Question

A parallel plate capacitor filled with air has a capacitance of $C$. The distance of separation between the plates is $d$ and the potential difference of $V$ is applied between the plates. Force of attraction between the plates of the parallel plate capacitor is

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

Answer 1

The correct option is C $\frac{C{V}^2}{2d}$

Force of attraction between the plates is $F=\frac{Q^2}{2A{ϵ}_0}$

or $F=\frac{C^2{V}^2}{2A{ϵ}_0}$ where $Q=CV$

also $C=\frac{A{ϵ}_0}{d}\Rightarrow A{ϵ}_0=Cd$

now, $F=\frac{C^2{V}^2}{2Cd}=\frac{C{V}^2}{2d}$