Main Concept

An inverse square law is a law that states that the influence (such as sound) of a point source (such as radio) is inversely proportional to the square of the distance from the source of the particular quantity. In other words:

$I\propto \frac{1}{r^2}$

where I is a physical quantity or intensity and r is an arbitrary distance. This law applies to several areas studied in mathematics and physics, such as gravity, electric field, light, sound, and radiation. The formulas of the aforementioned concepts that obey the inverse law are as follows:

Gravity:

$F_g\=\frac{{\mathrm{Gm}}_1{m}_2}{r^2}$

Electric Field:

$E\=\frac{Q}{4{\mathrm{\π\ϵ}}_0{r}^2}$

Light, Sound, and Radiation:

$I\=\frac{P}{4 \mathrm{\π} r^2}$

This law generally applies when some form of conserved quantity (such as force and energy) is radiated outwardly and uniformly in 3-D space from a point source.

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