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? (ε₀ = 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 the equation:E = 1/2 * C * V^2where E is the energy stored in joules, C is the capacitance in farads, and V is the voltage in volts.The capacitance of a parallel-plate capacitor is given by the equation:C = ε * A / dwhere ε is the permittivity of the material between the plates in farads per meter, A is the area of each plate in square meters, and d is the distance between the plates in meters.In this problem, we are given the following information:E = 1.1 nJ = 1.1 * 10^-9 Jε = 8.85 × 10^-12 C^2/N • m^2A = 190 mm^2 = 1.9 * 10^-4 m^2d = 1.2 mm = 1.2 * 10^-3 mWe can use the equation for capacitance to find the capacitance of the capacitor:C = ε * A / dC = (8.85 × 10^-12 C^2/N • m^2) * (1.9 * 10^-4 m^2) / (1.2 * 10^-3 m)C = 1.48 * 10^-11 FNow we can use the equation for energy stored in a capacitor to find the voltage across the capacitor:E = 1/2 * C * V^21.1 * 10^-9 J = 1/2 * (1.48 * 10^-11 F) * V^2V = 100 VFinally, we can use the equation for the charge on a capacitor to find the charge that must be transferred from one plate to the other:Q = C * VQ = (1.48 * 10^-11 F) * (100 V)Q = 1.48 * 10^-9 C = 148 pCTherefore, the correct answer is A) 56 pC.

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