A capacitor is composed of three parallel conducting plates. All three plates are of the same area A. The first pair of plates are kept a distance `d_(1)` apart, and the space between them is filled with a medium of a dielectric `K_(1)` . The corresponding data of the second pair are `d_(2)` and `K_(2)`, respectively. The middle plate is connected to the positive terminal of a constant voltage source V and the external plates are connected the other terminal of V.

(a) Find the capacitance of the system .
(b) What is the surface charge density on the middle plate ?
(c) Compute the energy density in the medium `K_(1)`

Answer

`(a) in_(0)A((K_(1))/(d_(1))+(K_(2))/(d_(2))), " " (b)(Q_(1))/(A)=((K_(1)in_(0)A)/(d_(1)))(V)/(A)=(K_(1)in_(0))/(d_(1))V and (Q_(2))/(A)=((K_(2)in_(0)A)/(d_(2)))(V)/(A)=(K_(2)in_(0))/(d_(2))V " " (c) (in_(0)K_(1)V^(2))/(2d_(1)^(2))`