Tilted parallel-plate capacitor at fixed charge ($C={ϵ}_0{s}^2\log [(a+\delta )/(a-\delta )]/(2\delta )$)

For square plates with a linearly varying gap from $a-\delta$ to $a+\delta$, the local-strip approximation gives the displayed capacitance for $|\delta |<a$. Its expansion is $C=({ϵ}_0{s}^2/a)[1+{\delta }^2/(3a^2)+O({\delta }^4/a^4)]$. An isolated capacitor has fixed electric charge, so $U=Q^2/(2C)$ decreases as $|\delta |$ increases. A sinusoidal small tilt therefore produces a leading energy variation at twice the tilt frequency.