Question

A parallel plate air capacitor has capacity $C$, distance of separation between plates is $d$ and potential difference $V$ is applied between the plates. Force of attraction between the plates of the parallel plate air capacitor is

• A. $\frac{C{V}^2}{d}$
• B. $\frac{C^2{V}^2}{2d^2}$
• C. $\frac{C^2{V}^2}{2d}$
• D. $\frac{C{V}^2}{2d}$

Answer 1

Answer: (D)

Force of attraction between the plates of the parallel plate air capacitor is
$F=\frac{Q^2}{2{\epsilon }_{0}A}$
where Q is the charge on the capacitor, ${\epsilon }_0$ is the permittivity of free space and A is the area of each plate.
But Q = CV and
$C=\frac{{\epsilon }_{0}A}{d}$ or ${\epsilon }_{0}A=Cd$
$\therefore F=\frac{C^2{V}^2}{2Cd}=\frac{C{V}^2}{2d}$