A parallel plate capacitor of plate area A and spac- ing between the plates d is filled with three dielectrics as shown in the Figure. The dielectric constants of the three dielectrics are `K_(1) = K, K_(2) = 2 K, K_(3) = 3 K`. The capacitor is connected to a cell of emf V.
(a) Write the ratio of maximum to minimum charge density on the surface of the capacitor plate.
(b) Calculate the surface charge density of bound (induced) charge on the middle dielectric.
(c) If the three dielectrics occupy equal volume between the plates, calculate the capacitance of the capacitor.

Answer

(a) `(sigma_(max))/(sigma_(min))`
(b) `sigma_(b)=(in_(0)V)/(d)(2K-1)`
(c) `C=(2K in_(0)A)/(d)`