Coulomb's Law
Simple Explanation
Coulomb's law gives the exact size of the electric force between two point charges: F = kq₁q₂/r². Like Newton's law of gravitation, this force follows an inverse-square pattern with distance — but the electric force is vastly stronger than gravity for typical charges and masses.
Why Do We Need It?
Coulomb's law lets you calculate exactly how strong the attraction or repulsion between charged objects is, not just which direction it acts — essential for anything from designing particle accelerators to understanding how atoms hold together.
Formula
Coulomb's Law
F = k q₁q₂ / r²
The electric force between two charges grows with the size of both charges, and shrinks rapidly (as the inverse square) with the distance between them — mirroring the same inverse-square pattern seen in gravity, but very much stronger.
- F
- — the electric force between the two charges, in newtons (N) — attractive for opposite charges, repulsive for like charges
- k
- — Coulomb's constant, about 9 × 10⁹ N·m²/C²
- q₁, q₂
- — the two charges, in coulombs (C)
- r
- — the distance between the two charges, in metres (m)
When to use it: Whenever the electric force between two known point charges at a known separation needs to be found.
Worked Example
Find the force between two charges
Two charges of +3 × 10⁻⁶ C and −2 × 10⁻⁶ C are 0.5 m apart. Using k = 9 × 10⁹ N·m²/C², find the size of the force between them.
Why Does This Work?
Like Newton's law of gravitation, this inverse-square relationship comes from the electric field spreading its influence out over the surface of an ever-larger sphere as distance increases — the same force is "spread thinner" over a much bigger area at greater distances.
Real-Life Example
Why electric forces hold atoms together
The negatively charged electrons in an atom are held in orbit by the positively charged nucleus.
Coulomb's law describes exactly this attractive force between the nucleus and electrons — despite being vastly weaker than the strong nuclear force at extremely short range, it is what governs the overall structure and chemistry of atoms.
Practice
Two charges of +4 × 10⁻⁶ C and +5 × 10⁻⁶ C are 0.2 m apart. Using k = 9 × 10⁹ N·m²/C², find the force between them.
HardCommon mistake
Forgetting to square the distance r — just like with gravitation, this equation uses r², not r, so halving the distance quadruples the force, not just doubles it.
Quick Review
- F = kq₁q₂/r²
- Same charges repel (F is repulsive); opposite charges attract (F is attractive).
- The electric force follows an inverse-square law, just like gravity.