A capacitor has two square plates each of side `l` making an angle `theta` between them as shown in Fig. Calculate capacitor of the arrangement for small values of `theta`

Explanation

At one side, distance between plates `d`,
At another side,
distance `= d + l sin alpha = d + l alpha`
Mean distance between the plates
`= (d(d+l alpha))/(2) =d +(l alpha)/(2)`
Capacity `C=(in_(0)A)/(d)=(in_(0)l^(2))/(d+(l alpha)/(2))`
`= =(in_(0)l^(2))/(d)[1+(l alpha)/(2d)]^(-1) =(in_(0) l^(2))/(d)[1-(l alpha)/(2d)]`.