
The electric potential difference between two points, driving the flow of current.Voltage, formally called electric potential difference, is the energy per unit charge required to move a charge between two points in an electric field. It is the driving force behind electric current: charges flow from higher to lower potential, much like water flows downhill. In physics and engineering, voltage is fundamental to circuits, from simple batteries to complex quantum control electronics.
Alessandro Volta invented the first battery, the voltaic pile, in 1800, providing a steady voltage source. The concept of potential difference was formalized by early 19th-century physicists like André-Marie Ampère and Georg Ohm, whose law (V = IR) remains central.
Voltage arises from the separation of positive and negative charges, creating an electric field. When a conductive path connects two points at different potentials, the field pushes free charges, producing current. The unit, the volt (V), equals one joule per coulomb. In practice, voltage can be generated by chemical reactions (batteries), electromagnetic induction (generators), or photovoltaic effects (solar cells), and it is controlled using resistors, capacitors, and transistors.
Voltage is ubiquitous: it powers all electronic devices, from microchips to power grids, and is used in quantum systems to control qubit states via microwave pulses or electrostatic gates.
The voltage across a typical lightning bolt can reach hundreds of millions of volts, yet the current lasts only microseconds—enough to power a city for a fraction of a second.
| V_dep | variable | Depolarizing field voltage — voltage volt |
| P | variable | Polarization of the dielectric — polarization coulomb per metre squared |
| d | variable | Thickness of the dielectric film — thickness metre |
| ε₀ | constant | Permittivity of free space, a fundamental constant — vacuum permittivity = 8.8541878128e-12 farad per metre |
| εᵣ | constant | Dimensionless ratio of the material's permittivity to vacuum permittivity — relative permittivity |











