Answer to Question #306688 in Physics for rust

Question

A capacitor of capacitance 20 micro-microfarads consists of two parallel plates each moving an area of 200 cm^2, separated in air a distance d apart. This condenser is charged to a difference in potential of 200 V and it is then disconnected from the source. Find (a) the distance of separation d, (b) the charge stored in the condenser, (c) the work done in storing this charge, and (d) the work needed to pull the plates apart to a distance of 3d.

Answer 1

Given:

$C=20*10^{-6}\:\rm F$

$A=200*10^{-4}\:\rm m^2$

$V=200\:\rm V$

(a)

$$C=\frac{\epsilon_0 A}{d}$$

$$d=\frac{\epsilon_0 A}{C}\\ =\frac{8.85*10^{-12}* 200*10^{-4}}{20*10^{-6}}=8.85*10^{-9}\:\rm m$$

(b)

$$q=CV=20*10^{-6}*200=0.004\:\rm C$$

(c)

$$E_p=\frac{CV^2}{2}=\frac{20*10^{-6}*200^2}{2}=0.4\:\rm J$$

(d)

$$W=\Delta E_p=E_p-\frac{1}{3}E_p=\frac{2}{3}E_p=0.26\:\rm J$$