# why is exchange force inversely proportional to square of distance? [duplicate]

Gravitational force is inversely proportional to the square of distance. Coulomb's force is inversely proportional to the square of distance. By biot savart law, magnetic field is inversely proportional to the square of distance. It can be explained by using field lines that these quantities are inversely proportional to the area (circle which is $\frac{1}{4}\pi \times$ diameter$^2$) produced by the two charges . But in reality they extend in three dimensions then it should be inversely proportional to cube of distance. It can also be explained using different data collected from experiments where all other quantities except distance is kept constant. What is the theoretical explaination for them to be inversely proportional to the square of distance ?

• – John Rennie Oct 12 '16 at 14:42
• Thanks John Rennie for the link. It was answered before. – selepsy Oct 13 '16 at 21:34

## 1 Answer

Your expectation of a cubic relationship between force and distance using the field lines model is based on the error of using the volume of a sphere rather than the surface of a sphere. The force is proportional to the flux, or field lines per unit area. That brings us back to r squared.

• For this an imaginary surface is to be imagined at some point on the line connecting the point charge or the centre of charged body . But r can be used to determine the distance between that surface and any one off the charge. So it will be proportional to square but not to square of r – selepsy Oct 13 '16 at 21:32