distance between the plates. In this problem, we have ε = ε0 = 8.85 × 10^-12 C^2/N ∙ m^2, A = 190 mm^2 = 1.9 × 10^-4 m^2, and d = 1.2 mm = 1.2 × 10^-3 m. Substituting these values into the equation for capacitance, we get C = 1.33 × 10^-12 F. Substituting this value of C into the equation for energy, we get U = 1/2 CV^2 = 1/2 (1.33 × 10^-12 F) V^2. Solving for V, we get V = 1.1 nJ / (1/2 (1.33 × 10^-12 F)) = 1650 V. The charge on each plate is given by Q = CV, so the charge that must be transferred from one plate to the other is Q = (1.33 × 10^-12 F) (1650 V) = 56 pC.

Two Square Air-Filled Parallel Plates That Are Initially Uncharged Are