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Hello I have a question:

Question

It is often said that if a point A has a potential higher than a point B, then A has a positive potential and B a negative potential.

Is it forcibly concluded that a point with a positive potential is positively charged, or that a point with a negative potential is negatively charged?

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2 Answers 2

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Potential talks about potential difference. You cannot just have potential, it is not like energy. We can define a potential difference between two points using the elementary definition: $$ V = V(A) - V(B) $$ In the case of $V(A)>V(B)>0$, you can say there is positive potential even though charges at points A and B are both positive. There is a convention we use in physics where we can talk about the potential of simply one charge alone. However, as before, we need a reference point. You can never talk about potential without analyzing the difference between two points. When we talk about the potential of one charge alone, it is usually assumed that $V=0$ at $\infty$. In this case, the only way to have negative potential is if the lone charge is negative. If the lone charge is positive it has positive potential.

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It is often said that if a point A has a potential higher than a point B, then A has a positive potential and B a negative potential.

All the statement means is that the potential at A is higher than B so that the potential difference $V_{A}-V_{B}$ is greater than zero. The terms negative potential and positive potential have no meaning by themselves. The potential at a point is always relative to some other point.

Is it forcibly concluded that a point with a positive potential is positively charged, or that a point with a negative potential is negatively charged?

No.

Consider two negatively charged objects. Object 1 has a negative charge of 1 coulomb. Object 2 has a negative charge of 2 coulombs. The potential of object 1 is higher than object 2 because it is more "positive", yet object 1 is negatively charged.

Hope this helps.

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