Coulomb's Law Calculator — Electrostatic Force

Coulomb's Law Guide

Coulomb's Law

F = kq₁q₂/r². k = 8.99×10⁹ N·m²/C² (Coulomb's constant = 1/(4πε₀)). q₁, q₂ = charges in coulombs (C). r = separation in metres. The force is repulsive if charges have the same sign, attractive if opposite. 1 microcoulomb (µC) = 10⁻⁶ C. Example: q₁ = +2µC, q₂ = −3µC, r = 10cm. F = 8.99×10⁹ × 2×10⁻⁶ × 3×10⁻⁶ / (0.10)² = 8.99×10⁹ × 6×10⁻¹² / 0.01 = 5.39N. Attractive force (opposite charges). Inverse square law: like gravity, force decreases with the square of distance.

Electric Field and Potential

Electric field E = F/q₀ = kq/r². Units: N/C or V/m (equivalent). The field points away from positive charges, toward negative charges. Electric potential V = kq/r (scalar, not vector). Potential energy U = kq₁q₂/r = q₂V. Relationship: E = −dV/dr (field is negative gradient of potential). Equipotential surfaces: spheres concentric with a point charge — no work done moving a charge along an equipotential.

Comparison with Gravity

Coulomb's law: F = kq₁q₂/r². Newton's gravitational law: F = Gm₁m₂/r². Both are inverse-square laws. The ratio k/G = 8.99×10⁹ / 6.67×10⁻¹¹ ≈ 10²⁰. Electrostatic force is approximately 10³⁶ times stronger than gravity for a proton-electron pair: F_electric = 8.99×10⁹ × (1.6×10⁻¹⁹)² / (5.3×10⁻¹¹)² = 8.2×10⁻⁸ N. F_gravity = 6.67×10⁻¹¹ × 1.67×10⁻²⁷ × 9.11×10⁻³¹ / (5.3×10⁻¹¹)² = 3.6×10⁻⁴⁷ N. Ratio: 2.3×10³⁹. Why gravity dominates cosmologically: matter is neutral overall, so electric forces cancel. G

Superposition Principle

The total electric force on a charge = vector sum of individual forces from all other charges. The total electric field at a point = vector sum of fields from all charges. This is the superposition principle — electric and gravitational fields both obey it. Dipole: two equal and opposite charges (+q and −q) separated by distance d. Electric dipole moment p = qd. Dipole fields decrease more rapidly with distance (1/r³ instead of 1/r²) than a monopole. Biological significance: many molecules are e