Is the potential difference between a point A and a point B equal to negative the potential difference between point B and point A? Or, are they the same?
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$\begingroup$ Are you referring to electrical or gravitational potential? $\endgroup$– Bob DSep 10, 2019 at 1:50
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$\begingroup$ I'm referring to Electric Potential. $\endgroup$– Shreyas ThakurSep 10, 2019 at 1:54
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2 Answers
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The potential difference $V$ between two points is the work per unit charge required to move the charge between the two points. The magnitude of the potential difference (work required per unit charge) from A is B is the same as from B to A. But the sign of the change in potential of one is the negative of the other. That is because if a given charge gains electrical potential moving from A to B (gaining electrical potential energy), that same charge loses the same amount of electrical potential moving from B to A (losing electrical potential energy).
Hope this helps.
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They are negatives of each other. The potential difference between two points is a signed quantity.
$$\varphi(\mathbf{r}_A)-\varphi(\mathbf{r}_B)=-[\varphi(\mathbf{r}_B)-\varphi(\mathbf{r}_A)]$$
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$\begingroup$ A long time ago, I too had the confusion of signs. $\endgroup$ Sep 11, 2019 at 22:24