Work of conservative forces is the opposite of potential energy difference

up:: Work

The work done by a conservative force releases/accumulates potential energy, depending on whether it follows a path alongside/opposite to the field lines.

Proof

For a Conservative Force $\vec{F}$, with potential $V(\vec{r})$, we have that it exerts work on a particle at a path $L$ as

$$W={\int }_L\vec{F}\cdot d\vec{l}=-{\int }_L\vec{\nabla }V\cdot d\vec{l}$$

By the Fundamental Theorem of Calculus, we have that it results into

$$W=-\left(V(\overrightarrow{r_2})-V(\overrightarrow{r_1})\right)\equiv -\Delta V$$