Four square metal plates of area A are arranged at an even spacing d as shown in the diagram. (Assume that A \gg d^{2}.)
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Plates 1 and 4 are first connected to a voltage source of magnitude V_{0}, with plate 1 positive; plates 2 and 3 are then connected together with a wire. The wire is subsequently removed. Finally, the voltage source attached between plates 1 and 4 is replaced with a wire. The steps are summarized in the diagrams below.
Find the resulting potential difference \Delta V_{12} between plates 1 and 2 ; like wise find \Delta V_{23} and \Delta V_{34}, defined similarly.
Assume, in each case, that a positive potential difference means that the top plate is at a higher potential than the bottom plate.