Coulomb's law
/ KOO-lom /
Coulomb's law is the rule for how strongly two electric charges push or pull on each other. It plays the same role for electricity that Newton's law of gravity plays for masses. It answers: if I know two charges and how far apart they are, exactly how big is the force between them, and which way does it point?
Coulomb's law says the electric force between two point charges is proportional to the product of the charges and inversely proportional to the square of the distance between them: F = k q1 q2 / r^2. Here q1 and q2 are the charges in coulombs, r is their separation, and k is Coulomb's constant, about 8.99 x 10^9 N m^2/C^2. The force points along the line joining the charges: it pushes them apart if the charges have the same sign, and pulls them together if the signs are opposite. Like gravity, it is an inverse-square law, so doubling the distance cuts the force to one quarter.
The law is stated for point charges (charges small enough to treat as points), and it is the starting point for all of electrostatics. Compared with gravity it is astonishingly strong: the electric repulsion between two protons is about 10^36 times their gravitational attraction. That is why matter is held together electrically, and why gravity only wins on the huge scale of planets, where charges cancel out but mass only adds up.
Two charges of 1 microcoulomb each, held 1 cm (0.01 m) apart, feel F = (8.99 x 10^9)(10^-6)(10^-6) / (0.01)^2 = about 90 N, roughly the weight of a 9 kg mass, from charges you cannot even see.
Even microcoulomb charges exert large forces at small separations.
Coulomb's law as written is exact only for point charges (or, by a theorem, for uniformly charged spheres viewed from outside). For charges that are close and spread out, you must add up the contributions piece by piece.