inverse square law
(a value's dependency upon reciprocal of the square of the distance from something)
An inverse square law is a scientific law (i.e., well-established
model) asserting that some value depends upon the distance from
something, more specifically on the reciprocal of the square
of that distance (1/d²). If that something is a point or spherically
symmetric body, then given any distance (i.e., the radius of
a sphere centered on the point), the sum (integral) of the
value across all points at any such distance is the same.
An inverse square law generally
implies three-dimensional Euclidean space,
and serves as an approximation if the space is close to that,
such as are current models of the universe.
Some common inverse-square examples:
- The density of things, e.g., particles, sprayed in all directions (or covering some specific solid angle) from a point.
- Electromagnetic radiation (EMR), similarly, from a point source.
- Sound waves from a point source.
- Electric force, e.g., associated with an electron or proton.
Phenomena that are not inverse square:
- The height of spreading ripples in a pond, e.g., from where something dropped into it. The ripples spread over just 2 dimensions instead of 3 and the height is related to 1/d rather than 1/d².
- gravitational waves, also 1/d, more like ripples in a pond than like EMR or sound waves.
electric field (E)
gravitational wave (GW)