Question

# 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 1st and 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 −Q, 2Q 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   p - 2, q - 1, r - 4, s - 3p - 1, q - 2, r - 4, s - 3p - 2, q - 1, r - 3, s - 4p - 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 =−(k−1)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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