1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Why is there an inverse square law in electrostatics?

  1. Dec 2, 2005 #1
    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?
  2. jcsd
  3. Dec 2, 2005 #2

    Tom Mattson

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    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:


    where [itex]m[/itex] 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 [itex]6\times10^{-17}eV[/itex] (source: http://pdg.lbl.gov/2005/listings/s000.pdf) [Broken]. So if the inverse square law doesn't hold exactly, it's pretty darn close.
    Last edited by a moderator: May 2, 2017
  4. Dec 8, 2005 #3


    User Avatar
    Science Advisor
    Homework Helper

    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.

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook