Formula & Calculator
Coulomb's Law
Force between two point charges.
Interpretation
Coulomb's law: the electrostatic force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
The force is attractive for opposite charges and repulsive for like charges.
Example: q₁=2µC, q₂=3µC, r=0.5m → F = (8.99×10⁹)×(6×10⁻¹²)/(0.5)² ≈ 0.216 N.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| F | Force | Newtons |
| k | Coulomb constant | N·m²/C² |
| q | Charge | Coulombs |
| r | Distance | meters |
What it means
Coulomb’s law describes the electrostatic force between two point charges. It states that the magnitude of the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. The formula F = k * |q1*q2| / r² applies, where k ≈ 8.99×10⁹ N·m²/C² is Coulomb’s constant. The force is attractive for opposite charges and repulsive for like charges. This law is the basis for electrostatics and is analogous to Newton’s law of gravitation. It explains the behaviour of charged particles, the structure of atoms, and the forces in molecules. In electrical engineering, Coulomb’s law is used to calculate forces on charges in electric fields, to design electrostatic precipitators, and to understand the electric field strength around conductors. The law also leads to the definition of the electric field (E = F/q) and the electric potential. Example: Two charges, q1=2µC, q2=3µC, separated by 0.5m, experience a force F = (8.99×10⁹)*(2×10⁻⁶)*(3×10⁻⁶)/(0.5)² = (8.99×10⁹ * 6×10⁻¹²)/0.25 = 0.05394/0.25 ≈ 0.216 N, repulsive since both are positive.
Worked example
Coulomb's Law – Practical Example
Real‑World| Parameter | Value |
|---|---|
| q₁ | 2 µC = 2×10⁻⁶ C |
| q₂ | 3 µC = 3×10⁻⁶ C |
| r | 0.1 m |
| k | 8.99×10⁹ N·m²/C² |
| Formula | F = k·q₁·q₂ / r² |
Common mistakes
- Units: Charge in coulombs, distance in metres, force in newtons.
- Sign: Like charges repel (force positive), opposite attract (force negative).
- Permittivity: In a medium, replace k with 1/(4πε), where ε = ε₀·ε_r.
- Point charges: The formula assumes charges are point‑like – not valid for extended distributions without integration.
- Superposition: For multiple charges, the net force is the vector sum of individual forces.
Applications
Coulomb's law describes the electrostatic force between two point charges, proportional to the product of charges and inversely proportional to the square of the distance between them. This law is fundamental to electrostatics and underpins the behaviour of electric fields and potentials. Electrical engineers apply it to design capacitors, to calculate forces in electrostatic actuators, and to understand the interaction of charged particles in semiconductors. In high‑voltage engineering, it helps predict corona discharge and breakdown phenomena. By applying Coulomb's law, professionals can quantify the forces acting on charges and design devices that rely on electrostatic attraction or repulsion. It is also essential for understanding the atomic structure of materials and the operation of electron microscopes.
- Design of electrostatic actuators and MEMS devices
- Capacitance calculation and capacitor design
- High‑voltage insulation and breakdown analysis
- Semiconductor physics and charge transport
- Educational foundation of electromagnetism
Frequently Asked Questions
Coulomb's Law gives the electric force between two point charges: F = k·q₁·q₂ / r², where k = 1/(4πε₀) ≈ 8.99×10⁹ N·m²/C². The force is attractive for opposite charges and repulsive for like charges.
k = 8.9875 × 10⁹ N·m²/C². It is also expressed as 1/(4πε₀), where ε₀ is the permittivity of free space.
The force is inversely proportional to the square of the distance (F ∝ 1/r²). Doubling the distance reduces the force to one-quarter. This is an inverse-square law.
The force is along the line joining the two charges. Like charges repel (positive force), opposite charges attract (negative force). The vector form includes a unit vector.
Yes, replace ε₀ with ε = ε₀·ε_r, where ε_r is the relative permittivity (dielectric constant) of the medium. The force is reduced by a factor of ε_r.
Coulomb's Law is valid for point charges or spherical charge distributions. It becomes less accurate when charges are moving at relativistic speeds or when quantum effects dominate.
The electric field E = F/q₀ (force per unit test charge). Coulomb's Law gives the force, and the electric field of a point charge is E = kQ/r².
Both are inverse-square laws. However, Coulomb's Law depends on charge (can be attractive or repulsive), while gravity depends on mass (always attractive). Coulomb's constant is much larger than G.
Use the principle of superposition: the net force on a charge is the vector sum of forces from each other charge individually, calculated using Coulomb's Law for each pair.
Common errors include: 1) using the wrong sign for charges, 2) forgetting to square the distance, 3) mixing up units (e.g., using cm instead of m), 4) ignoring the vector nature, and 5) applying the law to non-point charges without integration.