Problem 20.47

20.47
The work done to separate the two plates is given by
$W = \int_{0}^{x} F dx$
But, we know that the energy stored in the capacitor is given by
$U = \frac{1}{2} \frac{Q^{2}}{C}$
Equating these two and differentiating, we find that
$F = \frac{d}{dx} \frac{Q^{2}}{2C} = \frac{d}{dx} \frac{Q^{2}x}{2\epsilon_{0}A}$
$F = \frac{Q^{2}}{2\epsilon_{0}A}$