Some isolated metal plates with large surface areas are kept parallel to each other and total charges on each plate are as shown. Find the charge appearing on the surfaces of plates.
(a)

Explanation

1. The outer surfaces of extreme outer plates will have equal charges
`(Q_(1) + Q_(2) + …+Q_(n))/(2)`
2. The facing surfaces will have equal and opposite charges.
(a) Charge on outer surfaces of each plate `= (2Q + Q)/(2) = (3Q)/(2)`
Charge on inner surface of left plate
`= 2Q - (3Q)/(2) = (Q)/(2)`
Charge on inner surface of left plate
`= 2Q - (3Q)/(2) = (Q)/(2)`
Charge on inner surface of left plate
`2Q - (3Q)/(2) = (Q)/(2)`
Charge on inner surface of right plate `= -(Q)/(2)`
Check : Net charge on right plate `= (3Q)/(2) - (Q)/(2) = Q , O.K.`


(b) Charge on outer surfaces of extreme plates
`= (3Q - Q + 0)/(2) = Q`
Charge on inner surface of the left most plate `= 3Q - Q = 2Q`
Charge on the left surface of middle plate `= -2Q`
Charge on the right surface of middle plate` = - 2Q + x`
`= Q rArr x = Q`
Charge on inner surface of right most plats `= -x = - Q`
Check : Net charge on the right most plats `= - Q + Q = 0 , O.K.`