Are Coulomb's Law and Lorentz force always true for all phenomenon in physics?

Question

I saw two equation about charge:

• Coulomb's law

$$\mathbf F=k \frac{q_1q_2}{ r_{12}^{2} }\, \mathbf{\hat r} $$

• and magnetic Force

$$ \mathbf F=q \, \mathbf v\times \mathbf B$$

My question is:

Are these equations true for all cases, for example:

• like very fast movement?
• very tiny particle like basic particles?

Answer 1

These are classical equations of electromagnetism and hold for classical dimensions, i.e. where the Heisenberg's Uncertainty Principle is ignorable because $h$ is actually zero as far as measurements go. Coulomb's law is a law discovered in static conditions, and the Lorentz force in charge moving in a magnetic field. Maxwell's equations combine these and other phenomena in a coherent theory which is used for classical dimensions to describe and predict the behavior of charges and magnetic fields.

For elementary particles the concept of force is substituted by the concept of "interaction". In this case electromagnetic interaction, and is in the realm of quantum mechanics. See the answer in this question here.