(Solution) - Two large parallel metal plates -(2025 Original AI-Free Solution)

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Two large parallel metal plates are oriented horizontally and separated by a distance 3d. A grounded conducting wire joins them, and initially each plate carries no charge. Now a third identical plate carrying charge Q is inserted between the two plates, parallel to them and located a distance d from the upper plate, as in Figure P26.57.
(a) What induced charge appears on each of the two original plates?
(b) What potential difference appears between the middle plate and each of the other plates? Each plate has area A.