In 1785, Charles-Augustin de Coulomb measured the force between two charged objects and found it follows the same inverse-square pattern as gravity — but with two important differences: it can push as well as pull, and it is enormously stronger.
Who Was Charles Coulomb?
Charles-Augustin de Coulomb (1736–1806) was a French physicist and military engineer. Using a torsion balance — a thin wire that twists when a force is applied — he measured the tiny forces between charged spheres with remarkable precision. From those experiments he wrote down the law that now bears his name. The unit of electric charge, the coulomb (C), is named in his honor.
The Law
The electric force between two point charges depends on the size of each charge and the distance between them:
F = k · q₁q₂ / r²
F = electric force (Newtons, N)
k = Coulomb's constant ≈ 8.99 × 10⁹ N·m²/C²
q₁, q₂ = charges (Coulombs, C)
r = distance between charges (metres, m)
Vector idea: Coulomb's law does not just tell us how big the force is. It also tells us the force acts along the line joining the two charges. In coordinate-style models, positions like x₁ and x₂ determine r, and then the force direction follows from whether the charges attract or repel.
✅ Opposite charges attract
One positive (+) and one negative (−) charge pull toward each other. The force points from each charge toward the other.
🚫 Like charges repel
Two positive or two negative charges push away from each other. The force points outward from each charge.
Compare with gravity: Both gravity and Coulomb's law are inverse-square laws — double the distance and the force drops to one quarter. But Coulomb force can be millions of times stronger than gravity, and it has both attractive and repulsive versions. Gravity only attracts.
From Formula to Field Model
The companion files for this simulation hint at a more physical setup with regions labeled air, boundary, and conductor. That is a helpful reminder that Coulomb's law is often used inside a modeled space: charges sit somewhere, the surrounding region matters, and conductors or boundaries can shape what the electric field looks like.
Air region
The field fills the space around the charges, not just the line between them.
Boundaries
A simulation often defines the edges of the world so distances and field behavior stay measurable.
Conductors
Nearby conductive objects can redistribute charge and distort the simple two-charge picture.
Interactive Simulator
Drag the charges to change the distance. Use the panel controls to adjust charge magnitudes and signs.
q₁+2 μC
q₂−2 μC
Distance0.20 m
Force0.90 N
Real-World Applications
⚡
Lightning
Charge separation in storm clouds builds until the electric force is strong enough to drive a spark through the air — a lightning bolt.
🖨️
Laser Printers
A charged drum attracts toner particles to the right spots using Coulomb forces, then transfers them to paper to form the image.
🧲
Atomic Bonding
Coulomb attraction between protons and electrons holds atoms together. Chemistry is fundamentally Coulomb's law at atomic scale.
🩺
Electrostatic Filters
Air purifiers and surgical masks use electrostatic charge to attract and trap microscopic particles that would otherwise pass through.
Practice Problems
Use F = kq₁q₂/r². k = 9 × 10⁹ N·m²/C². Give answers to 2 significant figures.
Easy1. Two charges of +1 μC and −1 μC are 0.1 m apart. Is the force attractive or repulsive?
Hint: Opposite signs (+/−) always attract.
Easy2. Two identical +2 μC charges are 0.3 m apart. What is the force? (Round to 1 decimal.) [F = 9×10⁹ × (2×10⁻⁶)² / 0.09]
Hint: F = 9×10⁹ × 4×10⁻¹² / 0.09 = 0.4 N
Medium3. If the distance between two charges doubles, by what factor does the force change?
Hint: Inverse-square law: (2r)² = 4r², so force becomes F/4.
Medium4. A +3 μC charge and a +5 μC charge are 0.2 m apart. Calculate the force (in N, 1 decimal).
Hint: F = 9×10⁹ × 3×10⁻⁶ × 5×10⁻⁶ / 0.04 = 3.375 ≈ 3.4 N
Challenge5. Two charges exert a 10 N force on each other at 0.1 m. What distance would reduce the force to 2.5 N?