Coulomb's Law
Calculate the electrostatic force between two charged particles using Coulomb's law F = kq1*q2/r^2.
Solve for force, charge, or separation with worked examples.
The Formula
Coulomb's law gives the force between two point charges. Like charges repel each other. Opposite charges attract. The force weakens with the square of the distance.
Variables
| Symbol | Meaning |
|---|---|
| F | Electrostatic force (Newtons) |
| k | Coulomb's constant (8.99 × 10⁹ N⋅m²/C²) |
| q₁, q₂ | Charges of the two particles (Coulombs) |
| r | Distance between the charges (meters) |
Example 1
Two charges of +3 μC and -5 μC are 0.2 m apart. Find the force.
q₁ = 3 × 10⁻⁶ C, q₂ = 5 × 10⁻⁶ C, r = 0.2 m
F = 8.99 × 10⁹ × (3 × 10⁻⁶ × 5 × 10⁻⁶) / (0.2)²
F = 8.99 × 10⁹ × 1.5 × 10⁻¹¹ / 0.04
F ≈ 3.37 N (attractive, since charges are opposite)
Example 2
Two protons (q = 1.6 × 10⁻¹⁹ C) are 1 × 10⁻¹⁰ m apart
F = 8.99 × 10⁹ × (1.6 × 10⁻¹⁹)² / (10⁻¹⁰)²
F = 8.99 × 10⁹ × 2.56 × 10⁻³⁸ / 10⁻²⁰
F ≈ 2.30 × 10⁻⁸ N (repulsive — both positive)
When to Use It
Use Coulomb's law when:
- Calculating the force between static electric charges
- Analyzing electric forces in atoms and molecules
- Designing electrostatic systems and capacitors
- Comparing electric and gravitational forces
Key Notes
- Formula: F = kq₁q₂ / r²: k = 8.988 × 10⁹ N·m²/C² (Coulomb's constant). Charges in coulombs (C), distance in meters. For opposite signs, F is negative (attractive); same signs gives positive (repulsive).
- Inverse-square law: Like gravity, Coulomb's force follows an inverse-square law. Doubling the separation reduces the force to one-quarter. The mathematical form is identical to Newton's gravitational law.
- Electrostatic force is vastly stronger than gravity: Between two protons, the electrostatic repulsion is about 10³⁶ times stronger than their gravitational attraction. Gravity dominates at large scales only because matter is electrically neutral overall.
- Only valid in vacuum (or approximately in air): In a medium with permittivity ε, the force is reduced: F = q₁q₂ / (4πεr²). In water (ε_r ≈ 80), the electrostatic force is 80 times weaker than in vacuum.
- Superposition principle: The total force on a charge from multiple other charges is the vector sum of all individual Coulomb forces. Each pair interacts independently.