Four large parallel identical conducting plates of area A are arranged as shown in fig. The charges on each plate are given in the figure and the separation between the plates is d(d is very small). The surfaces of the plates are numbered (1), (2),....(8).

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Solution

As the plates are conducting so the electric field at points P,Q, R and S inside the plates should be zero.
At P, $\frac{1}{2 A ϵ_{0}} [4 Q - q_{2} - q_{2} - Q + q_{4} - q_{4} - 2 Q + q_{6} - q_{6} - 7 Q + q_{8} - q_{8}] = 0 \Rightarrow q_{2} = - 3 Q$
At Q, $\frac{1}{2 A ϵ_{0}} [4 Q - q_{2} + q_{2} + Q - q_{4} - q_{4} - 2 Q + q_{6} - q_{6} - 7 Q + q_{8} - q_{8}] = 0 \Rightarrow q_{4} = - 2 Q$
At R, $\frac{1}{2 A ϵ_{0}} [4 Q - q_{2} + q_{2} + Q - q_{4} + q_{4} + 2 Q - q_{6} - q_{6} - 7 Q + q_{8} - q_{8}] = 0 \Rightarrow q_{6} = 0$
At S, $\frac{1}{2 A ϵ_{0}} [4 Q - q_{2} + q_{2} + Q - q_{4} + q_{4} + 2 Q - q_{6} + q_{6} + 7 Q - q_{8} - q_{8}] = 0 \Rightarrow q_{8} = 7 Q$
Thus, $q_{1} = 4 Q - q_{2} = 4 Q - (- 3 Q) = 7 Q, q_{3} = Q - q_{4} = Q - (- 2 Q) = 3 Q, q_{5} = 2 Q - q_{6} = 2 Q, Q_{7} = 7 Q - q_{8} = 7 Q - 7 Q = 0$

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