Coulomb's Law

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

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