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)

Question

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)

Infinity Learn · Accepted Answer

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]

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