constant

coulomb constant

Electrostatic force constant in Coulomb's law
Value
\(k_{e} = 8.9875517923 \times 10^{9}\)newton metre squared per coulomb squared
21 related articles · 3 formulas

Description

The Coulomb constant (often denoted kₑ or 1/4πε₀) is the proportionality factor in Coulomb's law, which describes the electrostatic force between two point charges. It sets the strength of the electric interaction: for two charges of 1 coulomb each, separated by 1 meter, the force is about 8.99 × 10⁹ newtons — a colossal value that reflects how strong electric forces are compared to gravity. The constant appears throughout electrostatics, from the field of a point charge to the capacitance of a sphere, and its value is fixed by the definition of the ampere and the speed of light in the SI system.

History

The constant was implicit in Charles-Augustin de Coulomb's 1785 experiments, but the explicit form with kₑ emerged later as the metric system and the concept of charge were formalized in the 19th century. The modern SI definition ties its value to the speed of light and the magnetic constant.

How it works

In Coulomb's law, F = kₑ q₁q₂/r², the constant kₑ converts the product of charges and the inverse square of distance into a force in newtons. Its numerical value depends on the unit system: in SI, kₑ ≈ 8.9875517923 × 10⁹ N·m²/C². It is related to the vacuum permittivity ε₀ by kₑ = 1/(4πε₀), where ε₀ ≈ 8.854 × 10⁻¹² F/m. The factor 4π appears because of the spherical symmetry of the field from a point charge, making Gauss's law simpler in integral form.

In practice

It is used in designing capacitors, electrostatic precipitators, and in calculating forces in particle accelerators and semiconductor devices.

Fun fact

If you could hold two 1-coulomb charges one meter apart, the force between them would be about a billion newtons — roughly the weight of a large skyscraper.

Concept graph →

Formulas

$$\Xi = \frac{k_e Q^2}{G M^2}$$
Compares electrostatic to gravitational force strength.
What is in the formula
QvariableElectric charge of the body — electric charge coulomb
MvariableMass of the body — mass kilogram
k_econstantElectrostatic force constant in Coulomb's law — coulomb constant = 8.9875517923e9 newton metre squared per coulomb squared
GconstantNewtonian constant of gravitation — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared
$$f(r) = 1 - \frac{2GM}{c^2 r} + \frac{G k_e Q^2}{c^4 r^2}$$
Describes spacetime around a charged non-rotating mass.
What is in the formula
rvariableRadial coordinate from the center — radial distance metre
f(r)variableMetric function determining spacetime geometry — metric function
GconstantNewtonian constant of gravitation — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared
cconstantSpeed of light in vacuum — speed of light = 299792458 metre per second
k_econstantElectrostatic force constant in Coulomb's law — coulomb constant = 8.9875517923e9 newton metre squared per coulomb squared
$$r_{\pm} = \frac{GM}{c^2} \left(1 \pm \sqrt{1 - \frac{k_e Q^2}{G M^2}}\right)$$
Locations of event horizons in charged black holes.
What is in the formula
r_±variableInner and outer event horizon radii — horizon radius metre
QvariableElectric charge of the black hole — electric charge coulomb
MvariableMass of the black hole — mass kilogram
GconstantNewtonian constant of gravitation — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared
cconstantSpeed of light in vacuum — speed of light = 299792458 metre per second
k_econstantElectrostatic force constant in Coulomb's law — coulomb constant = 8.9875517923e9 newton metre squared per coulomb squared

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