# The inverse square law [duplicate]

Why the nature has chosen the inverse square law. For instance, the gravitational force as well as the Coulomb force is inversely proportional to the square of distances. Why not these forces are inversely related with power 1 or 3 or may be some higher power of distance?

## marked as duplicate by Floris, Qmechanic♦Feb 14 '17 at 6:26

• "Why" questions are always tricky to answer, but en.wikipedia.org/wiki/Gauss's_law may be what you're looking for. The electric/gravitational field spreads out as the surface area of a sphere, and the surface area of a sphere is proportional to $r^2$. – Jold Feb 14 '17 at 4:01
• – Floris Feb 14 '17 at 4:10

• I don't think the electroweak or strong forces are $1/r^2$.... Indeed the potential between quark has a part basically linear. – ZeroTheHero Feb 14 '17 at 5:50
While it is true that the Coulomb (electrostatic) and gravitational forces have a $1/r^2$ behaviour, the other two fundamental forces of nature, the weak and string forces, do not vary with distance in that way. In particular, the strong force has a constant part to it, meaning its potential $\sim r$. The residual strong interaction is described by a Yukawa-type potential: $e^{-\lambda r}/r$, thus producing a force that is not $1/r^2$.
So Nature has NOT chosen $1/r^2$ in 50% of the cases.
The $1/r^2$ is remarkable because of the geometrical relations that follows from this (basically Gauss's law), but it seems a coincidence rather than anything fundamental.