The Inverse Square Law

Suppose we have a point source of light. It will spreads its energy equally in all directions. Therefore if you wanted to find all of the points in space where the energy was of the same intensity you would have to draw a sphere around the source point. The bigger the radius of the sphere the greater the 'surface' over which the energy was spread.

The relationship between radius and sphere surface area is an inverse square relationship. That means that intensity will depend on 1/r2. If you double the distance from the source the intensity will not halve but drop to a quarter of its value, tripling the distance will make the intensity drop to a ninth and so on.


Any point source which spreads its influence equally in all directions without a limit to its range will obey the inverse square law. A simple experiment can illustrate this.

This comes from strictly geometrical considerations. The intensity of the influence at any given radius r is the source strength divided by the area of the sphere surface at that radius.

Being strictly geometric in its origin, the inverse square law applies to many different phenomena.

Point sources of gravitational force, electric field, light, sound or electromagnetic or nuclear radiation obey the inverse square law.


Inverse Square Law, Gravity

As one of the fields which obey the general inverse square law, the gravity field can be put in the form shown below, showing that the acceleration of gravity, g, is an expression of the intensity of the gravity field.


Inverse Square Law, Electric

As one of the fields which obey the general inverse square law, the electric field of a point charge can be put in the form shown below where point charge Q is the source of the field. The electric force in Coulomb's law follows the inverse square law.


Inverse Square Law, Radiation

As one of the fields which obey the general inverse square law, a point radiation source can be characterised by the relationship below whether you are talking about becquerels, Roentgens , rads, or rems . All measures of exposure will drop off by inverse square law.


Click here to go to a Java-Script interactive page that enables you to do a 'cyber-experiment'