Electrostatic force constant in Coulomb's lawThe 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.
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.
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.
It is used in designing capacitors, electrostatic precipitators, and in calculating forces in particle accelerators and semiconductor devices.
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.
| Q | variable | Electric charge of the body — electric charge coulomb |
| M | variable | Mass of the body — mass kilogram |
| k_e | constant | Electrostatic force constant in Coulomb's law — coulomb constant = 8.9875517923e9 newton metre squared per coulomb squared |
| G | constant | Newtonian constant of gravitation — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared |
| r | variable | Radial coordinate from the center — radial distance metre |
| f(r) | variable | Metric function determining spacetime geometry — metric function |
| G | constant | Newtonian constant of gravitation — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared |
| c | constant | Speed of light in vacuum — speed of light = 299792458 metre per second |
| k_e | constant | Electrostatic force constant in Coulomb's law — coulomb constant = 8.9875517923e9 newton metre squared per coulomb squared |
| r_± | variable | Inner and outer event horizon radii — horizon radius metre |
| Q | variable | Electric charge of the black hole — electric charge coulomb |
| M | variable | Mass of the black hole — mass kilogram |
| G | constant | Newtonian constant of gravitation — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared |
| c | constant | Speed of light in vacuum — speed of light = 299792458 metre per second |
| k_e | constant | Electrostatic force constant in Coulomb's law — coulomb constant = 8.9875517923e9 newton metre squared per coulomb squared |







