Three large identical conducting plates of area A are closely placed parallel to each other as shown (the area A is perpendicular to plane of diagram). The net charge on left , middle and right plates are Q_L, Q_M and Q_R respectively. Three infinitely large parallel surfaces S_L,S_M and S_R are drawn passing through middle of each plate such that surfaces are perpendicular to plane of diagram as shown. Then pick up the correct option(s).

 Since electric field at surface S_L is zero, net charge on left side of S_L is equal to net charge on right side of S_L. Further net charge between any two dotted surfaces (out of S_L, S_M and S_R) is zero from Gauss theorem.

$$\begin{gathered} \Rightarrow q_2=-q_3; q_3=-q_4; q_4=-q_5 \\ and, q_1=q_2+q_3+q_4+q_5+q_6 \end{gathered}$$

so, Charge on left most surface q₁ is equal to charge on right most surface q₆, that is, $q_1=q_6$.

$$\begin{gathered} \Rightarrow q_1+q_2+q_3+q_4+q_5+q_6=Q_L+Q_M+Q_R \\ \Rightarrow q_1=q_6=\frac{Q_L+Q_M+Q_R}{2} \\ \Rightarrow q_2=Q_L-q_1=\frac{{\displaystyle Q_L-\left(Q_M+Q_R\right)}}{{\displaystyle 2}} \\ \Rightarrow q_3=-q_2=-\frac{{\displaystyle Q_L-\left(Q_M+Q_R\right)}}{{\displaystyle 2}} \\ \Rightarrow q_4=Q_M-q_3=\frac{{\displaystyle Q_M-\left(Q_L+Q_R\right)}}{{\displaystyle 2}} \\ \Rightarrow q_5=-\frac{{\displaystyle Q_M-\left(Q_L+Q_R\right)}}{{\displaystyle 2}} \end{gathered}$$