A capacitor is formed by two square metal plate of edge a,separated by a distance d.Dielectric constants `K_1 and K_2`are filled in the gap as shown in figure(31-E25).Find the capacitance.

Explanation

Consider an elemental capacitor of which dx at a distance 'x' from one end. It is constituted of two capacitance elemnts of dielectric constants K_1 and K_2 with palte separartion x tan theata and d - x tan theata respectively in series.
Effective capacitance ` K = K_1 K_2 / K_1 - K_2 ln K_1 / K_2 `
So, `C = epsilon_0 KA / d `
` epsilon K_1 K_2 a^(2) / (K_1 - K_2 ) d in (K_1 /K_2) [where , A = a^(2)] `