Energy in capacitors: 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)

Question

Quizplus · Accepted Answer

The energy stored in a capacitor is given by:

$E=\frac{1}{2}CV^2$

We can rearrange this equation to solve for the charge Q:

$E=\frac{1}{2}CV^2=\frac{1}{2}\frac{\epsilon A}{d}V^2=\frac{1}{2}\frac{\epsilon A}{d}\left(\frac{Q}{C}ight)^2$

$1.1 nJ =\frac{1}{2}(8.85	imes10^{-12})(190 	imes 10^{-6})\left(\frac{Q}{1.2	imes10^{-3}}ight)^2$

$Q^2= \frac{2 	imes 1.1 	imes 10^{-9} 	imes 1.2 	imes 10^{-3}}{8.85 	imes 10^{-12} 	imes 190 	imes 10^{-6}}$

$Q^2=369.6 	imes 10^{-12}$

$Q= \sqrt{369.6} 	imes 10^{-6}$

$Q= 56 pC$

Therefore, the answer is (A) 56 pC.

Energy in Capacitors: Two Square Air-Filled Parallel Plates That Are