Coulomb's Law Calculator

Frequently Asked Questions

What is Coulomb's law?

F = k·q₁·q₂ / r², with k ≈ 8.988×10⁹ N·m²/C². The force is along the line joining the charges, repulsive for like signs and attractive for opposite.

How is it like gravity?

Both are inverse-square laws. Coulomb's is vastly stronger and can attract or repel, whereas gravity only attracts.

What does the medium change?

In a dielectric the force is reduced by the relative permittivity εᵣ (replace k with k/εᵣ). Water (εᵣ≈80) greatly weakens the force.

What is a coulomb in everyday terms?

A huge charge - two 1 C charges 1 m apart would repel with ~9×10⁹ N. Real static charges are micro- or nanocoulombs.

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How This Calculator Works

Coulomb's Law gives the electrostatic force between two point charges: F = k × q₁ × q₂ ÷ r², where k = 8.988 × 10⁹ N·m²/C² (Coulomb's constant), q₁ and q₂ are the charges in coulombs, and r is their separation in metres. The force magnitude uses the absolute value of the product; the sign of q₁ × q₂ sets the direction - positive (like charges) means repulsive, negative (opposite charges) means attractive. This calculator rearranges the equation four ways: force, either charge magnitude, or separation. The inverse-square r² in the denominator means halving the distance quadruples the force. An optional relative permittivity (dielectric constant εᵣ) divides the effective constant, modelling the force inside an insulating medium such as water (εᵣ ≈ 80) instead of vacuum.

Worked Example: Two Microcoulomb Charges

Place q₁ = +1 µC (1 × 10⁻⁶ C) and q₂ = −2 µC (−2 × 10⁻⁶ C) 5 cm (0.05 m) apart in vacuum. F = (8.988 × 10⁹) × |(1 × 10⁻⁶)(−2 × 10⁻⁶)| ÷ (0.05)² = (8.988 × 10⁹) × (2 × 10⁻¹²) ÷ 0.0025 ≈ 7.19 N. Because q₁ × q₂ is negative, the force is attractive - the charges pull toward each other with about 7 newtons, roughly the weight of a 0.7 kg object. Submerge the same pair in water (εᵣ ≈ 80) and the force drops ≈ 80× to under 0.1 N, because the polar water molecules screen the field.

Coulomb's Law vs. Gravity

Same form: both are inverse-square laws - F ∝ 1 ÷ r² - so orbits and field lines look similar.

Vastly stronger: the electrostatic force between two protons is ≈ 10⁶⁶ times their gravitational attraction.

Two signs: charge can attract or repel; gravity only attracts, which is why bulk matter is electrically neutral.

Superposition: with many charges, the net force is the vector sum of each pairwise Coulomb force.

Charge, Constant, and Permittivity

The coulomb (C) is a large unit - one elementary charge is only 1.602 × 10⁻⁹ C, so everyday static electricity involves micro- or nanocoulombs. Coulomb's constant relates to the permittivity of free space by k = 1 ÷ (4πε₀), with ε₀ ≈ 8.854 × 10⁻¹² F/m. Inside a dielectric, bound charges partially cancel the applied field, so the effective constant becomes k ÷ εᵣ; this is why capacitors are filled with high-permittivity insulators to store more charge at a given voltage. Air's εᵣ ≈ 1.0006, so treating it as vacuum is accurate.

Assumptions & Limits

Coulomb's Law strictly applies to point charges or, equivalently, uniformly charged spheres (treated as if all charge sits at the centre). For extended or irregular charge distributions you must integrate contributions or use Gauss's law. It describes static charges; accelerating charges radiate electromagnetic waves and require the full Maxwell equations. The law also assumes charges are at rest relative to each other and ignores magnetic forces, which appear once charges move. At subatomic scales quantum electrodynamics supersedes it, and the simple formula breaks down inside the atomic nucleus where the strong force dominates.

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