2017 charged plates

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

Plates 2 and 2016 are given charges 2Q2\mathbf Q and Q,\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 aQdbAϵ0\dfrac{a Qd}{bA\epsilon_0}, where aa and bb are coprime positive integers, then submit your answer as a+ba+b.

Details and Assumptions:

  • ϵ0\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.

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