Coulomb's Law Formula
Coulomb's Law calculates the electric force between two charges: F = kq1q2/r².
Learn about charge interaction with examples.
The Formula
Coulomb's Law describes the electrostatic force between two point charges. The force is proportional to the product of the charges and inversely proportional to the square of the distance between them.
Variables
| Symbol | Meaning |
|---|---|
| F | Electrostatic force (measured in newtons, N) |
| k | Coulomb's constant (8.9875 × 10⁹ N·m²/C²) |
| q₁ | First charge (measured in coulombs, C) |
| q₂ | Second charge (measured in coulombs, C) |
| r | Distance between the charges (measured in meters, m) |
Example 1
Two charges of +3 μC and +5 μC are 0.2 m apart. What is the force between them?
Convert to coulombs: q₁ = 3 × 10⁻⁶ C, q₂ = 5 × 10⁻⁶ C
F = (8.9875 × 10⁹) × (3 × 10⁻⁶ × 5 × 10⁻⁶) / (0.2)²
F = (8.9875 × 10⁹) × (15 × 10⁻¹²) / 0.04
F = 0.1348 / 0.04
F ≈ 3.37 N (repulsive, since both charges are positive)
Example 2
An electron and a proton are 5.3 × 10⁻¹¹ m apart (hydrogen atom). What is the attractive force?
q₁ = q₂ = 1.6 × 10⁻¹⁹ C, r = 5.3 × 10⁻¹¹ m
F = (8.9875 × 10⁹) × (1.6 × 10⁻¹⁹)² / (5.3 × 10⁻¹¹)²
F = (8.9875 × 10⁹) × (2.56 × 10⁻³⁸) / (2.809 × 10⁻²¹)
F ≈ 8.2 × 10⁻⁸ N (attractive, since charges are opposite)
When to Use It
Use Coulomb's Law when working with electrostatic forces:
- Calculating the force between charged particles or objects
- Analyzing electric fields and charge distributions
- Understanding atomic and molecular bonding forces
- Designing electrostatic devices like capacitors and sensors