Coulomb’s Law Calculator

Coulomb's law: F = k·q₁·q₂/r²

Coulomb's law describes the electrostatic force between two point charges: F = k·q₁·q₂/r², with k = 8.99·10⁹ N·m²/C² in vacuum. The form is mathematically identical to Newton's universal gravitation (1/r²), but the electric force is about 10³⁹ times stronger than gravity between two protons. Like charges repel, opposite charges attract. For multiple charges, use the superposition principle: the resulting force is the vector sum of the individual pairwise forces. The electric field at a distance r from a charge Q is E = F/q = k·Q/r² (N/C), and the electric potential is V = k·Q/r (volts). Example: two protons (q = 1.6·10⁻¹⁹ C) separated by 1 nm experience F ≈ 2.3·10⁻¹⁰ N — tiny in absolute terms, but enormous at atomic scale.

Applications

Chemistry (ionic bonds in NaCl, electronegativity), everyday electrostatics (carpet shock, plastic film cling), capacitors that store charge between plates, semiconductors (transistors, diodes — band physics at p-n junctions), and the historic Coulomb torsion balance (1785), which was the first device to measure the law directly.

FAQ

Why is the force negative when charges have opposite signs? In the scalar formula, the sign of the product q₁·q₂ encodes the direction: positive means repulsion, negative means attraction. In vector form the sign comes from the unit vector connecting the charges.

Does the law work in any medium? No — k depends on the medium. In water, the dielectric constant divides k by about 80, which is why ionic salts dissolve readily in water but not in oil.

How does Coulomb compare with gravity? Same 1/r² form, but only electrical: 10³⁹ stronger between two protons, and can be either attractive or repulsive. Gravity is always attractive — that's why it dominates on astronomical scales (planets are electrically neutral on average).