qv

qV denotes the product of a charge q (in coulombs) and an electric potential difference V (in volts). Because 1 volt equals 1 joule per coulomb, qV has units of energy (joules) and represents the work done on a charge as it moves through a potential difference, or the electric potential energy of that charge in the field. In formulas, the energy change is E = qV for a charge moving across a potential difference V.

The quantity qV is especially useful for understanding energy changes of discrete charges. If a charge q moves from a region of zero potential to a region at potential V, the energy gained is qV. If the charge moves in the opposite direction, the energy change is −qV. For a continuous flow of charge, energy transfer can be described using E = VIt, where I is current, V is voltage, and t is time, with instantaneous power P = IV.

Special case: when q equals the elementary charge e and V is 1 volt, qV equals 1 electron volt (1 eV), which is the kinetic energy gained by a single electron moving through 1 volt. In joules, 1 eV is approximately 1.602 × 10^−19 J.

Applications of the concept include energy accounting in electrical circuits, where work and energy transfer are analyzed at the level of individual charges or small charge packets, and in micro and nano-scale physics, where discrete charge considerations matter. qV is not a separate fundamental unit; it is a convenient label for the energy associated with moving charges through a potential difference.

See also: electron volt, electric potential energy, work done by electric field, potential difference, capacitance energy.