When the switch is closed find the charge flown through switch?

Explanation

`V_(A)=V_(C)`
`V_(A)-V_(C)=0`
`V_(A)-V_(B)+B_(B)-V_(C)=0`
`E_(1)d+E_(2)2d=0`
`q_(1)/(A epsilon_(0))d+((3Q+q_(1)))/(A epsilon_(0))xx2d=0`
`q_(1)=-2Q`

Final charge on plate `A=(3Q)/(2)+(-2Q)=-(Q)/(2)`
Initial charge on plate `A=Q`
Charge flown through switch `=Q-(-Q/2)=(3Q)/(2)`