Three identical square plates each of surface area A are arranged as shown in the figure. Plates 1, 2, and 3 are given charges $+ 2 Q, - Q$ and $- Q$ respectively. Find out the correct options

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Charges on the two forces of the middle plate are $- \frac{Q}{2}$ and $- \frac{Q}{2}$ , if plates 1 and 3 are connected through a conducting wire

Charge on the two faces of the middle plate are – 2Q and +Q

Energy of the system is $(\frac{5}{2} \frac{Q^{2} d}{ε_{0} A})$

Energy of the system is $(\frac{3}{2} \frac{Q^{2} d}{ε_{0} A})$

answer is A, B, C.

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Detailed Solution

In option A charges on outer surfaces of 1 and 3 plate will not change. $O + q_{1} - q_{2} + O = + Q$ [Conservation of charge on plates 1 and 3]
$q_{1} - q_{2} = Q$ ………….. (i)
$V_{1} - V_{3} = 0 = \frac{q_{1} d}{A ε_{0}} + \frac{q_{2} d}{A ε_{0}} ......... (i i i)$
By solving these two equations $q_{1} = q_{2} = \frac{Q}{2}$