constant

elementary charge

Magnitude of the electric charge of a single electron or proton
Value
\(e = 1.602176634 \times 10^{-19}\)coulomb
9 related articles · 6 formulas

Description

The 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.

History

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.

How it works

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.

In practice

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.

Fun fact

A typical lightning bolt transfers about 10²⁰ elementary charges — that's a hundred billion billion electrons.

Concept graph →

Formulas

$$V(z) = \phi - eFz - \frac{e^2}{4\pi\epsilon_0 z}$$
Potential energy for electron emission including work function and field.
What is in the formula
Vvariablepotential energy of electron — potential energy joule
zvariabledistance from the metal surface — position metre
φvariablework function of the metal — work function joule
Fvariableapplied electric field strength — electric field volt per metre
econstantcharge of a single proton — elementary charge = 1.602176634e-19 coulomb
ε0constantability of vacuum to permit electric field lines — vacuum permittivity = 8.8541878128e-12 farad per metre
$$\Delta Q = \nu \frac{e \Delta \Phi}{\Phi_0}$$
Charge quantization in superconductors relates flux change to accumulated charge.
What is in the formula
\Delta QvariableAccumulated charge change in the superconductor — electric charge coulomb
\Delta \PhivariableChange in magnetic flux through the superconducting loop — magnetic flux weber
\nuvariableFilling factor (integer or fractional) of the quantum Hall state — dimensionless
econstantMagnitude of the electric charge of a single electron or proton — elementary charge = 1.602176634e-19 coulomb
\Phi_0constantSuperconducting flux quantum, h/(2e), the fundamental unit of magnetic flux in a superconductor — magnetic flux quantum = 2.067833848e-15 weber
$$E = \frac{\hbar e B}{m c}$$
Energy of charged particle in magnetic field is proportional to B.
What is in the formula
EvariableEnergy of the charged particle — energy joule
BvariableMagnetic field strength — magnetic flux density tesla
mvariableMass of the charged particle — mass kilogram
\hbarconstantReduced Planck constant, quantum of angular momentum — reduced planck constant = 1.054571817e-34 joule second
econstantMagnitude of electric charge of a proton or electron — elementary charge = 1.602176634e-19 coulomb
cconstantSpeed of light in vacuum, universal constant — speed of light = 299792458 metre per second
$$\text{RM} = \frac{e^3}{2\pi m_e^2 c^4} \int n_e B_\parallel \, dl$$
Rotation measure is proportional to the integral of electron density times parallel magnetic field along the line of sight.
What is in the formula
n_evariableelectron number density — electron number density per cubic metre
B_parallelvariablemagnetic field component along line of sight — magnetic flux density tesla
dlvariableinfinitesimal path element along line of sight metre
econstantelementary charge — elementary charge = 1.602176634e-19 coulomb
m_econstantelectron rest mass — electron mass = 9.1093837015e-31 kilogram
cconstantspeed of light in vacuum — speed of light = 299792458 metre per second
∫operatorsummation over the line of sight — integral operator
$$F = \frac{h}{2\pi e} A$$
Relates magnetic oscillation frequency to Fermi surface cross-sectional area.
What is in the formula
Fvariablefrequency of magnetic oscillation — frequency hertz
Avariableextremal cross-sectional area of Fermi surface — area square metre
hconstantplanck constant = 6.62607015e-34 joule second
econstantelementary charge = 1.602176634e-19 coulomb
$$a_0 = \frac{e E_0}{m_e c \omega}$$
Dimensionless parameter comparing electron oscillation energy to rest mass.
What is in the formula
a_0variablerelativistic intensity parameter (normalized vector potential) — relativistic parameter
E_0variablepeak electric field amplitude of the laser — electric field volt per metre
ωvariableangular frequency of the laser — angular frequency radian per second
econstantcharge of a single proton — elementary charge = 1.602176634e-19 coulomb
m_econstantmass of an electron at rest — electron mass = 9.1093837015e-31 kilogram
cconstantuniversal speed limit of light in vacuum — speed of light = 299792458 metre per second

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