Two parallel plates that are initially uncharged are separated by $1.7 \mathrm {~mm}$, have only air between them, and each have surface areas of $16 \mathrm {~cm} ^ { 2 }$. How much charge must be transferred from one plate to the other if $1.9 \mathrm {~J}$ of energy are to be stored in the plates? $\left( \varepsilon _ { 0 } = 8.85 \times 10 ^ { - 12 } \mathrm { C } 2 / \mathrm { N } \cdot \mathrm { m } ^ { 2 } \right)$

Question

Quizplus · Accepted Answer

The energy stored in a capacitor is given by $ U = \frac{1}{2} \frac{Q^2}{C} $. The capacitance $ C $ of parallel plates is $ C = \frac{\varepsilon_0 A}{d} $. Solving for $ Q $ using $ U = 1.9 \mathrm{~J} $, $ A = 16 \times 10^{-4} \mathrm{~m}^2 $, $ d = 1.7 \times 10^{-3} \mathrm{~m} $, and $ \varepsilon_0 = 8.85 \times 10^{-12} \mathrm{~C}^2/\mathrm{N} \cdot \mathrm{m}^2 $, we find $ Q \approx 5.6 \mu \mathrm{C} $.

Two Parallel Plates That Are Initially Uncharged Are Separated By 1.7