Inverse-square law

The inverse-square law states that a quantity spreading uniformly from a point source has intensity proportional to the inverse square of distance. It describes effects such as gravitational and electric fields and radiated power per unit area.

Spherical spreading: The expansion of a wave or flow across spherical surfaces centered on its source. Each doubling of radius spreads the same output over four times the area.
Newton's law of universal gravitation: A law stating that two masses attract with force proportional to their product and inversely proportional to distance squared. Gravitational force between pointlike masses follows this distance dependence.
Euclidean space: A geometric space governed by the familiar rules of flat geometry. The law's usual area argument assumes three-dimensional Euclidean geometry.
Inverse-cube law: A scaling relation in which a quantity varies inversely with the cube of distance. It decreases faster than the inverse-square behavior of a freely spreading point-source field.
Surface area of a sphere: The area of a sphere with radius r, equal to 4πr². Its r² growth is the geometric basis of the law.
Coulomb's law: The electrostatic force between point charges, proportional to their charge product and inversely proportional to distance squared. Electric point charges exhibit the same spatial scaling as gravitating masses.
Dimensional analysis: A method for checking physical relations by tracking the dimensions of quantities. It distinguishes inverse-square intensity from inverse-square-root or other distance scalings.
Beer–Lambert law: A law describing exponential attenuation of light through an absorbing medium. Absorption adds exponential loss rather than the geometric inverse-square decrease.
Flux: The rate at which a physical quantity passes through a surface. Constant total flux across growing spheres makes flux per unit area fall as distance squared.
Illuminance: The luminous flux incident on a surface per unit area. For a point light source, illuminance falls with the square of distance.

Linked from 38 pages