Coulomb's Law Calculator
Calculate electrostatic force between two point charges using Coulomb's law F = k·q₁·q₂ / r². Enter charges in coulombs and distance in meters for instant force in newtons with charts and breakdown.
About This Calculator
The Coulomb's Law Calculator computes the electrostatic force between two stationary point charges using the fundamental inverse-square law of electrostatics. This tool is essential for physics students studying electromagnetism, electrical engineers designing circuits and components, and anyone curious about the forces that govern atomic interactions and static electricity.
Coulomb's law states that the 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 formula is F = k × q₁ × q₂ / r², where k = 8.9875517923 × 10⁹ N·m²/C² is the Coulomb constant (derived from the vacuum permittivity ε₀ as k = 1/(4πε₀)). A positive result indicates repulsion (like charges), while a negative result indicates attraction (opposite charges).
For example, the force between two protons (each with charge 1.602 × 10⁻¹⁹ C) separated by 1.0 × 10⁻¹⁵ m (a typical nuclear distance) is approximately 230 N — an enormous repulsive force at that scale. In contrast, the attractive force between an electron and a proton in a hydrogen atom (at the Bohr radius of 5.29 × 10⁻¹¹ m) is about 8.24 × 10⁻⁸ N.
How to use this calculator
Enter Charge 1 and Charge 2 in coulombs. Use scientific notation for convenience (e.g., 1.6e-19 for an electron, 1e-9 for a nanocoloumb charge). Enter the center-to-center distance in meters. Click Calculate to see the electrostatic force in newtons, with a detailed breakdown showing the Coulomb constant and an interactive chart.
Applications
Coulomb's law is fundamental to atomic physics (electron-proton interactions, atomic stability), chemistry (ionic and covalent bonds, molecular forces), electrical engineering (capacitor design, electrostatic discharge protection), and industrial applications (electrostatic painting, air purification, photocopier technology).
Frequently Asked Questions
What is Coulomb's law?
Coulomb's law describes the electrostatic force between two stationary point charges. The force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. It is repulsive for like charges and attractive for opposite charges.
What is the formula for Coulomb's law?
The Coulomb's law formula is F = k × q₁ × q₂ / r², where k = 8.988 × 10⁹ N·m²/C² is the Coulomb constant, q₁ and q₂ are the charges in coulombs, and r is the distance between them in meters. A positive force means repulsion, negative means attraction.
What units does this calculator use?
This calculator uses SI units: charges in coulombs (C), distance in meters (m), and force output in newtons (N). You can enter small charges like 1.6e-19 for a single proton charge or 1e-9 for typical static electricity values.
What is the Coulomb constant k?
The Coulomb constant k = 8.9875517923 × 10⁹ N·m²/C² is derived from the vacuum permittivity ε₀ as k = 1/(4πε₀). It converts the product of charges divided by distance squared into the electrostatic force in newtons.
What is the difference between Coulomb force and gravitational force?
Both are inverse-square laws, but Coulomb force can be attractive or repulsive while gravity is only attractive. Coulomb force is about 10⁴⁰ times stronger than gravity for elementary particles. The Coulomb constant k = 8.988×10⁹ is vastly larger than G = 6.674×10⁻¹¹.
What are some real-world applications of Coulomb's law?
Coulomb's law is used in designing capacitors, calculating atomic forces between electrons and protons, understanding chemical bonds, developing electrostatic precipitators for pollution control, designing photocopiers and laser printers, and studying plasma physics.
Does Coulomb's law work for moving charges?
Coulomb's law strictly applies only to stationary (static) point charges. For moving charges, magnetic effects also come into play, requiring the full Lorentz force law F = q(E + v × B) which combines electric and magnetic forces.
How do I calculate the force between an electron and a proton?
The charge of an electron and proton is ±1.602 × 10⁻¹⁹ C. In a hydrogen atom, they are about 5.29 × 10⁻¹¹ m apart (the Bohr radius). Using F = k·q₁·q₂/r², the attractive force is approximately 8.24 × 10⁻⁸ N, which is about 10⁴⁰ times stronger than their gravitational attraction.