
Magnitude of the electric charge of a single electron or protonThe elementary charge (e) is the magnitude of the electric charge carried by a single proton or electron — approximately 1.602 × 10⁻¹⁹ coulombs. It is the fundamental quantum of charge in nature: all free charges in the universe are integer multiples of e, a fact first demonstrated by Robert Millikan's oil-drop experiment in 1909. This quantization is a cornerstone of atomic physics, chemistry, and electronics, explaining why chemical reactions involve whole numbers of electrons and why currents in metals are carried by discrete particles.
The concept of a discrete charge unit dates to Michael Faraday's laws of electrolysis (1830s), but the first direct measurement was by Robert Millikan in 1909, who won the 1923 Nobel Prize for it. The exact value was refined over decades until the 2019 SI redefinition fixed it by definition.
The elementary charge is a fundamental constant of nature, not derived from other quantities. In the SI system, it was redefined in 2019 to be exactly 1.602176634 × 10⁻¹⁹ C, making the ampere and the kilogram depend on this fixed value. The charge of an electron is −e, and a proton is +e; quarks carry fractional charges (±1/3 e, ±2/3 e) but are never observed free due to confinement. The value of e sets the scale of electrostatic forces at atomic distances, determining binding energies and chemical bond strengths.
It underpins all electronics: the operation of transistors, diodes, and batteries relies on the movement of integer multiples of e. It also defines the unit of electric current (ampere) in the modern SI.
A typical lightning bolt transfers about 10²⁰ elementary charges — that's a hundred billion billion electrons.
| V | variable | potential energy of electron — potential energy joule |
| z | variable | distance from the metal surface — position metre |
| φ | variable | work function of the metal — work function joule |
| F | variable | applied electric field strength — electric field volt per metre |
| e | constant | charge of a single proton — elementary charge = 1.602176634e-19 coulomb |
| ε0 | constant | ability of vacuum to permit electric field lines — vacuum permittivity = 8.8541878128e-12 farad per metre |
| \Delta Q | variable | Accumulated charge change in the superconductor — electric charge coulomb |
| \Delta \Phi | variable | Change in magnetic flux through the superconducting loop — magnetic flux weber |
| \nu | variable | Filling factor (integer or fractional) of the quantum Hall state — dimensionless |
| e | constant | Magnitude of the electric charge of a single electron or proton — elementary charge = 1.602176634e-19 coulomb |
| \Phi_0 | constant | Superconducting flux quantum, h/(2e), the fundamental unit of magnetic flux in a superconductor — magnetic flux quantum = 2.067833848e-15 weber |
| E | variable | Energy of the charged particle — energy joule |
| B | variable | Magnetic field strength — magnetic flux density tesla |
| m | variable | Mass of the charged particle — mass kilogram |
| \hbar | constant | Reduced Planck constant, quantum of angular momentum — reduced planck constant = 1.054571817e-34 joule second |
| e | constant | Magnitude of electric charge of a proton or electron — elementary charge = 1.602176634e-19 coulomb |
| c | constant | Speed of light in vacuum, universal constant — speed of light = 299792458 metre per second |
| n_e | variable | electron number density — electron number density per cubic metre |
| B_parallel | variable | magnetic field component along line of sight — magnetic flux density tesla |
| dl | variable | infinitesimal path element along line of sight metre |
| e | constant | elementary charge — elementary charge = 1.602176634e-19 coulomb |
| m_e | constant | electron rest mass — electron mass = 9.1093837015e-31 kilogram |
| c | constant | speed of light in vacuum — speed of light = 299792458 metre per second |
| ∫ | operator | summation over the line of sight — integral operator |
| F | variable | frequency of magnetic oscillation — frequency hertz |
| A | variable | extremal cross-sectional area of Fermi surface — area square metre |
| h | constant | planck constant = 6.62607015e-34 joule second |
| e | constant | elementary charge = 1.602176634e-19 coulomb |
| a_0 | variable | relativistic intensity parameter (normalized vector potential) — relativistic parameter |
| E_0 | variable | peak electric field amplitude of the laser — electric field volt per metre |
| ω | variable | angular frequency of the laser — angular frequency radian per second |
| e | constant | charge of a single proton — elementary charge = 1.602176634e-19 coulomb |
| m_e | constant | mass of an electron at rest — electron mass = 9.1093837015e-31 kilogram |
| c | constant | universal speed limit of light in vacuum — speed of light = 299792458 metre per second |



