inversesquare

Inversesquare is a term commonly used to describe quantities whose strength decreases with distance according to the inverse square of the separation from a source. It is most often encountered as the inverse-square law in physics.

In physics, the inverse-square law applies to gravitational attraction between point masses, electrostatic force between point charges, and the radiant intensity from a point source. For gravitation and electrostatics, the force F scales as F ∝ 1/r^2, with F = G m1 m2 / r^2 in gravity and F = k q1 q2 / r^2 in electrostatics. For light and other radiation, the irradiance or flux at distance r falls off as E ∝ 1/r^2 (for a point source with total power P, E = P / (4π r^2)).

The r−2 dependence arises because the emitted energy or influence spreads uniformly over the surface area of a sphere with radius r, which is 4π r^2. As a result, the density decreases in proportion to 1/r^2.

Limitations and generalizations: The inverse-square law is an excellent model in the far field of a point or small source in open space. Real sources are extended, and near-field or shielding effects can alter the distance dependence. In d-dimensional space, the analogous law scales as 1/r^{d−1}.