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A capacitor is made of a flat plate of area ' $A$ ' and the second plate has staircase like structure. Width of each stair is ' $a$ ' and its height is ' $b$ '. The capacity of the capacitor is
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The correct answer is:
$\frac{\epsilon_0^A}{2 d}\left[\frac{2 d+b}{d+b}\right]$
Above capacitor can be considered as parallel combination of two capacitors of different width $\mathrm{d}$ and $\mathrm{b}+\mathrm{a}$ with each have cross-section $\frac{\mathrm{A}}{2}$.
$C=C_1+C_2=\frac{\varepsilon_0\left(\frac{A}{2}\right)}{d}+\frac{\varepsilon_0\left(\frac{A}{2}\right)}{d+b}=\frac{\varepsilon_0 A}{2 d}\left\{\frac{2 d+b}{(d+b)}\right\}$
$C=C_1+C_2=\frac{\varepsilon_0\left(\frac{A}{2}\right)}{d}+\frac{\varepsilon_0\left(\frac{A}{2}\right)}{d+b}=\frac{\varepsilon_0 A}{2 d}\left\{\frac{2 d+b}{(d+b)}\right\}$
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