Potential energy
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 F e = − 1 4 π ε 0 Q q r 2 r ^, {\displaystyle \mathbf {F} _{e}=-{\frac {1}{4\pi \varepsilon _{0}}}{\frac {Qq}{r^{2}}}\mathbf {\hat {r}},} where r ^ {\displaystyle \mathbf {\hat {r}} } is a vector of length 1 pointing from Q to q and ε 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 electrostatic potential energy is the energy of an electrically charged particle (at rest) in an electric field. It is defined as the 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 Δ U A B (r) = − ∫ A B F e ⋅ d r {\displaystyle \Delta U_{AB}({\mathbf {r} })=-\int _{A}^{B}\mathbf {F_{e}} \cdot d\mathbf {r} } 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.
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