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Q.

Two square metal plates of side 1 m are kept 0.01 m apart like a parallel plate capacitor in air in such a way that one of their edges is perpendicular to an oil surface in a tank filled with an insulating oil. The plates are connected to a battery of 500 V. The plates are then lowered vertically into the oil at a speed of 0.001 ms1. The current n×109A drawn from the battery during the process. Then find the value of n. (Dielectric constant of oil = 11], (0 = 8 × 1012 C2 N1 m1)

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answer is 4.

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Detailed Solution

Let a be the side of the square plate.  
As shown in figure, C1 and C2 are in parallel. Therefore,  total capacity of capacitors in the position shown is 
 C = C1 + C2 
 C =  0a(ax)d+K0axd
 q = CV = 0aVd  (a – x + Kx)
As plates are lowered in the oil, C increases hence charge stored will increase. 
Therefore, i =dqdt  =0aVd   (K–1) ·  dxdt
Substituting the values
 0= 8 × 1012 C2/Nm2
a = 1m, V = 500 volt, d = 0.01m, K = 11 and dxdt  = speed of plate = 0.001 m/s  
We get current  i =  (8×1012) 1    (500) (111 ) (0.001)(0.01)  Amp.
 i = 4

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