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Question

Two identical capacitors are connected as shown and having initial charge Q0. Separation between plates of each capacitor is d0. Suddenly, the left plate of upper capacitor and right plate of lower capacitor starts moving with speed v towards left while other plate of each capacitor remains fixed.
(given Q0V2d0=10 A). The value of current (in A) in the circuit is


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Solution

From conservation of charge,
q1+q2=2Q0....(1)
At time t
C1=ϵ0Ad0+Vt, C2=ϵ0Ad0Vt

q1C1=q2C2

q1q2=d0Vtd0+Vt
Substituting in (1)
q2+q2(d0Vtd0+Vt)=2Q0
q2(2d0d0+Vt)=2Q0
q2=2Q02d0(d0+Vt)I=dq2dt=Q0Vd0=20 A

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