# Potential Difference between A and B is negative the potential difference between B and A?

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?

• Are you referring to electrical or gravitational potential? – Bob D Sep 10 '19 at 1:50
• I'm referring to Electric Potential. – Shreyas Thakur Sep 10 '19 at 1:54

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).
$$\varphi(\mathbf{r}_A)-\varphi(\mathbf{r}_B)=-[\varphi(\mathbf{r}_B)-\varphi(\mathbf{r}_A)]$$