Does Coulomb's law work for moving charges?

Coulomb's law applies strictly to stationary charges. For moving charges, you must also consider magnetic forces, which are described by the Lorentz force law and Maxwell's equations.

What is a coulomb of charge?

One coulomb is the charge transported by one ampere of current in one second. It equals the charge of approximately 6.24 × 10^18 electrons. In practice, most static charges are measured in microcoulombs or nanocoulombs.

Why is the force inversely proportional to distance squared?

The inverse-square law arises because the electric field spreads uniformly over the surface of an expanding sphere. As distance doubles, the sphere's surface area quadruples, so the field strength at any point drops to one-quarter.

What is the permittivity of a medium?

Permittivity measures how easily a material allows electric field lines to pass through it. In a dielectric medium, the force between charges is reduced by the material's relative permittivity. Water has a high permittivity of about 80, which is why it dissolves ionic compounds readily.

Coulomb's Law Calculator

Calculate electrostatic force between charges

Coulomb's Law

F = k x |q1 x q2| / r^2

Charge 1 (C)

Charge 2 (C)

Distance (m)

Formula

F = k x |q1 x q2| / r^2, k = 8.9875 x 10^9

What Is Coulomb's Law?

Coulomb's Law describes the electrostatic force between two electrically charged particles. The force is proportional to the product of their charges and inversely proportional to the square of the distance between them. Like charges repel; opposite charges attract.

Named after French physicist Charles-Augustin de Coulomb (1736–1806), this law is fundamental to electrostatics and forms the basis for understanding atomic structure, chemical bonding, and electromagnetic field theory. It is the electrical analogue of Newton's law of gravitation.

How to Use Coulomb's Law Calculator

Enter the first charge (q₁) in Coulombs (C). Use scientific notation for small values, e.g. 1e-6 for 1 μC.
Enter the second charge (q₂) in Coulombs.
Enter the distance (r) between the charges in meters.
Click Calculate to get the electrostatic force in Newtons and its direction (attractive or repulsive).

Formula & Explanation

F = k × |q₁ × q₂| / r²

F  = electrostatic force (N)
k  = Coulomb's constant ≈ 8.988×10⁹ N·m²/C²
q₁ = first charge (C)
q₂ = second charge (C)
r  = distance between charges (m)

The force is attractive when charges have opposite signs and repulsive when they have the same sign. Coulomb's constant k = 1/(4πε₀) where ε₀ is the permittivity of free space.

Worked Examples

Two Electrons

Two electrons (q = −1.602×10⁻¹⁹ C each) are 1 nm apart (r = 10⁻⁹ m). F = 8.988×10⁹ × (1.602×10⁻¹⁹)² / (10⁻⁹)² = 2.31×10⁻¹⁰ N. Both carry the same charge sign, so the force is repulsive.

Proton and Electron in Hydrogen

In a hydrogen atom, the proton and electron are ~5.3×10⁻¹¹ m apart (Bohr radius). F = 8.988×10⁹ × (1.602×10⁻¹⁹)² / (5.3×10⁻¹¹)² ≈ 8.2×10⁻⁸ N. This attractive force holds the electron in its orbit.

Charged Spheres in a Lab

Two spheres carry +2 μC and −3 μC, placed 0.1 m apart. F = 8.988×10⁹ × |2×10⁻⁶ × (−3×10⁻⁶)| / 0.01 = 5.39 N. Opposite charges → attractive force of 5.39 N pulls them together.

Frequently Asked Questions

What is Coulomb's constant?▾

Coulomb's constant k ≈ 8.988×10⁹ N·m²/C² (often rounded to 9×10⁹). It equals 1/(4πε₀) where ε₀ = 8.854×10⁻¹² C²/(N·m²) is the permittivity of free space.

How does Coulomb's Law compare to gravity?▾

Both follow an inverse-square law: F ∝ 1/r². The key differences: Coulomb's force can be attractive or repulsive; gravity is always attractive. Electrostatic forces are enormously stronger — about 10³⁶ times stronger than gravity between an electron and proton.

Does Coulomb's Law work in materials?▾

In a medium with relative permittivity εᵣ (dielectric constant), the force is reduced: F = k × |q₁q₂| / (εᵣ × r²). Water (εᵣ ≈ 80) reduces electrostatic forces by 80x, explaining why ionic compounds dissolve in it.

What are the limits of Coulomb's Law?▾

Coulomb's Law is accurate for stationary or slowly moving point charges in vacuum. For moving charges (currents), magnetic forces also arise. At quantum scales, quantum electrodynamics (QED) replaces the classical treatment.

What is the SI unit of charge?▾

The SI unit of electric charge is the Coulomb (C), defined since 2019 as exactly 1/(1.602176634×10⁻¹⁹) elementary charges. The charge of a proton is +1.602×10⁻¹⁹ C; an electron is −1.602×10⁻¹⁹ C.