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
Key Notes
- Formula: F = kq₁q₂/r²: k = 8.99×10⁹ N·m²/C² (Coulomb's constant) = 1/(4πε₀). The force is repulsive between like charges (same sign) and attractive between opposite charges. It acts along the line joining the two charges.
- Inverse-square law — same form as gravity: Coulomb's law is mathematically identical to Newton's law of gravitation (F = Gm₁m₂/r²). However, the electrostatic force is approximately 10³⁶ times stronger than gravity for two protons — explaining why gravity dominates only at astronomical scales.
- Superposition principle: The total force on a charge from multiple sources is the vector sum of the individual Coulomb forces. This linearity allows analysis of complex charge distributions by decomposing them into point charge contributions.
- Electric field: E = F/q₀ = kq/r²: The electric field at a point is the force per unit positive test charge. It is a vector field that exists at all points in space around a charge, regardless of whether a test charge is present.
- Applications: Coulomb's law underlies atomic and molecular structure (electron-nucleus attraction), chemical bonding, electrostatic precipitators (air filtration), photocopier and laser printer operation (toner attraction), and the design of particle accelerators and ion traps.