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(A) For a system of parallel plates,the charge on the outermost surfaces is equal and is given by the sum of all charges divided by $2$.Let the charge

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$\frac{Q_1 + Q_2 + Q_3}{2}$

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(A) For a system of parallel plates,the charge on the outermost surfaces is equal and is given by the sum of all charges divided by $2$.Let the charge on surface '$a$' be $q_a$ and on surface '$f$' be $q_f$.By the property of parallel plates,$q_a = q_f$.Since the total charge on the system is $Q_{total} = Q_1 + Q_2 + Q_3$,and the charge on the outermost surfaces must be equal to maintain the electric field outside the system as zero,we have:$q_a + q_f = Q_1 + Q_2 + Q_3$Since $q_a = q_f$,we get:$2q_a = Q_1 + Q_2 + Q_3$$q_a = \frac{Q_1 + Q_2 + Q_3}{2}$Thus,the charge on both outermost surfaces '$a$' and '$f$' is $\frac{Q_1 + Q_2 + Q_3}{2}$.

Three parallel metal plates,each of area $A$,are placed as shown in the figure. Charges $Q_1$,$Q_2$,and $Q_3$ are given to them. Edge effects are negligible. Calculate the charge on the two outermost surfaces '$a$' and '$f$'.

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