Question

A parallel plate capacitor has plate of area A and separation d.Its charged to a potential difference $V_0$.The charging battery is disconnected and the plates are pulled apart to three times the initial separation. the work required to separate the plates is:

• A. $\frac{{\epsilon }_{0}A{V}_0^2}{3d}$
• B. $\frac{{\epsilon }_{0}A{V}_0^2}{2d}$
• C. $\frac{{\epsilon }_{0}A{V}_0^2}{d}$
• D. $\frac{{\epsilon }_{0}A{V}_0^2}{4d}$

Answer 1

The correct option is C $\frac{{\epsilon }_{0}A{V}_0^2}{d}$

Initial energy =$\frac{q^2}{2c}$
$C_0\to \frac{C_p}{3}$
Initial energy $=\frac{3q^2}{2c}$
$workdone=\frac{q^2}{c}=2\times \frac{AE}{2d}{V}^2$

$workdone=\frac{{\epsilon }_{0}A{V_0}^2}{d}$