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I am studying about electric potential, and in particular electric potential around a point charge, by the formula we get that:

$$V_E=\frac{1}{4\pi\epsilon_0}\frac{Q}{r}$$

My question is: Can the potential be negative? i.e. if the point charge is of some negative charge, say $-P$ is it true that $V_E=-\frac{1}{4\pi\epsilon_0}\frac{P}{r}$, or $V_E=\frac{1}{4\pi\epsilon_0}\frac{|-P\ |}{r}=\frac{1}{4\pi\epsilon_0}\frac{P}{r}$.

Furthermore when dealing with two charges and the potential energy $U_E=qV$, is it $|q|$ or $q$ itself ?

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Yes, the potential and the potential energy ($U=qV$, not with a $|q|$) can be negative.

This actually is an essential feature, because if not, the potential near a positive charge would be same as the potential near a negative charge. This causes a lot of problems, for example, if this were true, positive charges would move away from negative ones!

In simple terms, our current framework that describes electromagnetism would make no sense if this were the case.


A handy thing to keep in mind is always the definition of electric potential, i.e. The work per unit of charge required to move a positive charge from a reference point to a specified point. (as an edit suggested)

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  • $\begingroup$ "A handy thing to keep in mind is always the definition of electric potential, i.e. The work per unit of charge required to move a positive charge from a reference point to a specified point" Actually, infinity is the "specified point", isn't it? $\endgroup$ – Max Jun 11 '17 at 18:13
  • $\begingroup$ It usually is convenient to assume so! $\endgroup$ – Hritik Narayan Jun 11 '17 at 18:14

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