Formula and Method for Coulomb's Law
Coulomb's law describes the electrostatic force between two stationary point charges. First measured by Charles-Augustin de Coulomb in 1785, it states that the force is proportional to the product of the two charge magnitudes and inversely proportional to the square of the distance between them: F = k|q₁q₂| / r², where k is Coulomb's constant (about 8.9875 × 10⁹ N·m²/C² in a vacuum). This calculator also reports the force's direction (attractive or repulsive), the electric potential energy between the charges, and an intuitive equivalent-weight comparison.
Deriving the force from Coulomb's constant
Coulomb's constant is defined as k = 1/(4πε₀), where ε₀ ≈ 8.854 × 10⁻¹² F/m is the permittivity of free space. When the charges sit in a medium other than vacuum (an insulating dielectric such as glass, oil, or water), the force is reduced by the medium's relative permittivity εᵣ, giving the more general form F = k|q₁q₂| / (εᵣr²). The related potential energy stored between the charges is U = kq₁q₂ / (εᵣr) — note this version keeps the signs of q₁ and q₂, so U is negative for attracting charges (energy must be added to pull them apart) and positive for repelling charges.
Working with charge and distance units
- Real-world charges are almost always fractions of a coulomb — a coulomb is enormous, so most problems use microcoulombs (µC, 10⁻⁶) or nanocoulombs (nC, 10⁻⁹); pick the unit that matches your source and let the calculator convert to coulombs internally.
- Keep the distance as the straight-line separation between the two charge centers, not a path length, and convert it to meters before comparing results — 1 inch = 0.0254 m, 1 foot = 0.3048 m.
- Relative permittivity (εᵣ) is unitless: use 1 for vacuum or air, about 80 for water, and 2-8 for common insulators like glass or plastic.
Knowing the limits
Coulomb's law strictly applies to point charges (or spherically symmetric charge distributions) that are stationary relative to each other; it ignores magnetic effects that appear once charges move, which require the fuller framework of electrodynamics. It also assumes the two charges do not significantly redistribute each other's charge (a fair assumption for point charges, less so for nearby conductors). For charge distributions that are not point-like, the total force must be found by integrating Coulomb's law over the distribution rather than plugging in a single r.