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Feb 15, 2022 at 8:26 vote accept Solidification
Feb 15, 2022 at 7:55 comment added Yejus Hmm, I don't think so. You already have the equation for $\phi$, which is the whole point of solving Poisson's equation. To solve for the charge density on the plates, you must use an independent relation.
Feb 15, 2022 at 6:47 comment added Solidification nice, Thanks! But can we get this using Poisson's equation? I think we can do this by converting the surface charge $\sigma$ to a corresponding volume charge $\rho$ density using an appropriate delta function. It may be tedious but should in principle be doable.
Feb 15, 2022 at 6:40 history answered Yejus CC BY-SA 4.0