# Electric Potential Energy with Time (related to Electrical Work)

## Description

Electrical work is the work done on a charged particle by an electric field. The equation for 'electrical’ work is equivalent to that of 'mechanical’ work.

The electrical work per unit of charge, when moving a negligible test charge between two points, is defined as the voltage or electric potential difference between those points.

The concept of electric potential is closely linked with potential energy. A test charge q has an electric potential energy UE given by the formula shown here.

The potential energy and hence also the electric potential is only defined up to an additive constant: one must arbitrarily choose a position where the potential energy and the electric potential are zero.

These equations cannot be used if the curl ∇ × E ≠ 0, i.e., in the case of a nonconservative electric field (caused by a changing magnetic field; see Maxwell’s equations). The generalization of electric potential to this case is described below.

## Variables

U_{E} | electric potential energy (related to the work done by the electric charge) (joule) |

V | voltage or electric potential difference (V) |

I | electric current (A) |

t | time (s) |