2017 charged plates

2017 identical metallic plates (initially uncharged), each having area of cross section \(A\), are each separated by a distance of \(d,\) as shown in the figure above.

Plates 2 and 2016 are given charges \(2\mathbf Q\) and \(\mathbf Q,\) respectively. Plates 1 and 2017 are both earthed via a very thin conducting wire.

If the potential difference between plates 1728 and 1729 is of the form \(\dfrac{a Qd}{bA\epsilon_0}\), where \(a\) and \(b\) are coprime positive integers, then submit your answer as \(a+b\).

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Details and Assumptions:

• \(\epsilon_0\) denotes the permittivity of free space.
• The plates are very large, and the phenomena of fringing of electric field lines are neglected.
• Because of the large size, the electric field due to any particular plate is considered as that of an infinitely large, thin conducting plate.