We all remember calculating the electric force of interaction between a stationary nucleus and a revolving electron using Coulomb's law. The electron in this case is moving. Here's what I think about the law's validity in this case.
Considering two charges, if one is at rest and the other in motion, Coulomb's law still holds. Coulomb's law determines the electric force alone. Let us consider a Hydrogen atom at ground state. Considering the most probable states of an electron, the collection yields a circular orbit. In this case, the most probable distance is fixed. The revolving electron creates a magnetic field around it. However, the magnetic force acting on the nucleus is zero because the nucleus is stationary. And since the electron cannot exert a force on itself, the magnetic force acting on either is zero. This leaves us with the electric force alone that is given by Coulomb's law.
But if both the charges are in motion, the total force cannot be given by Coulomb's law alone. Relativistic effects come into the picture.
Here's a point I would like to make. In the case of moving charges( both moving slowly ), the total force acting on either, at some 'instant' can be given by the sum of the electric force( given by Coulombs law ) and the magnetic force. In the link given below, they have proceeded as I mentioned.
Electric and Magnetic force between moving charges
You see, Coulomb's law holds even in the case where charges move slowly. However a correction term( magnetic force ) was to be included.
So, in what sense does Coulomb's law not hold in the case of fast moving charges? What relativistic effects show up in the case of fast moving charges thereby, leading to a breakdown in Coulomb's law?
