Why is there an inverse square law in electrostatics?

[sruthisupriya]

I have a little doubt. why is there an inverse square law in electrostatics?why not some other than the inverse square? is there any relation/connection between the charges and the inverse square?

 

[quantumdude]

Good question! In quantum field theory, the inverse square law is shown to be a direct consequence of the masslessness of the carrier of the electromagnetic force, namely the photon. The field equations for a massive photon result in an expression for the electrostatic potential of the form:

$$\phi=C\frac{e^{-mr}}{r},$$

where $m$ is the photon mass. This potential is called the Yukawa potential (in case you feel like Googling for more information).

Currently the experimental upper bound on the mass of the photon is $6\times10^{-17}eV$ (source: http://pdg.lbl.gov/2005/listings/s000.pdf) . So if the inverse square law doesn't hold exactly, it's pretty darn close.

 

[CarlB]

A lot of things in physics have multiple explanations.

Classically, the inverse square law comes about because charges produce electric fields that can be modeled by little lines that begin only on + charges and end only on - charges. Since the area of the surface of a sphere is proportional to the square of the radius, you have to have the strength (the number of electric field lines per unit area) decrease as 1 over r squared.

Carl