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.

Related formulas

Variables

UEelectric potential energy (related to the work done by the electric charge) (joule)
Vvoltage or electric potential difference (V)
Ielectric current (A)
ttime (s)