Coulomb’s Law Calculator

Coulomb's Law Calculator

What would you like to calculate?

Medium:

Charge 1 (C): Examples: 1e-6 for 1 µC, -2e-9 for -2 nC

Charge 2 (C): Examples: 1e-6 for 1 µC, -2e-9 for -2 nC

Distance (m):

About Coulomb's Law

Coulomb's Law describes the electrostatic force between two electrically charged particles. The force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

F = k × |q₁ × q₂| / r²

Where:

F is the electrostatic force between the charges (in newtons, N)
k is Coulomb's constant (8.9875517923 × 10⁹ N·m²/C²)
q₁ and q₂ are the signed magnitudes of the charges (in coulombs, C)
r is the distance between the charges (in meters, m)

If the charges have the same sign (both positive or both negative), the force is repulsive. If they have opposite signs (one positive and one negative), the force is attractive.

+ Learn More About Coulomb's Law

Historical Background

Coulomb's Law was first published in 1785 by French physicist Charles-Augustin de Coulomb. He measured the force between charged objects using a torsion balance he invented.

Effect of Medium

The force between charges depends on the medium in which they are placed. In a medium other than vacuum, the force is reduced by a factor called the relative permittivity (εᵣ):

F = k × |q₁ × q₂| / (εᵣ × r²)

Relationship to Electric Field

Coulomb's Law is closely related to the concept of an electric field. The electric field (E) at a point due to a charge q is:

E = k × q / r²

This field exerts a force on any other charge placed in it, according to F = qE.

Applications

Coulomb's Law is fundamental in understanding:

Atomic and molecular structure
Electrostatic devices (e.g., photocopiers, electrostatic precipitators)
Electrical phenomena in biology (e.g., cell membranes)
Lightning and static electricity
Design of electrical components and devices

Limitations

Coulomb's Law applies exactly only to point charges at rest. For moving charges, magnetic effects must also be considered. Additionally, at the quantum level, the behavior of charges is described by quantum electrodynamics rather than classical electrostatics.