Effects of photons having a finite mass

[Saptarshi Sarkar]

TL;DR

Effect on Coulomb potential due to finite mass of photons

Few days back, our college professor told us that if a photon were to have a finite mass, then the Coulomb potential between two stationary charges separated by a distance r would be strictly zero beyond some distance.

He told us that it was due to the reason that photon is the elementary particle which is the reason behind Coulomb force. I didn't understand what he really meant as we haven't yet had the course on particle physics. Can anyone please explain it or refer to something that I can read?

 

[mfb]

then the Coulomb potential between two stationary charges separated by a distance r would be strictly zero beyond some distance.

That is not true. With a massive exchange particle you get a Yukawa potential. For large distances it is decreasing (approximately) exponentially, it quickly gets irrelevant, but never zero. The strong interaction has such a potential, and it can also arise in some cases from the electromagnetic interaction if additional particles shield a point charge.