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  4. A parallel plate capacitor whose capacitance C is 14 pF is charged by a battery to a potential difference V = 12 V between its plates. The charging battery is now disconnected and a porcelin 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)

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Q. A parallel plate capacitor whose capacitance $C$ is $14\, pF$ is charged by a battery to a potential difference $V = 12 V$ between its plates. The charging battery is now disconnected and a porcelin 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)

JEE MainJEE Main 2021Electrostatic Potential and Capacitance

Solution:

$U _{ i }=\frac{1}{2} \times 14 \times 12 \times 12\, pJ \left(\because U =\frac{1}{2} CV ^{2}\right)$
$=1008 \,pJ$
$U _{ f }=\frac{1008}{7} pJ =144 \,pJ \left(\because C _{ m }= kC _{0}\right)$
Mechanical energy $=\Delta U$
$=1008-144$
$=864\, pJ$