# Coulomb's law accuracy for small distances

My physic teacher told me that experimental deviations from the predictions of Coulomb's law occur at small separations because, being inverse square, Coulomb's law work best for larger values of r. Why is this the case?

• In, say, nucleus-on-nucleus scattering (Rutherford scattering), one does deviate from Coulomb's law, but that occurs when you penetrate the nucleus and nuclear physics starts happening. Electron-on-electron scattering shows no such deviations as of yet, which is how we place a (very small) upper limit on the size of the electron. – Jon Custer Nov 1 '16 at 20:08
• @JonCuster I am investigating the behaviour of charges spheres of radii 1.9cm. In the case of a 1:1 charge ratio, the experimentally measured force is lower than the force predicted by Coulomb's law at small separations. My teacher explained this was because the law works best at large distances. How would you justify this statement? – Maddie Nov 1 '16 at 20:18
• Ahhh... Once they get too close together, they stop looking like point sources at $1/r$ with respect to each other. – Jon Custer Nov 1 '16 at 20:30
• @JonCuster could you elaborate on this? – Maddie Nov 1 '16 at 20:33

There is a systematic way to approach to corrections of the pointe-like and spherically symmetric approximation, the multipole expansion. The idea is to expand the potential field in terms of $1/r$. The next correction to the $1/r^2$ electric field is the dipole