The magnitude of the forces between two charged spheres was first investigated in1785 by Coulomb, a French scientist. The law he discovered states:

The force between two point charges is directly proportional to the product of the charges divided by the square of their distance apart.

The law applies to point charges; subatomic particles may be regarded as approximating to point charges. Coulomb's law may be stated in mathematical terms as

F is propotional to Q'Q/r^2

where F is the electric (or coulomb) force between two point charges Q' and Q, distance r apart.


The force between two charges also depends on what separates them; its value is always reduced when an insulating material replaces a vacuum. To take this into account a medium is said to have permittivity, denoted by ε (epsilon). A material with high permittivity is one which reduces appreciably the force between two charges compared with the vacuum value.

Spherical symmetry is associated with point charges and so in Coulomb's law is rationalised by including 4π in the denominator, it becomes:

F = 1/4πε * Q'Q/r^2

The unit of ε is C^2*N^-1 m^-2, or more commonly is the farad per metre (Fm^-1).

The permittivity of a vacuum is called 'epsilon nought' and is called the permittivity of free space.

εᵒ = 8.85*10^-12 C^2*N^-1 m^-2.

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