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Three large conducting parallel plates each having same area are connected to a battery. E1 is the energy stored between the plates initially and E2 finally and F1 is the force between plates 1 and 3 initially and F2 is the force between them finally.  
Match List I with List II and select the correct answer using the codes given below the lists.
 
  List I List II  
p. Now, the middle plate shifts towards the third plate very slowly keeping 1sand 3rd plates fixed. Initial and final situations shown in figure. Then   1.E1E2>1  
q. Three large conducting parallel plates each having same area are connected to the battery and the space between the 2nd and 3rd plates is filled with dielectric. Now, the dielectric is removed very slowly. Then   2.E1E2<1  
r. Three large conducting parallel plates each having same area and having charges Q2Q and Q respectively initially. Now first plate shifts towards the left and 3rd towards right keeping 2nd fixed. Then
3.F1F2<1  
s. Three large conducting parallel plates each having same area, charge on 1st plate is Q, on 2nd plate is Q and the third is uncharged. Now, the switch is closed. If F1 is the force between plate 1 and 3 initially and F2 is the force between them finally, then 4.F1F2=1  

  1. p - 2, q - 1, r - 4, s - 3
  2. p - 1, q - 2, r - 4, s - 3
  3. p - 2, q - 1, r - 3, s - 4
  4. p - 1, q - 2, r - 3, s - 4


Solution

The correct option is A p - 2, q - 1, r - 4, s - 3
(a)
C=Aϵ0d
E1=12cϵ2+12cϵ2
E2=122c3ϵ2+122cϵ2
Force between plates is given by F=Q1Q22Aϵ0

F1=c2ϵ22Aϵ0 
F2=2cϵ3.2cϵ2Aϵ0=2c2ϵ23Aϵ0 

Net charge flowing through the battery =2cϵ3
Work done by battery = 2cϵ3ϵ=23cϵ2

(b) 

C=Aϵ0d
E1=12cϵ2+12kcϵ2 
E2=12cϵ2+12cϵ2
F1=kc2ϵ22Aϵ0
F2=c2ϵ22Aϵ0 

Net charge flowing through the battery =(k1)cϵ
Work done by battery is -ve

(c)

Charge doesn't change as it is an isolated system.
E1=Q22C+Q22C
E2=Q22C1+Q22C1   (C1<C)
F1=Q22Aϵ0
F2=Q22Aϵ0

(d)

E1=Q22C
E2=Q28C+Q28C=Q24C
F1=0
F2=Q2/42Aϵ0=Q28Aϵ0

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