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If we use uniqueness theorem then we know that if the boundary conditions and the charge distribution is same in 2 setups in a certain region then the electric field and potential in that region in both the setup are same.

What if we know that the electric field and potential of 2 setups have same function and have same charge distribution, then can we conclude that the boundary conditions are also same for the 2 setups?

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  • $\begingroup$ You should probably think a little bit about the definitions of the things you're talking about. The "function" already includes the boundary information. $\endgroup$
    – Danu
    Commented May 4, 2016 at 18:42
  • $\begingroup$ Ok. I actually meant the function defining only the points inside the region, not on the surface. $\endgroup$ Commented May 4, 2016 at 18:43
  • $\begingroup$ In general, I think you can treat the area outside the sources as though they were the same, but if you look inside the source charge distribution, your answer will differ if the charge density does. This is a way of understanding Gauss's Law, from outside any arbitrary constant source charge distribution, you can treat it like a point charge at it's center with a charge equal to the total charge, as long as you only consider solutions outside the charge distribution. $\endgroup$
    – ocket8888
    Commented May 4, 2016 at 18:52

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