Coulomb’s law is the inverse square law describing the electrostatic interaction between electrically charged particles. It was first published in 1785 and since then has been tested heavily and all observations are consistent with the law.
Coulomb’s law states that the magnitude of the electrostatic force of interaction between two point charges is directly proportional to the scalar multiplication of the magnitude of charges and inversely proportional to the square of the distances between them.
If the two charges have the same sign, the electrostatic force between them is repulsive. If they have different signed then the force between them is attractive.
The scalar for of the law is
|F| = ke|q1q2\/r2
The vector form of the law is
F = ke(q1q2r21)/r221
R21 = r21/|r21|
The magnitude of the electric field force in a vacuum is invertible from Coulomb’s law. Since E = F/Q it follows from the Coulomb’s law that the magnitude of the electric field E created by a single point charge q t a certain distance r in a vacuum is given by:
|E| = 1/(4πƐ0)(|q|/r2)