Coulomb constant

Beginner

k = 1/4πε₀.

Key relationk = 9×10⁹ N·m²/C²

k = 1/(4πε₀) = 8.99×10⁹ N·m²/C²; ε₀ = 8.85×10⁻¹² C²/N·m² is the permittivity of free space. In a medium ε₀ is replaced by ε = κε₀.

Worked example

Water's κ = 80 reduces the force 80-fold.

Common mistake

The huge size of k shows how strong electrostatics is.

In more detail

The Coulomb constant k = 1/(4πε0) ≈ 9 × 10⁹ N m²/C² sets the strength of electric forces. It is related to the permittivity of free space.

Calculating forces between charges in devices and atoms.
Relating electric fields to charge distributions.
Physicists use the Coulomb constant to convert between charges in coulombs and forces in newtons.

What is ε0?

The permittivity of free space, about 8.85 × 10⁻¹² F/m.

Why is k so large?

Because the coulomb is a large unit of charge, so the constant is big to produce everyday forces.

What is the relation between k and ε₀?

The Coulomb constant equals one over four pi times the permittivity of free space.