Coulomb's Law
Two charged objects push or pull on each other with an electric force. That force grows if either charge is bigger, but it fades very quickly as the charges move apart — doubling the distance between them cuts the force to just one quarter.
The formula
F = k · q₁ · q₂ / r²
- F — force (N): the electric push or pull between the two charges
- k — Coulomb's constant (N·m²/C²): a fixed number, about nine times ten to the ninth, that sets the strength of the electric force
- q₁ — first charge (C): the amount of electric charge on the first object
- q₂ — second charge (C): the amount of electric charge on the second object
- r — distance (m): the distance between the centers of the two charges
Worked example
Two small charges, q₁ = 2 μC and q₂ = 1 μC, sit 0.1 meters apart. What electric force do they exert on each other?
- q₁ = 2 μC
- q₂ = 1 μC
- r = 0.1 m
- F = k · q₁ · q₂ / r²
- F = (9×10⁹ · 2×10⁻⁶ · 1×10⁻⁶) / (0.1)²
F = 1.8 N
Test yourself
The same two charges are pulled apart to twice the distance, 0.2 meters. What is the new force?
- 0.9 N
- Correct answer: 0.45 N
- 3.6 N
Right! Doubling the distance divides the force by four, since distance is squared: 1.8 N ÷ 4 = 0.45 N.
Keeping r at 0.1 meters, q₁ is doubled to 4 μC while q₂ stays at 1 μC. What is the new force?
- 1.8 N
- 0.9 N
- Correct answer: 3.6 N
Exactly — force is directly proportional to each charge, so doubling q₁ doubles F: 1.8 N × 2 = 3.6 N.
Where you see this
Rub a balloon on your hair and it sticks to the wall; clothes fresh from the dryer cling to each other and spark; a photocopier pulls toner onto exactly the charged parts of the drum. In every case small separated charges are pushing and pulling with a force that is enormous up close and fades fast with distance.
Common mistakes
The reflex error is halving: double the distance, half the force — the distance is squared, so doubling it divides the force by four (1.8 N becomes 0.45 N), and tripling divides it by nine. The charges get no such exponent: doubling one charge simply doubles the force (1.8 N becomes 3.6 N), and only the r in F = k · q₁ · q₂ / r² carries the square. Remember the force can push apart or pull together — unlike gravity, charges come in two signs.
How it connects
This is gravitation's electric twin: F = k · q₁ · q₂ / r² has exactly the inverse-square geometry of Newton's law, swapping masses for charges and adding repulsion. It anchors the whole electromagnetism module — capacitance, next, is what happens when you store the charge this law pushes around, and every later lesson assumes charges interact this way.