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Can you add potentials if charge redistributes?

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Let say we have charged conductor M and we know its potential energy function Vm(r) when M is isolated from any charges. We also have charged conductor N with potential energy function Vn(r) when it is isolated.

Now we put objects M and N close together, the charges on their surfaces redistribute. I am interested in potential energy at every point in space, can I still add potential energy functions (Vm + Vn) to find that?

I'd like to think that it is possible to add functions like that, but I can't find a way of proving it mathematically yet. Any ideas of how to show this?

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