# Potential energy equations

**The potential energy** of an object in a force field is the **work** that should be done by the field to bring the object from one point to another. In other words, the field "drags" the object.

The force on a particle in a uniform field $$F$$ is equal to the negative of the gradient of the potential energy of the particle at that point: $$$\vecphy{F}=-\frac{dE_{\text{p}}}{d\vecphy{s}}=-\frac{\Delta E_{\text{p}}}{\Delta\vecphy{s}}$$$ This implies that the change in potential energy between two points in a uniform field is given by the negative of the product of the force with the change in displacement (i.e. work): $$$\Delta E_{\text{p}}=-\vecphy{F}\cdot\Delta\vecphy{s}$$$

$$E_{\text{p}}=$$potential energy; $$\vecphy{F}=$$force; $$\vecphy{s}=$$displacement.