What is Coulomb's Law?
Coulomb's law describes the electric force between two point charges: it grows with the product of the charges and shrinks rapidly with distance. It is the electrical analogue of Newton's law of gravitation and underpins all of electrostatics.
Coulomb's law states that the force between two point charges is F = k·q₁·q₂/r², where k ≈ 8.99 × 10⁹ N·m²/C² is Coulomb's constant, q₁ and q₂ are the charges, and r is the distance between them.
Try it: interactive calculator
Step-by-step worked examples
Two charges of +2 µC and +3 µC are 0.5 m apart. Find the force between them.
F = k q₁ q₂ / r² F = (8.99×10⁹)(2×10⁻⁶)(3×10⁻⁶) / (0.5)² F = (8.99×10⁹)(6×10⁻¹²) / 0.25 F = 0.0539 / 0.25 ≈ 0.216 N
A charge of 5 µC and a charge of 5 µC repel with a force of 0.05 N. Find their separation.
F = k q₁ q₂ / r² → r² = k q₁ q₂ / F r² = (8.99×10⁹)(5×10⁻⁶)(5×10⁻⁶) / 0.05 r² = 0.22475 / 0.05 = 4.495 r ≈ 2.12 m
If the distance between two fixed charges is doubled, what happens to the force?
F ∝ 1/r² Doubling r → F_new = F_old / 2² = F_old / 4 The force drops to one-quarter of its original value
Flashcards
Quick quiz
Q1.Coulomb's law formula is:
Q2.If the distance between two charges triples, the force becomes:
Q3.Two charges of the same sign will:
Q4.What is the approximate value of Coulomb's constant k?
The full card deck, worked steps and AI-tutor support for “What is Coulomb's Law?” are in Notek — study by hand before your exam.
Common mistakes
Forgetting to square the distance. — Correct: The distance term is r², not r — the force falls off much faster than linearly.
Using charge values in µC directly in the formula without converting to coulombs. — Correct: Convert µC to C (×10⁻⁶) before multiplying by k, or use a pre-scaled coefficient.
Assuming the force direction is always attractive. — Correct: Like charges repel; only unlike charges attract.
Confusing Coulomb's law with the electric field formula. — Correct: Coulomb's law gives the force between two charges; E = kQ/r² gives the field from one charge.
FAQ
What is Coulomb's law?
Coulomb's law describes the electric force between two point charges: F = k q₁q₂ / r².
What is the Coulomb's law formula?
F = k·q₁·q₂/r², where k ≈ 8.99 × 10⁹ N·m²/C², and r is the distance between the charges.
What are examples of Coulomb's law?
The repulsion between two electrons, the attraction between a proton and electron in a hydrogen atom, and static cling are everyday examples.
How do you calculate the force in Coulomb's law?
Multiply Coulomb's constant by both charges, then divide by the square of the distance between them: F = k q₁q₂ / r².