Two large parallel metal plates, each having area A`, are oriented horizontally and separated by a distance `3d`. A grounded conducting wire joins them, and initially each plate carries no chatege. Now a thirdidentical plate carrying charge `Q` is inserted between the two plates, parallel to them and lacated a distance (d) from the upper plate, as shown in. What induced charge appears on each of the two original plates?
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Explanation

`C=(epsilon_(0)A)/d rArrCprop1/d`
`C_(1)/C_(1)=(2d)/d=2`
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Potential of middle plate
`V=q/C_(1)=(Q-q)/C_(2)`
or `q/(q-q)=C_(1)/C_(2)=2` or `q=(2Q)/3`
So the induced charge on upper plate is `-2Q//3` and on lower plate is `-Q//3`.