Three identical metal plates are kept parallel to one another at a separation $a$ and $b$ as shown in the figure. The outer plates are connected by a thin conducting wire and charge $Q$ is placed on the central plate.

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Let the charge distribution be as shown Net charge on A and C is zero

$∴ q_{2} - q_{1} + q_{3} + q_{1} - Q = 0$

$\Rightarrow q_{2} + q_{3} = Q \to (1)$

$V_{A} = V_{C}$

$\Rightarrow E_{1} a = E_{2} b$

$q_{1} a = (Q - q_{1}) b$

$q_{1} = \frac{Qb}{a + b} \to (2)$

Electric field inside any conducting plate (C) is zero

$\Rightarrow q_{2} - q_{3} = 0 \to$ (3) solve (1), (2) and (3)

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