Q 12-02-076JEE MainJEE Main 2024 (9 Apr, Shift 1)Medium
A capacitor is made of a flat plate of area $A$ and a second plate having a stair-like structure as shown in the figure. If the area of each stair is $\dfrac A3$ and the height is $d$, the capacitance of the arrangement is:
Answer: (B) $\dfrac{11\epsilon_0A}{18d}$
The arrangement is three capacitors in parallel, each of area $\dfrac A3$, with separations $d$, $2d$ and $3d$:
$$C = \frac{\epsilon_0A}{3}\left(\frac1d + \frac1{2d} + \frac1{3d}\right) = \frac{\epsilon_0A}{3d}\times\frac{11}{6} = \frac{11\epsilon_0A}{18d}$$
Solution by Sreeraj P, M.Sc Physics