Coulomb's Law
Calculate the electrostatic force between two charged particles.
The electric equivalent of Newton's gravitational law.
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 ร 10โน Nโ mยฒ/Cยฒ) |
| qโ, qโ | Charges of the two particles (Coulombs) |
| r | Distance between the charges (meters) |
Example 1
Two charges of +3 ฮผC and -5 ฮผC are 0.2 m apart. Find the force.
qโ = 3 ร 10โปโถ C, qโ = 5 ร 10โปโถ C, r = 0.2 m
F = 8.99 ร 10โน ร (3 ร 10โปโถ ร 5 ร 10โปโถ) / (0.2)ยฒ
F = 8.99 ร 10โน ร 1.5 ร 10โปยนยน / 0.04
F โ 3.37 N (attractive, since charges are opposite)
Example 2
Two protons (q = 1.6 ร 10โปยนโน C) are 1 ร 10โปยนโฐ m apart
F = 8.99 ร 10โน ร (1.6 ร 10โปยนโน)ยฒ / (10โปยนโฐ)ยฒ
F = 8.99 ร 10โน ร 2.56 ร 10โปยณโธ / 10โปยฒโฐ
F โ 2.30 ร 10โปโธ N (repulsive โ 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