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Silly question that's been bugging me, please help:

(a) My understanding is that potential energy of a charge will increase when the charge is moved against the pull of electric-field.

If (a) is correct, what does the potential energy converge to when I move point charge Q- away from point charge Q+, eventually separating them by infinitely large distance ?

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(a) Is correct! The potential energy $U$ for equal but opposite charges is negative $$U=\frac{-|Q||Q|}{4\pi\epsilon_0 r}$$ Thus $U$ increases (becomes less negative) when you move one charge away from the other.

(b) When the distance between the charges goes to infinity $r → ∞$ $U → 0$. This is a conventional choice. You could add any arbitrary constant $U_0$ to the potential energy $U$.

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