Coulomb's Law Calculator — Electrostatic Force

Coulomb's Law Guide

What do I need to know about 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.

What do I need to know about 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.

What's the key thing to understand about 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 out. Gravity, unlike the electric force, is always attractive and never cancels, so it accumulates and dominates at the scale of planets, stars, and galaxies despite being enormously weaker at the level of individual particles.

What should I know about 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 electric dipoles, including water, which is why water is such an effective solvent for other charged or polar substances.