A parallel plate capacitor whose capacitance C is 14 pF is charged by a battery to a potential difference  V=12V between its plates. The charging battery is now disconnected and a porcelain plate with k=7 is inserted between the plates, then the plate would oscillate back and forth between the plates with a constant mechanical energy of ____ pJ. (Assume no friction)

The battery is charged to a potential U the energy stored in capacitor U=Q22C= 12CV2=12×14×12×12=7×144 pJ  When a dielectric plate is introduced the energy will change keeping charge constant as it is disconnected with batteryThe new energy of capacitor     U1=Q22C1=Q22C K=UK=7×1447=144pJThe change in energy will impose to the plate and it oscillates with energy of    U−U1=7×144−144 =6×144 =864pJ     [Note: Assume thickness of porcelain plate same as gap between capacitor plates]