What Is Coulomb's Law?
Coulomb's Law, established by Charles-Augustin de Coulomb in 1785, describes the electrostatic force between two point charges. The force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. Like charges repel each other, while unlike charges attract. This inverse-square law has the same mathematical form as Newton's law of gravitation.
Coulomb's Law is the foundation of electrostatics and one of the most fundamental laws in physics. It forms the basis of Gauss's Law and Maxwell's equations, which describe all electromagnetic phenomena. The constant k (Coulomb's constant) equals approximately 8.988 x 10^9 N·m²/C² and is related to the permittivity of free space by k = 1/(4πε0).
Coulomb's Law Formula
Force Examples
| q1 | q2 | Distance | Force | Direction |
|---|---|---|---|---|
| +1 μC | +1 μC | 1 m | 8.99 mN | Repulsive |
| +1 C | +1 C | 1 m | 8.99 GN | Repulsive |
| +1 μC | -1 μC | 0.1 m | 0.899 N | Attractive |
| Electron | Proton | 0.053 nm | 8.2 × 10-8 N | Attractive |
Comparison to Gravity
- The electrostatic force between an electron and proton is about 1039 times stronger than their gravitational attraction.
- Both follow inverse-square laws, but gravity is always attractive while electromagnetic force can be attractive or repulsive.
- Electromagnetic force has positive and negative charges that can cancel out; gravity has only one type of "charge" (mass).
- The enormous strength of electromagnetic force is why it dominates at atomic and molecular scales despite being so effectively screened at larger scales.
Frequently Asked Questions
Why don't we feel the electromagnetic force if it's so much stronger than gravity?
Matter is almost perfectly electrically neutral. The positive proton charges balance the negative electron charges with extraordinary precision (to better than 1 part in 10^21). This near-perfect cancellation means that at macroscopic scales, the net electromagnetic force between objects is essentially zero, allowing the much weaker gravitational force to dominate at astronomical distances.
Does Coulomb's Law work inside materials?
Inside a dielectric material, the effective force is reduced by the dielectric constant (κ): F = kq1q2/(κr²). In water (κ = 80), electrostatic forces are reduced by a factor of 80 compared to vacuum. This is why ionic compounds dissolve in water: the reduced electrostatic attraction between ions allows them to separate and dissolve.
What is the superposition principle?
When multiple charges are present, the total force on any charge is the vector sum of the individual Coulomb forces from each other charge. This superposition principle allows complex multi-charge problems to be solved by calculating and summing pairwise forces. It is one of the key features of the electromagnetic force in classical physics.