How to Calculate Coulomb's Law

Calculates the force between two charges as F = k × charge₁ × charge₂ ÷ distance². Like charges repel and unlike charges attract. As with gravitation, the force falls off with the square of the distance.

This finds the force between two electric charges.

F = k\dfrac{q_1 q_2}{r^2}

$k$ is Coulomb's constant, $8.988 \times 10^9$ , $q_1$ and $q_2$ are the charges and $r$ is the distance. Like charges repel, unlike charges attract.

The same shape as gravitation

Falling off with the square of the distance is exactly what gravitation does. Two things differ. One is the size of the constant: Coulomb's constant is some $10^{20}$ times the gravitational one. The other is the sign: gravitation only ever attracts, while the electric force can push apart.

Example

Charges of $+1$ μC and $-2$ μC sit 0.3 m apart. $F = 8.988 \times 10^9 \times (1 \times 10^{-6}) \times (-2 \times 10^{-6}) \div 0.3^2 = -0.2$ N. The negative sign means attraction, of size 0.2 N. Charges of $+1$ μC and $+2$ μC at the same distance repel with $+0.2$ N.

The field

The field a charge $q_1$ creates at a distance $r$ is $E = kq_1 \div r^2$ , which here is 99862 N/C. The force on a charge placed there is $F = q_2 E$ , so the field is the force a unit charge would feel at that point.

Notes

Charges here are in microcoulombs, millionths of a coulomb. One coulomb is an enormous charge; everyday static electricity is measured in microcoulombs.