Editing Potential energy (section)

=== Electrostatic potential energy ===
Electrostatic potential energy between two bodies in space is obtained from the force exerted by a charge ''Q'' on another charge ''q'', which is given by
<math display="block"> \mathbf{F}_{e} = -\frac{1}{4\pi\varepsilon_0} \frac{Qq}{r^2} \mathbf{\hat{r}},</math>
where <math>\mathbf{\hat{r}}</math> is a vector of length 1 pointing from ''Q'' to ''q'' and ''ε''<sub>0</sub> is the [[vacuum permittivity]].

If the electric charge of an object can be assumed to be at rest, then it has potential energy due to its position relative to other charged objects.  The [[electric potential energy|electrostatic potential energy]] is the energy of an electrically charged particle (at rest) in an electric field. It is defined as the [[work (physics)|work]] that must be done to move it from an infinite distance away to its present location, adjusted for non-electrical forces on the object. This energy will generally be non-zero if there is another electrically charged object nearby.

The work ''W'' required to move ''q'' from ''A'' to any point ''B'' in the electrostatic force field is given by
<math display="block">\Delta U_{AB}({\mathbf{r}})=-\int_{A}^{B} \mathbf{F_e} \cdot d\mathbf{r} </math>
typically given in J for Joules. A related quantity called ''[[electric potential]]'' (commonly denoted with a ''V'' for voltage) is equal to the electric potential energy per unit charge.