Inverse square law

A number of laws of physics involve inverse-square relations. For example:

The gravitational force that is exerted between two masses (m1 and m2) are seperated by a distance r given by Newtons law of gravitation, which is written as:

$F_g = \frac{G m_1 m_2}{r^2}$

This law, in words states that the gravitational force exerted between two bodies in fact decreases as one over the square of the distance separating the two masses. We know that the gravitational force is attractive, because the mass, distance and the gravitational constant always remain positive.

Charles Augustine de Coulomb in 1785 showed that the force of attraction and the force of repulsion between two electrically charged bodies and also between magnetic poles also obey an inverse square law. The force for two charged bodies are given as:

$F_E = \frac{1}{4\pi \epsilon_0}\frac{q_1 q_2}{r^2}$

where $\epsilon_0$ is a constant of proportionality known as the permittivity of free space, and $q_1$ and $q_2$ are the charges, and of course, r is the distance between the two charges.

A similar expression would apply for magnetic monopoles if they existed. However, none have ever been found in nature.