I Coulomb's Law and charge quantization

In Coulomb's Law, the magnitude of the force is normally written as $$F=\frac{1}{4 \pi\epsilon_0}\frac{q_1q_2}{r^2}$$Considering that charges usually come in integral numbers of the electron charge magnitude ##e##, you could write $$F=\frac{1}{4 \pi\epsilon_0}\frac{N_1N_2e^2}{r^2}$$ for the magnitude, where ##N_1## and ##N_2## are positive integers. However, in E&M one usually models charge distributions as continuously smooth, i.e. charges can have fractional values of ##e##.

This idea is analogous to thinking of mass as being continuous without worrying about the "graininess" of atoms.

 

The flaw here is that you seem to think that "particles" can only be either a proton or an electron. There's nothing that says that those two are the ONLY entities that can use the label "particles". What if the particle is a composite particle, such as the nucleus of an atom? What is the force between a gold nucleus and an electron? What is the charge on an alpha particle? And wait till you hear that there are entities that can have fractional charges!

The word particles are not exclusively reserved only for protons and electrons.

Zz.

 

Yes. The charges are additive.

If you have a collection of charges, it becomes important to assign a position to the associated net charge. As long as the clumps are small compared to the distance between the clumps, you can wave your hands and treat the net charge as if it is located in the center of the clump. If the clumps are large compared to the distance between and if the charges are not distributed in a spherically symmetric manner then things get more complex.