Electromagnetic force (thing)

The force between two charged particles is given by: F = Q₁Q₂ / 4πε₀r²

Where Q₁ and Q₂ are the charges on point charges 1 and 2 respectively, ε₀ is the permittivity of free space (8.85x10^-12 Fm^-1)
Sometimes the equation is simplified to: F = kQ₁Q₂ / r²
Where k = 1 / 4πε₀ = 8.988x10⁹

This simplified version only works when the permittivity of the space the interaction is taking place in is equal to that of free space.

Here is an example, an electron and an alpha particle (helium nucleus) are seperated by 1 centimetre, the force between them is:
F = 1.6x10^-19 x 3.2x10^-19 / 4πε₀0.01²
F = 5.12x10^-38 / 1.11212379x10^-10 x 0.01²
F = 5.12x10^-38 / 1.11212379x10^-14
F = 5.12x10^-38 / 1.11212379x10^-14
F = 4.603x10^-24 N, which is very small.

Suppose the seperation wasn't 1 centimetre, but 1 millimetre:
F = 1.6x10^-19 x 3.2x10^-19 / 4πε₀0.01²
F = 5.12x10^-38 / 1.11212379x10^-10 x 0.001²
F = 5.12x10^-38 / 1.11212379x10^-16
F = 5.12x10^-38 / 1.11212379x10^-16
F = 4.603x10^-22 N, which is 2 orders of magnitude higher for a 1 order of magnitude reduction in seperation. This is due to the inverse square law.