Q: Capacitor has square plates each of side ‘ l ‘ making an angle ‘ α ‘ with each other as shown. Then for small value of α , the capacitance ‘C’ is given by

Solution : At one side, distance between plates d,

At another side,

distance = d + l sinα ≅ d + l α

Mean distance between the plates

$\displaystyle = \frac{d + d + l \alpha}{2}$

$\displaystyle = d + \frac{l \alpha}{2}$

Capacity , $\displaystyle C = \frac{\epsilon_0 A}{d}$

$\displaystyle C = \frac{\epsilon_0 l^2 }{d + \frac{l \alpha}{2}}$

$\displaystyle C = \frac{\epsilon_0 l^2}{d} [1 + \frac{l \alpha}{2 d}]^{-1} $

$\displaystyle C = \frac{\epsilon_0 l^2}{d} [1 – \frac{l \alpha}{2 d}]$