Question

A capacitor is made of a flat plate of area $A$ and a plate having stair-like shape as shown in figure. The width of each stair is $A/3$ and the height is $d$. Calculate the capacity of the capacitor.

Answer 1

$C_{eq}=C_1+C_2+C_3$

$=\frac{{ϵ}_{0}A}{3d}+\frac{{ϵ}_{0}A}{3(b+d)}+\frac{{ϵ}_{0}A}{3(2b+d)}$

$=\frac{{ϵ}_{0}A}{3}(\frac{1}{d}+\frac{1}{b+d}+\frac{1}{2b+d})$

$=\frac{{ϵ}_{0}A(3d^2+6bd+2b^2)}{3(b+d)(2b+d)}$