Coulomb's law
The electrostatic force between two point charges is F = kₑ · q₁q₂ / r², directed along the line joining them: repulsive for like charges, attractive for opposite ones. The Coulomb constant is kₑ = 1/(4πε₀) ≈ 8.988 × 10⁹ N·m²·C⁻², with the vacuum permittivity ε₀ ≈ 8.854 × 10⁻¹² F·m⁻¹ (NIST/CODATA, NIST CODATA). The inverse-square form is why it mirrors Newtonian gravity.
The electric field
A charge q creates a field E = kₑ · q / r² pointing away from a positive charge and toward a negative one; the force on a test charge is F = qE. When several charges are present, their fields superpose vectorially — the simulator sums the contributions of every charge at each grid point to draw the field.
How to use the simulator
Add charges, drag them, and change their sign and magnitude. The tool reports the pairwise Coulomb force and renders the electric field as vectors or field lines, so you can see dipoles, shielding and the 1/r² falloff directly.
Note: the model treats ideal point charges in vacuum and is purely electrostatic (no magnetic effects or radiation). Field magnitudes are shown in model units scaled for on-screen visibility; the physics — inverse-square force and vector superposition — is exact.
Frequently asked questions
What is Coulomb's law?
Coulomb's law gives the electrostatic force between two point charges: F = k*q1*q2/r^2, along the line joining them. It is repulsive for like charges and attractive for opposite charges, and falls off as the inverse square of the distance.
What is the Coulomb constant?
The Coulomb constant is k = 1/(4*pi*epsilon0), approximately 8.988 x 10^9 N*m^2/C^2, where epsilon0 is the vacuum permittivity, about 8.854 x 10^-12 F/m (NIST/CODATA).
What is an electric field?
An electric field is the force per unit charge that a charge distribution exerts on a small test charge: E = F/q. A point charge q produces E = k*q/r^2, and fields from several charges add as vectors.
Is the Coulomb force attractive or repulsive?
It depends on the signs: like charges (both positive or both negative) repel, and opposite charges attract. The magnitude is the same in both cases for a given separation.
References
- National Institute of Standards and Technology, CODATA recommended values of the fundamental physical constants (NIST CODATA): vacuum permittivity ε₀ and Coulomb constant kₑ = 1/(4πε₀).
- D. J. Griffiths, Introduction to Electrodynamics, 4th ed. (Cambridge University Press) — Coulomb's law and the electric field.
- E. M. Purcell & D. J. Morin, Electricity and Magnetism, 3rd ed. (Cambridge University Press).