Coulomb's Law
Simple Explanation
Coulomb's law describes the electric force between two charged objects: the force is stronger when the charges are larger, and weaker when they are farther apart — specifically, the force decreases with the SQUARE of the distance. Like charges repel; opposite charges attract.
Why Do We Need It?
Coulomb's law is the foundation of electrostatics, playing the same role for electric charges that Newton's law of gravitation plays for masses — nearly everything else in this chapter builds on it.
Formula
Coulomb's Law
F = kq₁q₂ / r²
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
- — Electric force between the charges, in newtons (attractive if opposite signs, repulsive if same sign)
- k
- — Coulomb's constant, ≈ 8.99 × 10⁹ N·m²/C²
- q₁, q₂
- — Magnitudes of the two point charges, in coulombs (C)
- r
- — Distance between the charges, in metres
When to use it: Use to find the electric force between two point charges at a known separation.
Worked Example
Finding the force between two charges
Two charges of +3 × 10⁻⁶ C and -2 × 10⁻⁶ C are 0.5 m apart. Find the force between them (k = 8.99 × 10⁹ N·m²/C²).
Why Does This Work?
The inverse-square dependence on distance reflects how the influence of a charge spreads out over an ever-larger area as distance increases (similar to how gravity, light intensity, and other point-source effects also follow inverse-square laws) — this is a common geometric feature of any influence radiating outward from a point in three-dimensional space.
Real-Life Example
Static cling
Clothes fresh from a dryer often stick together due to static electricity.
Friction during drying transfers small amounts of charge between fabric pieces — the resulting attractive Coulomb force between the oppositely-charged surfaces is strong enough at close range (small r) to make the clothes cling together.
Practice
Two charges of magnitude 4 × 10⁻⁶ C each are 0.2 m apart. Find the force between them (k = 8.99 × 10⁹ N·m²/C²).
MediumCommon mistake
Forgetting the inverse-SQUARE relationship — doubling the distance does not halve the force; it reduces the force to one-quarter (since the distance term is squared in the denominator).
Quick Review
- Coulomb's law: F = kq₁q₂/r² — force between two point charges.
- Like charges repel; opposite charges attract.
- Force follows an inverse-square relationship with distance.