Definition:Inverse Square Law

Definition

Two real variables $x$ and $y$ are related by an inverse square law if and only if they fulfil the relationship:

$\forall x, y \in \R: x \propto \dfrac 1 {y^2} \iff \exists k \in \R, k \ne 0: x y^2 = k$

Examples

Forces of Interaction

Various forces of interaction between two particles in space obey the inverse square law, for example:

the force of gravitation

the electrostatic force.

Intensity of Effect

The inverse square law governs the intensity of an effect to the reciprocal of the square of the distance from its cause.

The illumination from a source of light is an everyday example of this.

Also see

• Results about the inverse square law can be found here.

Sources

• 1990: I.S. Grant and W.R. Phillips: Electromagnetism (2nd ed.) ... (previous) ... (next): Chapter $1$: Force and energy in electrostatics: $1.1$ Electric Charge
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): inverse square law
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): inverse square law